Solving a right triangle (round to the nearest tenth)
1 answer:
Answer:
see explanation
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Subtract the sum of the given angles from 180 for A
A = 180° - (90 + 46)° = 180° - 136° = 44°
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tan46° = =
Multiply both sides by 23
23 × tan46° = b, thus
b ≈ 23.8 ( to the nearest tenth )
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cos46° = =
Multiply both sides by c
c × cos46° = 23 ( divide both sides by cos46° )
c = ≈ 33.1 ( to the nearest tenth )
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Answer:
If we compare the the p value with the significance level provided , we see that
, so then we can reject the null hypothesis. and there is a significant increase in the miles per gallon from 2017 to 2019 at 10% of significance.
Step-by-step explanation:
Previous concepts
A paired t-test is used to compare two population means where you have two samples in which observations in one sample can be paired with observations in the other sample. For example if we have Before-and-after observations (This problem) we can use it.
Let put some notation :
x=test value 2017 , y = test value 2019
x: 28.7 32.1 29.6 30.5 31.9 30.9 32.3 33.1 29.6 30.8 31.1 31.6
y: 31.1 32.4 31.3 33.5 31.7 32.0 31.8 29.9 31.0 32.8 32.7 33.8
Solution to the problem
The system of hypothesis for this case are:
Null hypothesis:
Alternative hypothesis:
Because if we have an improvement we expect that the values for 2019 would be higher compared with the values for 2017
The first step is calculate the difference and we obtain this:
d: 2.4, 0.3, 1.7,3,-0.2, 1.1, -0.5, -3.2, 1.4, 2, 1.6, 2.2
The second step is calculate the mean difference
The third step would be calculate the standard deviation for the differences, and we got:
We assume that the true difference follows a normal distribution. The 4th step is calculate the statistic given by :
The next step is calculate the degrees of freedom given by:
Now we can calculate the p value, since we have a right tailed test the p value is given by:
If we compare the the p value with the significance level provided , we see that
, so then we can reject the null hypothesis. and there is a significant increase in the miles per gallon from 2017 to 2019 at 10% of significance.