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densk [106]
3 years ago
9

In a chess club the probability that Shaun will beat Mike is 3/8 .

Mathematics
1 answer:
romanna [79]3 years ago
3 0

Answer:

\frac{10}{56} = 0.1786 probability that Shaun loses both games

Step-by-step explanation:

Games are independent, so we find each separate probability, and multiply them.

In a chess club the probability that Shaun will beat Mike is 3/8.

So 1 - \frac{3}{8} = \frac{8}{8} - \frac{3}{8} = \frac{5}{8} probability that Shaun loses.

The probability that Shaun will beat Tim is 5/7 .

So 1 - \frac{5}{7} = \frac{2}{7} probability that Shaun loses.

What is the probability that Shaun loses both games?

This is:

p = \frac{5}{8} \times \frac{2}{7} = \frac{5*2}{8*7} = \frac{10}{56} = 0.1786

\frac{10}{56} = 0.1786 probability that Shaun loses both games

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If vector u = <-3.5, -1.5> and vector v = <-1.25, 2.25>, which graph shows the resulting vector for 2v − u?
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Answer:

D

Step-by-step explanation:

We know that vector addition is scalar addition.

Given vectors are u = <-3.5, -1.5> and v = <-1.25, 2.25>

2v = < -2.5, 4.5>

2v - u = < -2.5, 4.5> - <-3.5, -1.5> = < -2.5 - (-3.5) , 4.5 -(-1.5) >

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This vector is basically i + 6j which is drawn in option D

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3 years ago
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
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Answer:

x = 1, x = -1

Step-by-step explanation:

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Helena needs 3.5 cups of flour per loaf of bread and 2.5 cups of flour per batch of muffins. She also needs 0.75 cup of sugar pe
Alik [6]
The amount she has in hand, she can make 4 loaves of bread and 2 batches of muffins.
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3 years ago
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Oduvanchick [21]

Answer:

1/4 of the cake.

Step-by-step explanation:

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Therefore, he ate 1/4 of the entire cake.

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