Answer:
C. 
General Formulas and Concepts:
<u>Calculus</u>
- Mean Value Theorem (MVT) - If f is continuous on interval [a, b], then there is a c∈[a, b] such that
- MVT is also Average Value
Step-by-step explanation:
<u>Step 1: Define</u>
f'(c) = 20
Interval [1, b]
<u>Step 2: Check/Identify</u>
Function [1, b] is continuous.
Derivative [1, b] is continuous.
∴ There exists a c∈[1, b] such that
<u>Step 3: Mean Value Theorem</u>
- Substitute:
- Rewrite:
And we have our final answer!
The volume of the sphere is expressed in the formula V= 4/3 3.14r^3 and we are given the radius of the sphere. to find the volume, we can directly substitute r as the unit of the volume to be determined is consistent with the given. Hence, via subsitution, the answer is 1.7671 cubic feet
It helps to think of a simpler problem. Let's say mpg is 20 and 10% higher on a smooth road.
How many miles will you get with one gallon on a regular road?
How many more miles will you get on a smooth road? 10% more, right? How much is that?
OK - so you've now solved a simpler problem. Use the exact some process to solve your, more complicated, problem.
Answer:
E. 10 and 10
Step-by-step explanation:
Standard Deviation is the square root of sum of square of the distance of observation from the mean.
where, 
is mean of the distribution.
Here, since standard deviation is the ratio of the distance from the mean and sample size. So for decreasing the standard deviation we should keep numerator constant and increasing the denominator.
This can be only possible in option (E).
Hence, only Option (E) is correct.
Answer:
The second answer, and possibly the first answer as also true.
She did run a test that would indicate its an unbalanced dice, but this wasn't tried out with a different person throwing the dice.
Step-by-step explanation:
This is because from the computer generator results we see 11 of the 25 values are estimating at 1/5 when we know dice are 1/6 and more than 1/2 show just under 1/5 which balances this to be 1/6
But there are 9/25 tests that showed values under 10 throws found a 6 in 9/25 events = 1/3 approx out of 1/10 of the throws, and 1/3 is still a higher value than 1/6 of the multiple throws so indicates 100 throws would not be enough to tell as we cannot possibly assume her results are comparable with a computer generator.As the computer generator completed 25 x 100 throws and have just compared only x10 in relation to 1/10 of the events of the generated computer. This showing 9 of the 25 (100) throw events in relation scores 1/3 of the results a 6. The answer is she would need to throw somewhere between 1000 and 3000 to compare to the computers results.
