How do you simplify 8*1/10
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Answer:
1. The Venn diagrams are attached
2. When the statistics students number = 10·x + 3, we have;
The number of students that study
a. Algebra = 128/11
b. Statistic = 213/11
When the statistics students number = 2·x + 3, we have;
The number of students that study
a. Algebra = 16
b. Statistic = 15
Step-by-step explanation:
The parameters given are;
Total number of students = 30
Number of students that study algebra n(A) = x + 10
Number of students that study statistics n(B) = 10·x + 3
Number of student that study both algebra and statistics n(A∩B) = 4
Number of student that study only algebra n(A\B) = 2·x
Number of students that study neither algebra or statistics n(A∪B)' = 3
Therefore;
The number of students that study either algebra or statistics = n(A∪B)
From set theory we have;
n(A∪B) = n(A) + n(B) - n(A∩B)
n(A∪B) = 30 - 3 = 27
Therefore, we have;
n(A∪B) = x + 10 + 10·x + 3 - 4 = 27
11·x+13 = 27 + 4 = 31
11·x = 18
x = 18/11
The number of students that study
a. Algebra
n(A) = 18/11 + 10 = 128/11
b. Statistic
n(B) = 213/11
Hence, we have;
n(A - B) = n(A) - n(A∩B) = 128/11 - 4 = 84/11
Similarly, we have;
n(B - A) = n(B) - n(A∩B) = 213/11 - 4 = 169/11
However, assuming n(B) = (2·x + 3), we have;
n(A∪B) = n(A) + n(B) - n(A∩B)
n(A∪B) = 30 - 3 = 27
Therefore, we have;
n(A∪B) = x + 10 + 2·x + 3 - 4 = 27
2·x+3 + x + 10= 27 + 4 = 31
3·x = 18
x = 6
Therefore, the number of students that study
a. Algebra
n(A) = 16
b. Statistics
n(B) = 15
Hence, we have;
n(A - B) = n(A) - n(A∩B) = 16 - 4 = 12
Similarly, we have;
n(B - A) = n(B) - n(A∩B) = 15 - 4 = 11
The Venn diagrams can be presented as follows;
Answer:
The 99.7% confidence interval for the mean price of all new mobile homes is ($60,672, $65,622).
Step-by-step explanation:
<em>The question is incomplete:</em>
<em>The prices in thousands of dollar are:</em>
<em>66.6, 69.8, 58.4, 57.3, 63.1, 61.8, 56, 72.7, 61.8, </em>
<em>66.9, 72.6, 63.1, 58.7, 65.9, 61.1, 56.1, 49.9, 72.6, </em>
<em>49, 56.4, 72.6, 60.1, 65, 64.8, 56.5, 52, 53.2, </em>
<em>56.4, 75.4, 76.3, 60.5, 74.6, 57, 69.2, 62.7, 77.2.</em>
<em />
We have a sample of n=36 new mobile homes.
The mean of this sample is:
The population standard deviation is σ=7.5 (in thousands of dollars).
The critical value of z for a 99.7% CI is z=2.97.
Then, we can calculate the margin of error as:
Now we can calculate the lower and upper bound of the confidence interval as:
The 99.7% confidence interval for the mean price of all new mobile homes is ($60,672, $65,622).
