Answer:
a) 25
b) 67
c) 97
Step-by-step explanation:
We have that to find our
level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of
.
So it is z with a pvalue of
, so 
Now, find the margin of error M as such

In which
is the standard deviation of the population and n is the size of the sample. In this problem, 
(a) The desired margin of error is $0.10.
This is n when M = 0.1. So






Rounding up to the nearest whole number, 25.
(b) The desired margin of error is $0.06.
This is n when M = 0.06. So






Rounding up, 67
(c) The desired margin of error is $0.05.
This is n when M = 0.05. So






Rounding up, 97
The solution is that x = 26 and y = 9.
In order to find these, we need to note that since the two angles involving x's make a straight line, then they must equal 180 degrees. So we can add them together and set them equal to solve for x.
5x - 17 + 3x - 11 = 180 ----> combine like terms
8x - 28 = 180 ----> add 28 to both sides
8x = 208 -----> divide by 8
x = 26
Now that we have the value of x, we can find the value of the 3x - 11 term. That along with the right angle and the 2y + 5 angle combine to make another straight line. So we can solve by setting that equal to 180 as well.
3x - 11 + 90 + 2y + 5 = 180 ------> Combine like terms
3x + 2y + 84 = 180 -----> Put 26 in for x.
3(26) + 2y + 84 = 180 -----> Multiply
78 + 2y + 84 = 180 ------> Combine like terms again
2y + 162 = 180 ------> Subtract 162 from both sides
2y = 18 -----> Divide by 2
y = 9
Solve for
m by simplifying both sides of the inequality, then isolating the variable.
Inequality Form:
m≥−17
Interval Notation:
[−17,∞)
Answer:
36 cm
Step-by-step explanation:
arc length = r × θ
32π = r × 8/9π
r = 36