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3 years ago

Find the average rate of change of the parabola below over the interval [1,3]

Mathematics

1 answer:

weeeeeb [17]3 years ago

5 0

Answer:

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

$\frac{f(b)-f(a)}{b-a}$

Here (a, b ] = [ 1, 3 ], thus

f(b) = f(3) = 5 ← from graph

f(a) = f(1) = - 3 ← from graph

average rate of change = $\frac{5-(-3)}{3-1}$ = $\frac{8}{2}$ = 4 → D

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Answer:

39.2 square units is the answer

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2 years ago

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The average number of customers per day increased 25 percent during the sale. If the average number of customers per day before

Rasek [7]

Answer:

The average number of customers per day during the sale was 150.

Step-by-step explanation:

This question can be solved using a rule of three.

Before the sale, the average number of customers per day was 120, which is 100% = 1.

Now, there are x customers, and since it is an increase of 25%, it is 100+25 = 125% = 1.25. So

120 - 1

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The average number of customers per day during the sale was 150.

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4 years ago

The physical plant at the main campus of a large state university receives daily requests to replace fluorescent light bulbs. Th

ankoles [38]

We have been given that the distribution of the number of daily requests is bell-shaped and has a mean of 38 and a standard deviation of 6. We are asked to find the approximate percentage of lightbulb replacement requests numbering between 38 and 56.

First of all, we will find z-score corresponding to 38 and 56.

$z=\frac{x-\mu}{\sigma}$

$z=\frac{38-38}{6}=\frac{0}{6}=0$

Now we will find z-score corresponding to 56.

$z=\frac{56-38}{6}=\frac{18}{6}=3$

We know that according to Empirical rule approximately 68% data lies with-in standard deviation of mean, approximately 95% data lies within 2 standard deviation of mean and approximately 99.7% data lies within 3 standard deviation of mean that is $-3\sigma\text{ to }3\sigma$ .

We can see that data point 38 is at mean as it's z-score is 0 and z-score of 56 is 3. This means that 56 is 3 standard deviation above mean.

We know that mean is at center of normal distribution curve. So to find percentage of data points 3 SD above mean, we will divide 99.7% by 2.

$\frac{99.7\%}{2}=49.85\%$

Therefore, approximately $49.85\%$ of lightbulb replacement requests numbering between 38 and 56.

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3 years ago

You deposit $1200 in an account. The annual interest rate is 3%. How long will it take you to earn $108 in simple interest?

Kruka [31]

Answer:

<em>Interest = $3,888</em>

Step-by-step explanation:

Formula:

I = prt or I = p · r · t

what it stands for:

I = amount of interest

P = principal amount ($1,200)

R = interest rate (in years)(3% into decimal which would be .03)

T = amount of time (in years)($108)

so:

I = prt

I = (1,200)(.03)(108)

I = $3,888

Interest = $3,888

5 0

3 years ago