How much money is 10% of $500?

8) Write an absolute value equation that has 5 and 15 as its solutions?

marissa [1.9K]

(I'm going to use brackets as my absolute value bars lol)
[5 x -3]
[-15]
=15

7 0

3 years ago

6.Suppose the Gallup Organization wants to estimate the population proportion of those who think there should be a law that woul

drek231 [11]

Answer:

A sample of $n = (\frac{1.96\sqrt{0.3696*0.6304}}{E})^2$ is needed, in which E is the desired margin of error, as a proportion. If we find a decimal value, we round up to the next whole number.

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 of:

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

In a previous study of 1012 randomly chosen respondents, 374 said that there should be such a law.

This means that $n = 1012, \pi = \frac{374}{1012} = 0.3696$

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 $Z = 1.96$ .

How large a sample size is needed to be 95% confident with a margin of error of E?

A sample size of n is needed, and n is found when M = E.

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

$E = 1.96\sqrt{\frac{0.3696*0.6304}{n}}$

$E\sqrt{n} = 1.96\sqrt{0.3696*0.6304}$

$\sqrt{n} = \frac{1.96\sqrt{0.3696*0.6304}}{E}$

$(\sqrt{n})^2 = (\frac{1.96\sqrt{0.3696*0.6304}}{E})^2$

$n = (\frac{1.96\sqrt{0.3696*0.6304}}{E})^2$

A sample of $n = (\frac{1.96\sqrt{0.3696*0.6304}}{E})^2$ is needed, in which E is the desired margin of error, as a proportion. If we find a decimal value, we round up to the next whole number.

4 0

3 years ago

The first term of a geometric sequence is 32, and the 5th term of the sequence is 818 .

sammy [17]

Answer:

$32,24,18,\frac{27}{2} ,\frac{81}{8}$

Step-by-step explanation:

Let x, y , and z be the numbers.

Then the geometric sequence is $32,x,y,z,\frac{81}{8}$

Recall that term of a geometric sequence are generally in the form:

$a,ar,ar^2,ar^3,ar^4$

This implies that:

a=32 and $ar^4=\frac{81}{8}$

Substitute a=32 and solve for r.

$32r^3=\frac{81}{8}$

$r^4=\frac{81}{256}$

Take the fourth root to get:

$r=\sqrt[4]{\frac{81}{256} }$

$r=\frac{3}{4}$

Therefore $x=32*\frac{3}{4} =24$

$y=24*\frac{3}{4} =18$

$z=18*\frac{3}{4} =\frac{27}{2}$

8 0

3 years ago

How many equal sections divide a directed line segment if it is to be partitioned with a 2:7 ratio? 2, the least number given in

Elodia [21]

9514 1404 393

Answer:

9, the sum of the numbers given in the ratio

Step-by-step explanation:

The reduced ratio 2 : 7 means that two parts correspond to one length and 7 parts correspond to the other length. That is, there are a total of 2+7 = 9 parts in the full length of the segment.

It is convenient to think of the line segment as being divided into 9 equal parts.

_____

<em>Additional comments</em>

It is often helpful to consider the total number of "ratio units" in a given ratio. For example, in this problem, the shorter segment is 2/9 of the whole, and the longer one is 7/9 of the whole.

It can also be useful to consider what a "ratio unit" represents. If the whole segment is 27 inches long, then each of the 9 ratio units will represent 3 inches, for example. This means the division 2:7 is 2(3 in):7(3 in) = 6 in : 21 in.

3 0

2 years ago

Jay King, owner of a local Bed and Bath Store knows that his customers will only pay at most, $299 for a blow up bed. Assuming J

Roman55 [17]

If you would like to know the price Jay can pay the manufacturer for the blow up bed, you can calculate this using the following steps:

100% + 40% = 140%

140% of x is $299
140% * x = 299
140/100 * x = 299 /*100/140
x = 299 * 100 / 140
x = $213.6

40% of $213.6 = 40% * 213.6 = 40/100 * 213.6 = 85.44
$213.6 + $85.44 = $299

The correct result would be $213.6.

6 0

3 years ago