Product A requires 5 machine hours per unit to be produced, Product B requires only 3 machine hours per unit, and the company's
1 answer:
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Answer:
The confidence interval for the mean is given by the following formula:
(1)
And for this case the 95% confidence interval is given by (2.13; 2.37)
We have a point of estimate for the sample mean with this formula:
And for the margin of error we have the following estimation:
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
represent the sample mean
population mean (variable of interest)
s represent the sample standard deviation
n represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
(1)
And for this case the 95% confidence interval is given by (2.13; 2.37)
We have a point of estimate for the sample mean with this formula:
And for the margin of error we have the following estimation:
Answer:
So, the times the ball will be 48 feet above the ground are t = 0 and t = 2.
Step-by-step explanation:
The height h of the ball is modeled by the following equation
The problem want you to find the times the ball will be 48 feet above the ground.
It is going to be when:
We can simplify by 16t. So
It means that
16t = 0
t = 0
or
t - 2 = 0
t = 2
So, the times the ball will be 48 feet above the ground are t = 0 and t = 2.
Answer:
a) the length of the wire for the circle =
b)the length of the wire for the square =
c) the smallest possible area = 126.02 in² into two decimal places
Step-by-step explanation:
If one piece of wire for the square is y; and another piece of wire for circle is (60-y).
Then; we can say; let the side of the square be b
so 4(b)=y
b=
Area of the square which is L² can now be said to be;
On the otherhand; let the radius (r) of the circle be;
2πr = 60-y
Area of the circle which is πr² can now be;
Total Area (A);
A =
=
For the smallest possible area;
∴
If we divide through with (2) and each entity move to the opposite side; we have:
By cross multiplying; we have:
2πy = 480 - 8y
collect like terms
(2π + 8) y = 480
which can be reduced to (π + 4)y = 240 by dividing through with 2
∴ since , we can determine for the length of the circle ;
60-y can now be;
=
=
=
=
also, the length of wire for the square (y) ;
The smallest possible area (A) =
= 126.0223095 in²
≅ 126.02 in² ( to two decimal places)