Use the confidence interval to find the estimated margin of error. Then find the sample mean. A biologist reports a confidence i
1 answer:
Complete Question
A biologist reports a confidence interval of (3.5,4.9) when estimating the mean height (in centimeters) of a sample of seedlings. What is the estimated margin of error and the sample mean?
Answer:
The margin of error is
The sample mean is
Step-by-step explanation:
from the question we are told that
The upper limit is
The lower limit is
Generally the margin of error is mathematically represented as
Generally the sample mean is mathematically evaluated as
=>
=>
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Answer:
8/17≤m≤8 ; [8/17, 8]
Step-by-step explanation:
To solve the inequality you need to isolate the variable in the middle of the inequality.
When you are solving the inequality each operation has to be done to every part of the inequality.
To isolate the m in the middle we need to divide each part by 17.
8≤17m≤136
8/ 17 ≤ 17m/ 17 ≤ 136/ 17
8/17≤m≤8
[8/17,8]
Answer:
Step-by-step explanation:
The first thing we have to do is find the measure of angle A using the fact that the csc A = 2.5.
Csc is the inverse of sin. So we could rewrite as
or more easy to work with is this:
and cross multiply to get
2.5 sinA = 1 and
which simplifies to
sin A = .4
Using the 2nd and sin keys on your calculator, you'll get that the measure of angle A is 23.58 degrees.
We can find angle B now using the Triangle Angle-Sum Theorem that says that all the angles of a triangle have to add up to equal 180. Therefore,
angle B = 180 - 23.58 - 90 so
angle B = 66.42
The area of a triangle is
where h is the height of the triangle, namely side AC; and b is the base of the triangle, namely side BC. To find first the height, use the fact that angle B, the angle across from the height, is 66.42, and the hypotenuse is 3.9. Right triangle trig applies:
and
3.9 sin(66.42) = h so
h = 3.57
Now for the base. Use the fact that angle A, the angle across from the base, measures 23.58 degrees and the hypotenuse is 3.9. Right triangle trig again:
and
3.9 sin(23.58) = b so
b = 1.56
Now we can find the area:
so
A = 2.8 cm squared