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4 years ago

Simplify the following expression using properties of exponents. (4z)⁻³×(2z)⁵

Mathematics

1 answer:

Elena-2011 [213]4 years ago

8 0

Answer:

z²/2

Step-by-step explanation:

The applicable properties of exponents are ...

(ab)^c = (a^c)(b^c)

(a^b)(a^c) = a^(b+c)

a^-b = 1/a^b

$(4z)^{-3}\cdot(2z)^5=(4^{-3})(z^{-3})(2^5)(z^5)=\dfrac{32}{64}z^{-3+5}\\\\=\boxed{\dfrac{z^2}{2}}$

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Answer:

12.5h

Step-by-step explanation:

add all of the hours up

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3 years ago

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Aleonysh [2.5K]

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3 years ago

Ms. Turner is buying deli meat to make sandwiches for a class picnic. She buys 14 pounds of roast beef for $51.10. She also buys

Masja [62]

RB: $51.10/14=$3.65 per lb
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4 years ago

Read 2 more answers

Which of the following expressions is equivalent to the one shown below? (-5 x 4)3

salantis [7]

Answer:

-60

Step-by-step explanation:

<em>We'd solve anything inside the parentheses first:</em>

-5 * 4 = -20

<em>Now multiply:</em>

-20 * 3 = -60

Our answer would be -60

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3 years ago

Read 2 more answers

Suppose that a fast food restaurant decides to survey its customers to gauge interest in a breakfast menu. After surveying multi

Artemon [7]

Answer:

$\hat p = 0.727$ point of estimate for the proportion of customers interested in a breakfast menu

$ME= 0.039$ represent the margin of error.

Step-by-step explanation:

For this case we want to find a confidence interval for the proportion of customers interested in a breakfast menu.

The confidence interval for this case is given by this formula:

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

And the margin of error is given by:

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

The 95% confidence for this case is given by:

$0.688 \leq p \leq 0.766$

We can find the point of estimate for the proportion using the fact that the interval is symmetrical

$\hat p = \frac{Lower+Upper}{2} =\frac{0.688+0.766}{2}=0.727$

And we can find the margin of error with this difference:

$ME = Upper- \hat p = 0.766-0.727 = 0.039$

Or equivalently with:

$ME = \hat p -Lower = 0.727- 0.688 =0.039$

So then the final answer for this case would be:

$\hat p = 0.727$ point of estimate for the proportion of customers interested in a breakfast menu

$ME= 0.039$ represent the margin of error.

7 0

3 years ago