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3 years ago

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The library currently has 150 audio books. The library plans to purchase the same number of books each month. After 4 months, th

e library has 32 more audio books. Which equation can be used to determine t, the total number of audio books in the library after m months?

1 answer:

Andreas93 [3]3 years ago

6 0

Answer:

8 a month

Step-by-step explanation:

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A vehicle travels 57 kilometers north and then travels 26 kilometers south. What is the current position of the vehicle? (2 poin

solniwko [45]

Answer:

C. 31 kilometers north of its starting location

Step-by-step explanation:

<em>Please see attached a rough sketch of the situation for your reference</em>.

Step one:

Displacement North= 57km

Displacement South= 26km

Required

The final displacement

The current position is attained by subtracting 26km from 57km

=57-26= 31km

Therefore the current position is

C. 31 kilometers north of its starting location

5 0

3 years ago

Jessica is selling books during the summer to earn money for college. She

faltersainse [42]

It’s c I just took the test and got a hundred

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3 years ago

Find the average rate of change of the function from x=1 to x=2.<br><br><br><br> f(x)=−14/x^2

Irina-Kira [14]

Answer:

The average rate of change of the function from x=1 to x=2 will be: 10.5

Step-by-step explanation:

Given the function

$f\left(x\right)=-\frac{14}{x^2}$

at x₁ = 1,

f(x₁) = f(1) = -14/(1)² = -14/1 = -14

at x₂ = 2,

f(x₂) = f(2) = -14/(2)² = -14/(4) = -3.5

Using the formula to determine the average rate of change at which the total cost increases will be:

Average rate of change = [f(x₂) - f(x₁)] / [ x₂ - x₁]

= [-3.5 - (-14)] / [2 - 1]

= [-3.5 + 14] / [1]

= 10.5 / 1

= 10.5

Therefore, the average rate of change of the function from x=1 to x=2 will be: 10.5

6 0

3 years ago

Solve: x2 − x − 6/x2 = x − 6/2x + 2x + 12/x After multiplying each side of the equation by the LCD and simplifying, the resultin

Vesna [10]

The resulting equation after simplyfing the given equation is 3x^2 + 20x + 12 = 0 and whoose solutions are x = -2/3 or x = -6.

According to the given question.

We have an equation

$\frac{x^{2}-x-6 }{x^{2} } = \frac{x-6}{2x} +\frac{2x+12}{x}$

So, to find the resulting equation of the above equation we need to simplify.

First we will take LCD

$\frac{x^{2} -x - 6 }{x^{2} } = \frac{x -6+2(2x + 12)}{2x}$

$\implies \frac{x^{2}-x-6 }{x^{2} } =\frac{x-6+4x+24}{2x}$

$\implies \frac{x^{2}-x-6 }{x^{2} } = \frac{5x +18}{2x}$

Multiply both the sides by x.

$\frac{x^{2}-x-6 }{x} = \frac{5x+18}{2}$

Again multiply both the sides by x

$2x^{2} -2x-12 = 5x^{2} +18x$

$\implies 5x^{2} -2x^{2} +18x +2x +12 = 0$

$\implies 3x^{2} + 18x+2x + 12 = 0$

Factorize the above equation

⇒3x(x+6)+2(x+6) = 0

⇒(3x + 2)(x+6) = 0

⇒ x = -2/3 or x = -6

Hence, the resulting equation after simplyfing the given equation is 3x^2 + 20x + 12 = 0 and whoose solutions are x = -2/3 or x = -6.

Find out more information about equation here:

brainly.com/question/2976807

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1 year ago

The ability to find a job after graduation is very important to GSU students as it is to the students at most colleges and unive

gtnhenbr [62]

Answer: (0.8468, 0.8764)

Step-by-step explanation:

Formula to find the confidence interval for population proportion is given by :-

$\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

, where $\hat{p}$ = sample proportion.

z* = Critical value

n= Sample size.

Let p be the true proportion of GSU Juniors who believe that they will, immediately, be employed after graduation.

Given : Sample size = 3597

Number of students believe that they will find a job immediately after graduation= 3099

Then, $\hat{p}=\dfrac{3099}{3597}\approx0.8616$

We know that , Critical value for 99% confidence interval = z*=2.576 (By z-table)

The 99 % confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation will be

$0.8616\pm(2.576)\sqrt{\dfrac{0.8616(1-0.8616)}{3597}}$

$0.8616\pm (2.576)\sqrt{0.0000331513594662}$

$\approx0.8616\pm0.0148\\\\=(0.8616-0.0148,\ 0.8616+0.0148)=(0.8468,\ 0.8764)$

Hence, the 99 % confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation. = (0.8468, 0.8764)

4 0

3 years ago