Answer:
30 students are in the science class and 3 students recieved a failing grade.
Answer:
a) It can be used because np and n(1-p) are both greater than 5.
Step-by-step explanation:
Binomial distribution and approximation to the normal:
The binomial distribution has two parameters:
n, which is the number of trials.
p, which is the probability of a success on a single trial.
If np and n(1-p) are both greater than 5, the normal approximation to the binomial can appropriately be used.
In this question:

So, lets verify the conditions:
np = 201*0.45 = 90.45 > 5
n(1-p) = 201*(1-0.45) = 201*0.55 = 110.55 > 5
Since both np and n(1-p) are greater than 5, the approximation can be used.
The apothem is the distance from the center to the midpoint of one of the sides of a regular polygon. You can make a right triangle with the apothem, the line from the midpoint to the corner and the line from the center to the corner. An equilateral triangle has 60 degree angles (180/3). The right triangle has half of one of those angles so 30 degrees. Now we have a 30-60-90 triangle where the short leg is 5cm. The long leg, which is also half of one side of the triangle is thus

. A whole side of the triangle is

. Multiply that by 3 to get the perimeter of <span>

.</span>
In the standard form of the equation
![\\ \ f(t)=Acos[b(t\pm c)]+k\\ \\](https://tex.z-dn.net/?f=%20%5C%5C%20%5C%20f%28t%29%3DAcos%5Bb%28t%5Cpm%20c%29%5D%2Bk%5C%5C%20%5C%5C%20)
The middle line =k
For our given problem
f(t) = 40cos (80t + 20)
On comparison we get k=0
Hence middle line=0
x^2 = 16/100
We must solve for x by taking the square root of both sides.
But imagine x^2 = 9. x = 3 is a solution because 3^2 = 9. But x = -3 is also a solution because (-3)^2 = 9. So we need to add the plus and minus sign to account for all of our solutions.
√x^2 = √(16/100)
We square root both sides to remove the exponent 2 on x. Then
x = ±√(16/100)
Then we have to use a Property of Radicals which is √(x/y) = √(x) / √(y).
Then the square root of 16 is 4 and the square root of 100 is 10. 4/10 is 2/5 simplified.