Answer:
Yes, evidence shows that the cream will improve the skin of more than 40% of women over the age of 50 in 0.01 significance level.
Step-by-step explanation:
We need to make a hypothesis test.
Let p be the proportion of women who used cream report skin improvement.
: p=0.4
: p<0.4
To test the hypothesis, we need to calculate z-score of the sample mean and compare its probability with the significance level.
z= where
- p(s) is the sample proportion of women reported improvement (0.5)
- p is the proportion assumed under null hypothesis. (0.4)
- N is the sample size (70)
Putting the numbers:
z= ≈ 1.71
And P(z<1.71) ≈ 0.955. Since 0.955>0.01 we fail to reject the null hypothesis that the cream will improve the skin of more than 40% of women.
Answer:
3/4x - 1
Step-by-step explanation:
Answer:
The system of inequalities is
y\geq 3x-2
y<-(1/5)x+2
Step-by-step explanation:
step 1
Find the equation of the solid blue line
Let
A(0,-2), B(1,1)
Find the slope of AB
m=(1+2)/(1-0)=3
The equation of the line into slope intercept form is equal to
y=mx+b
we have
m=3
b=-2 - ----> the point A is the y-intercept
substitute
y=3x-2 - -----> equation of the solid blue line
The solution of the inequality is the shaded area above the solid line
therefore
The first inequality is
y\geq 3x-2
C(0,2), D(5,1)
step 2
Find the equation of the dashed red line
Let
Find the slope of CD
m=(1-2)/(5-0)=-1/5
The equation of the line into slope intercept form is equal to
y=mx+b
we have
m=-1/5
b=2 ----> the point C is the y-intercept
substitute
y=-(1/5)x+2 -----> equation of the dashed red line
The solution of the inequality is the shaded area below the dashed line
therefore
The second inequality is
y<-(1/5)x+2
The system of inequalities is
y\geq 3x-2
y<-(1/5)x+2