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3 years ago

Please help! Find the value of X. Round to the nearest tenth. acellus

Mathematics

1 answer:

just olya [345]3 years ago

7 0

9514 1404 393

Answer:

38.2°

Step-by-step explanation:

The law of sines tells you ...

sin(x)/15 = sin(27°)/11

sin(x) = (15/11)sin(27°) . . . . . multiply by 15

x = arcsin((15/11)sin(27°)) ≈ arcsin(0.619078) ≈ 38.2488°

x ≈ 38.2°

_____

Additional comment

In "law of sines" problems, you need to identify a side and opposite angle that you know both values of. Then, you need to identify whether you're looking for an angle or a side, and whether its opposite side or angle is known. If two angles are known, you can always figure the third from the sum of angles in a triangle.

Here, we have angle 27° opposite side 11. We are looking for an angle, and we know its opposite side. This lets us use the ratio formula directly. Since the angle is the unknown, it is useful to write the equation with sines on top and sides on the bottom.

The given angle is opposite the shorter of the given sides, so this triangle has two solutions. We assume that we want the solution that is an acute angle (141.8° is the other solution). That assumption is based on the drawing. Usually, you're cautioned not to take the drawings at face value.

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A manufacturer of coffee vending machines has designed a new, less expensive machine. The current machine is known to dispense (

cupoosta [38]

Answer:

$t=(15-1) [\frac{0.219}{0.2}]^2 =16.7864$

$p_v = 2*P(\chi^2_{14}>16.786)=0.5355$

And the 2 is because we are conducting a bilateral test.

$\alpha=0.05$ since the the $p_v >0.05$ we fail to reject the null hypothesis.

$\alpha=0.01$ since the the $p_v >0.01$ we fail to reject the null hypothesis.

Step-by-step explanation:

Data given

$\mu=7$ population mean (variable of interest)

$\sigma=0.2$ represent the population standard deviation

$s=0.219$ represent the sample deviation

n=15 represent the sample size

$\alpha=0.05,0.01$ represent the values for the significance level

Hypothesis test

On this case we want to check if the population standard deviation is equal or not to 0.2, so the system of hypothesis are:

H0: $\sigma = 0.2$

H1: $\sigma \neq 0.2$

In order to check the hypothesis we need to calculate the statistic given by the following formula:

$t=(n-1) [\frac{s}{\sigma_o}]^2$

This statistic have a Chi Square distribution distribution with n-1 degrees of freedom.

What is the value of your test statistic?

Now we have everything to replace into the formula for the statistic and we got:

$t=(15-1) [\frac{0.219}{0.2}]^2 =16.7864$

P value

We know the degrees of freedom of the distribution 14 on this case and we can find the p value like this:

$p_v = 2*P(\chi^2_{14}>16.786)=0.5355$

And the 2 is because we are conducting a bilateral test.

$\alpha=0.05$ since the the $p_v >0.05$ we fail to reject the null hypothesis.

$\alpha=0.01$ since the the $p_v >0.01$ we fail to reject the null hypothesis.

3 0

3 years ago

What is the slope of a line perpendicular to the line whose equation is 15x+18y=270. Fully simplify your answer.

In-s [12.5K]

Answer:

6/5

Step by step explanation:

Here we are provided with a equation which is ,

$\longrightarrow 15x + 18y = 270$

And we are interested in finding the slope of the line which is perpendicular to the given line. We may rewrite the equation as ,

$\longrightarrow 18y = -15x +270\\$

$\longrightarrow y =\dfrac{-15x+270}{18}\\$

$\longrightarrow y =\dfrac{-15}{18}x +\dfrac{270}{8}\\$

$\longrightarrow y =\dfrac{-5}{6}x +\dfrac{135}{4}$

Recall the slope intercept form of the line which is y = mx + c .On comparing to which we get ,

$\longrightarrow m =\dfrac{-5}{6}$

Again , recall that product of slopes of two perpendicular lines is -1. So that ,

$\longrightarrow m_{\perp} =-\bigg(\dfrac{1}{m}\bigg)$

Hence ,

$\longrightarrow\underline{\underline{ m_{\perp}= \dfrac{6}{5}}}$

And we are done !

6 0

3 years ago

Read 2 more answers

How many times greater is 2.125*10^4 than 1.25*10^3

suter [353]

2.125*10^4 x 10^4 / 1.25 x 10^3

= (2.125 / 1.25) x 10^(4 - 3)

= 1.7 x 10^1

= 17

Answer

17 times greater

8 0

3 years ago

Help please i can't do this

e-lub [12.9K]

You have to figure out how you got 26 from 2. They multiplied 13. So multiply 5 by 13. The answer is 26/65.

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3 years ago

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PLEASE HELP I HAVE A TIME LIMIT 17 Points and Brainlest to who answers first

Novay_Z [31]

A triangle is 180 degrees. 180-28=152. so if angle b and c are combined, your answer is 152 degrees.

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3 years ago

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Please help! Find the value of X. Round to the nearest tenth.￼ acellus

Please help! Find the value of X. Round to the nearest tenth. acellus