Answer:
(0.0706, 0.1294)
Step-by-step explanation:
Confidence interval of a proportion is:
CI = p ± CV × SE
where p is the proportion,
CV is the critical value (z score or t score),
and SE is the standard error.
The sample is large enough to estimate as normal. For 95% confidence level, CV = z = 1.96.
Standard error for a proportion is:
SE = √(pq/n)
SE = √(0.1 × 0.9 / 400)
SE = 0.015
The confidence interval is:
CI = 0.1 ± (1.96)(0.015)
CI = (0.0706, 0.1294)
Round as needed.
The answer is 105 because 180-75=105
Simplifying
2y + 5x + -1z = 4y + 6x
Reorder the terms:
5x + 2y + -1z = 4y + 6x
Reorder the terms:
5x + 2y + -1z = 6x + 4y
Solving
5x + 2y + -1z = 6x + 4y
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-6x' to each side of the equation.
5x + 2y + -6x + -1z = 6x + -6x + 4y
Reorder the terms:
5x + -6x + 2y + -1z = 6x + -6x + 4y
Combine like terms: 5x + -6x = -1x
-1x + 2y + -1z = 6x + -6x + 4y
Combine like terms: 6x + -6x = 0
-1x + 2y + -1z = 0 + 4y
-1x + 2y + -1z = 4y
Add '-2y' to each side of the equation.
-1x + 2y + -2y + -1z = 4y + -2y
Combine like terms: 2y + -2y = 0
-1x + 0 + -1z = 4y + -2y
-1x + -1z = 4y + -2y
Combine like terms: 4y + -2y = 2y
-1x + -1z = 2y
Add 'z' to each side of the equation.
-1x + -1z + z = 2y + z
Combine like terms: -1z + z = 0
-1x + 0 = 2y + z
-1x = 2y + z
Divide each side by '-1'.
x = -2y + -1z
Simplifying
x = -2y + -1z
The inverse function for the given function f(x) = 4x - 2 is x/4 + 2
or, f⁻¹(x) = x/4 + 2
Given function, f(x) = 4x-8
We have to find f⁻¹(x)
f(x) = 4x - 8
or, y = 4x - 8
Interchanging the x variable with y,
x = 4y - 8
Solving y,
x = 4(y - 2)
or, x/4 = y - 2
or, y = x/4 + 2
Now, replacing y with f⁻¹(x), we get;
f⁻¹(x) = x/4 + 2
For verifying, you can use
(f · f⁻¹ )(x) = x
Therefore, the inverse function of f(x) is x/4 + 2.
To learn more about the inverse functions, visit: brainly.com/question/14965513
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Answer:
H0: p(1980) = p(2010) ; H1 : P(1980) > P(2010)
0.02
Step-by-step explanation:
Given that:
Sample size in both 1980 and 2010 = 1000 samples :
Proportion in favor :
P(1980) = 0.66
P(2010) = 0.64
To test the hypothesis :
Null hypothesis :
Proportion in favor are the same in both years
Null hypothesis = H0 = p(1980) = p(2010)
Alternative hypothesis :
Proportion in favor in 1980 is greater than that in 2010
Alternative hypothesis = H1 : P(1980) > P(2010)
The sample statistic :
P(1980) - p(2010)
0.66 - 0.64
= 0.02
