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3 years ago

A cone has a height of 13 millimeters. Its base has a radius of 4

Mathematics

1 answer:

Talja [164]3 years ago

3 0

Answer:

Step-by-step explanation:radius r = 4 m

height h = 13 m

slant height s = 13.6014705 m

volume V = 217.817091 m3

lateral surface area L = 170.921119 m2

base surface area B = 50.2654825 m2

total surface area A = 221.186602 m2

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Please help me solve 216^x+1=6

Licemer1 [7]

It would be x=0.299415

4 0

3 years ago

Mr. Chin's hotel bill is $143. He leaves 12% of the hotel bill as a tip for the housekeeping service. What is the total amount M

Tema [17]

Answer:

$160.16

Step-by-step explanation:

Multiply $143 and 12%

Make 12% as decimal: 0.12

143*0.12

$160.16

6 0

3 years ago

A student measured the dimensions of a table and recorded the length as 103.50cm and the width as 73.75cm. according to the stud

PolarNik [594]

The table is usually the shape of a rectangle. The area is equal to the length times the width. To make sure, let's recalculate the solution.

Area = length × width
Area = 103.50 cm × 73.75 cm
Area = 7,633.125 cm²

So, we established that the answer is correct. Now, I'll introduce the concept of significant figures. There are rules regarding significant figures to be applied conventionally in measurements and calculations. This is to increase precision of the data. Significant figures are digits that carry meaning. When you are given data with a specific number of significant figures, the final answer should also contain the same number of significant figures. In convention, the rule says that the zero's after non-zero digits after the decimal point are significant. Also, all non-zero digits are significant. The value 103.50 has 5 significant figures, and 73.75 has 4. When it comes to multiplication, the answer should contain the least significant figures. So, we should have 4 significant figures. Therefore, the final answer to be reported should be 7,633 cm².

8 0

3 years ago

A student was asked to find a 90% confidence interval for the proportion of students who take notes using data from a random sam

Scorpion4ik [409]

Answer:

After use the formula we got the following result for the 90% confidence interval (0.13 <p<0.34)

And the conclusion for this case would be:

e. With 90% confidence, the proportion of all students who take notes is between 0.13 and 0.34.

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".

Description in words of the parameter p

$p$ represent the real population proportion of students who take notes

$\hat p$ represent the estimated proportion of students who take notes

n is the sample size required

$z_{\alpha/2}$ represent the critical value for the margin of error

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Numerical estimate for p

In order to estimate a proportion we use this formula:

$\hat p =\frac{X}{n}$ where X represent the number of people with a characteristic and n the total sample size selected.

Confidence interval

The confidence interval for a proportion is given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 90% confidence interval the value of $\alpha=1-0.90=0.1$ and $\alpha/2=0.05$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.64$

After use the formula we got the following result for the 90% confidence interval (0.13 <p<0.34)

And the conclusion for this case would be:

e. With 90% confidence, the proportion of all students who take notes is between 0.13 and 0.34.

6 0

3 years ago

The monthly profit for a small company that makes long-sleeve T-shirts depends on the price per shirt. If the price is too high,

Andrej [43]

Answer:

A. $18

B. $200

C. $p\in (16,20)$

Step-by-step explanation:

Function:

$f(p) = -50p^2 + 1,800p - 16,000$

Parts A and B:

The price that generates the maximum profit is ate vertex of parabola. Find the coordinates of the vertex:

$p_v=\dfrac{-b}{2a}=\dfrac{-1,800}{2\cdot (-50)}=\dfrac{1,800}{100}=18\\ \\f(p_v)=-50\cdot 18^2+1,800\cdot 18-16,000=200$

The price that generates the maximum profit is $18

The maximum profit is $200

Part C:

The company breaks even when the profit is positive. From the graph of the function you can see that the graph of the function is over p-axis for all $p\in (16,20)$ , so the positive profit is for $p\in (16,20)$

In p=16 and p=20, the profit is 0 and when p<16 and p>20, there will be a loss.

7 0

4 years ago