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dexar [7]
2 years ago
13

Which expression is equivalent to (x^-6/x^2)^3

Mathematics
2 answers:
goldenfox [79]2 years ago
8 0
For this problem, just apply the laws of exponents. When dividing variable with the same base, just subtract their exponents. Hence, x^-6 divided by x^2 would be x^-8. Then, multiply the exponent with 3, becoming x^-24. Or, in reciprocal form, 1/x^24.
ahrayia [7]2 years ago
5 0

Answer

Find the expression equivalent to

= (\frac{x^{-6}}{x^{2}})^{3}

To prove

The expression given in the question be

= (\frac{x^{-6}}{x^{2}})^{3}

Now using the properties of the exponent.

The quotient of powers property and tells us that when you divide powers with the same base you just have to subtract the exponents.

i.e

\frac{x^{a}}{x^{b}} = x ^{a - b}

Apply this properties in the above

= (x^{-6-2})^{3}

= (x^{-8})^{3}

Now using the property

To find a power of a power you just have to multiply the exponents.

i.e

(ab)^{2} = a^{2}. b ^{2}

Apply this property in the above

= x^{-24}

it is also written as

= \frac{1}{x^{24}}





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Select the correct location in the expression.
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Answer:

78

Correct term:60

Step-by-step explanation:

We are given that

\frac{4x^4-6x^3+6x+3}{x-3}

The quotient of this expression is given by

4x^3+6x^2+18x+78+\frac{183}{x-3}

We have to find the term in this expression  which contains an error.

\frac{4x^4-6x^3+6x+3}{x-3}

The quotient of this expression is given by

=4x^3+6x^2+18x+60

Dividend=Divisor\times quotient+ remainder

Using the formula

4x^4-6x^3+6x+3=(x-3)(4x^3+6x^2+18x+60)+\frac{183}{x-3}

We can see that in the given expression there is 60 in place of 78.

The error in the expression of quotient is 78.

Correct term is 60.

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The FBI wants to determine the effectiveness of their 10 Most Wanted list. To do so, they need to find out the fraction of peopl
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Answer:

<em>98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list</em>

(0.3583 , 0.4579)

Step-by-step explanation:

<u>Explanation</u>:-

<em>Given sample size 'n' = 517</em>

Given data Suppose a sample of 517 suspected criminals is drawn. Of these people, 211 were captured.

'x' =211

<em>The sample proportion</em>

                                   p^{-}  = \frac{x}{n} = \frac{211}{517} =0.4081

                                  q^{-} = 1-p^{-} = 1- 0.4081 = 0.5919

<em>98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list</em>

(p^{-}  - Z_{\frac{\alpha }{2}  } \sqrt{\frac{p^{-} (1-p^{-} )}{n} } , p^{-} + Z_{\frac{\alpha }{2} } \sqrt{\frac{p^{-} (1-p^{-} }{n} } )

(0.4081  - 2.326   \sqrt{\frac{0.4081 (0.5919 )}{517} } , 0.4081+ 2.326\sqrt{\frac{0.4081(0.5919 }{517} } )

(0.4081-0.0498 , 0.4081 +0.0498)

(0.3583 , 0.4579)

<u><em>Conclusion</em></u>:-

<em>98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list</em>

(0.3583 , 0.4579)

7 0
3 years ago
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