The sum of the angles of any triangle is

Many utility companies promote energy conservation by offering discount rates to consumers who keep their energy usage below cer

aleksley [76]

Answer:

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.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

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

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.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

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

This means that $p = 0.7$

Five residential subscribers are randomly selected from San Juan, Puerto Rico

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

This is

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

So

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

$P(X = 4) = C_{5,4}.(0.7)^{4}.(0.3)^{1} = 0.3602$

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

$P(X \geq 4) = P(X = 4) + P(X = 5) = 0.3602 + 0.1681 = 0.5283$

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

5 0

3 years ago

22 points !!! multiply. express your answer as a fraction simplest form. 8.33 x 144

dem82 [27]

Answer:

99 24/25

Step-by-step explanation:

8.33*√144=

8.33*12=99 24/25 or 100 with 8.33 bar

8 0

3 years ago

Read 2 more answers

Indicate whether the following congruence statement is true or false.<br> 50 points

Nostrana [21]

Step-by-step explanation:

Since line NL is not necessarily congruent to MQ (labelled with different congruent marks), triangle NLM is not congruent to triangle MQP.

Instead, triangles NLM and QPM are congruent.

8 0

3 years ago

Read 2 more answers

A customer brings a check of 2,941. he wants 100 in cash, put 20% of the remaining into her savings account then the rest into a

Goryan [66]

Answer:

Amount theta she is putting in Checking account is 2272.80

Step-by-step explanation:

Given:

Amount on check = 2941

Amount that he want in cash = 100

Amount she put in saving account = 20% of remaining after getting cash

Remaining Amount she put in checking account.

To find: Amount in her Checking Account.

Amount left after taking cash = 2941 - 100 = 2841

Amount that she put in saving account = 20% of 2841 = $\frac{20}{100}\times2841$ = 568.20

Amount in her checking account = 2941 - 100 - 568.20 = 2272.8

Therefore, Amount theta she is putting in Checking account is 2272.80

8 0

3 years ago

Please help, I have been trying for a while :(<br><br>question on photo

Zigmanuir [339]

Answer:

$\frac{x-22}{(x+2)(x-4)}$

Step-by-step explanation:

multiply the numerator/denominator of the first fraction by (x - 4)

multiply the numerator/denominator of the second fraction by (x + 2)

this ensures that the fractions have a common denominator

$\frac{4}{x+2}$ - $\frac{3}{x-4}$

= $\frac{4(x-4)}{(x+2)(x-4)}$ - $\frac{3(x+2)}{(x+2)(x-4)}$ ← subtract numerators leaving the common denominator

= $\frac{4x-16-3x-6}{(x+2)(x-4)}$

= $\frac{x-22}{(x+2)(x-4)}$

4 0

2 years ago