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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

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

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You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable preliminary estim

pogonyaev

Answer:

$n=\frac{0.5(1-0.5)}{(\frac{0.025}{1.28})^2}=655.36$

And rounded up we have that n=656

Step-by-step explanation:

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 80% of confidence, our significance level would be given by $\alpha=1-0.80=0.20$ and $\alpha/2 =0.10$ . And the critical value would be given by:

$z_{\alpha/2}=\pm 1.28$

Solution to the problem

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

Since we don't have prior info for the proportion of interest we can use $\hat p=0.5$ as estimator. And on this case we have that $ME =\pm 0.025$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.025}{1.28})^2}=655.36$

And rounded up we have that n=656

5 0

3 years ago

The volume of a cylindrical soap dispenser is modeled by the expression below.select the true statement.a. the expression (x + 1

bulgar [2K]

Answer:

The expression $(x+1)^2$ represents the radius of the soap dispenser.

The expression $4x+1$ represents the height of the soap dispenser.

Step-by-step explanation:

The question says that the soap dispenser is in the form of a cylinder.

Now, we find the volume of the cylinder by using the given formula:

$V= \pi r^2 h$ , where V represents the volume, 'r' represents the radius, and 'h' represents the height of the cylinder.

Now, the volume is the product of radius squared and the height, if they both are functions of $x$ , then the function to represent the volume must have cubic exponents.

Since, the radius is squared in the formula and it is a function of $x$ that implies that the function of radius must have square as the exponent of $x$ , therefore, the expression $(x+1)^2$ will represent the radius of the soap dispenser and the expression $(4x+1)$ represents the height of the soap dispenser.

8 0

3 years ago

Read 2 more answers

On the Algebra test the number of students who got a grade A was three more than twice the number of students who got lower grad

svlad2 [7]

X= # students who got lower grades
2x+3= # students with grade A

STEP 1:
Add the two sets above equal to 24.

x + (2x + 3)= 24
combine like terms

3x + 3= 24
subtract 3 from both sides

3x= 21
divide both sides by 3

x= 7 (# students lower than A)

STEP 2:
substitute x value from step 1 to find # grade A students

=2x + 3
=2(7) + 3
=14 + 3
=17 (# grade A students)

CHECK:
x + (2x + 3)= 24
7 + 2(7) + 3= 24
7 + 14 + 3= 24
24= 24

ANSWER: There were 17 students with grade A.

Hope this helps! :)

4 0

3 years ago

Simplify and explain how you got the answer:

timama [110]

Answer:

The answer is A

Step-by-step explanation: look at the picture for explanation