Answer:
154 students
Step-by-step explanation:
First get the total number of students .
This can be gotten by
12% of A = 21
Where A represents the total number of students.
12% represents the % of A that chose to study French and 21 is the number of students that studied French .
Therefore,
12% /100% x A = 21
0.12 x A = 21
Divide both sides by 0.12
0.12/0.12 x A = 21/0.12
A = 175
The total number of students is 175.
If 21 chose to study French their freshman year ,number of students that chose not to will be total number of students minus number of those who chose to study French.
That’s
175 - 21
= 154
154 students chose not to study French their freshman year
The expression of integral as a limit of Riemann sums of given integral 
is 4 
∑
from i=1 to i=n.
Given an integral .
We are required to express the integral as a limit of Riemann sums.
An integral basically assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinite data.
A Riemann sum is basically a certain kind of approximation of an integral by a finite sum.
Using Riemann sums, we have :
=∑f(a+iΔx)Δx ,here Δx=(b-a)/n
=f(x)=
⇒Δx=(5-1)/n=4/n
f(a+iΔx)=f(1+4i/n)
f(1+4i/n)=![[n^{2}(n+4i)]/2n^{3}+(n+4i)^{3}](https://tex.z-dn.net/?f=%5Bn%5E%7B2%7D%28n%2B4i%29%5D%2F2n%5E%7B3%7D%2B%28n%2B4i%29%5E%7B3%7D)
∑f(a+iΔx)Δx=
∑
=4∑
Hence the expression of integral as a limit of Riemann sums of given integral is 4 ∑ from i=1 to i=n.
Learn more about integral at brainly.com/question/27419605
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Answer: 16.5 hours
Step-by-step explanation:
distance=rate*time
132=8*x
Divide by 8 on both sides
x=16.5
