All categories

3 years ago

Find the average rate of change for f(x) = x^2 − 3x − 10 from x = −5 to x = 10.

Mathematics

1 answer:

Harman [31]3 years ago

8 0

Answer:

D) 2

The average rate of change of f(x)

A(x) =2

Step-by-step explanation:

Step(i):-

Given that the function f(x) = x² - 3x -10

Given x =a = -5 and y = b = 10

The average rate of change of f(x)

$A(x) = \frac{f(b)-f(a)}{b-a}$

Step(ii):-

f(x) = x² - 3x -10

f(-5) = (-5)² - 3(-5) -10 = 25+15-10=30

f(10) = (10)² -3(10)-10 = 100 -30 -10 =60

The average rate of change of f(x)

$A(x) = \frac{f(b)-f(a)}{b-a}$

$A(x) = \frac{60-30}{10-(-5)}= \frac{30}{15} = 2$

A(x) =2

You might be interested in

What is the value of y in the solution to the following system of equations? 5x − 3y = −11 2x − 6y = −14 −1 0 1 2

Alekssandra [29.7K]

5x - 3y = -11 (×2)
2x - 6y = -14 (x5)

10x - 6y = -22
10x - 30y = -70
---------------------- -
24y = 48
y = 2

5 0

3 years ago

THIS IS NOT A QUIZ!!! Drag the numbers to order them from least to greatest

snow_lady [41]

Answer:

LEAST TO GREATEST

-2.4

-0.8

0.2

0.9

1.6

4 0

3 years ago

The service department of a luxury car dealership conducted research on the amount of time its service technicians spend on each

mart [117]

Answer:

Probability that the mean service time is between 1 and 2 hours is 0.96764.

Step-by-step explanation:

We are given that a systematic random sample of 100 service appointments has been collected.

The 100 appointments showed an average preparation time of 90 minutes with a standard deviation of 140 minutes.

Let $\bar X$ = sample mean service time

The z-score probability distribution for sample mean is given by;

Z = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = average preparation time = 90 minutes

$\sigma$ = standard deviation = 140 minutes

n = sample of appointments = 100

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.

Now, probability that the mean service time is between 60 and 120 minutes is given by = P(60 minutes < $\bar X$ < 120 minutes)

P(60 minutes < $\bar X$ < 120 minutes) = P( $\bar X$ < 120 min) - P( $\bar X$ $\leq$ 60 min)

P( $\bar X$ < 120 min) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{120-90}{\frac{140}{\sqrt{100} } }$ ) = P(Z < 2.14) = 0.98382

P( $\bar X$ $\leq$ 60 min) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ $\leq$ $\frac{60-90}{\frac{140}{\sqrt{100} } }$ ) = P(Z $\leq$ -2.14) = 1 - P(Z < 2.14)

= 1 - 0.98382 = 0.01618

The above probability is calculated by looking at the value of x = 2.14 in the z table which has an area of 0.98382.

Therefore, P(60 min < $\bar X$ < 120 min) = 0.98382 - 0.01618 = 0.96764

7 0

4 years ago

Paul wants to deposit $600 today for a vacation he plans to take after graduation. Which formula should he use to determine the

Vitek1552 [10]

Answer:

Future value of a single amount

Step-by-step explanation:

Future value of a single amount - it is referred to as the amount of money that received after n year when money is deposit at the rate interest of i from the initial time. we can say that the total amount is the sum of principal money and interest value.

The formula used to calculate the Future Value of a single amount

Future value = Present value *[Future value factor]

6 0

3 years ago

Given a triangle JLM with vertices J(-4,3), L(-2,7), and M(2,7). What would the coordinates be if it was reflected across the li

topjm [15]

Answer: M'(2, - 5), L'(-2, -5), j'(-4, - 1)

Step-by-step explanation:

When we do a reflection over a given line, the distance between all the points (measured perpendicularly to the line) does not change.

The line is y = 1.

Notice that a reflection over a line y = a (for any real value a) only changes the value of the variable y.

Let's reflect the points:

J(-4, 3)

The distance between 3 and 1 is:

D = 3 - 1 = 2.

Then the new value of y must also be at a distance 2 of the line y = 1

1 - 2 = 1

The new point is:

j'(-4, - 1)

L(-2, 7)

The distance between 7 and 1 is:

7 - 1 = 6.

The new value of y will be:

1 - 6 = -5

The new point is:

L'(-2, -5)

M(2,7)

Same as above, the new point will be:

M'(2, - 5)

3 0

3 years ago