Answer:
The rate of change of radius is 0.0530 ft/sec.
Step-by-step explanation:
Given : Helium is pumped into a spherical balloon at a rate of 3 cubic feet per second.
To find : How fast is the radius increasing after 2 minutes?
Solution :
The volume of the sphere is
Differentiating w.r.t. r,
We have given, Helium is pumped into a spherical balloon at a rate of 3 cubic feet per second.
i.e.
Integrate w.r.t. t,
Assuming V=0 when t=0 then C=0
So,
Now, we apply chain rule
i.e.
The radius increasing after 2 minutes i.e. at
Therefore, the rate of change of radius is 0.0530 ft/sec.
Answer:
A. Multiply the purchase price by the tax rate. Then add the result to the purchase price.
Step-by-step explanation:
The amount of tax is found by multiplying the taxed amount by the tax rate. The customer generally pays the sales tax, so the amount the customer will pay will be the sum of the purchase price and the tax.
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Answer:
The 95% confidence interval obtained with a sample size of 64 will give greater precision.
Step-by-step explanation:
We are given the following in the question:
A 95% confidence interval is calculated with the following sample sizes
The population mean and standard deviation are unknown.
Effect of sample size on confidence interval:
- As the sample size increases the margin of error decreases.
- As the margin of error decreases the width of the confidence level decreases.
- Thus, with increased sample size the width of confidence level decreases.
If we want a confidence interval with greater precision that is smaller width, we have to choose the higher sample size.
Thus, the 95% confidence interval obtained with a sample size of 64 will give greater precision.