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1 year ago

11. A city engineer determines that 5,500 cubic meters of

Mathematics

1 answer:

PolarNik [594]1 year ago

3 0

The city do not have up to 5,500 cubic meters of sand that will be needed to combat erosion.

<h3>Volume</h3>

Volume is the amount of space occupied by a three dimensional object or figure. The volume (V) of a cone is given by:

V = (1/3)πr²h

Where h is the height, and r is the radius

Given that h = 35 m, the radius using Pythagoras theorem:

37² = r² + 35²

r = 12

V = (1/3)π(12)² * 35 = 5280 m³

The city do not have up to 5,500 cubic meters of sand that will be needed to combat erosion.

Find out more on Volume at: brainly.com/question/1972490

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3 years ago

A certain test preparation course is designed to help students improve their scores on the USMLE exam. A mock exam is given at t

e-lub [12.9K]

Answer:

$17.67-2.92\frac{2.517}{\sqrt{3}}=13.427$

$17.67+2.92\frac{2.517}{\sqrt{3}}=21.913$

So on this case the 90% confidence interval would be given by (13.427;21.913)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=17.67$

The sample deviation calculated $s=2.517$

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=3-1=2$

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,2)".And we see that $t_{\alpha/2}=2.92$

Now we have everything in order to replace into formula (1):

$17.67-2.92\frac{2.517}{\sqrt{3}}=13.427$

$17.67+2.92\frac{2.517}{\sqrt{3}}=21.913$

So on this case the 90% confidence interval would be given by (13.427;21.913)

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2 years ago

Which function goes with this graph?

harkovskaia [24]

From the given points on the graph we can find which function represents this graph.

A point on the graph is (3, 1). This means if we substitute x = 3 the answer must be 1.

The property of log is that $log_{a}(a)=1$

This suggests, if the base of log is equal to the number for which we are finding the log, the answer must be 1.

So, in this case we have:

$log_{a}(3)=1$

Since the answer is 1, the base of log must be 3.

In the given options, only option 3rd is with base 3.

So, the correct answer is option 3.

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