MATHEMATICS COLLEGE

The sphere at the right fits snugly inside a cube with 4-in. edges. What is the approximate volume of the space between the sphere and cube?
The sphere at the right fits snugly inside a cube - 1

Answers

Answer 1
Answer:

As given by the question

There are given that the inside edge is 4 in.

Now,

Since sphere fits snugly inside a cube therefore diameter of sphere will be equal to side of the cube

So,

\begin{gathered} \text{diameter}=4\text{ inches} \n \text{radius}=(dameter)/(2) \n \text{radius}=(4)/(2) \n \text{radius}=2 \end{gathered}

Then,

Volume of the sphere is given by:

\begin{gathered} (4)/(3)*\pi* r^3=(4)/(3)*3.14*2^3 \n =(4)/(3)*3.14*8 \n =33.5 \end{gathered}

And,

The volume of a cube is:

\begin{gathered} \text{Volume of cube=side}* side* side \n =4*4*4 \n =64\text{ inches} \end{gathered}

Then,

The volume of the space between the sphere and cube = 64-33.5 = 30.5.

Hence, the answer is 30.5 cube inches.

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QuestionIf $500 is borrowed with an interest of 21.0% compounded monthly, what is the total amount of money needed to pay itback in 1 year? Round your answer to the nearest dollar. Do not round at any other point in the solving process; only roundyour final answer.

In how many ways can a committee of two men and two women be formed from a group of twelve men and ten women?

Answers

Answer:

Step-by-step explanation:

number of ways=12c2×10c2

=(12 * 11)/(2 *1) * (10 *9)/(2 * 1) \n=2970~ways

4\7 equivalent fraction​

Answers

8/14 is also equivalent fraction :))) is

Answer:

Hope it helpsssssss

Step-by-step explanation:

4/7, 8/14, 12/21, 16/28, 20/35, 24/42, 28/49, 32/56, 36/63, 40/70, and so on

Explain how you get 608,149 to the nearest thousand place

Answers

Answer:

Step-by-step explanation:

608,000

you go to thousands look next number left and round up or down and the rest after the thousands becomes zeros

Final answer:

608,149 rounded to the nearest thousand is 608,000. The process involved looking at the digit in the hundreds place, determining it was less than 5, and therefore replacing it and all numbers to its right with zeroes.

Explanation:

To round 608,149 to the nearest thousand, you need to look at the digit in the hundreds place. This is the 1 in 608,149. Because 1 is less than 5, you leave the number in the thousands place (the 8 in 608,149) as it is, and change all the numbers to its right (149) in the original number to zeros. So 608,149 rounded to the nearest thousand is 608,000.

Learn more about Rounding Numbers here:

brainly.com/question/19166897

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A fatigue test was conducted in which the mean stress was 70 MPa, and the stress amplitude was 210 MPa. (a) Compute the maximum and minimum stress levels. (b) Compute the stress ratio. (c) Compute the magnitude of the stress range

Answers

Answer:

Step-by-step explanation:

https://tex.z-dn.net/?f=%5Csigma%20_%7Bmean%7D%3D70%20MPa%3D%5Cfrac%7B%5Csigma%20_%7Bmax%7D%2B%5Csigma%20_%7Bmin%7D%7D%7B2%7D

Rolling a 12 sided die find the odds in favor of rolling a 5
rolling a multiple of 3
rolling an odd number
rolling a number greater than 6

Find each probability of
P(5)
P(# less than 3)
P(odd)
P(13)

Answers

Answer:

1/12 , 1/3 , 1/2 , 1/2

Step-by-step explanation:

P(x) = favorable of x / total

plug in your conditions and you get the probablility

Answer:

1/12 for rolling a 5.

4/12 for multiples of 3. (3,6,9,12)

6/12 for rolling an odd number.(1,3,5,7,9,11)

6/12 for rolling a number greater than 6. (7,8,9,10,11,12)

Step-by-step explanation:

A data related to air pollution in 10 U.S. cities. The dependent variable Y is the annual mean concentration of sulfur dioxide, in micrograms per cubic meter. The explanatory variable X records the number of manufacturing enterprises employing 20 or more workers. Below is Routput of the relationship between X and Y. Coefficients: Estimate Std. Error t value Pro> tl) (Intercept) 9.4764 9.6266 0.98 0.354 2.0315 0.0070 4.51 0.CO2 ** X Signif. codes: 9 ****' 0.001 ***' 0.01 **' 0.05, 0.1' '1 Residual standard error: 17.9 on 8 degrees of freedom Multiple R-squared: 0.717, Adjusted R-squared: 0.682 F-statistic: 20.3 on 1 and 8 DF, p-value: 0.00198
a) Write the regression equation with parameters from the R output.b) Suppose that the number of manufacturing enterprises employing 20 or more workers in Irvine is 250, could you predict that the annual mean concentration of sulfur dioxide in Irvine?c) What is the residual if in Irvine the annual mean concentration of sulfur dioxide is 15 micrograms per cubic meter.d) What is the value of the correlation coefficient?e) Calculate a 95% confidence interval for the slope of the model.f) Based on the confidence interval, is there a linear relationship between X and Y?

Answers

Answer:

Y = 0.0315x + 9.4764

Residual = 2.35

Correlation Coefficient = 0.847

Step-by-step explanation:

From the R output given :

Intercept = 9.4764

Slope = 0.0315

x = number of manufacturing enterprise employing 20 or more workers

y = annual mean concentration of Sulphur dioxide

The regression equation :

y = bx + c

b = slope ; c = intercept

y = 0.0315x + 9.4764

Prediction using the regression equation :

The predicted y value, when x = 250

y = 0.0315(250) + 9.4764

y = 17.3514

The residual, if actual annual concentration = 15

Y residual = 17.35 - 15 = 2.35

The correlation Coefficient value, R

R = √R²

R = √0.717

R = 0.847
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