college mathematics assignment 7

1.1 Real Numbers: Algebra Essentials

• ⓐ 11 1 11 1
• ⓒ − 4 1 − 4 1
• ⓐ 4 (or 4.0), terminating;
• ⓑ 0. 615384 ¯ , 0. 615384 ¯ , repeating;
• ⓒ –0.85, terminating
• ⓐ rational and repeating;
• ⓑ rational and terminating;
• ⓒ irrational;
• ⓓ rational and terminating;
• ⓔ irrational
• ⓐ positive, irrational; right
• ⓑ negative, rational; left
• ⓒ positive, rational; right
• ⓓ negative, irrational; left
• ⓔ positive, rational; right
• ⓐ 11, commutative property of multiplication, associative property of multiplication, inverse property of multiplication, identity property of multiplication;
• ⓑ 33, distributive property;
• ⓒ 26, distributive property;
• ⓓ 4 9 , 4 9 , commutative property of addition, associative property of addition, inverse property of addition, identity property of addition;
• ⓔ 0, distributive property, inverse property of addition, identity property of addition
• ⓒ 121 3 π 121 3 π ;
• ⓐ −2 y −2 z or  −2 ( y + z ) ; −2 y −2 z or  −2 ( y + z ) ;
• ⓑ 2 t −1 ; 2 t −1 ;
• ⓒ 3 p q −4 p + q ; 3 p q −4 p + q ;
• ⓓ 7 r −2 s + 6 7 r −2 s + 6

A = P ( 1 + r t ) A = P ( 1 + r t )

1.2 Exponents and Scientific Notation

• ⓐ k 15 k 15
• ⓑ ( 2 y ) 5 ( 2 y ) 5
• ⓒ t 14 t 14
• ⓑ ( −3 ) 5 ( −3 ) 5
• ⓒ ( e f 2 ) 2 ( e f 2 ) 2
• ⓐ ( 3 y ) 24 ( 3 y ) 24
• ⓑ t 35 t 35
• ⓒ ( − g ) 16 ( − g ) 16
• ⓐ 1 ( −3 t ) 6 1 ( −3 t ) 6
• ⓑ 1 f 3 1 f 3
• ⓒ 2 5 k 3 2 5 k 3
• ⓐ t −5 = 1 t 5 t −5 = 1 t 5
• ⓑ 1 25 1 25
• ⓐ g 10 h 15 g 10 h 15
• ⓑ 125 t 3 125 t 3
• ⓒ −27 y 15 −27 y 15
• ⓓ 1 a 18 b 21 1 a 18 b 21
• ⓔ r 12 s 8 r 12 s 8
• ⓐ b 15 c 3 b 15 c 3
• ⓑ 625 u 32 625 u 32
• ⓒ −1 w 105 −1 w 105
• ⓓ q 24 p 32 q 24 p 32
• ⓔ 1 c 20 d 12 1 c 20 d 12
• ⓐ v 6 8 u 3 v 6 8 u 3
• ⓑ 1 x 3 1 x 3
• ⓒ e 4 f 4 e 4 f 4
• ⓓ 27 r s 27 r s
• ⓕ 16 h 10 49 16 h 10 49
• ⓐ $ 1.52 × 10 5 $ 1.52 × 10 5
• ⓑ 7.158 × 10 9 7.158 × 10 9
• ⓒ $ 8.55 × 10 13 $ 8.55 × 10 13
• ⓓ 3.34 × 10 −9 3.34 × 10 −9
• ⓔ 7.15 × 10 −8 7.15 × 10 −8
• ⓐ 703 , 000 703 , 000
• ⓑ −816 , 000 , 000 , 000 −816 , 000 , 000 , 000
• ⓒ −0.000 000 000 000 39 −0.000 000 000 000 39
• ⓓ 0.000008 0.000008
• ⓐ − 8.475 × 10 6 − 8.475 × 10 6
• ⓑ 8 × 10 − 8 8 × 10 − 8
• ⓒ 2.976 × 10 13 2.976 × 10 13
• ⓓ − 4.3 × 10 6 − 4.3 × 10 6
• ⓔ ≈ 1.24 × 10 15 ≈ 1.24 × 10 15

Number of cells: 3 × 10 13 ; 3 × 10 13 ; length of a cell: 8 × 10 −6 8 × 10 −6 m; total length: 2.4 × 10 8 2.4 × 10 8 m or 240 , 000 , 000 240 , 000 , 000 m.

1.3 Radicals and Rational Exponents

5 | x | | y | 2 y z . 5 | x | | y | 2 y z . Notice the absolute value signs around x and y ? That’s because their value must be positive!

10 | x | 10 | x |

x 2 3 y 2 . x 2 3 y 2 . We do not need the absolute value signs for y 2 y 2 because that term will always be nonnegative.

b 4 3 a b b 4 3 a b

14 −7 3 14 −7 3

• ⓒ 88 9 3 88 9 3

( 9 ) 5 = 3 5 = 243 ( 9 ) 5 = 3 5 = 243

x ( 5 y ) 9 2 x ( 5 y ) 9 2

28 x 23 15 28 x 23 15

1.4 Polynomials

The degree is 6, the leading term is − x 6 , − x 6 , and the leading coefficient is −1. −1.

2 x 3 + 7 x 2 −4 x −3 2 x 3 + 7 x 2 −4 x −3

−11 x 3 − x 2 + 7 x −9 −11 x 3 − x 2 + 7 x −9

3 x 4 −10 x 3 −8 x 2 + 21 x + 14 3 x 4 −10 x 3 −8 x 2 + 21 x + 14

3 x 2 + 16 x −35 3 x 2 + 16 x −35

16 x 2 −8 x + 1 16 x 2 −8 x + 1

4 x 2 −49 4 x 2 −49

6 x 2 + 21 x y −29 x −7 y + 9 6 x 2 + 21 x y −29 x −7 y + 9

1.5 Factoring Polynomials

( b 2 − a ) ( x + 6 ) ( b 2 − a ) ( x + 6 )

( x −6 ) ( x −1 ) ( x −6 ) ( x −1 )

• ⓐ ( 2 x + 3 ) ( x + 3 ) ( 2 x + 3 ) ( x + 3 )
• ⓑ ( 3 x −1 ) ( 2 x + 1 ) ( 3 x −1 ) ( 2 x + 1 )

( 7 x −1 ) 2 ( 7 x −1 ) 2

( 9 y + 10 ) ( 9 y − 10 ) ( 9 y + 10 ) ( 9 y − 10 )

( 6 a + b ) ( 36 a 2 −6 a b + b 2 ) ( 6 a + b ) ( 36 a 2 −6 a b + b 2 )

( 10 x − 1 ) ( 100 x 2 + 10 x + 1 ) ( 10 x − 1 ) ( 100 x 2 + 10 x + 1 )

( 5 a −1 ) − 1 4 ( 17 a −2 ) ( 5 a −1 ) − 1 4 ( 17 a −2 )

1.6 Rational Expressions

1 x + 6 1 x + 6

( x + 5 ) ( x + 6 ) ( x + 2 ) ( x + 4 ) ( x + 5 ) ( x + 6 ) ( x + 2 ) ( x + 4 )

2 ( x −7 ) ( x + 5 ) ( x −3 ) 2 ( x −7 ) ( x + 5 ) ( x −3 )

x 2 − y 2 x y 2 x 2 − y 2 x y 2

1.1 Section Exercises

irrational number. The square root of two does not terminate, and it does not repeat a pattern. It cannot be written as a quotient of two integers, so it is irrational.

The Associative Properties state that the sum or product of multiple numbers can be grouped differently without affecting the result. This is because the same operation is performed (either addition or subtraction), so the terms can be re-ordered.

−14 y − 11 −14 y − 11

−4 b + 1 −4 b + 1

43 z − 3 43 z − 3

9 y + 45 9 y + 45

−6 b + 6 −6 b + 6

16 x 3 16 x 3

1 2 ( 40 − 10 ) + 5 1 2 ( 40 − 10 ) + 5

irrational number

g + 400 − 2 ( 600 ) = 1200 g + 400 − 2 ( 600 ) = 1200

inverse property of addition

1.2 Section Exercises

No, the two expressions are not the same. An exponent tells how many times you multiply the base. So 2 3 2 3 is the same as 2 × 2 × 2 , 2 × 2 × 2 , which is 8. 3 2 3 2 is the same as 3 × 3 , 3 × 3 , which is 9.

It is a method of writing very small and very large numbers.

12 40 12 40

1 7 9 1 7 9

3.14 × 10 − 5 3.14 × 10 − 5

16,000,000,000

b 6 c 8 b 6 c 8

a b 2 d 3 a b 2 d 3

q 5 p 6 q 5 p 6

y 21 x 14 y 21 x 14

72 a 2 72 a 2

c 3 b 9 c 3 b 9

y 81 z 6 y 81 z 6

1.0995 × 10 12 1.0995 × 10 12

0.00000000003397 in.

12,230,590,464 m 66 m 66

a 14 1296 a 14 1296

n a 9 c n a 9 c

1 a 6 b 6 c 6 1 a 6 b 6 c 6

0.000000000000000000000000000000000662606957

1.3 Section Exercises

When there is no index, it is assumed to be 2 or the square root. The expression would only be equal to the radicand if the index were 1.

The principal square root is the nonnegative root of the number.

9 5 5 9 5 5

6 10 19 6 10 19

− 1 + 17 2 − 1 + 17 2

7 2 3 7 2 3

20 x 2 20 x 2

17 m 2 m 17 m 2 m

2 b a 2 b a

15 x 7 15 x 7

5 y 4 2 5 y 4 2

4 7 d 7 d 4 7 d 7 d

2 2 + 2 6 x 1 −3 x 2 2 + 2 6 x 1 −3 x

− w 2 w − w 2 w

3 x − 3 x 2 3 x − 3 x 2

5 n 5 5 5 n 5 5

9 m 19 m 9 m 19 m

2 3 d 2 3 d

3 2 x 2 4 2 3 2 x 2 4 2

6 z 2 3 6 z 2 3

−5 2 −6 7 −5 2 −6 7

m n c a 9 c m n m n c a 9 c m n

2 2 x + 2 4 2 2 x + 2 4

1.4 Section Exercises

The statement is true. In standard form, the polynomial with the highest value exponent is placed first and is the leading term. The degree of a polynomial is the value of the highest exponent, which in standard form is also the exponent of the leading term.

Use the distributive property, multiply, combine like terms, and simplify.

4 x 2 + 3 x + 19 4 x 2 + 3 x + 19

3 w 2 + 30 w + 21 3 w 2 + 30 w + 21

11 b 4 −9 b 3 + 12 b 2 −7 b + 8 11 b 4 −9 b 3 + 12 b 2 −7 b + 8

24 x 2 −4 x −8 24 x 2 −4 x −8

24 b 4 −48 b 2 + 24 24 b 4 −48 b 2 + 24

99 v 2 −202 v + 99 99 v 2 −202 v + 99

8 n 3 −4 n 2 + 72 n −36 8 n 3 −4 n 2 + 72 n −36

9 y 2 −42 y + 49 9 y 2 −42 y + 49

16 p 2 + 72 p + 81 16 p 2 + 72 p + 81

9 y 2 −36 y + 36 9 y 2 −36 y + 36

16 c 2 −1 16 c 2 −1

225 n 2 −36 225 n 2 −36

−16 m 2 + 16 −16 m 2 + 16

121 q 2 −100 121 q 2 −100

16 t 4 + 4 t 3 −32 t 2 − t + 7 16 t 4 + 4 t 3 −32 t 2 − t + 7

y 3 −6 y 2 − y + 18 y 3 −6 y 2 − y + 18

3 p 3 − p 2 −12 p + 10 3 p 3 − p 2 −12 p + 10

a 2 − b 2 a 2 − b 2

16 t 2 −40 t u + 25 u 2 16 t 2 −40 t u + 25 u 2

4 t 2 + x 2 + 4 t −5 t x − x 4 t 2 + x 2 + 4 t −5 t x − x

24 r 2 + 22 r d −7 d 2 24 r 2 + 22 r d −7 d 2

32 x 2 −4 x −3 32 x 2 −4 x −3 m 2

32 t 3 − 100 t 2 + 40 t + 38 32 t 3 − 100 t 2 + 40 t + 38

a 4 + 4 a 3 c −16 a c 3 −16 c 4 a 4 + 4 a 3 c −16 a c 3 −16 c 4

1.5 Section Exercises

The terms of a polynomial do not have to have a common factor for the entire polynomial to be factorable. For example, 4 x 2 4 x 2 and −9 y 2 −9 y 2 don’t have a common factor, but the whole polynomial is still factorable: 4 x 2 −9 y 2 = ( 2 x + 3 y ) ( 2 x −3 y ) . 4 x 2 −9 y 2 = ( 2 x + 3 y ) ( 2 x −3 y ) .

Divide the x x term into the sum of two terms, factor each portion of the expression separately, and then factor out the GCF of the entire expression.

10 m 3 10 m 3

( 2 a −3 ) ( a + 6 ) ( 2 a −3 ) ( a + 6 )

( 3 n −11 ) ( 2 n + 1 ) ( 3 n −11 ) ( 2 n + 1 )

( p + 1 ) ( 2 p −7 ) ( p + 1 ) ( 2 p −7 )

( 5 h + 3 ) ( 2 h −3 ) ( 5 h + 3 ) ( 2 h −3 )

( 9 d −1 ) ( d −8 ) ( 9 d −1 ) ( d −8 )

( 12 t + 13 ) ( t −1 ) ( 12 t + 13 ) ( t −1 )

( 4 x + 10 ) ( 4 x − 10 ) ( 4 x + 10 ) ( 4 x − 10 )

( 11 p + 13 ) ( 11 p − 13 ) ( 11 p + 13 ) ( 11 p − 13 )

( 19 d + 9 ) ( 19 d − 9 ) ( 19 d + 9 ) ( 19 d − 9 )

( 12 b + 5 c ) ( 12 b − 5 c ) ( 12 b + 5 c ) ( 12 b − 5 c )

( 7 n + 12 ) 2 ( 7 n + 12 ) 2

( 15 y + 4 ) 2 ( 15 y + 4 ) 2

( 5 p − 12 ) 2 ( 5 p − 12 ) 2

( x + 6 ) ( x 2 − 6 x + 36 ) ( x + 6 ) ( x 2 − 6 x + 36 )

( 5 a + 7 ) ( 25 a 2 − 35 a + 49 ) ( 5 a + 7 ) ( 25 a 2 − 35 a + 49 )

( 4 x − 5 ) ( 16 x 2 + 20 x + 25 ) ( 4 x − 5 ) ( 16 x 2 + 20 x + 25 )

( 5 r + 12 s ) ( 25 r 2 − 60 r s + 144 s 2 ) ( 5 r + 12 s ) ( 25 r 2 − 60 r s + 144 s 2 )

( 2 c + 3 ) − 1 4 ( −7 c − 15 ) ( 2 c + 3 ) − 1 4 ( −7 c − 15 )

( x + 2 ) − 2 5 ( 19 x + 10 ) ( x + 2 ) − 2 5 ( 19 x + 10 )

( 2 z − 9 ) − 3 2 ( 27 z − 99 ) ( 2 z − 9 ) − 3 2 ( 27 z − 99 )

( 14 x −3 ) ( 7 x + 9 ) ( 14 x −3 ) ( 7 x + 9 )

( 3 x + 5 ) ( 3 x −5 ) ( 3 x + 5 ) ( 3 x −5 )

( 2 x + 5 ) 2 ( 2 x − 5 ) 2 ( 2 x + 5 ) 2 ( 2 x − 5 ) 2

( 4 z 2 + 49 a 2 ) ( 2 z + 7 a ) ( 2 z − 7 a ) ( 4 z 2 + 49 a 2 ) ( 2 z + 7 a ) ( 2 z − 7 a )

1 ( 4 x + 9 ) ( 4 x −9 ) ( 2 x + 3 ) 1 ( 4 x + 9 ) ( 4 x −9 ) ( 2 x + 3 )

1.6 Section Exercises

You can factor the numerator and denominator to see if any of the terms can cancel one another out.

True. Multiplication and division do not require finding the LCD because the denominators can be combined through those operations, whereas addition and subtraction require like terms.

y + 5 y + 6 y + 5 y + 6

3 b + 3 3 b + 3

x + 4 2 x + 2 x + 4 2 x + 2

a + 3 a − 3 a + 3 a − 3

3 n − 8 7 n − 3 3 n − 8 7 n − 3

c − 6 c + 6 c − 6 c + 6

d 2 − 25 25 d 2 − 1 d 2 − 25 25 d 2 − 1

t + 5 t + 3 t + 5 t + 3

6 x − 5 6 x + 5 6 x − 5 6 x + 5

p + 6 4 p + 3 p + 6 4 p + 3

2 d + 9 d + 11 2 d + 9 d + 11

12 b + 5 3 b −1 12 b + 5 3 b −1

4 y −1 y + 4 4 y −1 y + 4

10 x + 4 y x y 10 x + 4 y x y

9 a − 7 a 2 − 2 a − 3 9 a − 7 a 2 − 2 a − 3

2 y 2 − y + 9 y 2 − y − 2 2 y 2 − y + 9 y 2 − y − 2

5 z 2 + z + 5 z 2 − z − 2 5 z 2 + z + 5 z 2 − z − 2

x + 2 x y + y x + x y + y + 1 x + 2 x y + y x + x y + y + 1

2 b + 7 a a b 2 2 b + 7 a a b 2

18 + a b 4 b 18 + a b 4 b

a − b a − b

3 c 2 + 3 c − 2 2 c 2 + 5 c + 2 3 c 2 + 3 c − 2 2 c 2 + 5 c + 2

15 x + 7 x −1 15 x + 7 x −1

x + 9 x −9 x + 9 x −9

1 y + 2 1 y + 2

Review Exercises

y = 24 y = 24

3 a 6 3 a 6

x 3 32 y 3 x 3 32 y 3

1.634 × 10 7 1.634 × 10 7

4 2 5 4 2 5

7 2 50 7 2 50

3 x 3 + 4 x 2 + 6 3 x 3 + 4 x 2 + 6

5 x 2 − x + 3 5 x 2 − x + 3

k 2 − 3 k − 18 k 2 − 3 k − 18

x 3 + x 2 + x + 1 x 3 + x 2 + x + 1

3 a 2 + 5 a b − 2 b 2 3 a 2 + 5 a b − 2 b 2

4 a 2 4 a 2

( 4 a − 3 ) ( 2 a + 9 ) ( 4 a − 3 ) ( 2 a + 9 )

( x + 5 ) 2 ( x + 5 ) 2

( 2 h − 3 k ) 2 ( 2 h − 3 k ) 2

( p + 6 ) ( p 2 − 6 p + 36 ) ( p + 6 ) ( p 2 − 6 p + 36 )

( 4 q − 3 p ) ( 16 q 2 + 12 p q + 9 p 2 ) ( 4 q − 3 p ) ( 16 q 2 + 12 p q + 9 p 2 )

( p + 3 ) 1 3 ( −5 p − 24 ) ( p + 3 ) 1 3 ( −5 p − 24 )

x + 3 x − 4 x + 3 x − 4

m + 2 m − 3 m + 2 m − 3

6 x + 10 y x y 6 x + 10 y x y

Practice Test

x = –2 x = –2

3 x 4 3 x 4

13 q 3 − 4 q 2 − 5 q 13 q 3 − 4 q 2 − 5 q

n 3 − 6 n 2 + 12 n − 8 n 3 − 6 n 2 + 12 n − 8

( 4 x + 9 ) ( 4 x − 9 ) ( 4 x + 9 ) ( 4 x − 9 )

( 3 c − 11 ) ( 9 c 2 + 33 c + 121 ) ( 3 c − 11 ) ( 9 c 2 + 33 c + 121 )

4 z − 3 2 z − 1 4 z − 3 2 z − 1

3 a + 2 b 3 b 3 a + 2 b 3 b

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Lab Assignment 7.1

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Name:__________________________________________Date:____________________Row:________

• An unknown distribution has a mean of 45 and a standard deviation of eight. Samples of size n = 30 are drawn randomly from the population. Find the probability that the sample mean is between 42 and 50.
• According to the Internal Revenue Service, the average length of time for an individual to complete (keep records for, learn, prepare, copy, assemble, and send) IRS Form 1040 is 10.53 hours (without any attached schedules). The distribution is unknown. Let us assume that the standard deviation is two hours. Suppose we randomly sample 36 taxpayers. a. In words, 𝑋 =
• In words, 𝑋̅ =
• Would you be surprised if the 36 taxpayers finished their Form 1040s in an average of more than 12 hours? Explain why or why not in complete sentences.
• Would you be surprised if one taxpayer finished his or her Form 1040 in more than 12 hours? In a complete sentence, explain why.

3. Suppose that a category of world-class runners are known to run a marathon (26 miles) in an average of 145 minutes with a standard deviation of 14 minutes. Consider 49 of the races. Let 𝑋̅ the average of the 49 races.

• Find the probability that the runner will average between 142 and 146 minutes in these 49 marathons.
• Find the 80th percentile for the average of these 49 marathons.

4. Cans of a cola beverage claim to contain 16 ounces. The amounts in a sample are measured and the statistics are n = 34, 𝑥̅ = 16.01 ounces. If the cans are filled so that μ = 16.00 ounces (as labeled) and σ = 0.143 ounces.

• Find the probability that a sample of 34 cans will have an average amount greater than 16.01 ounces.
• Do the results suggest that cans are filled with an amount greater than 16 ounces?

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College athletes set to get $2.8 billion, revenue-sharing model in landmark House v. NCAA settlement

Despite the landmark settlement nearing, details surrounding roster sizes and title ix remain unanswered.

A new era of college athletics is upon us, and leaders do not have much time to prepare for the transformative age.

College sports is on the precipice of changing forever after the NCAA Board of Governors and every Power Five conference agreed to destroy the amateurism model and share revenue with players by coming to terms on settling a multi-billion dollar lawsuit that threatened to bankrupt the collegiate athletics enterprise. 

"The five autonomy conferences and the NCAA agreeing to settlement terms is an important step in the continuing reform of college sports that will provide benefits to student-athletes and provide clarity in college athletics across all divisions for years to come," the NCAA and leaders from the Power Five conference wrote in a joint statement. "This settlement is also a road map for college sports leaders and Congress to ensure this uniquely American institution can continue to provide unmatched opportunity for millions of students." 

The $2.8 billion settlement in the House v. NCAA case, a landmark legal battle, has far-reaching implications anchored by revenue sharing and the expansion of roster sizes, which might also spark more legal battles with Title IX implications. In the immediate future, the legal settlement is transformative for players because not only will past athletes be compensated for prior restrictions on earning from their name, image, and likeness via the $2.8 billion settlement, but the agreement sets the stage for a future revenue-sharing model, a first in the NCAA's long history, benefiting thousands of collegiate athletes starting as soon as Fall 2025.

"For the first time in history, we will now have a fair and just economic system for college athletes. I could not be more delighted. But no celebrations until the system is in place," House lead attorney Jeffrey Kessler told CBS Sports.

The NCAA and its conferences will hammer out the details of new revenue-sharing and governance models over the next few months, but a framework was revealed in internal documents uncovered by multiple outlets in recent weeks. Athletic departments must now prepare for new line items that could balloon up to $30 million annually as the richest schools prepare to share upwards of $22 million in revenue with players while expanding roster sizes with unlimited scholarships, according to those documents.

The NCAA agreed to pay the past damages over the next 10 years ($277 million annually) and will fund the payments by cutting into its revenue shares with Division I schools. Had the case gone to trial in January 2025, the NCAA and its power conferences risked being on the hook for more than $4.2 billion because of a triple multiplier tied to antitrust law. Even worse, had a settlement not been reached, the parties risked $20 billion in back damages tied to several antitrust lawsuits that could have forced them into bankruptcy, according to documents circulated last week among conference presidents.

"The most important part about the settlement — and let's face it, there's still a lot of work to be done there — is it creates some clarity and some visibility on a whole bunch of issues that have sort of been roiling everybody for a while," NCAA president Charlie Baker said last week. "The other thing it does is create predictability and stability for schools. It creates a tremendous opportunity for student-athletes."

Discussions concerning a settlement structure have been ongoing for nearly a year. The NCAA is responsible for 40% of the $2.8 billion settlement, and the remaining 60% will come from reducing its revenue distributions to the 32 Division I conferences over the next 10 years ($1.6 billion). The NCAA is utilizing a formula based on revenue distribution presented to each league over a nine-year period starting in 2016, which leans heavily on basketball units tied to NCAA Tournament participation, according to Yahoo Sports . The Power Five conferences – ACC, Big Ten, Big 12, Pac-12 and SEC – will pay 24% of the overall damages, followed by the Group of Five at 10%.The FCS is on the hook for 14% and non-football conferences in Division I will pay 12% of the overall agreement, according to documents reviewed by CBS Sports.

The commissioners of the 22 non-FBS conferences made a late push Monday to flip the financial structure so that the Power Five conferences would be responsible for 60% of the withheld NCAA distributions over the next 10 years, but that effort failed in the 11th hour when the NCAA's Board of Directors approved the aforementioned settlement terms that evening. The 27 conferences outside the current Power Four leagues will be on the hook for 60% of the NCAA's withheld distributions.

Beyond the monetary figures and future revenue sharing, the settlement also further widens the gap between the four power conferences fueled by football revenue and the Group of Five conferences in the Football Bowl Subdivision. Power conferences are also expected to design a new governance structure to enforce rules that will be separate from its compatriots. The legislation is expected to provide unlimited scholarships while restructuring roster limits, which could cut down on the number of active football players but also allow programs to award more scholarships for sports like baseball, which has long been stuck on 11.7 scholarships to share with a team of nearly 40 players.

Further complicating the relationships among conferences is the financial gap exacerbated by a recently approved revenue structure with the College Football Playoff, which shares most of its revenue with the Big Ten and SEC.

Simply put, just because the biggest lawsuit in NCAA history is settled and players will soon be paid after years of carrying a multi-billion dollar industry on their backs, that doesn't mean the future will be without monumental challenges that could lead to the elimination of sports and further separation between the haves and have-nots among athletic departments in the FBS. 

How much will current and future players be paid?

The schools among the Power Four conferences are expected to pay current players roughly $20 million annually as part of a new revenue-sharing program. The figure will fluctuate from school to school, reflecting an estimated share of 22% of annual revenue generated by Power Four schools.

The agreement is expected to include a cap on revenue-sharing, which could start as high as $22 million annually per school, according to Yahoo Sports .

"Local decisions, I think, are good at times where schools that have more resources can do more," ACC commissioner Jim Phillips said last week. "... So some flexibility in a final decision and a final agreement will be helpful for our schools."

Former Pac-12 schools are included in the suit as part of the pay for past damages. According to multiple reports, the five power conferences are responsible for roughly 40% of the NCAA's school reductions for damages (between $597.6 million to $730.4 million). Those schools are expected to see an average drop between $1 million and $2 million in annual revenue from the NCAA to fund the settlement. 

Group of Five schools are responsible for 17% ($255.6 million to $312.4 million) and Football Championship Subdivision conferences will share 22% of the reductions ($327.6 million to $400.4 million).

Meanwhile, the NCAA is expected to reduce operating costs by $18 million a year, dipping into reserves and insurance to help fund its portion of the legal settlement ($1.1 billion), according to Yahoo Sports.

Will the math work in the Group of Five?

Many industry leaders, particularly those in the Group of Five conferences, are concerned revenue-sharing could send more athletic department budgets into the red, leading to the elimination of sports programs entirely. Many athletic departments are subsidized by student fees from the university and state funds, and some already operate at a deficit.

More than 50% of Group of Five schools earn less than $40 million annually in revenue. The Power Five conferences (then including the Pac-12) combined for more than $3.3 billion in revenue for the 2022 fiscal year, according to federal tax records. Ohio State earned $251.6 million in revenue last year to lead all Power Five schools.

"You really have to think about [Power Four] as different," House plaintiff attorney Jeffrey Kessler said during a panel at Howard University in April, according to Yahoo Sports . "The reason we get tied in knots is because we conflate those schools who have developed these gigantic independent commercial businesses with the schools who are still just educational institutions with extracurricular activities. When you try to come up with one rule for all, you go crazy. You have to look at the schools differently. For the ones with the money, there is plenty of money to compensate the athletes and share it with the women's sports."

Title IX and antitrust questions remain

Plaintiffs in the House suit are expected to give up their right to file antitrust lawsuits against the NCAA's rules for 10 years, and the plaintiff attorneys are expected to drop two additional pending antitrust cases against the NCAA. This agreement could be strengthened if the NCAA is finally successful in lobbying Congress, which could codify the settlement with legislation protecting the NCAA and its members with an antitrust exemption. Congress, however, has been slow to act after being presented with more than a dozen proposals concerning NIL guardrails over the last several years.

Title IX also complicates matters, and future court battles could loom. The unspoken truth among administrators is it seems unlikely they will advocate for equal pay for athletes whose sports earn less than football and men's basketball. 

"It's very likely we're going to see non-revenue sports get massacred," said Jason Belzer, president of Student Athlete NIL. "Title IX is going to be a very big battle. How are you going to stop it? It's going to be tough."

Many finer details are yet to be finalized. Attorneys will soon draft the terms of the settlement agreement, which they will then present to Senior District Judge Claudia Wilken in California's Northern District at a preliminary hearing yet to be scheduled. 

Roster sizes and scholarship limits will change

The new model will likely lift scholarship limits but also limit roster sizes. Those details are expected to be finalized in the coming months at the conference level and could vary within Division I.

Theoretically, football roster sizes could be trimmed from 120 to 100 players, but scholarships could be provided to all players instead of the currently mandated 85. For baseball-crazy conferences like those in the power structure, programs could finally provide scholarships to every player on the roster rather than often-criticized equivalencies of 11.7 scholarships that are shared among 27 players on a 39-man roster.

Again, there is much to consider and discuss before numbers are finalized on the conference level over the next year.

What happens to NIL collectives?

The NCAA has also proposed a new enforcement infrastructure to target pay-for-play and booster-led NIL collectives, though the details remain vague, according to documents obtained last week by Yahoo Sports . 

The documents contend the court will reaffirm rules around compensation, "including the prohibition on booster payments if they are not true NIL."  Schools will also be provided "economic incentives" to house NIL collectives within the university.

"Collectives aren't going to go away if there's a salary cap," said Russell White, president of The Collective Association. "Universities will continue to want to compete above and beyond (the base revenue shares)."

Ten-year NCAA revenue reduction projections

• FBS Power Five: $597.6 million to $730.4 million
• FBS Group of Five: $255.6 million to $312.4 million
• FCS: $327.6 million to $400.4 million
• Big Ten: $149 million to $182.6 million
• ACC: $141.3 million to $172.7 million
• SEC: $111.6 million to $136.4 million
• Big 12: $99 million to $121 million
• Pac-12: $96.3 million to $117.7 million

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NCAA | May 26, 2024

Sixteen regional sites selected for the 2024 ncaa di baseball championship.

INDIANAPOLIS – The NCAA Division I Baseball Committee announced the 16 regional sites for the 77th annual NCAA Division I Baseball Championship.

The 16 regional sites, with host institutions and records are as follows: 

• Athens, Georgia – Georgia (39-15)
• Chapel Hill, North Carolina – North Carolina (42-13)
• Charlottesville, Virginia – Virginia (41-15)
• Clemson, South Carolina – Clemson (41-14)
• Bryan-College Station, Texas – Texas A&M (44-13)
• Corvallis, Oregon – Oregon State (42-14)
• Fayetteville, Arkansas – Arkansas (43-14)
• Greenville, North Carolina – East Carolina (43-15)
• Knoxville, Tennessee – Tennessee (50-11) 
• Lexington, Kentucky – Kentucky (40-14) 
• Norman, Oklahoma – Oklahoma (37-19) 
• Raleigh, North Carolina – NC State (33-20) 
• Santa Barbara, California – UC Santa Barbara (42-12) 
• Stillwater, Oklahoma – Oklahoma State (40-17) 
• Tallahassee, Florida – Florida State (42-15)
• Tucson, Arizona – Arizona (36-21)

By being awarded a regional, all 16 host institutions have also been selected to the 64-team championship field.

Each regional field features four teams, playing in a double-elimination format. All 16 regionals are scheduled to be conducted from Friday, May 31 to Monday, June 3 (if necessary).

UC Santa Barbara is hosting for only the second time and for the first time in Santa Barbara (it hosted at a neutral site at Lake Elsinore in 2015).

Florida State is hosting a baseball regional for the 36th time in tournament history, the most by any school. Oklahoma is hosting for the first time since 2010.

Arkansas, Clemson, Kentucky, Oklahoma State and Virginia each hosted regionals in 2023 and Oklahoma State is hosting for a third consecutive season.

The full 64-team field, top-16 national seeds, first-round regional pairings and site assignments will be announced at Noon (ET), on Monday, May 27. The one-hour program will be shown live on ESPN2. The committee will set the entire 64-team bracket through both the super regionals and the first round of the Men’s College World Series and will not reseed the field after play begins. 

Selection of the eight super regional hosts will be announced on www.NCAA.com/mcws , Tuesday, June 4 at 10 a.m. (ET). 

There are 30 Division I Conferences which will receive an automatic berth in the field of 64, along with 34 at-large selections. The Men’s College World Series begins play Friday, June 14, at Charles Schwab Field Omaha in Omaha, Nebraska.  

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Whales Have an Alphabet

Until the 1960s, it was uncertain whether whales made any sounds at all..

This transcript was created using speech recognition software. While it has been reviewed by human transcribers, it may contain errors. Please review the episode audio before quoting from this transcript and email [email protected] with any questions.

[MUSIC PLAYING]

From “The New York Times,” I’m Michael Barbaro. This is “The Daily.”

Today, ever since the discovery that whales produce songs, scientists have been trying to find a way to decipher their lyrics. After 60 years, they may have finally done it. My colleague, Carl Zimmer, explains.

It’s Friday, May 24.

I have to say, after many years of working with you on everything from the pandemic to —

— CRISPR DNA technology, that it turns out your interests are even more varied than I had thought, and they include whales.

They do indeed.

And why? What is it about the whale that captures your imagination?

I don’t think I’ve ever met anybody who is not fascinated by whales. I mean, these are mammals like us, and they’re swimming around in the water. They have brains that are much bigger than ours. They can live maybe 200 years. These are incredible animals, and animals that we still don’t really understand.

Right. Well, it is this majestic creature that brings us together today, Carl, because you have been reporting on a big breakthrough in our understanding of how it is that whales communicate. But I think in order for that breakthrough to make sense, I think we’re going to have to start with what we have known up until now about how whales interact. So tell us about that.

Well, people knew that whales and dolphins traveled together in groups, but up until the 1960s, we didn’t really know that whales actually made any sounds at all. It was actually sort of an accident that we came across it. The American military was developing sophisticated microphones to put underwater. They wanted to listen for Russian submarines.

As one does. But there was an engineer in Bermuda, and he started hearing some weird stuff.

[WHALE SOUNDS]

And he wondered maybe if he was actually listening to whales.

What made him wonder if it was whales, of all things?

Well, this sound did not sound like something geological.

It didn’t sound like some underwater landslide or something like that. This sounded like a living animal making some kind of call. It has these incredible deep tones that rise up into these strange, almost falsetto type notes.

It was incredibly loud. And so it would have to be some really big animal. And so with humpback whales swimming around Bermuda, this engineer thought, well, maybe these are humpback whales.

And so he gets in touch with a husband and wife team of whale biologists, Roger and Katy Payne, and plays these recordings to them. And they’re pretty convinced that they’re hearing whales, too. And then they go on to go out and confirm that by putting microphones in the water, chasing after groups of whales and confirming, yes, indeed, that these sounds are coming from these humpback whales.

So once these scientists confirm in their minds that these are the sounds of a whale, what happens with this discovery?

Well, Roger and Katy Payne and their colleagues are astonished that this species of whale is swimming around singing all the time for hours on end. And it’s so inspirational to them that they actually help to produce a record that they release “The Song of the Humpback Whale” in 1970.

And so this is being sold in record stores, you know, along with Jimi Hendrix and Rolling Stones. And it is a huge hit.

Yeah, it sells like two million copies.

Well, at the time, it was a huge cultural event. This record, this became almost like an anthem of the environmental movement. And it led, for whales in particular, to a lot of protections for them because now people could appreciate that whales were a lot more marvelous and mysterious than they maybe had appreciated before.

And so you have legislation, like the Marine Mammal Act. The United States just agrees just to stop killing whales. It stops its whaling industry. And so you could argue that the discovery of these whale songs in Bermuda led to at least some species of whales escaping extinction.

Well, beyond the cultural impact of this discovery, which is quite meaningful, I wonder whether scientists and marine biologists are figuring out what these whale songs are actually communicating.

So the Paynes create a whole branch of science, the study of whale songs. It turns out that pretty much every species of whale that we know of sings in some way or another. And it turns out that within a species, different groups of whales in different parts of the world may sing with a different dialect. But the big question of what these whales are singing, what do these songs mean, that remains elusive into the 21st century. And things don’t really change until scientists decide to take a new look at the problem in a new way.

And what is that new way?

So in 2020, a group of whale biologists, including Roger Payne, come together with computer scientists from MIT. Instead of humpback whales, which were the whales where whale songs are first discovered, these scientists decide to study sperm whales in the Caribbean. And humpback whales and sperm whales have very, very different songs. So if you’re used to humpback whales with their crazy high and low singing voices —

Right, those best-selling sounds.

— those are rockin’ tunes of the humpback whales, that’s not what sperm whales do. Sperm whales have a totally different way of communicating with each other. And I actually have some recordings that were provided by the scientists who have been doing this research. And so we can take a listen to some of them.

Wow, It’s like a rhythmic clicking.

These are a group of sperm whales swimming together, communicating.

So whale biologists knew already that there was some structure to this sound. Those clicks that you hear, they come in little pulses. And each of those pulses is known as a coda. And whale biologists had given names to these different codas. So, for example, they call one coda, one plus one plus three —

— which is basically click, click, click, click, click, or four plus three, where you have four clicks in a row and a pause and then three clicks in a row.

Right. And the question would seem to be, is this decipherable communication, or is this just whale gibberish?

Well, this is where the computer scientists were able to come in and to help out. The whale biologists who were listening to the codas from the sperm whales in the Caribbean, they had identified about 21 types. And then that would seem to be about it.

But then, an MIT computer science graduate student named Prajusha Sharma was given the job of listening to them again.

And what does she hear?

In a way, it’s not so much what she heard, but what she saw.

Because when scientists record whale songs, you can look at it kind of like if you’re looking at an audio of a recording of your podcast, you will see the little squiggles of your voice.

And so whale biologists would just look at that ticker of whale songs going across the screen and try to compare them. And Sharma said, I don’t like this. I just — this is not how I look at data. And so what she decided to do is she decided to kind of just visualize the data differently. And essentially, she just kind of flipped these images on their side and saw something totally new.

And what she saw was that sperm whales were singing a whole bunch of things that nobody had actually been hearing.

One thing that she discovered was that you could have a whale that was producing a coda over and over and over again, but it was actually playing with it. It was actually stretching out the coda,

[CLICKING] So to get a little bit longer and a little bit longer, a little bit longer.

And then get shorter and shorter and shorter again. They could play with their codas in a way that nobody knew before. And she also started to see that a whale might throw in an extra click at the end of a coda. So it would be repeating a coda over and over again and then boom, add an extra one right at the end. What they would call an ornamentation. So now, you have yet another signal that these whales are using.

And if we just look at what the sperm whales are capable of producing in terms of different codas, we go from just 21 types that they had found in the Caribbean before to 156. So what the scientists are saying is that what we might be looking at is what they call a sperm whale phonetic alphabet.

Yeah, that’s a pretty big deal because the only species that we know of for sure that has a phonetic alphabet —

— is us, exactly. So the reason that we can use language is because we can make a huge range of sounds by just doing little things with our mouths. A little change in our lips can change a bah to a dah. And so we are able to produce a set of phonetic sounds. And we put those sounds together to make words.

So now, we have sperm whales, which have at least 150 of these different versions of sounds that they make just by making little adjustments to the existing way that they make sounds. And so you can make a chart of their phonetic alphabet, just like you make a chart of the human phonetic alphabet.

So then, that raises the question, do they combine their phonetic alphabet into words? Do they combine their words into sentences? In other words, do sperm whales have a language of their own?

Right. Are they talking to each other, really talking to each other?

If we could really show that whales had language on par with humans, that would be like finding intelligent life on another planet.

We’ll be right back.

So, Carl, how should we think about this phonetic alphabet and whether sperm whales are actually using it to talk to each other?

The scientists on this project are really careful to say that these results do not definitively prove what these sperm whale sounds are. There are a handful of possibilities here in terms of what this study could mean. And one of them is that the whales really are using full-blown language.

What they might be talking about, we don’t know. I mean, perhaps they like to talk about their travels over hundreds and thousands of miles. Maybe they’re talking about, you know, the giant squid that they caught last night. Maybe they’re gossiping about each other.

And you have to remember, sperm whales are incredibly social animals. They have relationships that last for decades. And they live in groups that are in clans of thousands of whales. I mean, imagine the opportunities for gossip.

These are all at least imaginable now. But it’s also possible that they are communicating with each other, but in a way that isn’t language as we know it. You know, maybe these sounds that they’re producing don’t add up to sentences. There’s no verb there. There’s no noun. There’s no structure to it in terms of how we think of language.

But maybe they’re still conveying information to each other. Maybe they’re somehow giving out who they are and what group they belong to. But it’s not in the form of language that we think of.

Right. Maybe it’s more kind of caveman like as in whale to whale, look, there, food.

It’s possible. But, you know, other species have evolved in other directions. And so you have to put yourself in the place of a sperm whale. You know, so think about this. They are communicating in the water. And actually, like sending sounds through water is a completely different experience than through the air like we do.

So a sperm whale might be communicating to the whale right next to it a few yards away, but it might be communicating with whales miles away, hundreds of miles away. They’re in the dark a lot of the time, so they don’t even see the whales right next to them. So it’s just this constant sound that they’re making because they’re in this dark water.

So we might want to imagine that such a species would talk the way we do, but there are just so many reasons to expect that whatever they’re communicating might be just profoundly different, so different that it’s actually hard for us to imagine. And so we need to really, you know, let ourselves be open to lots of possibilities.

And one possibility that some scientists have raised is that maybe language is just the wrong model to think about. Maybe we need to think about music. You know, maybe this strange typewriter, clickety clack is actually not like a Morse code message, but is actually a real song. It’s a kind of music that doesn’t necessarily convey information the way conversation does, but it brings the whales together.

In humans, like, when we humans sing together in choruses, it can be a very emotional experience. It’s a socially bonding experience, but it’s not really like the specific words that we’re singing that bring us together when we’re singing. It’s sharing the music together.

But at a certain point, we stop singing in the chorus, and we start asking each other questions like, hey, what are you doing for dinner? How are you going to get home? There’s a lot of traffic on the BQE. So we are really drawn to the possibility that whales are communicating in that same kind of a mode.

We’re exchanging information. We’re seeking out each other’s well-being and emotional state. And we’re building something together.

And I think that happens because, I mean, language is so fundamental to us as human beings. I mean, it’s like every moment of our waking life depends on language. We are talking to ourselves if we’re not talking to other people.

In our sleep, we dream, and there are words in our dreams. And we’re just stewing in language. And so it’s really, really hard for us to understand how other species might have a really complex communication system with hundreds of different little units of sound that they can use and they can deploy. And to think anything other than, well, they must be talking about traffic on the BQE. Like —

— we’re very human-centric. And we have to resist that.

So what we end up having here is a genuine breakthrough in our understanding of how whales interact. And that seems worth celebrating in and of itself. But it really kind of doubles as a lesson in humility for us humans when it comes to appreciating the idea that there are lots of non-human ways in which language can exist.

That’s right. Humility is always a good idea when we’re thinking about other animals.

So what now happens in this realm of research? And how is it that these scientists, these marine biologists and these computer scientists are going to try to figure out what exactly this alphabet amounts to and how it’s being used?

So what’s going to happen now is a real sea change in gathering data from whales.

So to speak.

So these scientists are now deploying a new generation of undersea microphones. They’re using drones to follow these whales. And what they want to do is they want to be recording sounds from the ocean where these whales live 24 hours a day, seven days a week. And so the hope is that instead of getting, say, a few 100 codas each year on recording, these scientists want to get several hundred million every year, maybe billions of codas every year.

And once you get that much data from whales, then you can start to do some really amazing stuff with artificial intelligence. So these scientists hope that they can use the same kind of artificial intelligence that is behind things like ChatGPT or these artificial intelligence systems that are able to take recordings of people talking and transcribing them into text. They want to use that on the whale communication.

They want to just grind through vast amounts of data, and maybe they will discover more phonetic letters in this alphabet. Who knows? Maybe they will actually find bigger structures, structures that could correspond to language.

If you go really far down this route of possibilities, the hope is that you would understand what sperm whales are saying to each other so well that you could actually create artificial sperm whale communication, and you could play it underwater. You could talk to the sperm whales. And they would talk back. They would react somehow in a way that you had predicted. If that happens, then maybe, indeed, sperm whales have something like language as we understand it.

And the only way we’re going to figure that out is if we figure out not just how they talk to themselves, but how we can perhaps talk to them, which, given everything we’ve been talking about here, Carl, is a little bit ironic because it’s pretty human-centric.

That’s right. This experiment could fail. It’s possible that sperm whales don’t do anything like language as we know it. Maybe they’re doing something that we can’t even imagine yet. But if sperm whales really are using codas in something like language, we are going to have to enter the conversation to really understand it.

Well, Carl, thank you very much. We appreciate it.

Thank you. Sorry. Can I say that again? My voice got really high all of a sudden.

A little bit like a whale’s. Ooh.

Yeah, exactly. Woot. Woot.

Thank yoooo. No. Thank you.

Here’s what else you need to know today.

We allege that Live Nation has illegally monopolized markets across the live concert industry in the United States for far too long. It is time to break it up.

On Thursday, the Justice Department sued the concert giant Live Nation Entertainment, which owns Ticketmaster, for violating federal antitrust laws and sought to break up the $23 billion conglomerate. During a news conference, Attorney General Merrick Garland said that Live Nation’s monopolistic tactics had hurt the entire industry of live events.

The result is that fans pay more in fees, artists have fewer opportunities to play concerts, smaller promoters get squeezed out, and venues have fewer real choices.

In a statement, Live Nation called the lawsuit baseless and vowed to fight it in court.

A reminder — tomorrow, we’ll be sharing the latest episode of our colleagues’ new show, “The Interview.” This week on “The Interview,” Lulu Garcia-Navarro talks with Ted Sarandos, the CEO of Netflix, about his plans to make the world’s largest streaming service even bigger.

I don’t agree with the premise that quantity and quality are somehow in conflict with each other. I think our content and our movie programming has been great, but it’s just not all for you.

Today’s episode was produced by Alex Stern, Stella Tan, Sydney Harper, and Nina Feldman. It was edited by MJ Davis, contains original music by Pat McCusker, Dan Powell, Elisheba Ittoop, Marion Lozano, and Sophia Lanman, and was engineered by Alyssa Moxley. Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly.

Special thanks to Project SETI for sharing their whale recordings.

That’s it for “The Daily.” I’m Michael Barbaro. See you on Tuesday after the holiday.

• May 30, 2024   •   25:21 The Government Takes On Ticketmaster
• May 29, 2024   •   29:46 The Closing Arguments in the Trump Trial
• May 28, 2024   •   25:56 The Alitos and Their Flags
• May 24, 2024   •   25:18 Whales Have an Alphabet
• May 23, 2024   •   34:24 I.C.C. Prosecutor Requests Warrants for Israeli and Hamas Leaders
• May 22, 2024   •   23:20 Biden’s Open War on Hidden Fees
• May 21, 2024   •   24:14 The Crypto Comeback
• May 20, 2024   •   31:51 Was the 401(k) a Mistake?
• May 19, 2024   •   33:23 The Sunday Read: ‘Why Did This Guy Put a Song About Me on Spotify?’
• May 17, 2024   •   51:10 The Campus Protesters Explain Themselves
• May 16, 2024   •   30:47 The Make-or-Break Testimony of Michael Cohen
• May 15, 2024   •   27:03 The Possible Collapse of the U.S. Home Insurance System

Hosted by Michael Barbaro

Featuring Carl Zimmer

Produced by Alex Stern ,  Stella Tan ,  Sydney Harper and Nina Feldman

Edited by MJ Davis Lin

Original music by Elisheba Ittoop ,  Dan Powell ,  Marion Lozano ,  Sophia Lanman and Pat McCusker

Engineered by Alyssa Moxley

Listen and follow The Daily Apple Podcasts | Spotify | Amazon Music | YouTube

Ever since the discovery of whale songs almost 60 years ago, scientists have been trying to decipher the lyrics.

But sperm whales don’t produce the eerie melodies sung by humpback whales, sounds that became a sensation in the 1960s. Instead, sperm whales rattle off clicks that sound like a cross between Morse code and a creaking door. Carl Zimmer, a science reporter, explains why it’s possible that the whales are communicating in a complex language.

On today’s episode

Carl Zimmer , a science reporter for The New York Times who also writes the Origins column .

Background reading

Scientists find an “alphabet” in whale songs.

These whales still use their vocal cords. But how?

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We aim to make transcripts available the next workday after an episode’s publication. You can find them at the top of the page.

The Daily is made by Rachel Quester, Lynsea Garrison, Clare Toeniskoetter, Paige Cowett, Michael Simon Johnson, Brad Fisher, Chris Wood, Jessica Cheung, Stella Tan, Alexandra Leigh Young, Lisa Chow, Eric Krupke, Marc Georges, Luke Vander Ploeg, M.J. Davis Lin, Dan Powell, Sydney Harper, Mike Benoist, Liz O. Baylen, Asthaa Chaturvedi, Rachelle Bonja, Diana Nguyen, Marion Lozano, Corey Schreppel, Rob Szypko, Elisheba Ittoop, Mooj Zadie, Patricia Willens, Rowan Niemisto, Jody Becker, Rikki Novetsky, John Ketchum, Nina Feldman, Will Reid, Carlos Prieto, Ben Calhoun, Susan Lee, Lexie Diao, Mary Wilson, Alex Stern, Dan Farrell, Sophia Lanman, Shannon Lin, Diane Wong, Devon Taylor, Alyssa Moxley, Summer Thomad, Olivia Natt, Daniel Ramirez and Brendan Klinkenberg.

Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly. Special thanks to Sam Dolnick, Paula Szuchman, Lisa Tobin, Larissa Anderson, Julia Simon, Sofia Milan, Mahima Chablani, Elizabeth Davis-Moorer, Jeffrey Miranda, Renan Borelli, Maddy Masiello, Isabella Anderson and Nina Lassam.

Carl Zimmer covers news about science for The Times and writes the Origins column . More about Carl Zimmer

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