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Alika [10]
3 years ago
8

Can someone walk me through it

Mathematics
1 answer:
Gre4nikov [31]3 years ago
6 0
Answer: x = 123
--------------------------------------------
--------------------------------------------

Here are the basic steps:

Step 1) Find the measure of angle 7 (near the 35 degree angle)
Step 2) Find angle 6 (in the center; bottom angle)
Step 3) Use angle 6 to find the value of x
-----------------
Let's go through those steps mentioned
-----------------
Step 1) Finding the measure of angle 7

We see that the 35 degree angle and angle 7 combine to form a 90 right angle. So they must add to 90 degrees

(angle 7) + 35 = 90
(angle 7) + 35 - 35 = 90 - 35
angle 7 = 55

So angle 7 is 55 degrees. We'll use it on the next step
-----------------
Step 2) Finding the measure of angle 6

We'll use the result from step 1. The triangle with angle 7, angle 6, and the 68 degree angle will be focused on here. Recall that for any triangle, the three angles must add to 180 degrees. 

So,
(angle 7) + (angle 6) + 68 = 180
(55) + (angle 6) + 68 = 180
(angle 6) + 55 + 68 = 180
(angle 6) + 123 = 180
(angle 6) + 123 - 123 = 180 - 123
angle 6 = 57

So we now know that angle 6 is 57 degrees
-----------------
Step 3) Find x

We now use the fact that angle 6 and angle x are a linear pair. They combine to form a straight line, or straight angle. In other words they add to 180 degrees (they are supplementary angles)

So,
(angle 6) + x = 180
(57) + x = 180
x + 57 = 180
x + 57 - 57 = 180 - 57
x + 57 - 57 = 123
x = 123
-----------------
Side note: we can use the exterior angle theorem to skip over step 2. To do this, we add up angle 7 (which was 55 degrees) to 68 to get 123 degrees which is the same answer. 

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Answer:

t=\frac{23500-20000}{\frac{3900}{\sqrt{100}}}=8.974      

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If we compare the p value and the significance level given for example \alpha=0.05 we see that p_v so we can conclude that we to reject the null hypothesis, and the actual mean is significantly higher than 20000.      

Step-by-step explanation:

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\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.      

We need to conduct a hypothesis in order to determine if the true mean is higher than 20000, the system of hypothesis would be:      

Null hypothesis:\mu \leq 2000      

Alternative hypothesis:\mu > 2000      

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".  

Calculate the statistic      

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

t=\frac{23500-20000}{\frac{3900}{\sqrt{100}}}=8.974      

Calculate the P-value      

First we need to calculate the degrees of freedom given by:  

df=n-1=100-1=99  

Since is a one-side upper test the p value would be:      

p_v =P(t_{99}>8.974)=9.43x10^{-15}  

Conclusion      

If we compare the p value and the significance level given for example \alpha=0.05 we see that p_v so we can conclude that we to reject the null hypothesis, and the actual mean is significantly higher than 20000.      

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