All categories

3 years ago

A pier forms an 85° angle with a straight shore. At a distance of 100 feet from the pier, the line of sight to the tip forms a 3

7° angle. Find the length of the pier to the nearest tenth of a foot. ...?

Mathematics

1 answer:

Troyanec [42]3 years ago

3 0

$\alpha=85^o,a=100,\beta=37^o,b=? \\ \\ \frac{a}{\sin\alpha}= \frac{b}{\sin\beta} 
\\
\\ \frac{100}{\sin85^o}= \frac{b}{\sin37^o} 
\\
\\b= \frac{100 \sin37^o}{\sin85^o} =60.4$

You might be interested in

Which of the following describes the graph of y=[x-2]?

kow [346]

Answer:

What are the answer choices, if you have any?.

Step-by-step explanation:

7 0

2 years ago

Hoochie [10]

Answer: 48 feet

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

According to Padgett Business Services, 20% of all small-business owners say the most important advice for starting a business i

elena-s [515]

Answer:

a) There is a 6.88% probability that none of the owners would say preparing for long hours and hard work is the most important advice.

b) There is a 1.93% probability that six or more owners would say preparing for long hours and hard work is the most important advice.

c) There is a 10.32% probability that exactly five owners would say having good financing ready is the most important advice.

d) The expected number of owners who would say having a good plan is the most important advice is 2.28

Step-by-step explanation:

Questions a), b), c) are all solved as binomial distribution problems.

Question d) is a simple calculation.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

In which C_{n,x} is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And $\pi$ is the probability of X happening.

For these problems

12 business owners were contacted, so $n = 12$ .

a. What is the probability that none of the owners would say preparing for long hours and hard work is the most important advice?

20% of all small-business owners say the most important advice for starting a business is to prepare for long hours and hard work, so $\pi = 0.2$ .

That is P(X=0) when $\pi = 0.2$ .

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 0) = C_{12,0}.(0.2)^{0}.(0.8)^{12} = 0.0688$

There is a 6.88% probability that none of the owners would say preparing for long hours and hard work is the most important advice.

b. What is the probability that six or more owners would say preparing for long hours and hard work is the most important advice?

20% of all small-business owners say the most important advice for starting a business is to prepare for long hours and hard work, so $\pi = 0.2$ .

This is:

$P = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)$

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 6) = C_{12,6}.(0.2)^{6}.(0.8)^{6} = 0.0155$

$P(X = 7) = C_{12,7}.(0.2)^{7}.(0.8)^{5} = 0.0033$

$P(X = 8) = C_{12,8}.(0.2)^{8}.(0.8)^{4} = 0.0005$

$P(X = 9) = C_{12,9}.(0.2)^{9}.(0.8)^{3} = 0.00006$

$P(X = 10) = C_{12,10}.(0.2)^{10}.(0.8)^{2} = 0.000004$

$P(X = 11) = C_{12,11}.(0.2)^{11}.(0.8)^{1} = 0.0000002$

$P(X = 12) = C_{12,12}.(0.2)^{12}.(0.8)^{0} = 0.000000004$

So:

$P = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) = 0.0155 + 0.0033 + 0.0005 + 0.000006 + 0.000004 + 0.0000002 + 0.000000004 = 0.0193$

There is a 1.93% probability that six or more owners would say preparing for long hours and hard work is the most important advice.

c. What is the probability that exactly five owners would say having good financing ready is the most important advice?

Twenty-five percent say the most important advice is to have good financing ready, so $\pi = 0.25$

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 5) = C_{12,5}.(0.25)^{5}.(0.75)^{7} = 0.1032$

There is a 10.32% probability that exactly five owners would say having good financing ready is the most important advice.

d. What is the expected number of owners who would say having a good plan is the most important advice?

Nineteen percent say having a good plan is the most important advice, so that is $0.19*12 = 2.28$

The expected number of owners who would say having a good plan is the most important advice is 2.28

4 0

3 years ago

Find the number of 4-digit numbers that contain exactly two even and two odd digits.

Dvinal [7]

Answer:

2,435

Step-by-step explanation:

find two even and two odd

7 0

3 years ago

Which of the choices below is not a possible correlation coefficient?

fiasKO [112]

Answer:

The condition for r is the following:

$-1 \leq r \leq 1$

And for this case if we analyze the options the only impossible value is given by:

1.0528

Because this value is higher than 1 and not satisfy the general limits for r

Step-by-step explanation:

The correlation coefficient is a measure of dispersion and is a value between -1 and 1, and is defined as:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

The condition for r is the following:

$-1 \leq r \leq 1$

And for this case if we analyze the options the only impossible value is given by:

1.0528

Because this value is higher than 1 and not satisfy the general limits for r

8 0

3 years ago