The family would buy the three pairs of shoes for $26.31 because you have to divide $52.62 in half since they bought half the amount of pairs of shoes that are given in the sale.
Answer:
B. y=-4x+2
Step-by-step explanation:
y-6=-4x-4
y=-4x-4+6
y=-4x+2
Answer:
A) A[p(t)] = 36πt²
B) 7234.56 square units
Step-by-step explanation:
<u>Given functions</u>:
<u>Part A</u>
To find the area of the circle of spilled paint as a function of time, substitute the function p(t) into the given function A(p):
![\begin{aligned}A(p) & = \pi p^2\\\\ \implies A[p(t)] & = \pi [p(t)]^2\\& = \pi (6t)^2\\& = \pi 6^2 t^2\\& = 36\pi t^2\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7DA%28p%29%20%26%20%3D%20%5Cpi%20p%5E2%5C%5C%5C%5C%20%5Cimplies%20A%5Bp%28t%29%5D%20%26%20%3D%20%5Cpi%20%5Bp%28t%29%5D%5E2%5C%5C%26%20%3D%20%5Cpi%20%286t%29%5E2%5C%5C%26%20%3D%20%5Cpi%206%5E2%20t%5E2%5C%5C%26%20%3D%2036%5Cpi%20t%5E2%5Cend%7Baligned%7D)
<u>Part B</u>
Given
Substitute the given values into the equation for A[p(t)} found in part A:
![\begin{aligned}A[p(8)] & = 36\pi t^2\\& = 36 \cdot 3.14 \cdot 8^2\\& = 36 \cdot 3.14 \cdot 64\\& = 113.04 \cdot 64\\& = 7234.56\:\: \sf square\:units\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7DA%5Bp%288%29%5D%20%26%20%3D%2036%5Cpi%20t%5E2%5C%5C%26%20%3D%2036%20%5Ccdot%203.14%20%5Ccdot%208%5E2%5C%5C%26%20%3D%2036%20%5Ccdot%203.14%20%5Ccdot%2064%5C%5C%26%20%3D%20113.04%20%5Ccdot%2064%5C%5C%26%20%3D%207234.56%5C%3A%5C%3A%20%5Csf%20square%5C%3Aunits%5Cend%7Baligned%7D)
Therefore, the area of spilled paint after 8 minutes if 7234.56 square units.
Answer:
a) 1/22
b) 3/44
c) 3/11.
Step-by-step explanation:
a).
Prob(picking a blue first) = 5/12.
Prob(picking a yellow next) = 4/11 ( as it is without replacement)
Prob(purple next) = 3/10
Probability of picking these in this order = 5/12 * 4/11 * 3/10
= 1/22 (answer).
Note the probabilities are multiplied because the 3 events are independent.
b)
Prob(all the same colour) = Prob(All are blue) + Prob(all are yellow) + Prob ( All are purple)
Prob(All are blue) = 5/12 * 4/11 * 3/10 = 1/22
Prob(all are yellow) = 4/12 * 3/11 * 2/10 = 1/55
Prob(all purple) = 3/12 * 2/11 * 1 /10 = 1/220
So probability there are all the same colour = the sum of the above
= 3/44 (answer).
c) I take this to mean that all 3 are a different colour.
This will be the number of combinations of blue, yellow and purple possible which is 3! = 6.
So the answer is 6 * 1/22 = 3/11.
