What you would do here is subtract.
The first day had 108 teams, and the second day had 10 less teams. 108-10 is 98, so there were 98 teams on the second day.
A.) Mark is correct as every increase in x of 2 equals a y increase of 4
9514 1404 393
Answer:
Perimeter: 17 inches
Area: 8 square inches
Step-by-step explanation:
The ratio of perimeters is the same as the similarity ratio.
JKLM perimeter / ABCD perimeter = P/68 = 1/4
Multiplying by 68, we get ...
P = 68/4 = 17 . . . . inches
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The ratio of areas is the square of the similarity ratio.
JKLM area / ABCD area = A/128 = (1/4)^2
Multiplying by 128, we get ...
A = 128/16 = 8 . . . . square inches
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Perimeter = 17 inches
Area = 8 square inches
Answer:
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Step-by-step explanation:
Answer:
P(x ≤ 5 ) = 0.9707
P ( x ≥ 6) = 0.0293
Step-by-step explanation:
The probability of a binomial mass distribution can be expressed with the formula:
![\mathtt{P(X=x) =(^{n}_{x} ) \ \pi^x \ (1-\pi)^{n-x}}](https://tex.z-dn.net/?f=%5Cmathtt%7BP%28X%3Dx%29%20%3D%28%5E%7Bn%7D_%7Bx%7D%20%29%20%20%20%5C%20%20%5Cpi%5Ex%20%5C%20%20%281-%5Cpi%29%5E%7Bn-x%7D%7D)
![\mathtt{P(X=x) =(\dfrac{n!}{x!(n-x)!} ) \ \pi^x \ (1-\pi)^{n-x}}](https://tex.z-dn.net/?f=%5Cmathtt%7BP%28X%3Dx%29%20%3D%28%5Cdfrac%7Bn%21%7D%7Bx%21%28n-x%29%21%7D%20%29%20%20%20%5C%20%20%5Cpi%5Ex%20%5C%20%20%281-%5Cpi%29%5E%7Bn-x%7D%7D)
where;
n = 8 and π = 0.36
For x = 5
The probability ![\mathtt{P(X=5) =(\dfrac{8!}{5!(8-5)!} ) \ 0.36^5 \ (1-0.36)^{8-5}}](https://tex.z-dn.net/?f=%5Cmathtt%7BP%28X%3D5%29%20%3D%28%5Cdfrac%7B8%21%7D%7B5%21%288-5%29%21%7D%20%29%20%20%20%5C%20%200.36%5E5%20%5C%20%20%281-0.36%29%5E%7B8-5%7D%7D)
![\mathtt{P(X=5) =(\dfrac{8!}{5!(3)!} ) \ 0.36^5 \ (0.64)^{3}}](https://tex.z-dn.net/?f=%5Cmathtt%7BP%28X%3D5%29%20%3D%28%5Cdfrac%7B8%21%7D%7B5%21%283%29%21%7D%20%29%20%20%20%5C%20%200.36%5E5%20%5C%20%20%280.64%29%5E%7B3%7D%7D)
![\mathtt{P(X=5) =(\dfrac{8 \times 7 \times 6 \times 5!}{5!(3)!} ) \times \ 0.0060466 \ \times 0.262144}](https://tex.z-dn.net/?f=%5Cmathtt%7BP%28X%3D5%29%20%3D%28%5Cdfrac%7B8%20%5Ctimes%207%20%5Ctimes%206%20%5Ctimes%205%21%7D%7B5%21%283%29%21%7D%20%29%20%20%5Ctimes%20%20%5C%200.0060466%20%5C%20%20%5Ctimes%200.262144%7D)
![\mathtt{P(X=5) =(\dfrac{8 \times 7 \times 6 }{3 \times 2 \times 1} ) \times \ 0.0060466 \ \times 0.262144}](https://tex.z-dn.net/?f=%5Cmathtt%7BP%28X%3D5%29%20%3D%28%5Cdfrac%7B8%20%5Ctimes%207%20%5Ctimes%206%20%7D%7B3%20%5Ctimes%202%20%5Ctimes%201%7D%20%29%20%20%5Ctimes%20%20%5C%200.0060466%20%5C%20%20%5Ctimes%200.262144%7D)
![\mathtt{P(X=5) =({8 \times 7 } ) \times \ 0.0060466 \ \times 0.262144}](https://tex.z-dn.net/?f=%5Cmathtt%7BP%28X%3D5%29%20%3D%28%7B8%20%5Ctimes%207%20%7D%20%29%20%20%5Ctimes%20%20%5C%200.0060466%20%5C%20%20%5Ctimes%200.262144%7D)
![\mathtt{P(X=5) =0.0887645}](https://tex.z-dn.net/?f=%5Cmathtt%7BP%28X%3D5%29%20%3D0.0887645%7D)
to 4 decimal places
b. x ≤ 5
The probability of P ( x ≤ 5)![\mathtt{P(x \leq 5) = P(x = 0)+ P(x = 1)+ P(x = 2)+ P(x = 3)+ P(x = 4)+ P(x = 5})](https://tex.z-dn.net/?f=%5Cmathtt%7BP%28x%20%5Cleq%205%29%20%3D%20P%28x%20%3D%200%29%2B%20P%28x%20%3D%201%29%2B%20P%28x%20%3D%202%29%2B%20P%28x%20%3D%203%29%2B%20P%28x%20%3D%204%29%2B%20P%28x%20%3D%205%7D%29)
![{P(x \leq 5) = ( \dfrac{8!}{0!(8!)} \times (0.36)^0 \times (1-0.36)^8 \ ) + \dfrac{8!}{1!(7!)} \times (0.36)^1 \times (1-0.36)^7 \ +](https://tex.z-dn.net/?f=%7BP%28x%20%5Cleq%205%29%20%3D%20%28%20%5Cdfrac%7B8%21%7D%7B0%21%288%21%29%7D%20%5Ctimes%20%20%280.36%29%5E0%20%20%5Ctimes%20%20%281-0.36%29%5E8%20%20%5C%20%29%20%20%2B%20%20%5Cdfrac%7B8%21%7D%7B1%21%287%21%29%7D%20%5Ctimes%20%20%280.36%29%5E1%20%20%5Ctimes%20%20%281-0.36%29%5E7%20%20%5C%20%2B)
![\dfrac{8!}{2!(6!)} \times (0.36)^2 \times (1-0.36)^6 \ + \dfrac{8!}{3!(5!)} \times (0.36)^3 \times (1-0.36)^5 + \dfrac{8!}{4!(4!)} \times (0.36)^4 \times (1-0.36)^4 \ + \dfrac{8!}{5!(3!)} \times (0.36)^5 \times (1-0.36)^3 \ )](https://tex.z-dn.net/?f=%5Cdfrac%7B8%21%7D%7B2%21%286%21%29%7D%20%5Ctimes%20%20%280.36%29%5E2%20%20%5Ctimes%20%20%281-0.36%29%5E6%20%20%5C%20%2B%20%20%5Cdfrac%7B8%21%7D%7B3%21%285%21%29%7D%20%5Ctimes%20%20%280.36%29%5E3%20%20%5Ctimes%20%20%281-0.36%29%5E5%20%2B%20%20%5Cdfrac%7B8%21%7D%7B4%21%284%21%29%7D%20%5Ctimes%20%20%280.36%29%5E4%20%20%5Ctimes%20%20%281-0.36%29%5E4%20%20%5C%20%20%2B%20%20%5Cdfrac%7B8%21%7D%7B5%21%283%21%29%7D%20%5Ctimes%20%20%280.36%29%5E5%20%20%5Ctimes%20%20%281-0.36%29%5E3%20%20%5C%20%29)
P(x ≤ 5 ) = 0.0281+0.1267+0.2494+0.2805+0.1972+0.0888
P(x ≤ 5 ) = 0.9707
c. x ≥ 6
The probability of P ( x ≥ 6) = 1 - P( x ≤ 5 )
P ( x ≥ 6) = 1 - 0.9707
P ( x ≥ 6) = 0.0293