Answer:
14.63% probability that a student scores between 82 and 90
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean
and standard deviation
, the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:

What is the probability that a student scores between 82 and 90?
This is the pvalue of Z when X = 90 subtracted by the pvalue of Z when X = 82. So
X = 90



has a pvalue of 0.9649
X = 82



has a pvalue of 0.8186
0.9649 - 0.8186 = 0.1463
14.63% probability that a student scores between 82 and 90
Cost of a sweatshirt = $32
Then
Cost of 14 sweatshirts = (32 * 14) dollars
= 448 dollars
Cost of a t-shirt = $14
Cost of 32 t-shirts = (32 * 14) dollars
= 448 dollars
So it can seen from the deduction that the cost of 14 sweatshirts and 32 t-shirts comes out to be same and equal to $448. I hope the answer and the procedure of doing this problem is clear to you. It is important to look at all the details given in the question and then start solving the problem.
Answer:

Step-by-step explanation:
We are given that a differential equation

We have to find the general solution of given differential equation


Compare with

We get


I.F=





Notice that 38 and 52 make a total of 90
sinA=cos(90-A)
sin38=cos52, therefore the answer is zero
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