Answer:
n
Step-by-step explanation:n
Answer: The waiting time will be 32 minutes when 240 people in line.
Step-by-step explanation:
Let us assume that the waiting time is directly proportional to the number of people in the queue.
Equation of direct proportion between variables x and y : ![\dfrac{x_1}{y_1}=\dfrac{x_2}{y_2}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx_1%7D%7By_1%7D%3D%5Cdfrac%7Bx_2%7D%7By_2%7D)
Put
to find
.
![\dfrac{20}{150}=\dfrac{x_2}{240}\\\\\Rightarrow\ x_2=\dfrac{20}{150}\times240\\\\\Rightarrow\ x_2=32](https://tex.z-dn.net/?f=%5Cdfrac%7B20%7D%7B150%7D%3D%5Cdfrac%7Bx_2%7D%7B240%7D%5C%5C%5C%5C%5CRightarrow%5C%20x_2%3D%5Cdfrac%7B20%7D%7B150%7D%5Ctimes240%5C%5C%5C%5C%5CRightarrow%5C%20x_2%3D32)
Hence, the waiting time will be 32 minutes when 240 people in line.
<h3>
Answer: -2</h3>
===============================================
Explanation:
We use the remainder theorem. This is the idea where if we divide P(x) over (x-k), then the remainder is P(k).
Comparing x+1 to x-k shows that k = -1
It might help to rewrite x+1 as x-(-1) to get it into the form x-k better.
Plug this k value into the function
f(x) = 2x^6 + 3x^5 - 1
f(-1) = 2(-1)^2 + 3(-1)^5 - 1
f(-1) = 2(1) + 3(-1) - 1
f(-1) = 2 - 3 - 1
f(-1) = -1 - 1
f(-1) =-2
The remainder is -2
We can confirm this through synthetic division or polynomial long division.