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garik1379 [7]
3 years ago
11

A 35-foot tall pole is leading towards a building. To stop the pole from leaning further, a 48-foot long cable is secured from t

he top of the pole to a stake in the ground opposite of the building. If the stake is 30 feet from the pole, what angle does the cable make with the pole?
Round the answer to the nearest tenth.

Mathematics
1 answer:
anygoal [31]3 years ago
6 0

9514 1404 393

Answer:

  38.5°

Step-by-step explanation:

A triangle solver can give an answer easily. The angle is 38.5°.

__

The law of cosines can be written to solve for an unknown angle C opposite side 'c' and flanked by sides 'a' and 'b'.

  C = arccos((a² +b² -c²)/(2ab))

Here, we have a=35, b=48, c=30, so the angle is ...

  C = arccos((35² +48² -30²)/(2·35·48)) = arccos(2629/3360) ≈ 38.515°

The angle the cable makes with the pole is about 38.5°.

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On a mountain, the temperature decreases by 18°F every 5000 feet. What integer represents the change in temperature at 20,000 ft
attashe74 [19]
<span>To find this answer, use multiples. For every 5000 feet ascended, deduct 18 degrees. For 20,000 feet, which is (4 * 5000), use (4 * -18). In this case, the answer is -72 degrees F, so the integer described would be -72.</span>
7 0
3 years ago
Based on historical data in Oxnard college, we believe that 37% of freshmen do not visit their counselors regularly. For this ye
slega [8]

Answer:

A sample size of 1031 is required.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

The margin of error is of:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

37% of freshmen do not visit their counselors regularly.

This means that \pi = 0.37

98% confidence level

So \alpha = 0.02, z is the value of Z that has a pvalue of 1 - \frac{0.02}{2} = 0.99, so Z = 2.327.

You would like to be 98% confident that your estimate is within 3.5% of the true population proportion. How large of a sample size is required?

A sample size of n is required.

n is found when M = 0.035. So

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.035 = 2.327\sqrt{\frac{0.37*0.63}{n}}

0.035\sqrt{n} = 2.327\sqrt{0.37*0.63}

\sqrt{n} = \frac{2.327\sqrt{0.37*0.63}}{0.035}

(\sqrt{n})^2 = (\frac{2.327\sqrt{0.37*0.63}}{0.035})^2

n = 1030.4

Rounding up:

A sample size of 1031 is required.

4 0
3 years ago
What is the distance between (8, -3) and (4, – 7)?
Dahasolnce [82]

Answer:

4

Step-by-step explanation:

using

\sqrt{(x2 - x1) + (y2 - y1)}

\sqrt{(8 - 3) + (4  - ( - 7)}

\sqrt{5 + 11}

\sqrt{16}

= 4

7 0
3 years ago
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Answer pls!! HURRY IT IS TIMED
alukav5142 [94]

Answer:

3 and 6

Step-by-step explanation:

4 0
2 years ago
Sid Upp is four years younger than his brother Tip. Let x stand for Tip's age . Write an equation stating that Sid's age is 32.
vlada-n [284]

Answer:

x+4=36

Step-by-step explanation:

you would subtract 4 on each side

x+4=36

  -4   -4

x=32

4 0
3 years ago
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