12a+14=302
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As a result, the rectangular prism's volume in fully factored form is:

V = (x - 1) * (l * w * h)

A 3D form with six rectangular faces is referred to as a rectangular solid. A rectangular solid's volume can be calculated using the formula V = lwh, where l denotes the solid's length, w its width, and h its height.

In this instance, we are informed that the rectangular solid's height is 17 units. Also, we are informed that the solid's base is a rectangle with an area of (x-1) square units. We can assume that the solid has length l and width w because its base is a rectangle.

Solids with six rectangular faces are known as rectangular solids. They go by the name rectangular prisms as well. Following are some examples of rectangular solids in daily life:

Laptops, school notebooks, fish tanks, cargo containers, rooms, storage sheds, refrigerators, cereal boxes, tissue boxes, cars, and more.

As a result, we have:

l * w = x - 1

The rectangular solid's volume is:

V = lwh

With l * w = x - 1 and h = 17 as substitutes, we obtain:

V = (x - 1)lw

This phrase can be factored as follows:

V = (x - 1)l * w * h

Since l * w = x - 1 and h = 17, we have:

V = (x - 1) * l * w * h

V = (x - 1) * (l * w * h)

As a result, the rectangular prism's volume in fully factored form is:

V = (x - 1) * (l * w * h)

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The quotient in simplest form is [tex]x^3 * (x+1)/(x-4).[/tex]

A fractiοn represents a part οf a whοle οr, mοre generally, any number οf equal parts. When spοken in everyday English, a fractiοn describes hοw many parts οf a certain size there are, fοr example, οne-half, eight-fifths, three-quarters.

Numeratοrs and denοminatοrs are alsο used in fractiοns that are nοt cοmmοn, including cοmpοund fractiοns, cοmplex fractiοns, and mixed numerals.

In pοsitive cοmmοn fractiοns, the numeratοr and denοminatοr are natural numbers. The numeratοr represents a number οf equal parts, and the denοminatοr indicates hοw many οf thοse parts make up a unit οr a whοle.

Tο divide fractiοns, we invert the secοnd fractiοn and multiply it by the first. Sο:

4x⁵/12x² ÷ (x²-3x-4)/(3x+3)= (4x⁵/12x²) * (3x+3)/(x²-3x-4)

Inverted secοnd fractiοn and multiplied

= (4/12) * (x⁵/x²) * (3(x+1)/(x-4)(x+1))

Factοred the denοminatοr οf the secοnd fractiοn

= (1/3) * [tex]x^{(5-2)[/tex] * (3(x+1)/(x-4))

Simplified and cancelled οut cοmmοn factοrs[tex]= (1/3) * x^3 * (3(x+1)/(x-4))= x^3 * (x+1)/(x-4)[/tex]

Therefοre, the quοtient in simplest fοrm is  [tex]x^3 * (x+1)/(x-4).[/tex]

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Kennedy's average speed was 3554 miles per hour by using the formula of average speed.

Average speed is a measure of how fast something travels over a period of time, calculated by dividing the total distance traveled by the total time taken. It is usually expressed in units of distance per unit of time, such as miles per hour (mph) or kilometers per hour (km/h).

Distance is a measure of the physical space between two points, objects, or locations. It is usually expressed in units such as meters, kilometers, miles, feet, or yards.

To find Kennedy's average speed, we can use the formula:

average speed = total distance / total time

In this case, Kennedy drove 9494 miles in 2 2/3 hours. To convert the mixed number to an improper fraction, we can multiply the whole number by the denominator and add the numerator, then put the result over the denominator:

2 2/3 = (2 × 3 + 2) / 3 = 8/3

So Kennedy's total time was:

total time = 8/3 hours

Using the formula, we get:

average speed = 9494 miles / (8/3 hours)

To divide by a fraction, we can multiply by its reciprocal:

average speed = 9494 miles × (3/8 hours)

Simplifying, we get:

average speed = 3554.25 miles per hour

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Thus, number of students in seventh grade who can play instrument out of 77 are 37.

In general, the term "proportion" refers to a part, share, or amount that is compared to a whole. Depending on the definition of proportion, two ratios are in proportion when they are equal. Two ratios as well as fractions are equal when an equation or a declaration to that effect is utilised.

Whereas if ratio between the initial and second is identical to the ratio between of second and third, then each three quantities are referred to as having a continuing proportion.

Given data for the  seventh grade students:

Out of 100 ---> 48 can play instruments.

Out of 77 ---> x (say) can play instruments.

So,

100/77 = 48/x

x = 48*77 / 100

x = 36.96

x = 37 (students)

Thus, number of students in seventh grade who can play instrument out of 77 are 37.

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A 14.2 million donation was made to a charity. The overall amount of the charity's contributed funds is 34 million if which amounts to 42% of those monies.

Let x represent the total amount of donations received by the charity.

According to the problem, 14.2 million represents 42% of the charity's donated funds:

14.2 million = 0.42x

We must isolate x on one side of the equation in order to find it. We can do this by dividing both sides of the equation by 0.42:

x = 14.2 million / 0.42

x = 33.80952381 million

Rounding this answer to the nearest million gives:

x ≈ 34 million

Therefore, the total amount of the charity's donated funds is approximately 34 million.

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The formula you need to use in order to find the volume of a cylinder is [tex]V = \pi r^{2} h[/tex]

Step 1) Take note of the information that has been provided to you.

The height is 8 yards

The radius is 2 years

Step 2) Substitute the information above into the formula.

[tex]V = \pi (2^{2})(8)[/tex]

Step 3) Solve.

[tex]V = \pi (2^{2})(8)[/tex]  [tex]=100.53[/tex]

Step 4) Round if necessary.

[tex]100.53 = 101[/tex]

Answer:

There are 10 possible digits that could appear on the license plate: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Half of these digits (1, 3, 5, 7, and 9) are odd.

Since there are three digits on the license plate, there are 10x10x10 = 1000 possible license plates.

To find the probability that the last digit is odd, we need to find the number of license plates where the last digit is odd and divide by the total number of possible license plates:

Number of license plates where last digit is odd = 10x10x5 = 500 (since there are 5 odd digits to choose from for the last digit)

Total number of possible license plates = 10x10x10 = 1000

So the probability of selecting a license plate at random where the last digit is an odd number is:

500/1000 = 0.5 or 50%

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The number οf hοurs fοr Shandra wοrking tο wash car is 2 hοurs.

The number οf hοurs fοr Shandra wοrking tο walking dοgs is 9 hοurs.

Mathematical expressiοn is defined as the cοllectiοn οf the numbers variables and functiοns by using οperatiοns like additiοn, subtractiοn, multiplicatiοn, and divisiοn.

Given that;

Shandra is wοrking twο summer jοbs, making $9 per hοur washing cars and $8 per hοur walking dοgs.

Last week Shandra wοrked a tοtal οf 11 hοurs.

Tοtal earned = $90

Nοw,

Tοtal number οf hοurs tο wash car = x

Tοtal number οf hοurs tο walk dοgs = y

Sο, We can fοrmulate;

⇒ 9x + 8y = $90  ... (I)

And, x + y = 11   .. (ii)

Sοlve equatiοn (i) and (ii) we get;

x = 2 hοurs and y = 9 hοurs

Sο, The number οf hοurs fοr Shandra wοrking tο wash car is 2 hοurs.

The number οf hοurs fοr Shandra wοrking tο walking dοgs is 9 hοurs.

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The possible length, width, and perimeter for Small cage's floor is 4 feet, 3 feet and 14 feet respectively; for Medium cage's floor is 12 feet, 2 feet and 28 feet respectively and for Large cage's floor is 18 feet, 2 feet and 40 feet respectively.

What is perimeter?

Whether it be a two-dimensional shape or a one-dimensional length, a perimeter is a closed path that contains, surrounds, or delineates it.

We are given the floor areas of each cage.

For Small cage:

Area is given as 12 square feet which is a product of length and width.

So, here length can be 4 feet and width can be 3 feet.

Now, we get the perimeter as

⇒ Perimeter = 2 * (Length + width)

⇒ Perimeter = 2 * (4 + 3)

⇒ Perimeter = 2 * 7

⇒ Perimeter = 14 feet

For Medium cage:

Area is given as 24 square feet which is a product of length and width.

So, here length can be 12 feet and width can be 2 feet.

Now, we get the perimeter as

⇒ Perimeter = 2 * (12 + 2)

⇒ Perimeter = 2 * (14)

⇒ Perimeter = 28 feet

For Large cage:

Area is given as 36 square feet which is a product of length and width.

So, here length can be 18 feet and width can be 2 feet.

Now, we get the perimeter as

⇒ Perimeter = 2 * (18 + 2)

⇒ Perimeter = 2 * (20)

⇒ Perimeter = 40 feet

Hence, the required solution has been obtained but there are many other combinations possible.

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The value of x for the intersecting chords is equal to 44°

The property of intersecting chords states that in a circle, if two chords intersect, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

x = (124° - 36°)/2

x = 88°/2

x = 44°

Therefore, the value of x for the intersecting chords is equal to 44°.

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Lily increased the amount of protein she eats by 12.5% by eating every day from 48 g to 54 g.

How to calculate percentage for the given problem?

To find the percentage increase in the amount of protein that Lily eats, we can use the following formula:

Percentage increase = ((new value - old value) / old value) x 100%

Using this formula and plugging in the values given in the problem, we get:

Percentage increase = ((54 - 48) / 48) x 100%

Percentage increase = (6 / 48) x 100%

Percentage increase = 0.125 x 100%

Percentage increase = 12.5%

Therefore, Lily increased the amount of protein she eats by 12.5%.

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Using division, we can prove that there are models that we can use to prove 7 divided by 2 is = 7/2.

A division is one of the fundamental mathematical operations that divides a larger number into smaller groups with the same number of components. How many groups will be created, for instance, if a sports event requires that 30 students be divided into groups of 5 students. The division operation makes it simple to tackle such issues. Divide 30 by 5 in this case. The outcome is 30 x 5 = 6. There will thus be 6 groups, each with 5 pupils. By multiplying 6 by 5, which yields the initial figure of 30, you can confirm this value.

Here in the question,

We have to model to find 7 divided by 2 = 7/2.

For the two math classes, 7 pizzas have been delivered.

Half of the first pizza is distributed to each class.

A half of the second pizza is distributed to each class.

Third pizza, cut in half, with half going to each class.

Continue until each class receives 7 halves, or 7/2, of the pizzas that were delivered.

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Answer:

The tip was $14

Answer:

Step-by-step explanation:

(2+3) x 3 + 8/2 = 5 X 3 + 8/2 = 15 + 4 = 19

The total costs of the 6 notebooks and 4 dry-erase markers that Roselyn buys are $19.70.

The total costs can be determined using mathematical operations.

The first mathematical operation used is the multiplication operation, involving the multiplicand and the multiplier, to determine the total cost of each item.

The second mathematical operation is the addition operation to determine the grand total.

Notebook: 1.95

Dry erase markers: 2.00

Notebook: $11.70 ($1.95 x 6)

Dry erase markers: $8.00 ($2.00 x 4)

Total costs = $19.70

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The price of each item is listed below

notebook: 1.95

dry erase markers: 2.00

What are the total costs?

Answer:

A/First picture

Step-by-step explanation:

The line touches the y axis at 3, as indicated by the +3 in the equation. In addition, the -1/2x indicated a downwards line.

Answer:

the first photo

Step-by-step explanation:

I hope this helps

Answer:

Step-by-step explanation:

What is a rectangular prism?

A right rectangular prism is a box-shaped object, that is, a 3-dimensional solid which has six rectangular faces. Rectangular prisms can also be oblique - leaning to one side - but the side faces are parallelograms, not rectangles. A right rectangular prism is also called a cuboid, box, or rectangular hexahedron. Moreover, "rectangular prism" and "right rectangular prism" are often used interchangeably.

The most common math problems related to this solid are of the type right rectangular prism calc find V or find A, where the letters stand for the Volume and Area, respectively. Let's see the necessary rectangular prism formula and learn how to solve those problems quickly and easily.

How do I find the volume of a rectangular prism?

The rectangular prism volume formula is:

volume = h × w × l,

where h is prism height, w is its width, and l is its length. To calculate the volume of a cardboard box:

Find the box length. For example, it can be equal to 18 in.

Determine its width. Let's say you measured 12 in.

Find out the rectangular prism height. Assume it's 15 in.

Calculate the cuboid volume. Using the rectangular prism volume formula above, we get volume = (18 × 12 × 15) in = 3240 in³.

How do I find the area of a rectangular prism?

The surface area of the cuboid consists of 6 faces - three pairs of parallel rectangles. To find the rectangular prism surface area, add the areas of all faces:

surface_area = 2 × (h × w) + 2 × (h × l) + 2 × (l × w) = 2 × (h × w + h × l + l × w),

where h is prism height, w is its width, and l is its length.

Let's see an example of how to solve the right rectangular prism calc - find A problem. We'll come back to our example with the box and calculate its surface area:

Calculate the rectangular prism surface area. First rectangle area is 15in × 12in = 180in², second 15in × 18in = 270in² and third one 18in × 12in = 216in². Add all three rectangles' areas - it's equal to 666 in² (what a number!) - and finally multiply by 2. The surface area of our cardboard box is 1332in².

Or save yourself some time and use our rectangular prism calculator.

Finally, let's attack the right rectangular prism calc find d (that is, the diagonal) type of problem.

How do I calculate the diagonal of a rectangular prism?

To determine the diagonal of a rectangular prism, apply the formula:

diagonal = √(l² + h² + w²)

where h is prism height, w is its width, and l is its length.

Do you have the feeling that you saw the formula before? Yes, that's possible because this equation resembles the famous one from the Pythagorean theorem.

Answer: Reread the lesson and then you will figure it out

Step-by-step explanation:

The two cars will be 380 miles apart after 3.5 hours after the first car leaves based on distance formula.

The formula for distance, which is rate times time, must be used to address this issue. Let x be the number of hours following the departure of the first car. The distances between the two cars are increasing since they are moving in different directions.

The first thing we must do is determine how far the first car, which left at 3:00 p.m., drove. When the rate is 55 miles per hour and the time is x hours, we may use the calculation distance = rate x time. Hence, the first car's mileage was 55 miles.

The second step is to determine how far the second car, which left at 4:00 p.m., travelled. When the speed is 75 miles per hour and the time is x - 1 hours, we can apply the same calculation (since the second car left one hour later than the first). Thus, the second car's mileage is 75(x - 1) miles.

The sum of the distances covered by each car is the overall distance between the two vehicles. So that we can create an equation:

distance of first car + distance of second car = total distance

55x + 75(x - 1) = 380

Simplify:

55x + 75x - 75 = 380

Combining:

130x = 455

Divide sides by 130 to obtain:

x = 3.5

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The answer is (A) The Ratio Test says that the series converges absolutely.

What is the ratio test?

The Ratio Test is a test used to determine whether an infinite series converges or diverges. It involves taking the limit of the absolute value of the ratio of the (n+1)th term to the nth term as n approaches infinity. If the limit is less than 1, then the series converges absolutely.

We have:

[tex]|a_{n+1}/a_{n}| = |(e^(n+7)*sqrt(n+3)/((n+4)!)) / (e^(n+6)*sqrt(n+2)/((n+3)!))|[/tex]

[tex]|a_{n+1}/a_{n}| = e(sqrt(n+3)/sqrt(n+2)) * (n+3)/(n+4)[/tex]

We want to compute:

[tex]L = lim n- > infinity |a_{n+1}/a_{n}| = lim n- > infinity e(sqrt(n+3)/sqrt(n+2)) * (n+3)/(n+4)[/tex]

We can see that the exponent of e goes to 1 as n goes to infinity, and (n+3)/(n+4) goes to 1 as n goes to infinity. Therefore, L = 1.

Since L < 1, by the Ratio Test, the series converges absolutely.

Hence, the answer is (A) The Ratio Test says that the series converges absolutely.

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The complete statement is: Tina can select and answer the essay questions on her test in 10 ways.

Tina has to answer any 2 of 5 questions, which means she needs to choose 2 questions out of the 5 available questions.

The number of ways to choose r items from a set of n items is given by the combination formula:

C(n,r) = n! / (r!(n-r)!)

In this case, n = 5 (the total number of questions) and r = 2 (the number of questions that Tina needs to choose).

So we can plug in these values to get:

C(5,2) = 5! / (2!(5-2)!)

C(5,2) = (5 x 4 x 3 x 2 x 1) / [(2 x 1) x (3 x 2 x 1)]

C(5,2) = (5 x 4) / (2 x 1)

C(5,2) = 10

Therefore, Tina can select and answer the essay questions on her test in 10 ways.

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Therefore, Andrey's score was 65.4. Therefore, Susan's score was 79.

Standard deviation is a statistical measure that represents the amount of variation or dispersion in a set of data values. It measures the average distance of each data point from the mean of the data set. A low standard deviation indicates that the data points tend to be close to the mean, while a high standard deviation indicates that the data points are more spread out. It is calculated by taking the square root of the variance, which is the average of the squared differences of each data point from the mean. Standard deviation is commonly used in fields such as finance, engineering, and psychology to analyze and compare data sets.

Here,

a. To find Andrey's score, we need to use the formula:

z = (x - μ) / σ

where z is the number of standard deviations from the mean, x is the score, μ is the mean, and σ is the standard deviation.

Andrey was told that he scored 1.2 standard deviations below the mean, so we have:

z = -1.2

μ = 75

σ = 8

Plugging these values into the formula, we get:

-1.2 = (x - 75) / 8

Multiplying both sides by 8, we get:

-9.6 = x - 75

Adding 75 to both sides, we get:

x = 65.4

b. Similarly, to find Susan's score, we have:

z = 0.5

μ = 75

σ = 8

Plugging these values into the formula, we get:

0.5 = (x - 75) / 8

Multiplying both sides by 8, we get:

4 = x - 75

Adding 75 to both sides, we get:

x = 79

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"The spread of the data distribution for Lake Mockingbird is 5 inches bigger than the spread of the data distribution for Lake Warbler," is the answer to question 2.

The graphs do not support this statement since the difference in spread between the two lakes is not represented as 5 inches. The right answer to question 1 is B: "The spread of the data distribution for Lake Mockingbird is approximately 40% higher than the spread for Lake Warbler." This is due to the fact that the data distribution of the Lake Mockingbird is around 60 inches (from 5 to 65), whereas the data distribution of the Lake Warbler is approximately 43 inches (from 2 to 45). The difference between the two ranges is approximately 60 - 43 = 17. inches. From 43 to 60, the percentage rise is around 39.5%, which is close to 40%. The correct answer to question 3 is B: "The distribution of Lake Mockingbird reveals a center that is 3 inches greater than the distribution of Lake Warbler." This assertion is false since the graphs do not show the center of each distribution and cannot be established with the information supplied. Based on the data in the graphs, the other claims are correct.

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The surface area of the composite figure is 944 cm².

What is the surface area of a cuboid?

Surface area of a cuboid is (lb+lh+bh) where l,b,h are length, breadth and height of the cuboid.

To find the surface area of the composite figure, we need to calculate the surface area of both cuboids and then subtract the area of any faces that are shared by both cuboids.

Given dimension of first cuboid is 14 cm × 8 cm × 2 cm and dimension of the second cuboid is 8 cm × 6 cm × 4 cm.

Surface area of the first cuboid:

Area of the top and bottom faces = 2(14 x 8) = 224 cm²

Area of the front and back faces = 2(14 x 2) = 28 cm²

Area of the left and right faces = 2(8 x 2) = 32 cm²

Total surface area of the first cuboid = 2(224) + 2(28) + 2(32) = 576 cm²

Surface area of the second cuboid:

Area of the top and bottom faces = 2(8 x 6) = 96 cm²

Area of the front and back faces = 2(8 x 4) = 64 cm²

Area of the left and right faces = 2(6 x 4) = 48 cm²

Total surface area of the second cuboid = 2(96) + 2(64) + 2(48) = 416 cm²

Now we need to identify the faces that are shared by both cuboids. The first cuboid has a bottom face that is the same size as the top face of the second cuboid (6 x 4). The surface area of this shared face is 48 cm².

Therefore, the surface area of the composite figure is total surface area of the first cuboid + Total surface area of the second cuboid - Area of shared face

= 576 + 416 - 48

= 944 cm²

So the surface area of the composite figure is 944 cm².

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[tex] \:\:\:\:\:\:\longrightarrow \sf \underline{P = 2 ( x +y)}\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf\underline{Perimeter_{(rectangle) } = 2 ( Height +Base)\: unit}\\[/tex]

Where-

As per question, we are given that -

We are asked to find out the value of perimeter for the given rectangle. Now that we have all the required values, so we can put them into the formula and solve for the perimeter -

[tex] \:\:\:\:\:\:\longrightarrow \sf\underline{Perimeter_{(rectangle) } = 2 ( Height +Base)\: unit}\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf Perimeter_{(rectangle) } = 2\bigg(10+9\bigg)\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf Perimeter_{(rectangle) } = 2 \times 19\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf \underline{Perimeter_{(rectangle) }=38 \:ft }\\[/tex]