Answer:
Probability that a house has a hot tub given that it has a pool is 55%.
Step-by-step explanation:
We are given that in New York State, 38% of the houses have a pool and 21% of the houses have both a pool and a hot tub.
Let the probability that houses have a pool = P(A) = 0.38
Also, let B = event that houses have a hot tub
Probability that houses have both a pool and a hot tub = 
= 0.21
Now, the conditional probability that a house has a hot tub given that it has a pool is given by = P(B / A)
<u>As we know that</u>; P(B / A) = 
= 
= 0.553 ≈ 55%
Hence, the probability that a house has a hot tub given that it has a pool is 55%.
Answer:(2,4)
Step-by-step explanation:
you can make a grid to check
Answer:
−60n−116p
Step-by-step explanation:
6)
A quadratic function has the form
y = ax^2 + bx + c
Use point (3, 5) in the equation above:
5 = a(3^2) + 3b + c
5 = 9a + 3b + c
9a + 3b + c = 5 Equation 1
Use point (4, 3) in the equation above:
3 = a(4^2) + 4b + c
16a + 4b + c = 3 Equation 2
Use point (5, 3) in the equation above.
5 = a(5^2) + 5b + c
25a + 5b + c = 5 Equation 3.
Now solve the system of equations of equations 1, 2, and 3 to find the coefficients, a, b, and c.
9a + 3b + c = 5
16a + 4b + c = 3
25a + 5b + c = 5
Subtract the first equation from the second equation.
Subtract the second equation from the third equation.
You get
7a + b = -2
9a + b = 2
Subtract the first equation above from the second equation to get.
2a = 4
a = 2
Substitute:
7a + b = -2
7(2) + b = -2
b = -16
9a + 3b + c = 5
9(2) + 3(-16) + c = 5
18 - 48 + c = 5
c - 30 = 5
c = 35
The equation in standard form is
y = 2x^2 - 16x + 35
We can find it in vertex form:
y = 2(x^2 - 8x) + 35
y = 2(x^2 - 8x + 16) + 35 - 32
y = 2(x - 4)^2 + 3
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