Answer:
-1.92 cm³
Step-by-step explanation:
The formula for the volume of a cube in terms of side length is ...
V = s³
Then the first-order approximation of volume for a small change ∆s in side length is ...
V(s +∆s) ≈ V(s) + V'(s)·∆s
and the change in volume is ...
∆V ≈ V(s +∆s) -V(s) = V'(s)·∆s
The derivative V'(s) is ...
V'(s) = 3s²
so the change in volume for s = 8 cm and ∆s = -0.01 cm is ...
∆V ≈ 3s²·∆s = 3(8 cm)²(-0.01 cm) = -1.92 cm³
Answer:
5 hours
Step-by-step explanation:
This is a classic pre-algebra question.

Answer:
Null hypothesis = 
Alternate hypothesis =
Step-by-step explanation:
Given : In a recent semester, the proportion who earned a bachelor's degree within six years was 0.395.
The president of a certain college believes that the proportion of students who enroll in her institution have a higher completion rate.
To Find : Determine the null and alternative hypotheses.
Solution:
In a recent semester, the proportion who earned a bachelor's degree within six years was<u> 0.395. </u>
Claim : the proportion of students who enroll in her institution <u>have a higher completion rate.</u>
So,null hypothesis = 
Alternate hypothesis =
Answer:
The 90% confidence interval of the population proportion is (0.43, 0.56).
Step-by-step explanation:
The (1 - <em>α</em>)% confidence interval for population proportion <em>p</em> is:

The information provided is:
<em>X</em> = 74
<em>n</em> = 150
Confidence level = 90%
Compute the value of sample proportion as follows:

Compute the critical value of <em>z</em> for 90% confidence level as follows:

*Use a <em>z</em>-table.
Compute the 90% confidence interval of the population proportion as follows:


Thus, the 90% confidence interval of the population proportion is (0.43, 0.56).