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3 years ago

PLEASE HELP FIRST CORRECT ANSWER GETS BRAINLIEST!!!!!!!!!

Mathematics

1 answer:

andreev551 [17]3 years ago

7 0

1st calculate the hypotenuse of the right triangle with one side =|-7| and the second side = |-14|
(Hypotenuse)² = 7² + 14² = 625 & Hypotenuse = √625 = 25; now that we have the hypotenuse we can calculate all 6 trigo values:

a) sin Ф = (opposite side) / (hypotenuse) = -14/25 (the student gave a wrong answer).

b) cos Ф = (adjacent) /(hypotenuse) = -7/25 (Right answer)

c) tan Ф = (opposite side) / (adjacent) = -14/ -7 = 14/7 = 2 (the student gave a wrong answer)

d) csc Ф = 1/sin Ф = (1) : (-14/25) = - 25/14 (the student gave a wrong answer)

e) sec Ф = 1/cos Ф = -25/7 ( Right question)

f) cot Ф = 1/tan Ф = 1/2 (the student gave a wrong answer)

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Answer:

We conclude that the proportion of Americans who prefer to drink DD coffee is actually more than what was advertised.

Step-by-step explanation:

We are given that in a recent Dunkin Donuts (DD) commercial, it states that 58% of Americans prefer to drink their coffee.

Of the five hundred randomly selected people who were asked if they preferred DD coffees, 325 said they did.

Let p = proportion of Americans who prefer to drink DD coffee

SO, Null Hypothesis, $H_0$ : p $\leq$ 58% {means that the proportion of Americans who prefer to drink DD coffee is actually less than or equal to what was advertised}

Alternate Hypothesis, $H_A$ : p > 58% {means that the proportion of Americans who prefer to drink DD coffee is actually more than what was advertised}

The test statistics that will be used here is One-sample z proportion statistics;

T.S. = $\frac{\hat p-p}{{\sqrt{\frac{\hat p(1-\hat p)}{n} } } } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of people who prefer to drink DD coffee in a sample of 500 people = $\frac{325}{500}$ = 65% or 0.65

n = sample of people = 500

So, test statistics = $\frac{0.65-0.58}{{\sqrt{\frac{0.65(1-0.65)}{500} } } } }$

= 3.282

Now at 0.05 significance level, the z table gives critical value of 1.6449 for right-tailed test. Since our test statistics is more than the critical value of z so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the proportion of Americans who prefer to drink DD coffee is actually more than what was advertised.

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