Please Help me this is the first part of 4 in this question. I will be posting the other 3 shortly. I need the answer. This is v
ital for me to pass math class
1 answer:
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Answer:
The formula for the area of the triangle is:
When <em>x</em> = 3, the area is 216 square centimeters.
When <em>x </em>= 2.4, the area is 138.24 square centimeters.
And when <em>x</em> = 5, the hypotenuse of the triangle is 50 centimeters.
Step-by-step explanation:
We are given a right triangle with a height of 8<em>x</em> and a base of 6<em>x</em>.
The area of a triangle is given by the formula:
So, by substitution:
When <em>x </em>= 3, the area will be:
And when <em>x</em> = 2.4, the area will be:
When <em>x </em>= 5, the height will be 8(5) = 40 cm and the base will be 6(5) = 30 cm.
By the Pythagorean Theorem:
So:
The hypotenuse will be:
Part A
Given info:
- xbar = sample mean = 4.90 ppm
- s = sample standard deviation = 1.12 ppm
- n = 23 = sample size
Because n > 30 is not true, and we don't know the population standard deviation (sigma), this means we must use a T distribution.
The degrees of freedom here are n-1 = 23-1 = 22.
At 90% confidence and the degrees of freedom mentioned, the t critical value is roughly t = 1.717
Use a T distribution table or calculator to determine this. If you don't have a calculator for the task, then you can search out "inverse T calculator" and there are tons of free options to pick from.
The margin of error E is
E = t*s/sqrt(n)
E = 1.717*1.12/sqrt(23)
E = 0.400982
This is approximate and accurate to 6 decimal places.
The confidence interval is going to be xbar plus or minus that E value
L = lower bound = xbar - E = 4.90 - 0.400982 = 4.499018 = 4.50
U = upper bound = xbar + E = 4.90 + 0.400982 = 5.300982 = 5.30
The confidence interval in the format of (L, U) is (4.50, 5.30)
You could also express it as the format L < mu < U and it would be 4.50 < mu < 5.30; however, I'll stick to the first method.
<h3>Answer: (4.50, 5.30)</h3>=====================================================
Part B
Since we know sigma = 2.6 is the population standard deviation, we can use a Z distribution now.
At 90% confidence, the z critical value is roughly 1.645; use a table or calculator to determine this.
Round this up to the nearest integer to get 20326. For min sample size problems, <u>always</u> round up.
<h3>Answer: 20326</h3>