Answer:
27. 18.62
28. 200%
29. 136
30. 50
31. 12.5%
32. 750
33. 5.4
Step-by-step explanation:
Ratios can be written 3 ways...
14:1 or 14/1 or 14 to 1
Domain: (-6, 0, 3) Range: (-9, -7, 3, 5)
Answer:
The population standard deviation is not known.
90% Confidence interval by T₁₀-distribution: (38.3, 53.7).
Step-by-step explanation:
The "standard deviation" of $14 comes from a survey. In other words, the true population standard deviation is not known, and the $14 here is an estimate. Thus, find the confidence interval with the Student t-distribution. The sample size is 11. The degree of freedom is thus
.
Start by finding 1/2 the width of this confidence interval. The confidence level of this interval is 90%. In other words, the area under the bell curve within this interval is 0.90. However, this curve is symmetric. As a result,
- The area to the left of the lower end of the interval shall be
. - The area to the left of the upper end of the interval shall be
.
Look up the t-score of the upper end on an inverse t-table. Focus on the entry with
- a degree of freedom of 10, and
- a cumulative probability of 0.95.
.
This value can also be found with technology.
The formula for 1/2 the width of a confidence interval where standard deviation is unknown (only an estimate) is:
,
where
is the t-score at the upper end of the interval,
is the unbiased estimate for the standard deviation, and
is the sample size.
For this confidence interval:
Hence the width of the 90% confidence interval is
.
The confidence interval is centered at the unbiased estimate of the population mean. The 90% confidence interval will be approximately:
.
Volume of a cone:


r²h
Plug the radius and volume in the formula.


10²h = 942
Divide both sides by

.

10²h = 2,826
Divide both sides by pi.
10²h = 900
Divide both sides by 10² (100).
h = 9
The cone's height is 9 units.