Answer:
Step-by-step explanation:
The -4 makes the waves taller (Amplitude 4), and the negitive flips over x-axis.
In (3x-pi) The three compresses horizontally making the waves tighter. The -pi shifts the funtion pi to the right.
The +5 shifts up five.
Answer:
The probability that at least 280 of these students are smokers is 0.9664.
Step-by-step explanation:
Let the random variable <em>X</em> be defined as the number of students at a particular college who are smokers
The random variable <em>X</em> follows a Binomial distribution with parameters n = 500 and p = 0.60.
But the sample selected is too large and the probability of success is close to 0.50.
So a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:
1. np ≥ 10
2. n(1 - p) ≥ 10
Check the conditions as follows:

Thus, a Normal approximation to binomial can be applied.
So,

Compute the probability that at least 280 of these students are smokers as follows:
Apply continuity correction:
P (X ≥ 280) = P (X > 280 + 0.50)
= P (X > 280.50)

*Use a <em>z</em>-table for the probability.
Thus, the probability that at least 280 of these students are smokers is 0.9664.
Answer:
Assuming 1/20 is a 5% late fee:
$21.211
Step-by-step explanation:
67.82 x 1/20 = 3.391
67.82 + 3.391 = 71.211
Answer: P(x) = {(x-4)^2} (x) (x+4)
Step-by-step explanation:
Let's start with the multiplicity of 2;
At multiplicity of 2; x=4.
Therefore, x - 4 is a factor of the function P(x).
Since it has a multiplicity of 2, we will rewrite the factor as (x-4)^2
Now for the multiplicity of 1.
At this multiplicity of 1, x= 0 and - 4.
Therefore, the factors are x-0 and x+4
Since multiplicity of 1, the factors remain as they are without any additional root on top.
Therefore, the factors of the polynomial p(x) are (x-4)^2 and x and x+4.
And solution of P(x) in factor form will be: P(x) = {(x-4)^2} (x) (x+4)