X = # of perfomances
y = total amount of money
Income: y = 7500x
Expense: y = 5900x + 88000
Substitution:
7500x = 5900x + 88000
1600x = 88000
x = 55
y = 7500(55) = $412,500
55 performances are needed to break-even.
9514 1404 393
Answer:
28 square units
Step-by-step explanation:
The rectangle is 7-0 = 7 units high and 6-2 = 4 units wide. Its area is the product of these dimensions:
A = LW
A = (7)(4) = 28 . . . square units
<span>x + 9 = 2(x - 1)^2
x + 9 = 2(x^2 - 2x + 1)
x + 9 = 2x^2 - 4x + 2
</span>2x^2 - 4x + 2 - x - 9 = 0
2x^2 - 5x -7 =0
Answer:
10%
Step-by-step explanation:
Answer:
a. proportions have not changed significantly
Step-by-step explanation:
Given
Business College= 35 %
Arts College= 35 %
Education College = 30%
Calculated
Business College = 90/300= 9/30= 0.3 or 30%
Arts College= 120/300= 12/30= 2/5= 0.4 or 40%
Education College= 90/300= 9/30 = 0.3 or 30%
First we find the mean and variance of the three colleges using the formulas :
Mean = np
Standard Deviation= s= 
Business College
Mean = np =300*0.3= 90
Standard Deviation= s=
=
= 7.94
Arts College
Mean = np =300*0.4= 120
Standard Deviation= s=
=
= 8.49
Education College
Mean = np =300*0.3= 90
Standard Deviation= s=
=
= 7.94
Now calculating the previous means with the same number of students
Business College
Mean = np =300*0.35= 105
Arts College
Mean = np =300*0.35= 105
Education College:
Mean = np =300*0.3= 90
Now formulate the null and alternative hypothesis
Business College
90≤ Mean≥105
Arts College
105 ≤ Mean≥ 120
Education College
U0 : mean= 90 U1: mean ≠ 90
From these we conclude that the proportions have not changed significantly meaning that it falls outside the critical region.