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3 years ago

Calculate the average rate of change of y=x2+3x−2 on the interval 1≤x≤2

Mathematics

1 answer:

Artyom0805 [142]3 years ago

3 0

Answer:

The rate of change for the given function is 6.

Step-by-step explanation:

Given function is:

$y = x^2+3x-2$

The interval on which we have to find the rate of change is:

1≤x≤2

Here

a = 1

b = 2

We have to find the values of function on both points

Putting 1 in place of input (x)

$y_a= (1)^2+3(1)-2\\= 1+3-2\\=2$

Putting x = 2

$y_b = (2)^2+3(2)-2\\= 4+6-2\\=8$

The rate of change is calculated by using the following formula

$Rate\ of\ change = \frac{y_b-y_a}{b-a}\\=\frac{8-2}{2-1}\\= \frac{6}{1}\\=6$

Hence,

The rate of change for the given function is 6.

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Keith ... x hours a week
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7 0

3 years ago

Read 2 more answers

A math professor notices that scores from a recent exam are normally distributed with a mean of 61 and a standard deviation of 8

Alexeev081 [22]

Answer:

a) 25% of the students exam scores fall below 55.6.

b) The minimum score for an A is 84.68.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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 p-value, we get the probability that the value of the measure is greater than X.

Mean of 61 and a standard deviation of 8.

This means that $\mu = 61, \sigma = 8$

(a) What score do 25% of the students exam scores fall below?

Below the 25th percentile, which is X when Z has a p-value of 0.25, that is, X when Z = -0.675.

$Z = \frac{X - \mu}{\sigma}$

$-0.675 = \frac{X - 61}{8}$

$X - 61 = -0.675*8$

$X = 55.6$

25% of the students exam scores fall below 55.6.

(b) Suppose the professor decides to grade on a curve. If the professor wants 0.15% of the students to get an A, what is the minimum score for an A?

This is the 100 - 0.15 = 99.85th percentile, which is X when Z has a p-value of 0.9985. So X when Z = 2.96.

$Z = \frac{X - \mu}{\sigma}$

$2.96 = \frac{X - 61}{8}$