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3 years ago

Select all ratios equivalent to 2:3. 14:6 10:12 12:18

Mathematics

1 answer:

Nataly [62]3 years ago

8 0

Answer:

12 : 18

Step-by-step explanation:

because 2x6 =12

and 3x6 = 18

since other numbers cant be multiplied by the same number for both sides

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There are currently 16 teams in the National Football Conference (NFC). Of those teams, 11 have won at least one super bowl and

svp [43]

You are given 16 teams, 11 have won at least one super bowl and 5 have not.

A. The probability that both selected teams have won at least 1 super bowl is

$Pr(A)=\dfrac{C_{11}^2}{C_{16}^2}=\dfrac{\dfrac{11!}{2!(11-2)!}}{\dfrac{16!}{2!(16-2)!}}=\dfrac{\dfrac{10\cdot 11}{2}}{\dfrac{15\cdot 16}{2}}=\dfrac{55}{120}=\dfrac{11}{24}.$

B. The probability that neither selected team has won at least 1 super bowl is

$Pr(B)=\dfrac{C_{5}^2}{C_{16}^2}=\dfrac{\dfrac{5!}{2!(5-2)!}}{\dfrac{16!}{2!(16-2)!}}=\dfrac{\dfrac{4\cdot 5}{2}}{\dfrac{15\cdot 16}{2}}=\dfrac{10}{120}=\dfrac{1}{12}.$

C. The probability that at least one selected team has won at least 1 super bowl is

$Pr(C)=1-Pr(B)=1-\dfrac{1}{12}=\dfrac{11}{12}.$

D. to find the probability that the second team selected has won at least 1 super bowl given that the first team selected has not won a super bowl, consider such events:

P - the second team selected has won at least 1 super bowl;

Q - the first team selected has not won a super bowl.

Then

$Pr(P|Q)=\dfrac{Pr(P\cap Q)}{Pr(Q)}=\dfrac{\dfrac{5\cdot 11}{C_{16}^2}}{\dfrac{C_5^1\cdot C_{15}^1}{C_{16}^2}}=\dfrac{55}{75}=\dfrac{11}{15}.$

E. To find the probability that the second team selected has won at least 1 super bowl given that the first team selected has won at least 1 super bowl, consider events:

M - the second team selected has won at least 1 super bowl;

N - the first team selected has won at least 1 super bowl.

Then

$Pr(M|N)=\dfrac{Pr(M\cap N)}{Pr(N)}=\dfrac{\dfrac{11\cdot 10}{C_{16}^2}}{\dfrac{C_{11}^1\cdot C_{15}^1}{C_{16}^2}}=\dfrac{110}{165}=\dfrac{2}{3}.$

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3 years ago

A rocking horse has a weight limit of 60 pounds what percentage is 95% of the weight

yaroslaw [1]

Answer:

57 lbs is your answer

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3 years ago

If papers were 60 cents per hundred papers, if you purchase 50 papers how much did you spend?PLEASE HELP I NEED THIS ANSWER STAT

Darina [25.2K]

Answer:

$83.33

Step-by-step explanation:

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3 years ago

The cross country coach later determines that the length of the football field is 120 yards. all students must run 5 laps. using

Sloan [31]

First we will need your answer for part A!

3 0

4 years ago

Read 2 more answers

What is the solution of the system of equations shown below? y = 4x + 4 y<br> = x^2 - 5x + 18 *

melisa1 [442]

Answer:

(7, 32) and (2, 12)

Step-by-step explanation:

y = 4x + 4

y = x² - 5x + 18

4x + 4 = x² - 5x + 18

x² - 9x + 14 = 0

14 = (-7)(-2)

-9 = -7 + (-2)

(x - 7)(x - 2)=0

x= 7, x = 2

For x = 7

y = 4x + 4 = 4*7 + 4 = 32

(7, 32)

For x = 2

y = 4x + 4 = 4*2 + 4 = 12

(2, 12)

Check:

y = x² - 5x + 18

(7, 32)

32 = 7² - 5*7 + 18

32= 32 true

(2, 12)

12 = 2² - 5*2 + 18

12 = 12 true

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3 years ago

Read 2 more answers