Answer:
The 95% confidence interval would be given (0.622;0.644).
We are confident (95%) that the true proportion of people that said that they change their nail polish once a week is between 0.622 and 0.644
Step-by-step explanation:
Data given and notation
n=7000 represent the random sample taken
X=4431 represent the people that said that they change their nail polish once a week
estimated proportion of people that said that they change their nail polish once a week
represent the significance level
Confidence =0.95 or 95%
p= population proportion of people that said that they change their nail polish once a week
Solution to the problem
The confidence interval would be given by this formula
For the 95% confidence interval the value of 
and 
, with that value we can find the quantile required for the interval in the normal standard distribution.
And replacing into the confidence interval formula we got:
And the 95% confidence interval would be given (0.622;0.644).
We are confident (95%) that the true proportion of people that said that they change their nail polish once a week is between 0.622 and 0.644
Answer: a) 3 and -3 b) 4 and 2
c) 3.5 and 2.5 d) 5.5 and 0.5 e) This is due to the difference in the coefficient of (x-3)² and the value at the right side of each equation.
Step-by-step explanation:
a) 3x²-9 = 0
3x² = 0+9
3x² = 9
Dividing both sides by 3
x² = 9/3
x² = 3
x = √3
x = +3 and -3
b) (x-3)² = 1
Taking square root of both sides to remove the square,
√(x-3)² = √1
x-3 = √1
x-3 = 1 and x-3 = -1 (note that √1 is +1 and -1)
x = 4 and x = 2
c) 4(x-3)² = 1
Dividing both sides by 4 we have;
(x-3)² = 1/4
Taking the square root of both sides to eliminate the square.
√(x-3)² = √1/4
x-3 = √1/4
x-3 = +1/2 and x-3 = -1/2
x = 1/2+3 and x = -1/2+3
x = 3.5 and 2.5
d) 2(x-3)² = 12
Dividing both sides by 2 we have;
(x-3)² = 12/2
Taking the square root of both sides to eliminate the square.
√(x-3)² = √12/2
x-3 = √6
x-3 = 2.5 and x-3 = -2.5
x = 2.5+3 and x = -2.5+3
x = 5.5 and 0.5
e) The answers to questions 1 to 4 has different solutions due to the different value of the coefficient of (x-3)² and also the value at the right hand side of the equations also differs, hence, the reason for the difference in their answers.
Answer:
180
Explanation:
20 x 9 = 180
That is the correct graph that represents
{3y≥x−9 3x+y>−3
hope i helped =D
They don’t have anything in common
