Study link 4.1 answers

Highschool level trigonometry!!! Need help knowing step by step how to find answer!

Goshia [24]

Answer:

$\theta \approx 82.34^\circ$

Step-by-step explanation:

Please refer to the attached diagram. (Apologies if the shading or resolution is a bit off.)

So, we want to find θ.

Since we formed a right triangle, we can use right triangle ratios.

We know the measure of the adjacent side to θ and the hypotenuse.

Therefore, we will use the cosine ratio:

$\displaystyle \cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$

The adjacent side is 2 and the hypotenuse is 15. By substitution:

$\displaystyle \cos(\theta)=\frac{2}{15}$

Now, we will take the inverse cosine of both sides. So:

$\displaystyle \theta=\cos^{-1}\Big(\frac{2}{15}\Big)$

Use a calculator. Hence:

$\theta \approx 82.34^\circ$

The angle between the ground and the ladder is about 82.34°.

5 0

3 years ago

three vertices of a rectangle are located at (5,3), (7,1), and (1,-1). what are the coordinates of the fourth vertex?

SVETLANKA909090 [29]

I first plotted the three points and from from their position it was clear which pairs to join to start a rectangle.

At this point you need to check to make sure the angle at B is a right angle. Find the slope of the line segments AB and BC and check that the product of the slopes is -1.

From the diagram you can now see where the fourth point D has to be. If AB and CD are parallel then D must be 3 units to the left of C and 2 units above C. Find the coordinates of D and then check by finding the slopes of CD and DA and showing that the angle at D is a right angle.

I hope this helps

3 0

3 years ago

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-3 | -8n – 8 | = -120 Can you guys solve for absolute value??

alexandr1967 [171]

Answer:

n = -6 or n = 4.

Step-by-step explanation:

-3 | -8n – 8 | = -120

Divide both sides by -3:

| -8n – 8 | = 40

This gives us 2 equations because the expression in the absolute signs can be positive or negative:

-8n - 8 = 40

so -8n = 48

n = -6.

and

-8n - 8 = -40

-8n = -32

n = 4.

3 0

3 years ago

Unlike most packaged food products, alcohol beverage container labels are not required to show calorie or nutrient content. An a

zhenek [66]

Answer:

We conclude that the true average estimated calorie content in the population sampled exceeds the actual content.

Step-by-step explanation:

We are given that an article reported on a pilot study in which each of 58 individuals in a sample was asked to estimate the calorie content of a 12 oz can of beer known to contain 153 calories.

The resulting sample mean estimated calorie level was 193 and the sample standard deviation was 88.

Let $\mu$ = true average estimated calorie content in the population sampled.

So, Null Hypothesis, $H_0$ : $\mu$ $\leq$ 153 calories {means that the true average estimated calorie content in the population sampled does not exceeds the actual content}

Alternate Hypothesis, $H_A$ : $\mu$ > 153 calories {means that the true average estimated calorie content in the population sampled exceeds the actual content}

The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean estimated calorie level = 193 calories

s = sample standard deviation = 88

n = sample of individuals = 58

So, the test statistics = $\frac{193-153}{\frac{88}{\sqrt{58} } }$ ~ $t_5_7$

= 3.462

The value of t test statistics is 3.462.

Since, in the question we are not given the level of significance so we assume it to be 5%. Now, at 0.05 significance level the t table gives critical value of 1.6725 at 57 degree of freedom for right-tailed test.

Since our test statistic is more than the critical value of t as 3.462 > 1.6725, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the true average estimated calorie content in the population sampled exceeds the actual content.

8 0

3 years ago

Arts I meant sorry I clicked the wrong one

Ivahew [28]

Wow that looks so cool!, is that toothless?

5 0

4 years ago

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