Answer:
The system of equations is :
Equation 1- 
Equation 2- 
Number of vinyl doghouse = 5
Number of treated lumber doghouse =12.5
Step-by-step explanation:
Let x be the number of vinyl doghouses
y be the number of treated lumber doghouses
→If it takes the company 5 hours to build a vinyl doghouses and 2 hours to build a treated lumber doghouse. The company dedicates 50 hours every week towards assembling and painting doghouses.
Equation 1- 
→It takes an additional hour to paint each vinyl doghouse and an additional 2 hours to assemble each treated lumber doghouse. The company dedicates 30 hours every week towards assembling and paining dog houses.
Equation 2- 
→When we solve these equation we get the number of vinyl doghouse and treated lumber doghouse.
Subtract equation 2 from equation 1




Put value of x in equation 2





Therefore, number of vinyl doghouse = 5, number of treated lumber doghouse =12.5
Answer:
x = 0 , 5
Step-by-step explanation:

Cross multiply,
2x* ( x - 2) = 3x *(x - 3)
2x*x - 2*2x = x*3x - 3*3x
2x² - 4x = 3x² - 9x
subtract 2x² from both sides
-4x = 3x² - 2x² - 9x {Combine like terms}
-4x = x² - 9x
Add 9x to both sides
-4x+ 9x = x²
x² = 5x
x² - 5x = 0
x(x - 5) = 0
x = 0 ; x - 5 = 0
x = 5
Answer:
H0 : σ²= 7.2²
H1 : σ² < 7.2
We can conclude that the mean waiting time of customers vary less, Than 7.2 minutes.
Step-by-step explanation:
H0 : σ²= 7.2²
H1 : σ² < 7.2²
The test statistic :
X² = [(n - 1)*s² ÷ σ²]
s² = 3.5
n = sample size = 25. ; s²
X² = [(25 -1)*3.5² ÷ 7.2²
X² = (24 * 3.5^2) / 7.2^2
X² = 5.67
Pvalue from Chisquare statistic :
P(X² < 5.67) = 0.000042
Pvalue < α ; we reject the Null.
Hence, we can conclude that the mean waiting time of customers vary less, Than 7.2 minutes.
Simple, it is equal to |4|, you have to draw the lines around the 4 on the worksheet.