Answer: The 95% confidence interval is approximately (55.57, 58.43)
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Explanation:
At 95% confidence, the z critical value is about z = 1.960 which you find using a table or a calculator.
The sample size is n = 17
The sample mean is xbar = 57
The population standard deviation is sigma = 3
The lower bound of the confidence interval is
L = xbar - z*sigma/sqrt(n)
L = 57 - 1.960*3/sqrt(17)
L = 55.5738905247863
L = 55.57
The upper bound is
U = xbar + z*sigma/sqrt(n)
U = 57 + 1.960*3/sqrt(17)
U = 58.4261094752137
U = 58.43
Therefore the confidence interval (L, U) turns into (55.57, 58.43) which is approximate.
The inverse of this function is f(x) = 2x - 12.
You can find the inverse of any function by switching the f(x) and x values in the equation. Then you can solve for the new f(x) value. The result is your inverse function. The work for this one is below.
f(x) = 1/2x + 6 ----> switch f(x) and x
x = 1/2f(x) + 6 ----> subtract 6
x - 6 = 1/2f(x) ----> multiply by 2
2x - 12 = f(x) ----> change the order for consistency.
f(x) = 2x - 12
Answer:
gradient = 2
line: y = 2x - 4
Step-by-step explanation:
Find the slope from the slope intercept formula
y = mx + b
b is the y intercept
b = -4 and the point is (0,-4)
So far the equation looks like this.
y = mx - 4
Use the other intercept (x intercept) to find m
x = 2
y = 0
0 = m*2 - 4 Add 4 to both sides
4 = 2m Divide by 2
4/2 = m
m = 2
So the gradient or slope is 2
<u>Answer:</u>
7th Place
<u>Step-by-step explanation:</u>
Seeing as how the number of runners in front of Paula is 
the number of runners behind her,
Assign the number of people behind Paula to a variable:
# of people behind Paula = b, which means
# of people ahead of Paula = b
Use the variable to make an equation:
b (people behind Paula) + b (people ahead of Paula) + 1 (Paula) = 25
b + b + 1 = 25
Solve for b:
b + b + 1 = 25
b + b = 24
b = 24
b = 18
If there are 18 people behind Paula, there are * 18 people in front of her, which is 6; This puts Paula in 7th place.
