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2 years ago

6

Find the distance traveled in 35 seconds by an object traveling at a velocity of v(t) = 20 + 5cos(t) feet per second

1 answer:

rosijanka [135]2 years ago

8 0

$s(t)= \int\limits^{35}_0 {v(t)} \, dt \\ =\int\limits^{35}_0 {(20+5cos(t))} \, dt \\ =[20t+5sin(t)]^{35}_0 \\ =(20(35)+5sin(35))-(20(0)+5sin(0)) \\ =700+2.868=702.868 \, feet$

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How many computers must the AB Computer Company sell to break even? Let x be the number of computers.

Eduardwww [97]

Answer:

The Company AB must sell 116 computers to break even

Step-by-step explanation:

we have

$R(x)=1.5x$ -----> equation A

$C(x)=145+\frac{1}{4}x$ ----> equation B

where

C is the cost function

R is the revenue function

x is the number of computers sold

we know that

Break even is when the cost is equal to the revenue

so

equate equation A and equation B

$1.5x=145+\frac{1}{4}x$

Solve for x

subtract 1/4x both sides

$1.5x-\frac{1}{4}x=145$

$1.5x-0.25x=145$

$1.25x=145$

Divide by 1.25 both sides

$x=116$

therefore

The Company AB must sell 116 computers to break even

7 0

3 years ago

A simple random sample of items resulted in a sample mean of . The population standard deviation is . a. Compute the confidence

Varvara68 [4.7K]

Answer:

(a): The 95% confidence interval is (46.4, 53.6)

(b): The 95% confidence interval is (47.9, 52.1)

(c): Larger sample gives a smaller margin of error.

Step-by-step explanation:

Given

$n = 30$ -- sample size

$\bar x = 50$ -- sample mean

$\sigma = 10$ --- sample standard deviation

Solving (a): The confidence interval of the population mean

Calculate the standard error

$\sigma_x = \frac{\sigma}{\sqrt n}$

$\sigma_x = \frac{10}{\sqrt {30}}$

$\sigma_x = \frac{10}{5.478}$

$\sigma_x = 1.825$

The 95% confidence interval for the z value is:

$z = 1.960$

Calculate margin of error (E)

$E = z * \sigma_x$

$E = 1.960 * 1.825$

$E = 3.577$

The confidence bound is:

$Lower = \bar x - E$

$Lower = 50 - 3.577$

$Lower = 46.423$

$Lower = 46.4$ --- approximated

$Upper = \bar x + E$

$Upper = 50 + 3.577$

$Upper = 53.577$

$Upper = 53.6$ --- approximated

<em>So, the 95% confidence interval is (46.4, 53.6)</em>

Solving (b): The confidence interval of the population mean if mean = 90

First, calculate the standard error of the mean

$\sigma_x = \frac{\sigma}{\sqrt n}$

$\sigma_x = \frac{10}{\sqrt {90}}$

$\sigma_x = \frac{10}{9.49}$

$\sigma_x = 1.054$

The 95% confidence interval for the z value is:

$z = 1.960$

Calculate margin of error (E)

$E = z * \sigma_x$

$E = 1.960 * 1.054$

$E = 2.06584$

The confidence bound is:

$Lower = \bar x - E$

$Lower = 50 - 2.06584$

$Lower = 47.93416$

$Lower = 47.9$ --- approximated

$Upper = \bar x + E$

$Upper = 50 + 2.06584$

$Upper = 52.06584$

$Upper = 52.1$ --- approximated

<em>So, the 95% confidence interval is (47.9, 52.1)</em>

Solving (c): Effect of larger sample size on margin of error

In (a), we have:

$n = 30$ $E = 3.577$

In (b), we have:

$n = 90$ $E = 2.06584$

<em>Notice that the margin of error decreases when the sample size increases.</em>

4 0

2 years ago

|x+8|=x+8 what is x?

Darya [45]

Answer:

x ≥ 0

Step-by-step explanation:

The absolute value of x+8 equals itself, thus x must be a real number (0 or any positive number).

7 0

2 years ago

6th grade math (answer both) .... :D

LekaFEV [45]

Answer:

Question 2: Option B

Step-by-step explanation:

The number of ounces and the total price for yogurt cup A is not stated, therefore, I can not answer question 1 properly.

<h3>For question 2:</h3><h3 />

Unit rate formula for price is: $\frac{price}{quantity}$

32 ounces of yogurt sell for 1.62.

So:

$\frac{1.62}{32} =0.050625$

0.050625 ≈ 0.05

<em>Option B should be the best answer. </em>

7 0

2 years ago

The expression 10a+6c gives the cost (in dollars) for a adults and c children to eat at a buffet restaurant. A. The cost for 1 a

Liono4ka [1.6K]

Answer: The total cost is $\$62$ assuming the cost for 1 adult is $\$5$ and the cost for 1 child is $\$2$

Step-by-step explanation:

Assuming the cost for 1 adult is $\$5$ and the cost for 1 child is $\$2$ :

$a=\$5$ and $c=\$2$

Then the expression that gives the total cost $10 a+6c$ is solved as:

$10(\$5)+6(\$2)=\$62$

4 0

3 years ago