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Sloan [31]
3 years ago
10

When the sum of 8 and a certain number is increased by 12, the result is the same as the product of 3 and the number. What is th

e number?

Mathematics
1 answer:
Roman55 [17]3 years ago
6 0
ANSWER: The number is 10.
Hope this helps!!

I used the variable n as the number we needed to find. The equation was n + 8 + 12 = 3n

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1. A 2002 poll reported that 61​% of people worried that they would be exposed to SARS.
Mama L [17]

Answer:

Part 1

a)ME=1.96 \sqrt{\frac{0.61 (1-0.61)}{100}}=0.0956  

b) ME=1.96 \sqrt{\frac{0.61 (1-0.61)}{363}}=0.0502

c) ME=1.96 \sqrt{\frac{0.61 (1-0.61)}{1551}}=0.0243

Part 2

We can see that if we increase the sample size the margin of error decrease and that makes sense since n is on the denominator in the formula for the margin of error and if we increase the denominator the result needs to decrease.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})

Part 1

For this case in order to find the margin of error we need to assume a confidence level fixed, let's assume 95% for example. The Margin of error is given by this formula:

ME= z_{\alpha/2}\sqrt{\frac{p(1-p)}{n}}

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. And the critical value would be given by:

z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96

The margin of error for the proportion interval is given by this formula:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}    (a)  

And on this case we have that \hat p = 0.61 and we are interested in order to find the value of ME.

So we can replace for each case and see what we got:

a)ME=1.96 \sqrt{\frac{0.61 (1-0.61)}{100}}=0.0956  

b) ME=1.96 \sqrt{\frac{0.61 (1-0.61)}{363}}=0.0502

c) ME=1.96 \sqrt{\frac{0.61 (1-0.61)}{1551}}=0.0243

Part 2

We can see that if we increase the sample size the margin of error decrease and that makes sense since n is on the denominator in the formula for the margin of error and if we increase the denominator the result needs to decrease.

7 0
3 years ago
A map use the scale 3/4 of an inch to represent 3 miles .if the actual distance between two cities is25 miles ,then what is the
slega [8]
<h3><em><u>given</u></em><em><u>:</u></em></h3>

<em><u>3</u></em><em><u>/</u></em><em><u>4</u></em><em><u> </u></em><em><u>inch</u></em>

<em><u>3</u></em><em><u> </u></em><em><u>miles</u></em>

<h3><em><u>to</u></em><em><u> </u></em><em><u>find</u></em><em><u>:</u></em></h3>

<em><u>the</u></em><em><u> </u></em><em><u>length</u></em><em><u> </u></em><em><u>of</u></em><em><u> </u></em><em><u>the</u></em><em><u> </u></em><em><u>map</u></em>

<h3><em><u>solution</u></em><em><u>:</u></em></h3>

<em><u>Based on the given conditions, write: </u></em>

<em><u>x=</u></em><em><u> </u></em><em><u>34</u></em><em><u>/</u></em><em><u> 4 · 25</u></em><em><u>/</u></em><em><u> </u></em><em><u>3</u></em>

<em><u>Write as a single fraction:</u></em>

<em><u>x</u></em><em><u>=</u></em><em><u> </u></em><em><u>3 × 25</u></em><em><u>/</u></em><em><u> </u></em><em><u>4</u></em><em><u>/</u></em><em><u> </u></em><em><u>3</u></em>

<em><u>Divide a fraction by multiplying its reciprocal:</u></em>

<em><u>x</u></em><em><u>=</u></em><em><u> </u></em><em><u>3 x 25</u></em><em><u>/</u></em><em><u> </u></em><em><u>4</u></em><em><u> </u></em><em><u>×</u></em><em><u> </u></em><em><u>1</u></em><em><u>/</u></em><em><u> </u></em><em><u>3</u></em>

<em><u>Write as a single fraction: </u></em>

<em><u>x=</u></em><em><u> </u></em><em><u>3 x 25</u></em><em><u>/</u></em><em><u> </u></em><em><u>4</u></em><em><u> </u></em><em><u>×</u></em><em><u> </u></em><em><u>3</u></em>

<em><u>Reduce fraction to the lowest term by canceling 25 the greatest common factor:</u></em>

<em><u>x</u></em><em><u>=</u></em><em><u> </u></em><em><u>2</u></em><em><u>5</u></em><em><u>/</u></em><em><u>4</u></em>

<em><u>therefore</u></em><em><u>,</u></em><em><u>the</u></em><em><u> </u></em><em><u>length</u></em><em><u> </u></em><em><u>of</u></em><em><u> </u></em><em><u>the</u></em><em><u> </u></em><em><u>map</u></em><em><u> </u></em><em><u>is</u></em><em><u> </u></em><em><u>2</u></em><em><u>5</u></em><em><u>/</u></em><em><u> </u></em><em><u>4</u></em><em><u>.</u></em>

5 0
2 years ago
A roll of carpet that contains 250 yd of carpet will cover how many rooms if each room requires 7 3/4 yards of carpet?
iren [92.7K]

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Step-by-step explanation:

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Use proportions & cross-multiply to solve:

\frac{1}{7.75} =\frac{x}{250}\\7.75x=250\\x=\frac{250}{7.75} =32.258

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Answer:

x = -2

Step-by-step explanation:

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