456.98-10-14.95-6.07-109.10-30=<span>286.86
So her new </span>checkbook balance is $286.86
<h3>
Answer: Choice D</h3><h3>
m = n</h3><h3>
b = sqrt(pi)*a</h3>
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Explanation:
Each circle has a radius of 'a'. So r = a.
The area of each circle is pi*r^2 = pi*a^2
The area of each square with side length b is b^2
The two stacks have the same volume only when the circle area is equal to the square area, so whenever pi*a^2 = b^2 is true.
Solving for b leads to b = sqrt(pi*a^2) = sqrt(pi)*a
The stacks must also be the same height for the volumes to be the same, so m = n as well.
Answer:16
Step-by-step explanation:
Let n = required random sample size.
Assume that the population standard deviation is known as σ.
Let m = sample mean.
At the 95% confidence level, the expected range is
(m - k(σ/√n), m + k(σ/√n))
where k = 1.96.
Therefore the error margin is 1.96(σ/√n).
Because the error margin is specified as 3% or 0.03, therefore
(1.96σ)/√n = 0.03
√n = (1.96σ)/0.03
n = 128.05σ²
This means that the sample size is about 128 times the population variance.
Answer:
Smallest sample size = 128.05σ², where σ = population standard deviation.
Answer:
Morning's average rate = 50 mph, and Afternoon's average rate = 25 mph.
Step-by-step explanation:
Suppose he drove 150 miles for X hours, then his average rate in the morning was (150/X) mph.
Given that he spent 5 hours in driving.
And he drove 50 miles for (5-X) hours, then his average rate in the afternoon was 50/(5-X) mph.
Given that his average rate in the morning was twice his average rate in the afternoon.
(150/x) = 2 * 50/(5-x)
150/x = 100/(5-x)
Cross multiplying terms, we get:-
150*(5-x) = 100*x
750 - 150x = 100x
750 = 100x + 150x
750 = 250x
x = 750/250 = 3.
It means he spent 3 hours in the morning and 2 hours in the afternoon.
So morning's average rate = 150/3 = 50 mph.
and afternoon's average rate = 50/(5-3) = 25 mph.
