What are the new dimensions if we shrink the triangle below by a scale factor of 1/3
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Answer:
There are 38 premium tickets and 82 regular tickets in a pile.
Step-by-step explanation:
Given,
Total number of tickets = 120
Total amount = $5812
Solution,
Let the number of premium tickets be x.
And the number of regular tickets be y.
Total number of tickets is the sum of total number of premium tickets and total number of regular tickets.
So the equation can be written as;
Again,total amount is the sum of total number of premium tickets multiplied by cost of each premium ticket and total number of regular tickets multiplied by cost of each regular ticket.
So the equation can be written as;
Now We will multiply equation 1 by 25 we get;
Now Subtracting equation 3 from equation 2 we get;
We will now substitute the value of x in equation 1 we get;
Hence There are 38 premium tickets and 82 regular tickets in a pile.
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>