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3 years ago

Multiplying a number by 2 and then dividing by 3 is the same as multiplying by what number

Mathematics

1 answer:

Anestetic [448]3 years ago

7 0

That is the same as multiplying by 3

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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

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

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

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

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

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

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

5 0

3 years ago

Solve the Inequality for M:<br> 1 + m/3 < 6

Nookie1986 [14]

1 + m/3 < 6

Take 1 off both sides:

m / 3 < 5

Times both sides by 3:

m < 15

7 0

3 years ago

What value is added to both sides of the equation x2 − 8x = −10 in order to solve by completing the square? −8 16 −4 4?

ivanzaharov [21]

X^2 - 8x = -10 .....u would add 16 to both sides
x^2 - 8x + 16 = -10 + 16

take half of ur x term, ur x term is -8, half of it is -4, then u square it...-4^2 = 16, and that is what u add to both sides

7 0

3 years ago

Y-intercept for the graph or 3x-5y=6

mr Goodwill [35]

The answer is B. -6/5

4 0

3 years ago

Read 2 more answers

1. Describe the relationship between the following lines:

Anestetic [448]

I believe your answer is B

4 0

4 years ago