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2 years ago

6

Scarlett is going to invest in an account paying an interest rate of 4% compounded daily. How much would Scarlett need to invest

, to the nearest ten dollars, for the value of the account to reach $54,000 in 8 years?

1 answer:

IrinaVladis [17]2 years ago

4 0

Answer: 39210

Step-by-step explanation:

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A candidate for a US Representative seat from Indiana hires a polling firm to gauge her percentage of support among voters in he

UkoKoshka [18]

Answer:

a) The minimum sample size is 601.

b) The minimum sample size is 2401.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

For this problem, we have that:

We dont know the true proportion, so we use $\pi = 0.5$ , which is when we are are going to need the largest sample size.

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

a. If a 95% confidence interval with a margin of error of no more than 0.04 is desired, give a close estimate of the minimum sample size that will guarantee that the desired margin of error is achieved. (Remember to round up any result, if necessary.)

This is n for which M = 0.04. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.04 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.04\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.04}$

$(\sqrt{n})^2 = (\frac{1.96*0.5}{0.04})^2$

$n = 600.25$

Rounding up

The minimum sample size is 601.

b. If a 95% confidence interval with a margin of error of no more than 0.02 is desired, give a close estimate of the minimum sample size necessary to achieve the desired margin of error.

Now we want n for which M = 0.02. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.02 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.02\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.02}$

$(\sqrt{n})^2 = (\frac{1.96*0.5}{0.02})^2$

$n = 2401$

The minimum sample size is 2401.

4 0

3 years ago

An augmented matrix for a system of linear equations in x, y, and z is given. Find the solution of the system.

Angelina_Jolie [31]

Answer:

(x, y, z) = (-4, 2, 1)

Step-by-step explanation:

See the attachment for the output of a calculator that produces the reduced row-echelon form of the matrix.

The [x, y, z] result vector is the column on the right.

(x, y, z) = (-4, 2, 1)

_____

Numerous web sites are available for computing the row-reduced form of the matrix, or for solving the system of equations. Your graphing calculator will do it as well.

8 0

3 years ago

Line a is parallel to line b, m 6=85, and m 3=2x. Find m 1.

Paladinen [302]

Since a line =180 degrees you could set it up as (180-85) and you would get <u><em>95.
Hope this helps!!!</em></u>

3 0

3 years ago

Read 2 more answers

What is 12/21 divided by 3/14

sladkih [1.3K]

To do this problem, you gotta cross-multiply. SO, $\frac{12}{21}$ multiplied by $\frac{14}{3}$

12 times 14 = 168
21 times 3 = 63
Then the final answer is $\frac{168}{3}$

5 0

3 years ago

Jack's house is located at the origin (0,0). He walks 2 blocks right. Then, he walks 6 blocks up. Finally, he walks 3 blocks rig

attashe74 [19]

Answer: 5, 6

Step-by-step explanation:

0 + 2 = 2

2 , 0

0 + 6 = 6

2, 6

2 + 3 = 5

5, 6

5 0

3 years ago