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3 years ago

Solve for n. (Thank you!)

Mathematics

2 answers:

Katena32 [7]3 years ago

7 0

Answer:

n = 5

Step-by-step explanation:

To solve this find what can be multiplied by 2 to get 10. The answer is 5 because 2 x 5 = 10. You have to multiply the exponents to get the answer.

sdas [7]3 years ago

3 0

Answer:

n = 5

Step-by-step explanation:

$(z^{2})^{n}$ = $z^{10}$

Now, apply the exponent rule $(a^{b})^{c}$ = $a^{bc}$ :

$z^{2n}$ = $z^{10}$

If $a^{f(x)}$ = $a^{g(x)}$ , then f(x) = g(x):

2n = 10

n = 5

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a. 0.1681 = 16.81% probability that all five qualify for the favorable rate.

b. 0.5283 = 52.83% probability that at least four qualify for the favorable rates

Step-by-step explanation:

For each Puerto Rico resident, there are only two possible outcomes. Either they qualify for discounted rates, or they do not. The probability of a person in the sample qualifying for discounted rates is independent of any other person in the sample. This means that the binomial probability distribution is used to solve this question.

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In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

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70% of the island residents of Puerto Rico have reduced their electricity usage sufficiently to qualify for discounted rates.

This means that $p = 0.7$

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This means that $n = 5$

a. All five qualify for the favorable rate

This is P(X = 5). So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 5) = C_{5,5}.(0.7)^{5}.(0.3)^{0} = 0.1681$

0.1681 = 16.81% probability that all five qualify for the favorable rate.

b. At least four qualify for the favorable rates

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$P(X \geq 4) = P(X = 4) + P(X = 5)$

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