You must show all steps and provide any evidence needed in your solution to receive full credit.

4. The company is building a scale model of the theater’s main show tank for an investor's presentation. Each dimension will be made one eight of the original dimension to accommodate the mock-up in the presentation room. What is the volume of the smaller mock-up tank?

5. Using the information from #4, answer the following question by filling in the blank: The volume of the original main show tank is ____% of the mock-up of the tank.

Answer:

I think it's $216

Step-by-step explanation:

0.3 times 720

Answer:

2.875 mi  

Step-by-step explanation:

A scale factor (SF) is the ratio of two corresponding lengths in similar figures.

SF = actual distance/map distance = 5.75 mi/2 in

or 1 in = 2.875 mi

On the map, the distance from the library to the park is 1 in, so the actual distance is 2.875 mi.

A model's scale ratio is the proportionate ratio of a linear dimension. The actual distance from the library to the park is 2.875 miles.

A model's scale ratio is the proportionate ratio of a linear dimension of the model to the equivalent characteristic of the original.

Given that the actual distance from Micah's house to school is 5.75 miles, while the same distance on the map is represented by 2 inches. Therefore, the scale ratio can be written as,

Scale Ratio = Distance on Map/ Distance in real

                   = 2 inches / 5.75 miles

Now, the distance between the library and the park is given 1 inch on the map. Therefore, using the scale ratio, the actual distance from the library to the park is,

Scale Ratio = Distance on Map/ Distance in real

2inches /5.75 miles = 1 inch/ Distance in real

Distance in real = (5.75 miles×1 inch)/2 inches

Distance in real = 2.875 miles

Hence, the actual distance from the library to the park is 2.875 miles.

Learn more about Scale ratio here:

https://brainly.com/question/13770371

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Answer:

mean absolute deviation

Step-by-step explanation:

The mean absolute deviation of a data set is the average distance between each data point and the mean. It gives us an idea about the variability in a data set since it is a measure of dispersion

Final answer:

The average distance of all data values from the mean of the data is called the 'standard deviation'. It measures how data points vary from the mean and indicates the data's spread. Standard deviation is calculated by finding the square root of the average squared deviations from the mean.

Explanation:

The Average Distance of Data Values from the Mean

The average distance of all data values from the mean of the data is referred to as the standard deviation. This statistical measure expresses the extent to which data points in a data set diverge from the average, or mean, value. When the standard deviation is small, it indicates that the data points are clustered closely around the mean, showing little variation. Conversely, a large standard deviation suggests that the data points are spread out over a wider range, signifying greater dispersion in the data set.

The calculation of the standard deviation starts with computing the variance, which is the average of the squared deviations from the mean. The formula for variance is s² = Σ(Yi - Y)² / (n - 1), where s² is the variance, Yi represents each data point, Y is the mean of the data, and n is the sample size. After calculating the variance, the standard deviation is found by taking the square root of the variance.

c ÷ 3.14=d

907.46 ÷3.14= 289

Answer:

Diameter = 289 units

Step-by-step explanation:

A circle has a circumference of 907.46 units

The circumference of a circle is outer boundary.

[tex]\text{Circumference (C)}=\pi d[/tex]

where, d is diameter, C=907.46

Put the value of C

[tex]907.46=\pi d[/tex]

[tex]907.46=3.14\times d[/tex]

[tex]d=289[/tex]

Hence, The diameter is 289 units

Answer:

x = 13 and y = 13√3

Step-by-step explanation:

Recall that sin Ф = opposite side / hypotenuse, and that

                   cos Ф = adjacent sice / hypotenuse.

if we recognize that the angle Ф is 30° here, then we know that:

x = opposite side = hypotenuse * sin 30° = 26*(1/2) = 13.

and....

y = adjacent side = hypotenuse*cos 30° = 26*√3/2 = 13√3

In summary, x = 13 and y = 13√3

Answer: 265

Step-by-step explanation: In order to find the sum of the first 10 terms in the series you need to first identify what the series is. The numbers are being reduced by 3 for each number, so the the first 10 terms would be 40, 37, 34, 31, 28, 25, 22, 19, 16, 13

The sum means the total of them all added together, which is 265.

The answer to this question is 265

Answer:

[tex]\frac{x}{x(x - 6)}\\\\\frac{1}{x-6}[/tex]

6 is excluded

Step-by-step explanation:

The expression [tex]\frac{x}{x^2 - 6x}[/tex] can be simplified by factoring the denominator and dividing out the x term.

x² - 6x = x(x-6)

It simplifies the expression by:

[tex]\frac{x}{x(x - 6)}\\\\\frac{1}{x-6}[/tex]

The excluded value is any value which makes the denominator 0.

x - 6 = 0

x = 6

6 is excluded.

Answer:

x=-4

Step-by-step explanation:

6(2x-1)-12=3(7x+6)

Distribute

12x -6 -12 = 21x +18

Combine like terms

12x-18 = 21x+18

Subtract 12x from each side

12x-12x-18 = 21x-12x+18

-18 = 9x+18

Subtract 18 from each side

-18-18 = 9x+18-18

-36 = 9x

Divide by 9

-36/9 = 9x/9

-4 =x

Answer:

7

Step-by-step explanation:

Find the greatest common factor of 28 and 35, which is 7. That means that each group will have seven people.

To go more into detail, there will be 4 groups of 6th graders and 5 groups of 7th graders.

Answer:

5 withdrawals

Step-by-step explanation:

Since $10.50 ends in $0.50, you know that she must have made at least one $2.50 transaction.

10.50 - 2.50 = 8

8/2 = 4 (she made four $2 transactions)

She made 4 $2 transactions and 1 $2.50 transaction.

4 + 1 = 5

She made 5 transactions total.

Answer:

64v

Step-by-step explanation:

2(5v+6)-6(-9v+2)

Distribute the 2 to everything in the parentheses.

10v+12-6(-9v+2)

Distribute the -6 to everything in the parentheses.

10v+12+54v-12

Combine like terms

64v

I think the answer might be 64v

HEYA

since perimeter of ΔABC=27.6cm

AB=9.6cm

BC=6cm

therefore AC= 12cm

[tex]27.6cm - 9.6cm - 6cm = 12cm[/tex]

since ΔABC~ΔBCD

therefore the sides will be proportional

let the perimeter of ΔBCD=x

[tex] \frac{9.6}{6} = \frac{27.6}{x} [/tex]

[tex]x = \frac{27.6 \times 6}{9.6} cm[/tex]

x=17.25cm

hope it helps you mate thanks for the question and if possible please mark it as brainliest

To solve the data distribution problem among four devices, we use a system of equations representing the conditions given for the data storage among devices A, B, C, and D. By expressing all variables in terms of the amount on device B and solving, we determine the data distribution to be 35 GB, 70 GB, 105 GB, and 15 GB for devices A, B, C, and D respectively.

Solving the Data Distribution Problem

Let's represent the amount of data on devices A, B, C, and D as a, b, c, and d respectively. Given that the total amount of data is 225 GB, we have:

From these equations, we can express everything in terms of b and subsequently find the values of a, b, c, and d. To demonstrate, let's substitute (2) and (3) into (1) and solve for b:

Now, using equation (3), we can express d in terms of b and substitute into (5):

Substitute c from (3) into (4), and then d from (6) into the result:

Simplify (7) and solve for b:

We calculate a = 35GB, b = 70GB, c = 105GB, and d = 15GB. These are the amounts of data on devices A, B, C, and D respectively.

Devices A, B, C, and D contain approximately 9.0 GB, 18.1 GB, 157.4 GB, and 13.4 GB, respectively.

Let's denote:

- The amount of data on device A as [tex]\(x\)[/tex] GB.

- The amount of data on device B as [tex]\(y\)[/tex] GB.

- The amount of data on device C as [tex]\(z\)[/tex] GB.

- The amount of data on device D as [tex]\(w\)[/tex] GB.

Given:

1. [tex]\(x = \frac{1}{2}y\)[/tex]

2. [tex]\(z = 5(y + w)\)[/tex]

3. [tex]\(2z + 4w = 500 - y\)[/tex]

We know that the total amount of data on all devices is 225 GB:

[tex]\[x + y + z + w = 225\][/tex]

We'll use these equations to solve for [tex]\(x\), \(y\), \(z\), and \(w\)[/tex].

Substituting [tex]\(x = \frac{1}{2}y\)[/tex] into the equation for the total amount of data:

[tex]\[\frac{1}{2}y + y + z + w = 225\][/tex]

[tex]\[y + 2y + z + w = 225\][/tex]

[tex]\[3y + z + w = 225\][/tex]

[tex]\[y = \frac{225 - z - w}{3}\][/tex]

Now, we'll use this expression for [tex]\(y\)[/tex] to rewrite the other equations:

From equation 2:

[tex]\[z = 5\left(\frac{225 - z - w}{3} + w\right)\][/tex]

[tex]\[z = \frac{5}{3}(225 - z - w) + 5w\][/tex]

[tex]\[z = \frac{5}{3}(225) - \frac{5}{3}z - \frac{5}{3}w + 5w\][/tex]

[tex]\[z + \frac{5}{3}z + \frac{5}{3}w = \frac{5}{3}(225) + 5w\][/tex]

[tex]\[\frac{8}{3}z + \frac{5}{3}w = \frac{1125}{3} + \frac{15}{3}w\][/tex]

[tex]\[8z + 5w = 1125 + 15w\][/tex]

[tex]\[8z = 1125 + 10w\][/tex]

[tex]\[z = \frac{1125 + 10w}{8}\][/tex]

From equation 3:

[tex]\[2z + 4w = 500 - \frac{225 - z - w}{3}\][/tex]

[tex]\[2z + 4w = 500 - \frac{225}{3} + \frac{1}{3}z + \frac{1}{3}w\][/tex]

[tex]\[2z + \frac{1}{3}z + \frac{1}{3}w + 4w = \frac{1500 - 225}{3}\][/tex]

[tex]\[2z + \frac{1}{3}z + \frac{13}{3}w = \frac{1275}{3}\][/tex]

[tex]\[\frac{7}{3}z + \frac{13}{3}w = \frac{1275}{3}\][/tex]

[tex]\[7z + 13w = 1275\][/tex]

[tex]\[7\left(\frac{1125 + 10w}{8}\right) + 13w = 1275\][/tex]

[tex]\[7(1125 + 10w) + 104w = 10200\][/tex]

[tex]\[7875 + 70w + 104w = 10200\][/tex]

[tex]\[174w = 2325\][/tex]

[tex]\[w = \frac{2325}{174}\][/tex]

[tex]\[w = 13.4\][/tex]

Substituting [tex]\(w = 13.4\)[/tex] into the equation for [tex]\(z\)[/tex]:

[tex]\[z = \frac{1125 + 10(13.4)}{8}\][/tex]

[tex]\[z = \frac{1125 + 134}{8}\][/tex]

[tex]\[z = \frac{1259}{8}\][/tex]

[tex]\[z = 157.375\][/tex]

Substituting [tex]\(w = 13.4\)[/tex] into the expression for [tex]\(y\)[/tex]:

[tex]\[y = \frac{225 - z - w}{3}\][/tex]

[tex]\[y = \frac{225 - 157.375 - 13.4}{3}\][/tex]

[tex]\[y = \frac{54.225}{3}\][/tex]

[tex]\[y = 18.075\][/tex]

Substituting [tex]\(y = 18.075\)[/tex] into the equation for [tex]\(x\)[/tex]:

[tex]\[x = \frac{1}{2}y\][/tex]

[tex]\[x = \frac{1}{2}(18.075)\][/tex]

[tex]\[x = 9.0375\][/tex]

So, the amount of data on each device is approximately:

- Device A: [tex]\(9.0\)[/tex] GB

- Device B: [tex]\(18.1\)[/tex] GB

- Device C: [tex]\(157.4\)[/tex] GB

- Device D: [tex]\(13.4\)[/tex] GB

Answer:

The slope would be -0.8 and 5.6 would be the intercept.

Step-by-step explanation:

The constant at the end of the equation is always the intercept.

The coefficient of x is the slope.

This just means that the graph starts at (0. 5.6) and has a rate of change of -0.8 y for every change in x.

Answer:

B and D

Step-by-step explanation:

The surface area is the area of each face of the cube. The volume is the amount that will fill the cube. These are two separate processes which cannot give you the same measurement by calculating one part of the surface area. B is false.

Doubling the sides of the cube will not double the surface area. It will quadruple it. D is false too.

The exact volume of the figure made up of two cones and a cylinder with a 4 cm diameter is [tex]\(76 \pi \, \text{cm}^3\)[/tex], which is approximately 238.64.

1. Volume of the Cylinder:

  [tex]\[ V_{\text{cylinder}} = \pi \times (2 \, \text{cm})^2 \times 17 \, \text{cm} \][/tex]

  [tex]\[ V_{\text{cylinder}} = \pi \times 4 \, \text{cm}^2 \times 17 \, \text{cm} \][/tex]

  [tex]\[ V_{\text{cylinder}} = 68 \pi \, \text{cm}^3 \][/tex]

2. **Volume of each Cone:**

 [tex]\[ V_{\text{cone}} = \frac{1}{3} \pi \times (2 \, \text{cm})^2 \times 3 \, \text{cm} \][/tex]

[tex]\[ V_{\text{cone}} = \frac{1}{3} \pi \times 4 \, \text{cm}^2 \times 3 \, \text{cm} \][/tex]

[tex]\[ V_{\text{cone}} = 4 \pi \, \text{cm}^3 \][/tex]

  Since there are two cones, the total volume for the cones is [tex]\(2 \times V_{\text{cone}} = 8 \pi \, \text{cm}^3\)[/tex].

3. Total Volume:

[tex]\[ V_{\text{total}} = V_{\text{cylinder}} + 2 \times V_{\text{cone}} \][/tex]

[tex]\[ V_{\text{total}} = 68 \pi + 8 \pi \, \text{cm}^3 \][/tex]

[tex]\[ V_{\text{total}} = 76 \pi \, \text{cm}^3 \][/tex]

Now, the exact volume is [tex]\(76 \pi \, \text{cm}^3\)[/tex]. To find the numerical approximation, you can use the value of [tex]\(\pi\)[/tex], which is approximately 3.14.

[tex]\[ V_{\text{total}} \approx 76 \times 3.14 \, \text{cm}^3 \approx 238.64 \, \text{cm}^3 \][/tex]

Red - 5/10

Green - 3/10

Yellow 2/10

Easyyy

♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫

➷ You replace the balls, so the type of probability is independent.

First of all, the probability of getting a red ball is:

5/10 or 1/2

As you can see, the probability of getting a green ball is:

3/10

Lastly, the probability of getting a yellow ball is:

2/10 or 1/5

The sum of all of them added together is always:

10/10, or 1

✽

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬TROLLER (don't worry i didn't troll you)

The answers are:

B.   [tex]\frac{-3-\sqrt{29}}{2}[/tex]

C.   [tex]\frac{-3+\sqrt{29}}{2}[/tex]

We can use the quadratic equation to find the two values of x that are roots of the given equation. We must remember that most of the quadratic equations have two roots, however, we could find quadratic equations with just one root or even with no roots, at least in the real numbers.

Quadratic equation:

[tex]\frac{-b+-\sqrt{b^{2}-4ac} }{2a}[/tex]

So,

From the given equation we have:

[tex]a=1\\b=3\\c=-5[/tex]

Substituting it into the quadratic equation to find the roots, we have:

[tex]\frac{-b+-\sqrt{b^{2}-4ac} }{2a}=\frac{-3+-\sqrt{3^{2}-4*1*-5} }{2*1}\\\\\frac{-3+-\sqrt{3^{2}-4*1*-5} }{2*1}=\frac{-3+-\sqrt{9+20} }{2}\\\\\frac{-3+-\sqrt{29}}{2}[/tex]

So,

[tex]x_{1}=\frac{-3-\sqrt{29}}{2}\\\\x_{2}=\frac{-3+\sqrt{29}}{2}[/tex]

Hence, the correct options are B and C.

Answer:

Step-by-step explanation:

Okay so solve this this is how you do it

[tex]-2x-y=-4[/tex] and [tex]x+2y=5[/tex]

To cancel out the X we have to make x into 2 x

[tex]1(-2x-y=-4)\\2(x+2y=5)\\\\[/tex]

[tex]-2x-y=-4\\2x+4y=10[/tex]

we can cancel out -2x and 2x now leaving us with

[tex]-y=-4\\4y=10[/tex]

add them both and solve for y

[tex]3y=6\\y=\frac{6}{3}\\y=2[/tex]

Now just substitute 2 for y

[tex]-2x-2=-4\\-2x=-4+2\\-2x=-2\\x=\frac{-2}{-2} \\x= 1[/tex]

Or

[tex]x+2(2)=5\\x+4=5\\x=5-4\\x=1[/tex]

In both the equations your answer will be the same

Hope this helps :)

If you have an doubt or need further help just reply :)

Look at the picture.

The x-intercepts are where the graph crosses the x-axis, and the y-intercepts are where the graph crosses the y-axis.

Final answer:

To find the y-intercept of a line, set x to zero in the equation y = mx + b, and the y-intercept is the value of b. To find the x-intercept, set y to zero and solve for x. The intercepts are the coordinates where the line crosses respective axes.

Explanation:

To determine the intercepts of a line, you need to find the points where the line crosses the axes. The y-intercept is the point where the line crosses the y-axis, and it is found when the value of x is 0. If we have a linear equation in the form y = mx + b, the y-intercept is the value of b, which is the y-coordinate when x is zero.

To find the x-intercept, we need to find the value of x when y is zero. This can be done by setting the y-value in the equation y = mx + b to zero and solving for x. The resulting x-value will be the x-coordinate of the x-intercept.

For example, if we have a linear equation y = -2x + 3, the y-intercept occurs when x is zero, which means y = 3. So the y-intercept is (0,3). To find the x-intercept, we set y to 0 and solve for x: 0 = -2x + 3, resulting in x = 1.5. Thus, the x-intercept is (1.5,0).

Answer:

1 1/4

Step-by-step explanation:

subtract 1 1/2 from 2 3/4

After using part of his flour, Henry subtracts the amount used from the initial amount to find that he has 1 cup of flour left.

The question asks about subtracting fractions in order to determine how much flour is left after some is used. We start with Henry's initial amount of flour, which is 2 3/4 cups, and subtract the amount he used to bake muffins, which is 1 1/2 cups. To perform this subtraction, we first need to have the fractions with a common denominator. Since 4 is the least common multiple of 4 and 2, we convert 1 1/2 to 3/4. Now, we have 2 3/4 cups - 1 3/4 cups, which can be simplified step-by-step:

Therefore, Henry has 1 cup of flour left after making muffins.

To provide another example, if we were to reference a cooking equation like the one for biscuits, where 2 cups of flour make 12 biscuits, we could determine how much product we can make with a given amount of reactants (flour). Similarly, with the given measurements in the question, we are finding the remainder of the reactant (flour) after it's been partially used.

Answer:

a⁻⁵

Step-by-step explanation:

1/a²·1/a³

Multiply numerators and denominators

= (1 × 1)/(a² × a³)

= 1/a⁵

= a⁻⁵

the answer is D. (4.24,pi/4)

The mistake in the table is located at point [tex](r, \theta) = \left(4.24, \frac{\pi}{4} \right)[/tex].

In this question we must evaluate the function [tex]r(\theta) = 1 + 2\cdot \sin \theta[/tex], where [tex]\theta[/tex] in radians, for all [tex]\theta[/tex] set in the table and looks that all values of [tex]r[/tex] match with all corresponding values in the table.

According to the table, [tex]r\left(\frac{\pi}{4} \right) = 4.24[/tex] but the evaluation of the function brings out a different result:

[tex]r\left(\frac{\pi}{4} \right) = 1 + 2\cdot \sin \frac{\pi}{4}[/tex]

[tex]r\left(\frac{\pi}{4} \right) = 1 + 2\cdot \left(\frac{\sqrt{2}}{2} \right)[/tex]

[tex]r\left(\frac{\pi}{4} \right) = 1 + \sqrt{2}[/tex]

[tex]r\left(\frac{\pi}{4} \right) \approx 2.414[/tex]

The mistake in the table is located at point [tex](r, \theta) = \left(4.24, \frac{\pi}{4} \right)[/tex]. [tex]\blacksquare[/tex]

To learn more on polar functions, we kindly invite to check this verified question: https://brainly.com/question/9547138

We can use the vertical line test to check if each graph is a function. If the line passes through two points, it is not a function. If it only passes through one point then it is a function.

Graph 1:

It is a function because the line doesn't pass through more than one point. (yellow)

Graph 2:

It is not a function because the line does pass through more than one point. (orange)

Graph 3:

Horizontal lines are not functions. (orange)

Graph 4:

It is a function because the line doesn't pass through more than one point. (yellow)

Best of Luck!

Answer:

Graph 1:

It is a function because line don't pass more than one point. (yellow)

Graph 2:

It is not a function because line does pass through more than one point. (orange)

Graph 3:

Horizontal lines are not functions. (orange)

Graph 4:

It is a function because the line doesn't pass through more than one point. (yellow)

Step-by-step explanation:

please mark as brainliest

Answer:

[tex]m\angle 5=76\degree[/tex].

Step-by-step explanation:

In the given parallelogram, line AC is a transversal.

Using the alternate interior angles theorem,

[tex]m\angle 5=76\degree[/tex].

You can observe this by tracing a Z-pattern.

You will then observe that m<5 and the [tex]76\degree[/tex] angles are alternate interior angles.

Answer:

4x(3y + 7z) = 12xy + 28xz

Step-by-step explanation:

Factoring is the decomposition of an expression into a product of factors, which when multiplied together give the original expression.

Final answer:

The expression 12xy + 28xz can be factored using the distributive property by taking out the greatest common factor, which is 4x, resulting in the factored form 4x(3y + 7z).

Explanation:

To use the distributive property to factor the expression 12xy + 28xz, we need to find the greatest common factor (GCF) that is common to both terms. Here, the GCF for the numerical coefficients 12 and 28 is 4, and both terms have the variable x. Thus, we factor out 4x from both terms.

The factored expression is 4x(3y + 7z). We get this by dividing each term by the GCF:

For 12xy: (12xy)/(4x) = 3y

For 28xz: (28xz)/(4x) = 7z

Finally, we write the expression as the GCF multiplied by the sum of these quotients: 4x(3y + 7z).

the answer would be 47.5

Answer:

6 runners

Step-by-step explanation:

the total divided by the distance each runner will run

1.5/0.25=6

Answer:

3

Step-by-step explanation:

just take any 2 points (since it is linear) and do the slope formula.

slope is y2-y1/x2-x1

The slope is gonna be positive 3 for this question!