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2 years ago

Solve for m 2/3=m/42

Mathematics

1 answer:

almond37 [142]2 years ago

4 0

$\frac{2}{3}=\frac{m}{42}\ \ \ \ | multiply\ by\ 42\\\\ \frac{2*42}{3}=m\\\\
28=m\\\\Solution\ is\ m=28.$

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One of the legs of a right triangle measures 8 cm and its hypotenuse measures 14 cm.

Ugo [173]

Answer:

about 11.5 cm.

Step-by-step explanation:

I know the measurement of the other leg is about 11.5 cm. I know because I used the Pythagorean theorem.

a^2+b^2=c^2.

"a" and "b" are the values of the legs of the triangle, while "c" is the measure of the hypotenuse. We know that 8cm is the measure of one of the legs, and 14 cm is a measure of the hypotenuse.

8^2+b^2=14^2 simplified: 64+b^2=196

Then, I subtracted 64 on both sides, so I would have "b" by itself.

b^2=132

Next, I found the square root of both b^2 and 132, so I would find the true value of "b."

b=11.4891252931

So, the measure of the other leg rounded to the nearest tenth is about 11.5.

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2 years ago

Which is the value of the expression (StartFraction (10 Superscript 4 Baseline) (5 squared) Over (10 cubed) (5 cubed)) cubed?

Flura [38]

Answer:

The value to the given expression is 8

Therefore $\left[\frac{(10^4)(5^2)}{(10^3)(5^3)}\right]^3=8$

Step-by-step explanation:

Given expression is (StartFraction (10 Superscript 4 Baseline) (5 squared) Over (10 cubed) (5 cubed)) cubed

Given expression can be written as below

$\left[\frac{(10^4)(5^2)}{(10^3)(5^3)}\right]^3$

To find the value of the given expression:

$\left[\frac{(10^4)(5^2)}{(10^3)(5^3)}\right]^3=\frac{((10^4)(5^2))^3}{((10^3)(5^3))^3}$

( By using the property ( $(\frac{a}{b})^m=\frac{a^m}{b^m}$ )

$=\frac{(10^4)^3(5^2)^3}{(10^3)^3(5^3)^3}$

( By using the property $(ab)^m=a^mb^m$ )

$=\frac{(10^{12})(5^6)}{(10^9)(5^9)}$

( By using the property $(a^m)^n=a^{mn}$ )

$=(10^{12})(5^6)(10^{-9})(5^{-9})$

( By using the property $\frac{1}{a^m}=a^{-m}$ )

$=(10^{12-9})(5^{6-9})$ (By using the property $a^m.b^n=a^{m+n}$ )

$=(10^3)(5^{-3})$

$=\frac{10^3}{5^3}$ ( By using the property $a^{-m}=\frac{1}{a^m}$ )

$=\frac{1000}{125}$

$=8$

Therefore $\left[\frac{(10^4)(5^2)}{(10^3)(5^3)}\right]^3=8$

Therefore the value to the given expression is 8

3 0

2 years ago

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Is 48 a perfect cube? Explain your reasoning.

Ksivusya [100]

Answer:

Reasoning:

If something is a perfect cube, it is able to be put under a cube root ( $\sqrt[3]{..}$ ) and will result in an integer (a non-decimal number > 0, basically).

So let's calculate $\sqrt[3]{48}$ , and see if the result is an integer.

$\sqrt[3]{48}$ = 3.634.......

As you can see, the result is not an integer, therefore 48 is not a perfect cube.

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2 years ago

TIME REMAINING37:15How many square inches are in 60 square feet?

Firlakuza [10]

60 square feet = 8640 square inchs

So, 60 square feet = 60 × 144 = 8640 square inchs.

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2 years ago

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A recent poll of 80 randomly selected Californians showed that 38% ( = 0.38) believe they are doing all that they can to conserv

Elanso [62]

The margin of error given the proportion can be found using the formula

$z* \sqrt{ \frac{p(1-p)}{n} }$

Where
$z*$ is the z-score of the confidence level
$p$ is the sample proportion
$n$ is the sample size

We have
$z*=2.58$
$p=0.38$
$n=80$

Plugging these values into the formula, we have:
$2.58 \sqrt{ \frac{0.38(1-0.38)}{80} } =0.14$

The result 0.14 as percentage is 14%

Margin error is 38% ⁺/₋ 14%

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3 years ago

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