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2 years ago

Use the Distributive Property to expand (−2x−7)4

Mathematics

1 answer:

Westkost [7]2 years ago

5 0

Answer:

Step-by-step explanation:

4(-2x - 7)

4*-2x -8x

4*-7 = -28

-8x - 28

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Find the minimum sample size necessary to be 99% confident that the population mean is within 3 units of the sample mean given t

SVEN [57.7K]

Answer:

The minimum sample size required is 207.

Step-by-step explanation:

The (1 - α) % confidence interval for population mean μ is:

$CI=\bar x\pm z_{\alpha /2}\frac{\sigma}{\sqrt{n}}$

The margin of error of this confidence interval is:

$MOE=z_{\alpha /2}\frac{\sigma}{\sqrt{n}}$

Given:

$MOE=3\\\sigma=29\\z_{\alpha /2}=z_{0.01/2}=z_{0.05}=2.576$

*Use a z-table for the critical value.

Compute the value of n as follows:

$MOE=z_{\alpha /2}\frac{\sigma}{\sqrt{n}}\\3=2.576\times \frac{29}{\sqrt{n}} \\n=[\frac{2.576\times29}{3} ]^{2}\\=206.69\\\approx207$

Thus, the minimum sample size required is 207.

3 0

2 years ago

When you receive a loan to make a purchase, you often must make a down payment in cash. The amount of the loan is the purchase c

emmainna [20.7K]

Summarizing the problem, there are three terms that you have to deal with: purchasing cost, down payment and loan. So, you would expect that the answer would contain these quantities. Among them, the unknown is the purchasing cost, therefore, we denote this as x.

Based on the statement, "The amount of the loan is the purchase cost minus the down payment", we can formulate an equation for this.

Amount of Loan = x - Down payment

This will be our working equation. Moving on, the down payment was mentioned to be equal to $1500. The lean received is equal to $2600. Substituting these values to the working equation, we can now determine the value of x.

2600 = x - 1500

Solving for x by transposing it to one side,

x = 2600-1500
x = $1,100

Therefore, the purchasing cost of the car is $1,100.

6 0

3 years ago

Help pls lord jesus

Reil [10]

Answer:

The answer is on the paper. Hope it's correct :)

6 0

2 years ago

Are the ratios 25/45 and 15/27 proportional? Explain.

liberstina [14]

Write them out as a fraction then reduce them. If theyre the same then its proportional.

25/45 can be cancelled down to 5/9

15/27 can be cancelled down to 3/9

So no theyre not.

6 0

2 years ago

Sally lives in City A and works for the department of transportation. She needs to inspect the weigh stations in each of four di

galben [10]

Answer:

She can visit the cities in 192 ways

Step-by-step explanation:

If Sally starts from city A and after going to 4 cities she returns to home,

then that can be in 4! = 24 ways. (permutation of 4 distinct objects)

If between the time she visits cities, she comes home once,

then cities can be visited in,

$4! \times 3_{C_{1}}$ = 72 ways. (permutation of 4 distinct objects and choosing 1 gap among the 3 )

If between the time she visits cities, she comes home twice,

then cities can be visited in,

$4! \times 3_{C_{2}}$ =72 ways. (permutation of 4 distinct objects and finding 2 gaps among the 3)

If between the time she visits cities, she comes home thrice,

then cities can be visited in,

$4! \times 3_{C_{3}}$ = 24 ways. (permutation of 4 distinct objects and choosing 3 gaps among the 3)

Now, she can't come home more than thrice in between the time she visits cities (since there are 4 cities to visit only)

So, the number of ways she can visit cities = (24+ 72 + 72 + 24)

= 192

6 0

2 years ago