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Molodets [167]
2 years ago
6

One number is 6 more than twice the other number. If the sum of the two numbers is ​21, find the two numbers

Mathematics
1 answer:
hichkok12 [17]2 years ago
4 0

Answer:

One number, let's call it x, is 6 more than twice the other number, let's say this number is y.

x= 2y+6

x+y=21

We're left with a system of equations.

If we substitute the first equation in the second we find the value of y.

(2y+6)+y=21

3y+6=21

3y=15

<u><em>y=5</em></u>

Now that we have found the value of y, we can take that value and substitute it in the second equation (since it's easier) to find the value of x.

x+ (5)=21

<u><em>x=16</em></u>

<u><em>Now to check if our answers are correct, we plug in both values into any equation and see if they equate.</em></u>

x+y=21

(16)+(5)=21

21=21

Our solution is correct!

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3 years ago
Darren wants to estimate the mean age in a population of trees. He'll sample nnn trees and build a 90\%90%90, percent confidence
Alchen [17]

Using the z-distribution, as we have the standard deviation for the population, it is found that the smallest sample size required to obtain the desired margin of error is of 77.

<h3>What is a z-distribution confidence interval?</h3>

The confidence interval is:

\overline{x} \pm z\frac{\sigma}{\sqrt{n}}

In which:

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  • z is the critical value.
  • n is the sample size.
  • \sigma is the standard deviation for the population.

The margin of error is given by:

M = z\frac{\sigma}{\sqrt{n}}

In this problem, we have that the parameters are given as follows:

M = 3, z = 1.645, \sigma = 16.

Hence, solving for n, we find the sample size.

M = z\frac{\sigma}{\sqrt{n}}

3 = 1.645\frac{16}{\sqrt{n}}

3\sqrt{n} = 1.645 \times 16

\sqrt{n} = \frac{1.645 \times 16}{3}

(\sqrt{n})^2 = \left(\frac{1.645 \times 16}{3}\right)^2

n = 76.97

Rounding up, the smallest sample size required to obtain the desired margin of error is of 77.

More can be learned about the z-distribution at brainly.com/question/25890103

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2 years ago
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3 years ago
What is the solution, vertex , and y-intercept ?
MrMuchimi
F(x) = -(x+7)² + 4

f(x) = -(x+7)(x+7) + 4
f(x) = -(x² + 7x + 7x + 49) + 4
f(x) = -x² - 14x - 49 + 4
f(x) = -x² - 14x - 45

True for f(x)
<span>the equation is quadratic. 
the vertex is (7,4)
</span><span>the y-intercept is (0,4)</span>
7 0
3 years ago
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