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3 years ago

What makes the statement true? 8^-2=?

2 answers:

6 0

I think the correct answer would be 1/64. <span>A </span>negative exponent<span> just means that the base is on the wrong side of the fraction line, so you need to flip the base to the other side. It is calculated as follows:

8^-2 = 1/8^2 = 1/64

Hope this answers the question. Have a nice day.</span>

loris [4]3 years ago

4 0

Answer:

$\frac{1}{64}$ makes the statement true.

Step-by-step explanation:

Given expression,

$8^{-2}$

By using the property of exponent, i.e. $a^m=\frac{1}{a^{-m}}$

$\implies 8^{-2}=\frac{1}{8^{2}}$

$=\frac{1}{64}$

Hence, the true statement would be,

$8^{-2}=\frac{1}{64}$

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What are 3 interesting facts about David Hilbert

faust18 [17]

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3 0

3 years ago

What is the slope of the line NP

Luba_88 [7]

Answer:

The slope of NP is $\frac{-5}{7}$ ⇒ B

Step-by-step explanation:

In any square, every two opposite sides are parallel and every two consecutive sides are perpendicular

Parallel lines have the same slope

The product of the slopes of the perpendicular lines is -1, which means if the slope of one m, then the slope of the other is $\frac{-1}{m}$ (reciprocal m and change its sign)

The rule of the slope of the line which passes through the points (x1, y1) and (x2, y2) is m = $\frac{y2-y1}{x2-x1}$

In square MNPR

∵ MN and NP are adjacent sides

∴ MN ⊥ NP

∵ M = (3, 8) and N = (-2, 1)

∴ x1 = 3 and y1 = 8

∴ x2 = -2 and y2 = 1

→ Use the rule of the slope above to find the slope of MN

∴ m(MN) = $\frac{1-8}{-2-3}$

∴ m(MN) = $\frac{-7}{-5}$

∴ m(MN) = $\frac{7}{5}$

∵ MN ⊥ NP

∴ The product of their slopes = -1

→ Reciprocal the slope of MN and change its sign

∴ m(NP) = $\frac{-5}{7}$

∴ The slope of NP is $\frac{-5}{7}$

8 0

3 years ago

Complete the following table for f(a) = -8(5/2)*

marusya05 [52]

Replace x in the equation with the x values in the table and solve for y.

-8(5/2)^-3 = -64/125

-8(5/2)^-1 = -16/5

-8(5/2)^0 = -8

-8(5/2)^2 = -40

6 0

3 years ago

Devont had a handful of dimes and quarters in his pocket. He counted 41 coins and realized they were worth $7.55. Write and solv

MatroZZZ [7]

Answer:D:18 Q:23

Step-by-step explanation:

6 0

3 years ago

Noise levels at 5 volcanoes were measured in decibels yielding the following data: 127,174,157,120,161 Construct the 98% confide

slavikrds [6]

Answer:

The critical value used is T = 3.747.

The 98% confidence interval for the mean noise level at such locations is (108.944, 186.656).

Step-by-step explanation:

Before building the confidence interval, we need to find the sample mean and the sample standard deviation.

Sample mean:

$\overline{x} = \frac{127+174+157+120+161}{5} = 147.8$

Sample standard deviation:

$s = \sqrt{\frac{(127-147.8)^2+(174-147.8)^2+(157-147.8)^2+(120-147.8)^2+(161-147.8)^2}{4}} = 23.188$

Confidence interval:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 5 - 1 = 4

98% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 4 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.98}{2} = 0.99$ . So we have T = 3.747, which is the critical value used.

The margin of error is:

$M = T\frac{s}{\sqrt{n}} = 3.747\frac{23.188}{\sqrt{5}} = 38.856$

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 147.8 - 38.856 = 108.944

The upper end of the interval is the sample mean added to M. So it is 147.8 + 38.856 = 186.656.

The 98% confidence interval for the mean noise level at such locations is (108.944, 186.656).

8 0

4 years ago