What are the steps for this equation?: 6x-5=3x+4
2 answers:
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Answer:
The 99% confidence interval is (3.0493, 3.4907).
We are 99% sure that the true mean of the students Perry score is in the above interval.
Step-by-step explanation:
Our sample size is 21.
The first step to solve this problem is finding our degrees of freedom, that is, the sample size subtracted by 1. So
.
Then, we need to subtract one by the confidence level and divide by 2. So:
Now, we need our answers from both steps above to find a value T in the t-distribution table. So, with 20 and 0.005 in the two-sided t-distribution table, we have
Now, we find the standard deviation of the sample. This is the division of the standard deviation by the square root of the sample size. So
Now, we multiply T and s
Then
The lower end of the interval is the mean subtracted by M. So:
The upper end of the interval is the mean added to M. So:
The 99% confidence interval is (3.0493, 3.4907).
Interpretation:
We are 99% sure that the true mean of the students Perry score is in the above interval.
Answer:
Step-by-step explanation:
Please refer to the attached diagram. (Apologies if the shading or resolution is a bit off.)
So, we want to find θ.
Since we formed a right triangle, we can use right triangle ratios.
We know the measure of the adjacent side to θ and the hypotenuse.
Therefore, we will use the cosine ratio:
The adjacent side is 2 and the hypotenuse is 15. By substitution:
Now, we will take the inverse cosine of both sides. So:
Use a calculator. Hence:
The angle between the ground and the ladder is about 82.34°.
