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Natalija [7]
3 years ago
15

The sales manager of a company awarded a total of \$3000$3000 in bonuses to the most productive salespeople. The bonuses were aw

arded in amounts of \$250$250 or \$750$750. If at least one \$250$250 bonus and at least one \$750$750 bonus were awarded, what is one possible number of \$250$250 bonuses awarded?
Mathematics
1 answer:
alisha [4.7K]3 years ago
4 0

Answer:

one possible number of bonus is 9.

Step-by-step explanation:

Let, the number of $250 bonus = x and number of $750 bonus = y.

We have that bonuses are given in amounts $250 and $750.

Since, the total bonus is $3000.

So, we get,

250x + 750y = 3000.

As, there is atleast one $250 bonus and atleast one $750 bonus.

Let, the minimum number of bonus of $750 be 1 i.e. y = 1.

Substitute in the equation gives,

250x + 750 × 1 = 3000

i.e. 250x = 3000 - 750

i.e. 250x = 2250

i.e. x = 9

Thus, the maximum number of $250 bonus are 9.

Hence, one possible number of bonus is 9.

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Answer:

Option B is correct.

The alternative hypothesis is given Mathematically as

Ha: pA - pB > 0

Step-by-step explanation:

For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis takes the other side of the hypothesis; that there is indeed a significant difference between two proportions being compared. It usually confirms the the theory being tested by the experimental setup.

For this question, we want to test if students who are "Greek" (those who belong to a sorority/fraternity) have a tendency to be more involved in student government events than students who are "Not Greek" by checking the proportion of each group of students that turn out to vote in the student government elections.

If the proportion of Greek students that turn out to vote in the student government elections = pA

And

The proportion of non-Greek students that turn out to vote in the student government elections = pB

And the difference between them is given as

μ₀ = pA - pB

The theory to be tested that pA > pB, would constitute the alternative hypothesis and the null hypothesis would say that either the proportions are equal or proportion of non-greek students that turn out to vote is more than the proportion of Greek students that turn out to vote in the student government elections.

Mathematically,

The null hypothesis would be that

H₀: μ₀ = pA - pB ≤ 0

or

H₀: pA = pB

And the alternative hypothesis would be that

Hₐ: μ₀ = pA - pB > 0

or

Hₐ: pA > pB

Thereby, confirming the theory to be tested.

Hope this Helps!!!

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Step-by-step explanation:

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