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3 years ago

One number is eight less than three times another number. If the sum of the numbers is 20, find the numbers.

Mathematics

1 answer:

mamaluj [8]3 years ago

4 0

Answer:

7 & 13

Step-by-step explanation:

Let the first number be x

2nd number = 8 less than 3 times the other

2nd number = 3x - 8

Their sum = 20

X + 3x - 8 = 20

4x -8 = 20

Collect like terms

4x = 20+8

4x = 28

Divide both sides by 4

4x/4 = 28/4

X = 7

First number = 7

2nd number = 3x - 8

= 3(7) - 8

= 21 -8

= 13.

Therefore the numbers are 7 and 13

Pls mark as brainliest

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kakasveta [241]

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3 years ago

Suppose a production facility purchases a particular component part in large lots from a supplier. The production manager wants

musickatia [10]

Answer:

We need a sample size of at least 1161.

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

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The margin of error for the interval is:

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For this problem, we have that:

$\pi = 0.22$

90% confidence level

So $\alpha = 0.1$ , z is the value of Z that has a pvalue of $1 - \frac{0.1}{2} = 0.95$ , so $Z = 1.645$ .

How large a sample should she take?

We need a sample size of at least n.

n is found when $M = 0.02$

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

$0.02 = 1.645\sqrt{\frac{0.22*0.78}{n}}$

$0.02\sqrt{n} = 1.645\sqrt{0.22*0.78}$

$\sqrt{n} = \frac{1.645\sqrt{0.22*0.78}}{0.02}$

$(\sqrt{n})^{2} = (\frac{1.645\sqrt{0.22*0.78}}{0.02})^{2}$

$n = 1160.88$

Rounding up

We need a sample size of at least 1161.

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