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3 years ago

Will name brainliest

Mathematics

2 answers:

slega [8]3 years ago

7 0

Answer:

x = 14.1 (Rounded to the nearest tenths)

Step-by-step explanation:

Since the opposite side of the angle given needs to be found out and hypotenuse, Sin ratio would be used;

Sin(42) = $\frac{x}{21}$

=> Now multiply 21 on both sides of =, in order to isolate x;

Sin(42) * 21 = x

14.1 = x

Hope this helps!

exis [7]3 years ago

3 0

Answer:

14.1 =x

Step-by-step explanation:

Since this is right triangle, we can use trig functions

sin theta = opp/ hypotenuse

sin 42 = x /21

21 sin 42 = x

14.05174273 =x

Rounding to the nearest tenth

14.1 =x

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$t=\frac{5.63-5}{\frac{1.61}{\sqrt{15}}}=1.516$

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Since is a right tailed test the p value would be:

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Step-by-step explanation:

Data given and notation

$\bar X=5.63$ represent the sample mean

$s=1.61$ represent the standard deviation for the sample

$n=15$ sample size

$\mu_o =15/tex] represent the value that we want to test 
[tex]\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses to be tested

We need to conduct a hypothesis in order to determine if the average is more than 5.63, the system of hypothesis would be:

Null hypothesis: $\mu \leq 5.63$

Alternative hypothesis: $\mu > 5.63$

Compute the test statistic

We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

We can replace in formula (1) the info given like this:

$t=\frac{5.63-5}{\frac{1.61}{\sqrt{15}}}=1.516$

Now we need to find the degrees of freedom for the t distribution given by:

$df=n-1=15-1=14$

P value

Since is a right tailed test the p value would be:

$p_v =P(t_{14}>1.516)=0.076$

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