Answer:
(k ∘ p)(x) = 2x^2 − 12x + 13
Step-by-step explanation:
k(x) = 2x^2 − 5 and p(x) = x − 3,
(k ∘ p)(x).= k(p(x))
This means put the function p(x) in for x in the function k(x)
(k ∘ p)(x) = 2(p(x)^2) -5
= 2(x-3)^2 -5
= 2 (x-3)(x-3) -5
FOIL
=2(x^2 -3x -3x+9) -5
=2 (x^2 -6x+9) -5
= 2x^2 -12x +18 -5
Combine like terms
= 2x^2 -12x +13
The side opposite the left 45 degree angle is 8 as well since the 2 base angles are equal.
Use s^2 + b^2 = c^2
Solve for c
8^2 + 8^2 = c^2
64 + 64 = c^2
128 = c^2
c = sqrt(128)
c = sqrt(64 * 2)
c = 8 sqrt(2)
c = 11.31
Answer:
Step A. 3(m - 2) + 2(m - 2) and 5(m - 2) are equivalent expressions.
Step-by-step explanation:
Step B. If you calculate 3(m - 2) + 2(m - 2) you will see it will equal to 5(m - 2) therefore, they are equal.
Hope I Helped I'm New! :D
Answer: 297
Step-by-step explanation: 33,000 divided by 1000 = 33. So 33 x 9 = 297
Answer:
(a) The value of P (X = 2) is 0.3571.
(b) The value of P (X ≤ 1) is 0.5952.
Step-by-step explanation:
A Hypergeometric distribution is used to describe the probability distribution of <em>x</em> successes in <em>n</em> random draws from a population of size <em>N </em>that contains exactly <em>r</em> items that are considered as success. In this distribution each draw results in either a success or a failure.
The probability mass function of Hypergeometric distribution is:
![P(X=x)=\frac{{r\choose x}{N-r\choose n-x}}{{N\choose n}}](https://tex.z-dn.net/?f=P%28X%3Dx%29%3D%5Cfrac%7B%7Br%5Cchoose%20x%7D%7BN-r%5Cchoose%20n-x%7D%7D%7B%7BN%5Cchoose%20n%7D%7D)
Given:
N = 9
r = 3
n = 4
(a)
Compute the value of P (X = 2) as follows:
![P(X=2)=\frac{{3\choose 2}{9-3\choose 4-2}}{{9\choose 4}}=\frac{3\times 15}{126}=0.3571](https://tex.z-dn.net/?f=P%28X%3D2%29%3D%5Cfrac%7B%7B3%5Cchoose%202%7D%7B9-3%5Cchoose%204-2%7D%7D%7B%7B9%5Cchoose%204%7D%7D%3D%5Cfrac%7B3%5Ctimes%2015%7D%7B126%7D%3D0.3571)
Thus, the value of P (X = 2) is 0.3571.
(b)
Compute the value of P (X ≤ 1) as follows:
P (X ≤ 1) = P (X = 0) + P (X = 1)
![=\frac{{3\choose 0}{9-3\choose 4-0}}{{9\choose 4}}+\frac{{3\choose 1}{9-3\choose 4-1}}{{9\choose 4}}\\=0.1190+0.4762\\=0.5952](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%7B3%5Cchoose%200%7D%7B9-3%5Cchoose%204-0%7D%7D%7B%7B9%5Cchoose%204%7D%7D%2B%5Cfrac%7B%7B3%5Cchoose%201%7D%7B9-3%5Cchoose%204-1%7D%7D%7B%7B9%5Cchoose%204%7D%7D%5C%5C%3D0.1190%2B0.4762%5C%5C%3D0.5952)
Thus, the value of P (X ≤ 1) is 0.5952.