To express
5
−
2
as a positive exponent we will use this rule of exponents:
x
a
=
1
x
−
a
5
−
2
=
1
5
−
−
2
=
1
5
2
Answer:
Height of cylinder is 
.
Step-by-step explanation:
Diameter of cylinder, D = 6 feet
Relation between Radius, R and diameter, D is given by:
So, radius, R = 
feet
Let height of cylinder be 
feet.
Formula for volume of cylinder is given by:
Where, R is the radius of base of cylinder
and H is the height of cylinder
We are given that,
Using formula for volume,
Hence, Height of cylinder is .
Part A
Answers:
Mean = 5.7
Standard Deviation = 0.046
-----------------------
The mean is given to us, which was 5.7, so there's no need to do any work there.
To get the standard deviation of the sample distribution, we divide the given standard deviation s = 0.26 by the square root of the sample size n = 32
So, we get s/sqrt(n) = 0.26/sqrt(32) = 0.0459619 which rounds to 0.046
================================================
Part B
The 95% confidence interval is roughly (3.73, 7.67)
The margin of error expression is z*s/sqrt(n)
The interpretation is that if we generated 100 confidence intervals, then roughly 95% of them will have the mean between 3.73 and 7.67
-----------------------
At 95% confidence, the critical value is z = 1.96 approximately
ME = margin of error
ME = z*s/sqrt(n)
ME = 1.96*5.7/sqrt(32)
ME = 1.974949
The margin of error is roughly 1.974949
The lower and upper boundaries (L and U respectively) are:
L = xbar-ME
L = 5.7-1.974949
L = 3.725051
L = 3.73
and
U = xbar+ME
U = 5.7+1.974949
U = 7.674949
U = 7.67
================================================
Part C
Confidence interval is (5.99, 6.21)
Margin of Error expression is z*s/sqrt(n)
If we generate 100 intervals, then roughly 95 of them will have the mean between 5.99 and 6.21. We are 95% confident that the mean is between those values.
-----------------------
At 95% confidence, the critical value is z = 1.96 approximately
ME = margin of error
ME = z*s/sqrt(n)
ME = 1.96*0.34/sqrt(34)
ME = 0.114286657
The margin of error is roughly 0.114286657
L = lower limit
L = xbar-ME
L = 6.1-0.114286657
L = 5.985713343
L = 5.99
U = upper limit
U = xbar+ME
U = 6.1+0.114286657
U = 6.214286657
U = 6.21
Making 10 chairs would take Marjorie and Blaine<u> </u><u>21 hours and 40 minutes</u>.
<h3>How long does it take to make 10 chairs?</h3>
The total time it takes Marjorie and Blaine to perform their respective tasks in building a chair is multiplied by 10 chairs, respectively. This time is known as their speed.
The resulting figures are summed to get the total time.
<h3>Data and Calculations:</h3>
The total time it takes Marjorie to build a chair is 15 hours (1.5 hours x 10)
The total time it takes Baline to sew cushions per chair is 400 minutes (40 x 10) or 6 hours and 40 minutes.
Therefore, the total time to build 10 chairs is 21 hours, 40 minutes (15 hours + 6 hours and 40 minutes).
Thus, making 10 chairs would take Marjorie and Blaine <u>21 hours and 40 minutes</u>.
Learn more about the time consumed at brainly.com/question/17146782
#SPJ1
