Answer:
f(x) = 0.5(x + 3)^2 + 5.
Step-by-step explanation:
The horizontal stretch is given by multiplying by 1/2 or 0.5:
f(x) = 0.5x^2
Now a shift of 3 to the left gives f(x) = 0.5(x + 3)^2.
5 units up gives 0.5(x + 3)^2 + 5.
Answer:
The test statistics is 
The critical value is 
The null hypothesis is rejected
Step-by-step explanation:
From the question we are told that
The sample size for men is 
The sample proportion of men that own a cat is 
The sample size for women is 
The sample proportion of women that own a cat is 
The level of significance is 
The null hypothesis is 
The alternative hypothesis is 
Generally the test statistic is mathematically represented as

=> 
=> 
The critical value of
from the normal distribution table is

The p-value is obtained from the z-table ,the value is

=> 
Given that the
then we reject the null hypothesis
Gross earning = $8,000
FICA tax = 8000*0.0765 = $612
Federal income tax = $1,270
Sate income tax = 8000*0.02 = $160
Voluntary deductions = $20
Total deductions = 612+1270+160+20 = $2,062
Net pay = 8000-2062 = $5,938