I need an explanation on how to do this one

\( \textsf{\qquad\qquad\huge\underline{{\sf Answer}}} \)

Volume of a rectangular prism is ~

\( \sf{Volume_{cuboid}= Length × Width × Height} \)

\(\qquad \sf  \dashrightarrow \: v = (4x + 2) \times (3x - 5) \times (7x + 4)\)

\(\qquad \sf  \dashrightarrow \: v = (12 {x}^{2} - 20x + 6x - 10) \times (7x + 4) \)

\(\qquad \sf  \dashrightarrow \: v = (12 {x}^{2} - 14x- 10) \times (7x + 4)\)

\(\qquad \sf  \dashrightarrow \: v = 84 {x}^{3} + 48 {x}^{2} - 98x {}^{2} - 56x - 70x - 40\)

\(\qquad \sf  \dashrightarrow \: v = 84 {x}^{3} - 50 {x}^{2} - 126x - 40\)

So, the correct choice is B

Answer:

I got 5,192.775

Step-by-step explanation:

Volume of a cylinder is V=πr^2h

Diameter is 2r

The standard deviation of the salaries for the company's 80 employees is calculated to be X, where X represents the numerical value of the standard deviation.

The standard deviation measures the dispersion or variability of a set of data points. In order to calculate the standard deviation, we need to first find the mean (average) of the salaries. Then, for each salary, we calculate the difference between the salary and the mean, square that difference, and sum up all the squared differences. Next, we divide the sum by the total number of salaries (80 in this case) minus 1 to obtain the variance. Finally, the standard deviation is obtained by taking the square root of the variance. This accounts for the fact that the squared differences are in squared units, while the standard deviation should be in the original units (currency in this case).

By following this process, we can find the standard deviation of the salaries for the 80 employees in the company. This value represents the measure of variability or spread in the salary distribution, providing insights into how salaries deviate from the mean.

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The probability that a randomly selected freshman has English as the first class of the day is 1/5 or 20%.

The expression that represents the conditional probability that a randomly selected freshman has English as the first class of the day is: p(E|Fr), where E represents English and Fr represents freshman.

To calculate this probability, we need to use the information from the two-way table. The total number of freshmen is given in the table as 150. The number of freshmen with English as their first class is 30.

So, the probability that a randomly selected freshman has English as the first class of the day can be calculated as:

p(E|Fr) = Number of freshmen with English as first class / Total number of freshmen

p(E|Fr) = 30 / 150

Simplifying the expression:

p(E|Fr) = 1/5

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Answer:

5

230

3

0

3

Step-by-step explanation:

1)5.2 estimated is 5

2)229.9 estimated is 230

3)37.1 estimated is 3

4)0.0 estimated is 0

5)2.9 estimated is 3

Answer:

Step-by-step explanation:

Denominators of the fractions are 7 and 3, which are mutually prime numbers.

The LCD is the product of 7 and 3:

Simplify into mixed fraction

\(\\ \sf\longmapsto 6\dfrac{5}{7}=\dfrac{47}{7}\)

\(\\ \sf\longmapsto 6\dfrac{1}{3}=\dfrac{19}{3}\)

Find LCD

\(\\ \sf\longmapsto 7(3)\)

\(\\ \sf\longmapsto 21\)

Two events are independent if the result of the second event is not affected by the result of the first event.

Two events are dependent if the result of the first event affects the outcome of the second event so that the probability is changed.

In the problem in the question, the first marble drawn is not replaced, and thus the probability of the second draw will change because the sample size reduces.

Therefore, both events are DEPENDENT.

Answer:

Step-by-step explanation:

Army DA administrative publications and forms by the Army Publishing Directorate APD. The latest technologies high quality electronic pubs and forms view ...

Convert 2500mg to kg

step 1: convert 2500mg to g

step 2: Convert 2.5 g to kg

Therefore, 2500mg is equivalent to 0.0025kg

Answer:

50% 250x2=450

Step-by-step explanation:

Answer:

50%

Step-by-step explanation:

$225 x 2 = 450

this means the cell phones price was reduced by 50%

glad to help ;)

Step-by-step explanation:

variable x = bats

variable y = balls

3x + 6y = 3900

1x + 3y = 1300

I believe this is what they meant by represent it algebraically, but I'm not sure exactly what your class is learning right now. Geometrically, I do not know what they mean. I hope this helps you in some way

Answer:

8t+2=8(4)+2

   =32+2

Step-by-step explanation:

I was on the same problem and this was correct. Hope this helps!!

To find the asymptotes of a graph, first determine the type of asymptote (horizontal, vertical, or slant) and identify the conditions that must be satisfied. Then, set the numerator or denominator equal to zero and solve for y or x, or divide the numerator by the denominator and find the equation of the line that the graph approaches as x approaches infinity.

To find the asymptotes of a graph, you can follow these steps:

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The estimated regression equation for the given data is ŷ = -0.0025 Length - 0.2171 Width - 0.0004 Weight - 0.6806 ManTran

In regression analysis, the estimated regression equation is obtained by fitting a model to the data. In this case, the equation is ŷ = -0.0025 Length - 0.2171 Width - 0.0004 Weight - 0.6806 ManTran, where ŷ represents the predicted value of the response variable (CityMPG) based on the given predictor variables (Length, Width, Weight, ManTran).

The coefficient signs in the estimated regression equation indicate the direction and magnitude of the relationship between each predictor variable and the response variable. Based on a priori expectations, negative signs were expected for Length, Width, and Weight, as these variables are typically associated with decreased fuel efficiency (lower CityMPG). However, the estimated coefficients for these variables have negative values, indicating that an increase in Length, Width, or Weight is associated with a decrease in CityMPG, which aligns with expectations.

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Answer: The perimeter is 76 inches

We need to write the equation for the expression "nine less than a number n":

Answer:

the number of miles run on Thursday is 5.60 miles

Step-by-step explanation:

The computation of the number of miles run on Thursday is shown below

Here we assume the number of miles be x

3 ÷ 4 ÷ 1 = 4.2 ÷ x

3 ÷ 4 ÷ x = 4.2

3x = 16.8

x = 5.6

Hence, the number of miles run on Thursday is 5.60 miles

see the attachment for solution

hope it helps...!!!

Answer:

  $5.83

Step-by-step explanation:

The total amount of money is the sum of the values of the various denomination coins.

__

Let p, n, d, q represent the numbers of pennies, nickels, dimes, and quarters, respectively.

  p + n + d + q = 50 . . . . . . there are 50 coins in all

  16% × 50 = p . . . . . . . . . . 16% are pennies

  34% × 50 = d . . . . . . . . . . 34% are dimes

  n = p +3 . . . . . . . . . . . . . . there are 3 more nickels than dimes

The total value is ...

  v = 0.01p +0.05n +0.10d + 0.25q

__

The numbers of pennies and dimes are found easily:

  0.16 × 50 = p = 8

  0.34 × 50 = d = 17

Then the number of nickels can be found:

  n = p +3 = 8 +3 = 11

Finally, the number of quarters is found from the total number of coins:

  p + n + d + q = 50

  8 + 11 + 17 + q = 50 . . . substitute known values

  q = 14 . . . . . . . . . . . . . subtract 36 from both sides

The total value is then ...

  v = 0.01(8) +0.05(11) +0.10(17) +0.25(14) = 0.08 +0.55 +1.70 +3.50

  v = 5.83

The bag contains $5.83.

The probability that a postdated cheque is forged is 0.8  .

In the question ,

it is given that ,

there is 1 cheque forged in 10000 cheques.

the percent of postdated cheques = 5% ,

So , the number of Post-dated cheque = 0.05*10,000 = 500

the percent of cheques that the postdated cheque is forged is = 80%

the number of Forged cheque that are post-dated = 0.8*500 = 400

So , Probability (post-dated check is forged) = (Forged check that are post-dated)/(post dated checks)

Substituting the values ,

we get ,

= 400/500

= 0.8

Therefore , the required probability is 0.8  .

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Answer: y is 7 and x is 17

Step-by-step explanation:

x is the bigger numbr

y is the smol numbr

x + y = 24

x - y = 10

x = 17

y = 7

Answer:

A: 12.50 dollars

B: y=12.50x

C: 62.50 dollars

Step-by-step explanation:

The test statistics based on the information given will be -0.6329.

It should be noted that that test statistics simply means a method that's used in statistics for hypothesis testing.

From the information given, a standard weight that is known to weigh 1 gram is repeatedly weighed 4 times and the resulting measurements (in grams) are: {0.95,1.02, 1.01, 0.98}.

The computed standard deviation is 0.p

0316, the sample size is 4, degree of freedom is 3. The test statistic will be:

= (0.99 - 1)/(0.0316/✓4)

= -0.6329

In conclusion, the test statistics based on the information given will be -0.6329.

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The distribution used to obtain the critical value in this situation is the Student's t-distribution.

Critical value is a statistical value used to determine whether a hypothesis test result is statistically significant or not. It is the value that is compared to the test statistic to determine whether the null hypothesis should be rejected or not. The critical value is determined by the level of significance chosen for the study, the sampling distribution of the test statistic, and the degrees of freedom.

The Student's t-distribution is a symmetric probability distribution that is used when the population standard deviation is unknown. It is used in situations where there is a small sample size (less than 30) and the sample is drawn from a normally distributed population. In this case, the owner is interested in developing a 90% confidence interval estimate, so the critical value will be obtained from the Student's t-distribution.

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Answer:

Refer to the step-by-step.

Step-by-step explanation:

To determine the radius of a circle, you need to have some information about the circle. There are a few different ways to determine the radius depending on the information available to you. Here are some common methods...

The circumference of a circle is the distance around its edge. If you know the circumference of the circle, you can use the formula for circumference to calculate the radius.

\(\boxed{\left\begin{array}{ccc}\text{\underline{Circumference of a Circle:}}\\\\C=2\pi r\rightarrow \boxed{r=\dfrac{C}{2\pi}} \end{array}\right}\)

The area of a circle is the measure of the region enclosed by the circle. If you know the area of the circle, you can use the formula for the area to calculate the radius.

\(\boxed{\left\begin{array}{ccc}\text{\underline{Area of a Circle:}}\\\\A=\pi r^2\rightarrow \boxed{r=\sqrt{\frac{A}{\pi} } } \end{array}\right}\)

The diameter of a circle is a straight line passing through the center, and it is equal to twice the radius. If you know the diameter of the circle, you can divide it by 2 to find the radius.

\(\boxed{\left\begin{array}{ccc}\text{\underline{Diameter of a Circle:}}\\\\d=2r\rightarrow \boxed{r=\frac{d}{2} } \end{array}\right}\)

If you have the coordinates of the center of the circle and a point on the circle's circumference, you can calculate the distance between them using the distance formula. The distance between the center and any point on the circle will be equal to the radius.

\(\boxed{\left\begin{array}{ccc}\text{\underline{The Distance Formula:}}\\\\d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \end{array}\right}\)

Other methods include:

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Answer:

  $12.50

Step-by-step explanation:

The cost of 5 bags will be 5/3 times the cost of 3 bags:

  5-bag cost = (5/3)($750) = $12.50

Marco would spend $12.50 on 5 bags of cat food.

_____

If you like, you can find the "unit rate" -- the cost of one bag of cat food:

  $7.50 / (3 bags) = $2.50 /bag

Then, multiply that rate by 5 bags:

  (5 bags)($2.50/bag) = $12.50

Note that we have multiplied by 5 and divided by 3, the same as if we had multiplied by 5/3.

Answer:

X=17

Step-by-step explanation:

When you input x as 17 into the equation you get angle 2 is equal to 142 and angle 3 is equal to 38.

142+38=180

so 17 is x

The given series in the sigma notation can be written as \(\sum_{n = 1} ^ 5 10n - 8\).

An arithmetic series is a set of integers where each term is made up of the common difference, a fixed amount, and the sum of the terms before it. In other words, the terms of the series may be represented as follows if the first term of an arithmetic series is a and the common difference is d:

a, a + d, a + 2d, a + 3d, ...

The given series is 2 + 12 + 22 + 32 + 42.

The total number of terms are 5.

The first term is 2, and the common difference is:

d = 12 - 2 = 10

Now, using the nth term of sequence we have:

an = 2 + (n - 1) 10

= 10n - 8

= \(\sum_{n = 1} ^ 5 10n - 8\)

Hence, the given series in the sigma notation can be written as \(\sum_{n = 1} ^ 5 10n - 8\).

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