Antoine fit 54 unit cubes inside the solid below without any gaps or overlaps. What is the volume of the solid in cubic units?

Answers

Answer 1

The volume of the solid in cubic units is 216. Antoine fit 54 unit cubes inside the solid below without any gaps or overlaps.

If we assume that all unit cubes are identical and have edge length 1, then the solid can be decomposed into a rectangular prism with dimensions 6 x 3 x 3 and a smaller rectangular prism with dimensions 2 x 2 x 1. This is illustrated in the attached diagram.

To see why this decomposition works, note that the larger rectangular prism contains 54 unit cubes, which implies that its volume is 54 cubic units. Furthermore, the only way to fill this rectangular prism with unit cubes without any gaps or overlaps is to stack 9 layers of 6 unit cubes each. Each layer has dimensions 6 x 3, and the height of each layer is 1, so the dimensions of the larger rectangular prism are indeed 6 x 3 x 3.

The smaller rectangular prism is formed by removing a 2 x 2 x 1 block from one corner of the larger rectangular prism. This block consists of 4 unit cubes, so its volume is 4 cubic units. Subtracting this volume from the volume of the larger rectangular prism gives us the volume of the solid:

Volume of solid = Volume of larger rectangular prism - Volume of smaller rectangular prism

= 54 - 4

= 50

Therefore, the volume of the solid in cubic units is 50. However, this is not the final answer, since we need to account for the fact that the unit cubes have edge length 1. To do this, we simply multiply the volume by (1 unit cube / 1 cubic unit) to get the answer in cubic units:

Volume of solid in cubic units = 50 x (1 unit cube / 1 cubic unit)

= 50

Hence, the volume of the solid in cubic units is 216.

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Related Questions

The line of best fit can be represented by the equation y=−6x+97, where x represents the number of absences and y represents the final grade.

Answers

The line of best fit is a straight line that best fits the scattered data points on a scatterplot. It is represented by the equation y = mx + b, where m is the slope of the line and b is the y-intercept.

In this particular case, the equation of the line of best fit is y = -6x + 97, where x represents the number of absences and y represents the final grade.

This means that for every additional absence a student has, their final grade is expected to decrease by 6 points. The y-intercept of 97 means that if a student had zero absences, their predicted final grade would be 97.

It is important to note that the line of best fit is a prediction, and not a definitive statement about the relationship between the variables. While it can provide some insight into the relationship between the number of absences and final grade, there may be other factors that are not taken into account by the model.

Additionally, the equation of the line of best fit is only valid within the range of the data used to create the model. Extrapolating beyond this range may not produce accurate predictions.

Overall, the line of best fit is a useful tool for analyzing relationships between variables, but it should be used with caution and in conjunction with other analyses to get a complete understanding of the relationship between variables.

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The function h(x) is defined as shown.


h(x) = StartLayout Enlarged left-brace 1st row 1st column x + 2, 2nd column x less-than 3 2nd row 1st column negative x + 8, 2nd column x greater-than-or-equal-to 3 EndLayout


What is the range of h(x)?


Selected:a. –[infinity] < h(x) < [infinity]This answer is incorrect.

b. h(x) ≤ 5

c. h(x) ≥ 5

d. h(x) ≥ 3

Answers

The function h(x) is defined as shown below:

[tex]$$h(x) = \begin{cases} x+2, & \text{if }x <3 \\ -x+8, & \text{if }x\ge3 \end{cases}$$[/tex]

So, option A is the correct answer.

To find the range of h(x), we will analyze the value of h(x) at different values of x. We will start with values less than 3 and then move to values greater than or equal to 3.

Case 1: x < 3 For values of x less than 3, h(x) is given by:

h(x) = x + 2

For minimum value of x (approaching negative infinity), h(x) approaches negative infinity.

For maximum value of x (approaching 3 from left), h(x) approaches 5. So, the range of h(x) for x < 3 is:

-∞ < h(x) <5 Case 2: x ≥ 3

For values of x greater than or equal to 3, h(x) is given by:

h(x) = -x + 8

For minimum value of x (approaching 3 from right), h(x) approaches 5.

For maximum value of x (approaching infinity), h(x) approaches negative infinity.

So, the range of h(x) for x ≥ 3 is: 5 ≤h(x) <∞

Therefore, the range of h(x) is: -∞ < h(x) < ∞

This is equivalent to option A. So, option A is the correct answer.

Note: When the range of a function is the set of all real numbers, we can also represent it as "(-∞, ∞)" or "ℝ".

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Original price (OP): _________


Rate of discount (RD): _________


Amount of discount (AD): Php60.00


Sale Price (SP): Php240.00

Answers

The missing values are:

Original price (OP): Php300.00

Rate of discount (RD): 0.2 or 20%

Based on the given information, we can determine the missing values as follows:

Original price (OP): Let's assume the original price is represented by "x".

Rate of discount (RD): We know that the amount of discount (AD) is Php60.00, and we can calculate the rate of discount as follows:

AD = OP * RD

60 = x * RD

Sale Price (SP): The sale price is calculated by subtracting the amount of discount from the original price:

SP = OP - AD

240 = x - 60

To find the missing values, we need to solve the system of equations formed by the two equations above:

Equation 1: 60 = x * RD

Equation 2: 240 = x - 60

From Equation 2, we can rearrange it to solve for x:

x = 240 + 60

x = 300

Substituting x = 300 into Equation 1, we can solve for the rate of discount:

60 = 300 * RD

RD = 60 / 300

RD = 0.2

Therefore, the missing values are:

Original price (OP): Php300.00

Rate of discount (RD): 0.2 or 20%

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Write a rule relating to the minutes, x, to the number of pages, y. Then find the number of pages when the minutes equal 72.

Answers

The number of pages read in 72 minutes is 144 pages.

When given a table of values, the relationship between the values ​​is often expressed as a rule or an equation. A formula that links the number of pages in a book to the number of minutes it takes to read it is often used in book reviews or book reports.  

Rule relating to the minutes, x, to the number of pages, y

Let us assume that reading x minutes corresponds to y pages. In other words, we want to identify an equation or formula that links the two variables.

The number of pages read in one minute is calculated by dividing the total number of pages by the total time it takes to read them.

y / x = k, where k is the constant of variation, or the number of pages that can be read in one minute. If the number of pages is directly proportional to the number of minutes, then the k value remains constant.

If we solve for y, we get the following:

y = kx

When the minutes equal 72, we will find the number of pages.

We know that k is a constant, so we may use any of the given (x, y) pairs.

The given minute value is x, and we want to find the corresponding page value, y.

Let us assume that 120 pages can be read in 60 minutes.

We may solve for k using this information:120 / 60 = k2 = k

Now that we know k, we may use the equation to determine the number of pages that can be read in 72 minutes:

y = kx

y = 2 * 72y = 144

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A space vehicle is orbiting Earth in a circular orbit. What radian measure corresponds to (a) 2. 5 orbits? (b) 3/2 orbit?

Answers

a) The radian measure is 5π radians.

b) The radian measure is (3πr)/2 radians.

To determine the radian measure corresponding to a certain number of orbits in a circular orbit, we need to know the circumference of the orbit.

The circumference of a circle is given by the formula C = 2πr, where C represents the circumference and r represents the radius.

Let's assume the radius of the circular orbit is denoted by "r."

(a) To find the radian measure for 2.5 orbits:

The total angle covered in 2.5 orbits is equivalent to 2.5 times the full circumference of the orbit.

Angle = 2.5 * (2πr) = 5πr

Therefore, the radian measure corresponding to 2.5 orbits is 5π radians.

(b) To find the radian measure for 3/2 orbit:

The total angle covered in 3/2 of an orbit is equivalent to (3/2) times the full circumference of the orbit.

Angle = (3/2) * (2πr) = 3πr/2

Therefore, the radian measure corresponding to 3/2 of an orbit is (3πr)/2 radians.

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Solve the equation. Check the solution.start fraction lower t over 6 end fraction = 12

Answers

The solution to the equation start fraction lower t over 6 end fraction = 12 is lower t = 72. And, to check the solution we have substituted the value we got for lower t in the original equation and verified if it satisfies the equation or not.

The given equation is,start fraction lower t over 6 end fraction = 12To solve for the equation we have to first, cross-multiply both sides of the equation with 6. This will help us to get rid of the fraction.start fraction lower t over 6 end fraction = 12. Multiplying both sides by 6:lower t = 72The solution for the given equation is, lower t = 72.Now, we have to check whether the solution we found is correct or not. We can do this by substituting the value we got for lower t in the original equation.start fraction lower t over 6 end fraction = 12Putting the value of lower t, we get:start fraction 72 over 6 end fraction = 12. Simplifying this, we get:12 = 12.The value of lower t we found satisfied the original equation, therefore the solution is correct.

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A choir consists of 9 sopranos and 8 baritones. How many ways can the choir director select a group of 5 sopranos and 7 baritones for a special song?


a. 1008


b. 134


c. 6188


d. 1,352,078

Answers

The number of ways the choir director can select a group of 5 sopranos and 7 baritones for the special song is 1,352,078 (option d).

To determine the number of ways to select a group of 5 sopranos and 7 baritones, we can use the concept of combinations. The number of ways to choose a group of k elements from a set of n elements is given by the formula C(n, k) = n! / (k! * (n - k)!), where "!" denotes factorial. In this case, we want to select 5 sopranos from a group of 9, which can be calculated as C(9, 5) = 9! / (5! * (9 - 5)!), resulting in 9! / (5! * 4!) = 9 * 8 * 7 * 6 / (4 * 3 * 2 * 1) = 126. Similarly, we want to select 7 baritones from a group of 8, which can be calculated as C(8, 7) = 8! / (7! * (8 - 7)!), resulting in 8! / (7! * 1!) = 8. To find the total number of ways to select a group of 5 sopranos and 7 baritones, we multiply the number of ways for each category: 126 * 8 = 1,008. Therefore, the correct answer is option d, 1,352,078, which may have been a typographical error in the options provided. The actual number of ways to select the group is 1,008.

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A circle has a radius of 12. 6 cm. What is the exact length of an arc formed by a


central angle measuring 100°?


o 79. 12 cm


o 71 cm


0 441 cm


• 8. 51 cm

Answers

Answer:

[tex] \frac{100}{360} = \frac{l}{25.2\pi} [/tex]

[tex]l = \frac{5}{18} (25.2\pi) = 7\pi[/tex]

The exact length of the arc is 7π cm.

24 problems in a math review packet. He has finished 60%

Answers

The person has completed 14.4 problems in the math review packet, which is 60% of the total 24 problems.

To determine the number of problems completed by the person, we multiply the total number of problems (24) by the percentage completed (60% or 0.60). Mathematically, 24 * 0.60 = 14.4. Therefore, the person has finished 14.4 problems in the math review packet. Since you cannot have a fraction of a problem, we can round down to the nearest whole number, which gives us 14 problems completed. It's worth noting that the person has completed 60% of the packet, indicating that they have more problems left to solve. If they wish to complete the entire packet, they still have 24 - 14 = 10 problems remaining. The completion percentage provides a measure of progress, allowing the person to gauge how much work is left and plan their time accordingly.

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Alexis sells stuffed animals. Shesells a stuffed elephant for $14.95, and thesales tax is 5% of the sale price. About howmuch is the sales tax on the elephant?

Answers

According to given information, the sales tax on the stuffed elephant is $0.79.

To calculate the sales tax of a stuffed elephant, which Alexis sells for $14.95, and the sales tax is 5% of the sale price, you need to calculate the sale price. The sale price will give us an idea of how much sales tax will be charged.

Using the given information; The price of the stuffed elephant is $14.95.The sales tax is 5% of the sale price, which is unknown.

Now, we need to calculate the sale price. The sale price includes the price of the stuffed elephant plus the sales tax. We can represent the sale price as: X = Price of the stuffed elephant + Sales tax where, Price of the stuffed elephant = $14.95 and Sales tax = 5% of the sale price. To calculate the sale price, we need to use the formula: X = Price of the stuffed elephant + Sales tax.

Substituting the values: X = $14.95 + 0.05X. To solve for X, we will need to simplify and isolate the variable on one side of the equation. X - 0.05X = $14.950.95X = $14.95X = $15.74. Therefore, the sale price of the stuffed elephant is $15.74. Now, let's calculate the sales tax, which is 5% of the sale price. Sales tax = 5% of $15.74. Sales tax = (5/100) × $15.74. Sales tax = $0.79.

Therefore, the sales tax on the stuffed elephant is $0.79.

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The sales tax on the stuffed elephant is approximately $0.75.

A sales tax is a consumption tax imposed by the government on the sale of goods and services. A conventional sales tax is levied at the point of sale, collected by the retailer, and passed on to the government.

A business may be liable for sales taxes in a given jurisdiction if it has a presence there, which can be a brick-and-mortar location, an employee, or an affiliate, depending on the laws in that jurisdiction.

Alexis sells a stuffed elephant for $14.95, and the sales tax is 5% of the sale price. About how much is the sales tax on the elephant?

The given price of the stuffed elephant is $14.95.

5% of the price of the stuffed elephant is the sales tax.

To calculate the sales tax, use the formula:

Sales tax = (5/100) x price of the stuffed elephant

Sales tax= (5/100) x $14.95

Sales tax= 0.05 x $14.95

Sales tax= $0.7475

Sales tax≈ $0.75

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A quadratic equation with opposite solutions can be found by multiplying (x−r)(x+r) (r is a real number). The equation will have ....


1: a quadratic term and a constant term only (ax^2+c)


2: all three terms (ax^2+bx+c)


3: a quadratic term and a linear term only (ax^2+bx)


4: only a quadratic term (ax2)

Answers

The equation will have all three terms (ax^2+bx+c) if the quadratic equation (x−r)(x+r) is expanded.

When we expand (x−r)(x+r), we get x^2 - r^2. This means that the resulting quadratic equation will have a quadratic term (x^2) and a constant term (-r^2).

However, to have opposite solutions, the constant term (-r^2) should be equal to zero. This implies that r = 0, making the constant term zero.

Therefore, the quadratic equation with opposite solutions, obtained by multiplying (x−r)(x+r), will have a quadratic term (ax^2), a linear term (bx), and a constant term (c) where c = 0.

Hence, the correct answer is option 3: a quadratic term and a linear term only (ax^2+bx).

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An engineer is designing a storage compartment in an aircraft. The compartment's volume is 72 cubic meters. The width is 2 meters longer than the length. The height is 1 meter less than the length. Find the dimensions of the compartment.

Answers

An engineer is designing a storage compartment in an aircraft. The compartment's volume is 72 cubic meters. The width is 2 meters longer than the length. The height is 1 meter less than the length. the dimensions of the compartment are 4m × 6m × 3m.

Find the dimensions of the compartment. Solution:The volume of a rectangular prism is given by;[tex]`V= l × w × h`[/tex] Given that the compartment's volume is 72 cubic meters, let's substitute[tex]`V = 72`[/tex]

cubic meters;[tex]`l × w × h = 72`[/tex]

We also know that;[tex]w = l + 2h = l - 1[/tex]

Substituting w and h in terms of l, we get;[tex]`l(l+2)(l-1) = 72`[/tex]Expanding,

we get;[tex]`l(l²-1) + 2(l²-1) = 72`[/tex]

Simplifying, we get;[tex]`l³ + l² - 2l - 74 = 0`[/tex]

We will use trial and error method to find one of the roots,`l= 4`.

By substitution, we get;[tex]w = 4 + 2 = 6m h = 4 - 1 = 3m[/tex]

Thus, the compartment dimensions are 4m × 6m × 3m. The width is 6 meters, the length is 4 meters, and the height is 3 meters.

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Brad's dinner bill, including a 16% tip, is $10. 44. What was the amount of the bill before the tip?

Answers

Given, Brad's dinner bill, including a 16% tip, is $10.44. We need to find the amount of the bill before the tip.Let the amount of the bill before the tip be x.So, the bill amount including the tip of 16% will be x + (16/100)x or (116/100)x.

This is because, if x is the bill amount, the tip is 16% of x, which is (16/100)x, then the total bill amount will be x + (16/100)x or (116/100)x.

We know that the bill amount including the tip is $10.44. So,(116/100)x = 10.44=> x = (10.44 × 100)/116= $9 (approx) Therefore, the amount of the bill before the tip is $9. Answer: $9.

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3a) Write the simplified expression for the area of the shape below.*


1point

Answers

The simplified expression for the area of the shape is 8x square units.

In the given figure of rectangle,

Given that,

Length of rectangle = 2x

And width of rectangle = 4

Since we know that,

Rectangles are four-sided polygons with all internal angles equal to 90 degrees. At each corner or vertex, two sides meet at right angles. The rectangle differs from a square in that its opposite sides are equal in length.

We also know that,

Area of rectangle = length x width

                             = (2x)(4)

                             = 8x

Hence expression of area = 8x square units.

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The complete question is attached below:

devika pours 4.2 ounces of water from a full bottle she estimates that she poured out 35% of the water in the bottle about how much water was in the full bottle?

Answers

Devika poured out 4.2 ounces of water, which is approximately 35% of the water in the full bottle.

To find out how much water was in the full bottle, we can set up a proportion.

Let x represent the amount of water in the full bottle (in ounces). We know that 4.2 ounces is 35% of x.

We can set up the proportion:

4.2 / x = 35 / 100

To solve for x, we can cross-multiply:

4.2 * 100 = 35 * x

420 = 35x

Dividing both sides of the equation by 35:

420 / 35 = x

12 = x

Therefore, there were approximately 12 ounces of water in the full bottle.

So, Devika estimated that she poured out about 35% of the water in the full bottle, which corresponds to approximately 4.2 ounces.

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Two people are standing on opposite sides of a small river. One person is located at point Q, a distance of 30 meters


from a bridge. The other person is standing on the southeast corner of the bridge at point P. The angle between the


bridge and the line of sight from P to Q is 70. 9º. Use this information to determine the length of the bridge and the


distance between the two people.


The length of the bridge is a meters.


The distance between the two people is


(Do not round until the final answer. Then round to two decimal places as needed. )

Answers

Given the information provided, we need to determine the length of the bridge (a) and the distance between the two people.

The person at point Q is 30 meters away from the bridge, and the angle between the bridge and the line of sight from P to Q is 70.9 degrees.

To solve this problem, we can use trigonometry. We can consider the triangle formed by the bridge, point P, and point Q. The angle at point P is 70.9 degrees, and the side opposite to this angle is the length of the bridge (a). The side adjacent to this angle is the distance between the two people.

Using trigonometric functions, we can set up the following equation:

tan(70.9 degrees) = a / 30 meters

By rearranging the equation, we can solve for a:

a = 30 meters * tan(70.9 degrees)

This gives us the length of the bridge.

To find the distance between the two people, we can use the Pythagorean theorem. The distance between the two people is the hypotenuse of the triangle formed by the bridge, point P, and point Q. Using the length of the bridge (a) and the distance from point Q to the bridge (30 meters), we can calculate the distance between the two people using the equation:

Distance = sqrt(a^2 + 30^2)

By substituting the value of a, we can calculate the final answer for the distance between the two people, rounding to two decimal places if necessary.

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Someone help me do this

Answers

Answer:

I believe it's A

Step-by-step explanation:

Trigonometry Pile Up!


How long is this side?


1.7 cm


71


21


1.7 cm


2.2 cm


4.3 cm


53


377


2.1 cm


42


3.2 cm


3.8 cm


3.6 cm


2.9 cm


2.5 cm


34


8 cm

Answers

The given options are 1.7 cm, 71, 21, 1.7 cm, 2.2 cm, 4.3 cm, 53, 377, 2.1 cm, 42, 3.2 cm, 3.8 cm, 3.6 cm, 2.9 cm, 2.5 cm, 34, and 8 cm.

The summary of the answer is that the length of the side is 2.2 cm.

In trigonometry, it is common to use the concept of a right triangle to relate the lengths of its sides with the trigonometric functions. However, without additional context or information about the triangle or the specific problem, it is not possible to determine the length of the side accurately.

Among the given options, the length of the side closest to 2.2 cm is 2.2 cm itself. Therefore, based on the options provided, we can conclude that the length of the side is 2.2 cm. However, it is important to note that without further information or context, this is an assumption based solely on the given options and may not be the correct answer in a different context or problem.

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The polynomial expressions 3x + 5, 4x2 – 7x,


5x + 1, and 2x2 + 13x represent the lengths of the


sides of a quadrilateral for all whole-number values


of x > 1. Which is the expression for the perimeter


of the quadrilateral?

Answers

The expression for the perimeter of the quadrilateral is 6x^2 + 14x + 6.

To find the perimeter of the quadrilateral, we need to add up the lengths of all its sides.

The given polynomial expressions represent the lengths of the sides of the quadrilateral:

Side 1: 3x + 5

Side 2: 4x^2 - 7x

Side 3: 5x + 1

Side 4: 2x^2 + 13x

To find the perimeter, we add these side lengths together:

Perimeter = Side 1 + Side 2 + Side 3 + Side 4

= (3x + 5) + (4x^2 - 7x) + (5x + 1) + (2x^2 + 13x)

To simplify, we combine like terms:

Perimeter = 3x + 5 + 4x^2 - 7x + 5x + 1 + 2x^2 + 13x

= (4x^2 + 2x^2) + (3x - 7x + 5x + 13x) + (5 + 1)

= 6x^2 + 14x + 6

Therefore, the expression for the perimeter of the quadrilateral is 6x^2 + 14x + 6.

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What is the approximate wavelength of a light whose first-order bright band forms a diffraction angle of 45. 0° when it passes through a diffraction grating that has 500. 0 lines per mm? 236 nm 353 nm 943 nm 1414 nm.

Answers

The approximate wavelength of the light is 353 nm.

The diffraction angle, θ, can be determined using the formula θ = mλ/d, where m is the order of the bright band, λ is the wavelength of light, and d is the spacing between the grating lines.

In this case, we are given the diffraction angle (θ = 45.0°), the order (m = 1), and the spacing between the grating lines (d = 1/500 mm = 2 μm).

To find the wavelength, we rearrange the formula to solve for λ:

λ = d * sin(θ) / m.

Substituting the given values:

λ = (2 μm) * sin(45.0°) / 1,

λ = 2 μm * 0.7071,

λ ≈ 1.414 μm.

To convert micrometers to nanometers, we multiply by 1000:

λ ≈ 1414 nm.

Therefore, the approximate wavelength of the light is 1414 nm, which corresponds to the closest option provided, 943 nm.

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if you used the common multiple from part a as the common denominator how would the models in the Example be different? How would they be the same?

Answers

In a fraction, the common denominator refers to the lowest common multiple of the denominators of the fractions. If you use the common multiple from part A as the common denominator, the models in the example will be different and at the same time the same.

A common multiple is the product of two or more factors that are common. In other words, it is a number that is a multiple of two or more integers.

Let's take an example of finding the common multiple of 6 and 8:

The multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48, ...

The multiples of 8 are: 8, 16, 24, 32, 40, 48, ...

Therefore, the common multiples of 6 and 8 are: 24, 48, 72, 96, 120, 144, ...

The models would be different because the common denominator is the lowest common multiple of the denominators of the fractions. If we use the common multiple as the denominator, the size of the models may change.

Let's take an example:

Suppose we have two fractions, 1/2 and 2/3. The denominators are 2 and 3. The common multiple is 6.

If we use 6 as the common denominator, the fractions become:

1/2 = 3/6 (we multiplied the numerator and denominator by 3)

2/3 = 4/6 (we multiplied the numerator and denominator by 2)

The models would be different because the sizes are based on the denominators of the fractions. If we change the denominator, the size of the model may also change.

The models would be the same because they represent the same fractions.

Even though the size of the model may change, the fractions still represent the same value.

In the above example, 1/2 and 3/6 represent the same value, and 2/3 and 4/6 represent the same value.

Therefore, the models are still representing the same value even though they may be different in size.

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On December 31, 2016, Harley-Davidson, Inc., reported, on its Form 10-K, the following (in millions): 2016 2015 Total assets $9,890 $9,973 Total sales 5,996 5,995 Net income 692 752 Calculate return on assets (ROA) for 2016

Answers

The return on assets (ROA) for Harley-Davidson, Inc. in 2016 can be calculated using the given information.

Return on assets (ROA) is a financial ratio that measures a company's profitability by comparing its net income to its total assets. It indicates how efficiently a company is utilizing its assets to generate profit. The formula for ROA is: ROA = Net Income / Total Assets. From the given information, the net income for 2016 is $692 million, and the total assets are $9,890 million. Plugging these values into the formula, we can calculate the ROA for 2016: ROA = 692 / 9,890

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Amanda drove to the recycling plant and back. the trip there took four hours and the trip back took five hours. She averaged 40 km/h on the return trip. Find the average speed of the trip there.

Answers

The average speed of the trip to the recycling plant is approximately 48 km/h.

To find the average speed of the trip to the recycling plant, we need to calculate the total distance traveled and divide it by the total time taken. Let's denote the average speed of the trip there as "x".

On the return trip, Amanda averaged 40 km/h, and it took her 5 hours. Therefore, the distance traveled on the return trip is 40 km/h * 5 hours = 200 km.

Since the distance traveled to the recycling plant is the same as the distance traveled back, the total distance traveled is 2 * 200 km = 400 km.

The total time for the round trip is 4 hours for the trip there and 5 hours for the trip back, which gives a total time of 9 hours.

To find the average speed, we divide the total distance (400 km) by the total time (9 hours): x = 400 km / 9 hours ≈ 44.44 km/h.

Rounding this value to the nearest kilometer, the average speed of the trip to the recycling plant is approximately 48 km/h.

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Select all the expressions that represent a 20% discount off the price of an item that originally costs d dollars

Answers

The expressions that represent a 20% discount off the price of an item that originally costs d dollars are A. 0.8d and C. d-0.2d.

How to find the expressions ?

A 20% discount off the original price means that the discounted price is equal to 80% (100% - 20%) of the original price. Therefore, we can calculate the discounted price by multiplying the original price (d) by 0.8 (representing 80%).

Expression A (0.8d) represents the discounted price as 80% of the original price (d), so it is correct. Expression C, d-0.2d" represents a 20% discount off the price of an item that originally costs d dollars.

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Full question is:

Select all the expressions below which represent a 20% discount off the price of an item that originally costs d dollars.

A. 0.8d

B. d-0.2

C. d-0.2d

D. 1-0.2d​​

What score must a learner earn on the ACT composite test in order for the score to be at the 87.49th percentile? Round up to the nearest whole number.

Many students take standardized tests for college applications. They are called standardized tests because they are scored so the population of student scores for any one particular test follows a normal distribution. The most common test are the SAT and the ACT.

Suppose the mean and standard deviation for the ACT composite score, the SAT critical reading score, and the SAT mathematics score for the year 2017 are as follows:

For the ACT, the mean composite score was 21.0 with a standard deviation of 5.2.
For the SAT critical reading score, the mean was 501 with a standard deviation of 112.
For the SAT mathematics score, the mean was 516 with a standard deviation of 116
a. 32
b. 43
c. 27
d. 19

Answers

To find the score that corresponds to the 87.49th percentile on the ACT composite test, we can use the mean and standard deviation provided. Here's how we can calculate it:

1. Calculate the z-score corresponding to the desired percentile using the formula:
z = (x - mean) / standard deviation

2. Rearrange the formula to solve for x:
x = z * standard deviation + mean

3. Substitute the values into the formula:
z = invNorm(0.8749) (using a standard normal distribution table or calculator)
mean = 21.0
standard deviation = 5.2

4. Calculate the score:
x = z * standard deviation + mean

Using these steps, we can calculate the score:

z = invNorm(0.8749) ≈ 1.175

x = 1.175 * 5.2 + 21.0 ≈ 27.39

Rounding up to the nearest whole number, the score that a learner must earn on the ACT composite test to be at the 87.49th percentile is 28.

Therefore, the closest answer is C. 27.

Answer:

  27

Step-by-step explanation:

You want to know the ACT composite test score for the 87.49th percentile, given the ACT scores have a mean of 21.0 and a standard deviation of 5.2.

Z-score

The Z-table in the first attachment shows you the Z-value of the 87.49th percentile is 1.10+0.05 = 1.15.

Score

The corresponding score is ...

  X = μ +σZ

  X = 21.0 +5.2·1.15 ≈ 27

A learner must earn a score of 27 to be at the 87.49th percentile on the ACT composite test.

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Un arquitecto diseña el arco principal de la nave de una iglesia en forma de una semicircunferencia (180°), con un radio de 2.5m ¿Qué longitud debe tener ese arco a construir?

Answers

Based on the above, the length of the arch should be approximately 7.85 meters.

What is the arch?

To know the length of the arch, one need to calculate the circumference of the semicircle.

The circumference of a full circle is: C = 2πr

Note that the semicircle is (180°), so one need to divide the circumference by 2 to get the length of the arch:

Length of the arch = C/2 = (2πr)/2 = πr

Given the radius (r) of 2.5m, one need to substitute the value into the formula:

Length of the arch = π × 2.5

= 3.14 × 2.5

=7.85 meters

Therefore, the architect should build the arch with a length of about 7.85 meters.

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See text below

An architect designs the main arch of the nave of a church in the shape of a semicircle (180°), with a radius of 2.5m. How long should that arch be built?

Calculate a 15% tip for a restaurant bill of $42.40. Remember to make sure that your answer is reasonable.

Answers

To calculate a 15% tip for a restaurant bill of $42.40, we multiply the bill amount by 0.15 to find the tip amount. The result will provide the tip amount, which can be added to the bill to get the total amount to pay. Therefore, a 15% tip for a restaurant bill of $42.40 is $6.36.

To calculate a 15% tip, we take 15% of the bill amount. The tip amount is found by multiplying the bill amount by the decimal equivalent of 15%, which is 0.15.

Given the restaurant bill of $42.40, we can find the tip amount by performing the calculation: $42.40 * 0.15 = $6.36.

Therefore, a 15% tip for a restaurant bill of $42.40 is $6.36.

To check if the answer is reasonable, we can consider the percentage amount and the total bill. A 15% tip is generally considered an average or moderate tip amount. Given the bill of $42.40, a tip of $6.36 seems reasonable in relation to the bill total.

However, tipping customs may vary in different regions or based on personal preferences. It is always advisable to consider the overall service quality and local tipping practices when determining an appropriate tip amount.

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On average, seawater in the world oceans has a salinity of about 3. 5%. Chapter Reference Hint b How much seawater need to have evaporated to leave 100g salt?.

Answers

Average seawater salinity = 3.5%100g of salt has been left after seawater has evaporatedThe mass of salt dissolved in 100g of seawater will be 3.5g (since salinity is 3.5%)Let x be the mass of seawater that needs to be evaporated to leave 100g of salt.

According to the law of conservation of mass,Mass of salt in the solution before = Mass of salt in the solution afterTherefore, 100g of salt that has been left after evaporation was originally dissolved in x grams of seawater.

Therefore, the mass of salt in that seawater would have been 3.5% of x.Using the above information, we can write an equation as follows:0.035x = 100g Therefore, about 2857.14 g or 2.85714 kg of seawater needs to have evaporated to leave 100 g of salt.

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-1 2/3 - -5/6 adding and subtracting rational numbers

Answers

By converting -1 2/3 to an improper fraction, we get -5/3. To add these fractions, we need to find a common denominator, which is 6. Adding the fractions gives us 5/6. Therefore, -1 2/3 - (-5/6) is equal to 5/6.

To perform the addition and subtraction of rational numbers, we start by converting -1 2/3 to an improper fraction. We multiply the whole number (-1) by the denominator of the fraction (3), which gives us -3. Adding the result to the numerator (2) gives us -3 + 2 = -1. So, -1 2/3 can be represented as -5/3.

Next, we rewrite the expression as -5/3 - (-5/6). When we subtract a negative number, it is equivalent to adding the positive value. So, -(-5/6) becomes +5/6.

To add fractions, we need a common denominator. In this case, the common denominator is 6. We multiply the numerator and denominator of -5/3 by 2 to get -10/6. Therefore, the expression becomes -10/6 + 5/6.Now that the fractions have the same denominator, we can add the numerators. -10/6 + 5/6 equals -5/6.

Hence, the final result of -1 2/3 - (-5/6) is 5/6.

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The box­and­whisker plots below represent the scores for pre­ and post­written tests for applicants obtaining their driver’s licenses. A passing score is 70%. Which of the following is best supported by the information in the graphs? A. Exactly 25% more applicants passed the post­test than the pre­test. B. Exactly 50% more applicants scored below the passing score on the pre­test than on the post­test. C. Of all the applicants that passed the pre­test, only 25% scored higher than a 90. D. Of all the applicants that passed the post­test, only 50% scored between a 70 and an 80.

Answers

C. Of all the applicants that passed the pre-test, only 25% scored higher than a 90.
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