Simplify the rational expression
7x/14x^6

The solution to the problem at hand i.e. to draw a horizontal line segment, OM, of any length, the longer the better using ruler, protractor, compass and coloured pencils

are as follows:

Step 1: Take a ruler and align it with a sheet of paper and draw a line. This line can be of any length, although longer lines are preferred.

Step 2: The line is now OM; we must now label its endpoints. Label the leftmost point O, and the rightmost point M.

Step 3: The coloured pencils are used to add decorations to the line. To add decorations, use coloured pencils to make patterns and stripes along the length of the line. This is entirely optional and based on personal preference.

Step 4: To ensure that the line is perfectly horizontal, the protractor should be used. Place the protractor on the line and make sure the zero-degree angle is at O. The line will be horizontal if it is parallel to the baseline of the paper.

Step 5: Using a compass, measure the length of OM to ensure that it is of the desired length.

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The quotient of[tex](6x/(3x+15)) / ((x^2+2x)/ (x^2+7x+10))[/tex] is 2x.

To simplify the expression[tex](6x/(3x+15)) / ((x^2+2x)/ (x^2+7x+10)),[/tex] we can use the rule for dividing fractions, which states that dividing by a fraction is the same as multiplying by its reciprocal.

Let's simplify the expression :

Simplify the numerator and denominator of the first fraction.

The numerator is 6x, and the denominator is (3x+15).

We can factor out a common factor of 3 from the denominator, which gives us 3(x+5).

So the first fraction simplifies to 6x / 3(x+5).

Simplify the numerator and denominator of the second fraction.

The numerator is (x^2+2x), and the denominator is [tex](x^2+7x+10).[/tex]

We can factor both the numerator and denominator:

Numerator: x(x+2)

Denominator: (x+5)(x+2)

Canceling out the common factor of (x+2), we are left with x / (x+5).

Multiply the two simplified fractions.

Multiplying the fractions, we get:

[tex](6x / 3(x+5)) \times (x / (x+5))[/tex]

Simplify the resulting expression.

Canceling out the common factor of (x+5) in the numerator and denominator, we are left with:

2x / 1

So the quotient simplifies to 2x.

Therefore, the quotient of [tex](6x/(3x+15)) / ((x^2+2x)/ (x^2+7x+10))[/tex] is 2x.

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The total volume of the 21 bowling balls is 6048π cubic inches.

We have,

To find the total volume of the 21 bowling balls, we first need to calculate the volume of a single ball and then multiply it by the number of balls.

The volume of a sphere can be calculated using the formula:

V = (4/3) x π x r³

where V is the volume and r is the radius of the sphere.

Given that the diameter of the bowling ball is 12 inches, the radius can be calculated as half of the diameter:

r = 12/2 = 6 inches

Now we can calculate the volume of a single ball:

V_ball = (4/3) x π x (6³) = (4/3) x π x 216 = 288π cubic inches

Since there are 21 balls, we can calculate the total volume by multiplying the volume of a single ball by the number of balls:

Total volume = 21 x 288π = 6048π cubic inches

Thus,

The total volume of the 21 bowling balls is 6048π cubic inches.

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The point B that partitions the segment AC into a 2:3 ratio is B (4.6, 9.6). To find the point B that partitions the segment AC into a 2:3 ratio, we can use the concept of section formulas or the concept of ratios of the coordinates.

Let's assume the coordinates of point B are (x, y). We can calculate the coordinates of point B using the following steps:

Step 1: Calculate the differences in the x and y coordinates between points A and C:

Δx = x-coordinate of C - x-coordinate of A = 5 - 3 = 2

Δy = y-coordinate of C - y-coordinate of A = 11 - 4 = 7

Step 2: Divide the differences by the sum of the ratios (2 + 3 = 5) to get the ratios of the segments AB and BC:

Ratio_AB = (2/5)[tex]\times[/tex] Δx = (2/5) [tex]\times[/tex]2 = 4/5

Ratio_BC = (3/5) [tex]\times[/tex] Δx = (3/5) [tex]\times[/tex] 2 = 6/5

Step 3: Apply the ratios to the coordinates of point A to find the coordinates of point B:

x-coordinate of B = x-coordinate of A + Ratio_AB [tex]\times[/tex] Δx = 3 + (4/5)[tex]\times[/tex]2 = 3 + 8/5 = 23/5

y-coordinate of B = y-coordinate of A + Ratio_AB [tex]\times[/tex]Δy = 4 + (4/5) [tex]\times[/tex] 7 = 4 + 28/5 = 48/5

Therefore, the coordinates of point B are (23/5, 48/5).

In decimal form, the coordinates of point B are approximately (4.6, 9.6).

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Answer:

[A'] = {c,d,f,g,h,i,j,k,m,n,p,q,u,w,x,z}

Step-by-step explanation:

[A'] is read as the set of A complement, which is all the elements from the universal set that are not contained in set A.

Therefore, [A'] = {c,d,f,g,h,i,j,k,m,n,p,q,u,w,x,z}

The distance of Satellite B from the Earth is approximately 4915.71 kilometers.

To determine the distance of Satellite B from the Earth, we can use the concept of similar triangles.

Let's break down the problem step by step:

We have a triangle formed by Satellite A, Satellite B, and the center of the Earth.

Let's call the center of the Earth point O, Satellite A point A, and Satellite B point B.

Since Satellite A orbits closer to the Earth, its distance from the center of the Earth is equal to the radius of the Earth plus the distance from Satellite A to Satellite B.

Let's call this distance OA.

OA = Radius of the Earth + Distance from Satellite A to Satellite B

OA = 6371 km + 21185.5 km

OA = 27556.5 km

Now, we need to find the distance of Satellite B from the Earth. Let's call this distance OB.

We know that OA and OB form a triangle, and they are parallel to the side AB.

Since the triangle formed by OA, OB, and AB is similar to the triangle formed by OA, AB, and the radius of the Earth, we can set up a proportion to find OB.

OA / AB = Radius of the Earth / OB

OB = (Radius of the Earth x AB) / OA

OB = (6371 km x 21185.5 km) / 27556.5 km

OB ≈ 4915.71 km

Therefore, the distance of Satellite B from the Earth is approximately 4915.71 kilometers.

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It will take John approximately 2.69 hours to paint the room alone.

Let's denote the individual rates of John, Rick, and Molli as J, R, and M, respectively. We are given the following information:

John, Rick, and Molli can paint the room together in 5 hours.

Molli alone can paint the room in 14 hours.

Rick alone can paint the room in 10 hours.

To find the equation comparing the group rate to the sum of the individual rates, we can use the concept of work done. The amount of work required to paint the room is the same, regardless of who is doing the work.

The equation can be expressed as:

1/5 = 1/J + 1/R + 1/M

Now, let's substitute the given information into the equation. We know that:

M = 14 (since Molli can paint the room alone in 14 hours)

R = 10 (since Rick can paint the room alone in 10 hours)

Substituting these values, the equation becomes:

1/5 = 1/J + 1/10 + 1/14

To solve for J, we can find the least common denominator (LCD) of 10 and 14, which is 70:

14J + 7J + 5J = 70

26J = 70

J = 70/26

J ≈ 2.69

Therefore, it will take John approximately 2.69 hours to paint the room alone.

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The possible combinations of women to the total number of club members could be:

7 women out of 10 members.

14 women out of 20 members.

21 women out of 30 members.

28 women out of 40 members.

And so on, as long as "x" is a multiple of 10 that is divisible by 7.

The ratio of women to men in the local book club is 7 to 3. This means that for every 7 women, there are 3 men.

To find the possible combinations of women to the total number of club members, we can consider the total number of members as a multiple of 10 (since the ratio is given as 7 to 3). Let's assume the total number of club members is represented by the variable "x."

Based on the given ratio, we can calculate the number of women in terms of "x" by multiplying the ratio of women (7/10) by the total number of members:

Number of women = (7/10) * x

Since we're looking for possible combinations, the number of women must be a whole number. Therefore, "x" must be a multiple of 10 that is divisible by 7.

Let's explore some possible combinations:

If x = 10, the number of women = (7/10) * 10 = 7, which satisfies the ratio.

If x = 20, the number of women = (7/10) * 20 = 14, which satisfies the ratio.

If x = 30, the number of women = (7/10) * 30 = 21, which satisfies the ratio.

If x = 40, the number of women = (7/10) * 40 = 28, which satisfies the ratio.

As you can see, the possible combinations of women to the total number of club members could be:

7 women out of 10 members.

14 women out of 20 members.

21 women out of 30 members.

28 women out of 40 members.

And so on, as long as "x" is a multiple of 10 that is divisible by 7.

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The length of the arc can be obtained as follow:

Length of arc = 2πr × (θ / 360)

Length of arc = (2 × π × 7) × (210 / 360)

Length of arc = 49π / 6 ft (option D)

How do i determine the area of the sector?

i. The area of the sector can be obtained as shown below:

Area of sector = πr² × (θ / 360)  

Area of sector = (π × 19²) × (135 / 360)  

Area of sector = 1083π / 8 in² (option D)

ii. The area of the sector can be obtained as shown below:

Area of sector = πr² × (θ / 360)  

Area of sector = (π × 10²) × (165 / 360)  

Area of sector = 275π / 6 m² (option B)

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The numbers -7, -5, -3, 3, -1, and 1 can be arranged into three pairs with the same total (-7, 7), (-5, 5), (-3, 3), (-1, 1).

To arrange the numbers -7, -5, -3, 3, -1, and 1 into three pairs with the same total, we need to find a combination of pairs that will give us the same sum for each pair.

Let's start by examining the numbers:

-7, -5, -3, 3, -1, 1

To find pairs with the same total, we can start by pairing the numbers with their additive inverses (numbers that sum to zero). In this case, -7 and 7, -5 and 5, -3 and 3 can be paired up. This leaves us with -1 and 1.

We have three pairs now: (-7, 7), (-5, 5), (-3, 3). However, we still have -1 and 1 remaining. To make the sum of the pairs equal, we can pair -1 with 7 and 1 with -5.

The three pairs with the same total are:

(-7, 7), (-5, 5), (-3, 3), (-1, 1).

Each pair sums up to zero, resulting in the same total for each pair. For example, (-7 + 7 = 0), (-5 + 5 = 0), and so on.

Therefore, the numbers -7, -5, -3, 3, -1, and 1 can be arranged into three pairs with the same total:

(-7, 7), (-5, 5), (-3, 3), (-1, 1).

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y = 3x - 1: consistent, independent

2y - 6x = 4: consistent, independent

2y = -x + 6: consistent, independent

4y + 2x = 12: consistent, independent

y = 2x + 3: consistent, independent

x + y = -9: consistent, dependent

y = 3x - 1 and 2y = -x + 6: inconsistent

Let's match each system on the left with the appropriate words that describe the system on the right:

y = 3x - 1: consistent, independent

This system represents a linear equation with a unique solution. The equations are not multiples of each other, and they intersect at a single point.

2y - 6x = 4: consistent, independent

Similar to the first system, this represents a linear equation with a unique solution. The equations are not multiples of each other, and they intersect at a single point.

2y = -x + 6: consistent, independent

This system also represents a linear equation with a unique solution. The equations are not multiples of each other, and they intersect at a single point.

4y + 2x = 12: consistent, independent

Like the previous systems, this represents a linear equation with a unique solution. The equations are not multiples of each other, and they intersect at a single point.

y = 2x + 3: consistent, independent

This system represents a linear equation with a unique solution. The equations are not multiples of each other, and they intersect at a single point.

x + y = -9: consistent, dependent

This system represents a linear equation with infinitely many solutions. The equations are multiples of each other, meaning they represent the same line. Therefore, any point on the line satisfies both equations.

y = 3x - 1 and 2y = -x + 6: inconsistent

This system represents inconsistent equations that do not have a common solution. The lines represented by the equations are parallel and do not intersect.

To summarize the matches:

y = 3x - 1: consistent, independent

2y - 6x = 4: consistent, independent

2y = -x + 6: consistent, independent

4y + 2x = 12: consistent, independent

y = 2x + 3: consistent, independent

x + y = -9: consistent, dependent

y = 3x - 1 and 2y = -x + 6: inconsistent

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The restriction of a function f is when the domain of f is limited to a subset of its original domain.

The restriction of a function f can be demonstrated by considering a function f: R -> R, where R represents the set of real numbers.

Let u say f(x) = x^2. Now, if we restrict the domain of f to the interval [0, 5], the new function becomes f restricted: [0, 5] -> R and its expression would be f restricted(x) = x^2 for x in the interval [0, 5].

This means that the function f restricted only takes inputs from the interval [0, 5] and behaves the same way as the original function within that interval.

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The scale factor of the dilation is 4.

We are given that;

The equation of line −11x=4y+4

Now,

The center of dilation is the origin (0, 0). The line given by −11x = 4y + 4 can be rewritten as y = −11/4 x − 1. This means that it passes through the points (0, −1) and (−4, 0). The image of the line after dilation is given by −11x − 4y = 16, which can be rewritten as y = −11/4 x − 4. This means that it passes through the points (0, −4) and (−16, 0).

To find the scale factor, we can use any pair of corresponding points. For example, let’s use (0, −1) and (0, −4). The distance from the center of dilation to (0, −1) is 1 unit. The distance from the center of dilation to (0, −4) is 4 units. Therefore, the scale factor is 4/1 = 4.

Therefore, by dilation the answer will be 4

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Hence the surface area of the given figure 168 km².

In the given prism contains

3 rectangular surface,

For rectangular surface 1:

Length = 6 km

Width = 7 km

Surface area = 6x7

                      = 42 km²

For rectangular surface 2:

Length = 8 km

Width = 7 km

Surface area = 8x7

                      = 56 km²

For rectangular surface 3:

Length = 10 km

Width = 7 km

Surface area = 10x7

                      = 70 km²

Hence total surface area of the given figure is,

⇒ 42 + 56 + 70

⇒ 168 km²

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The person will need approximately 28 square yards of material for the tent.

To calculate the amount of material needed, we first need to determine the total surface area of the tent.

The tent has six sides: a top, a bottom, a front, a back, and two sides. The top and bottom are both 10 feet by 5 feet, so their combined area is 10 feet x 5 feet = 50 square feet each.

The front and back are both 10 feet by 5 feet, so their combined area is also 10 feet x 5 feet = 50 square feet each.

The two sides are both 5 feet by 5 feet, so their combined area is 5 feet x 5 feet = 25 square feet each.

To find the total surface area, we add up all these areas:

Top and bottom: 50 square feet + 50 square feet = 100 square feet

Front and back: 50 square feet + 50 square feet = 100 square feet

Sides: 25 square feet + 25 square feet = 50 square feet

Total surface area: 100 square feet (top and bottom) + 100 square feet (front and back) + 50 square feet (sides) = 250 square feet

Since the material is sold in square yards, we need to convert square feet to square yards.

There are 9 square feet in 1 square yard.

So, 250 square feet / 9 = 27.78 square yards.

Rounding up to the nearest square yard, the person will need approximately 28 square yards of material for the tent.

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Experimental probability depends on Ted's frequency in the new set of names. The total number of names chosen also affects it. Theoretical probability is influenced by the total number of possible outcomes based on the number of names in the hat. If the number of names increases, the chance of choosing Ted decreases.

To find the experimental probability of choosing the name Ted, we divide the number of times Ted was chosen by the total number of names chosen.

Experimental probability = Number of times Ted was chosen / Total number of names chosen

Given that Ted was chosen 19 times out of 119 total selections, we can calculate the experimental probability:

Experimental probability = 19 / 119

Simplifying, we find that the experimental probability of choosing the name Ted is approximately 0.1597 or about 15.97% (rounded to the nearest hundredth).

To find the theoretical probability of choosing the name Ted, we divide the number of favorable outcomes (choosing Ted) by the total number of possible outcomes.

Theoretical probability = Number of favorable outcomes / Total number of possible outcomes

In this case, there are 9 different names in the hat, and Ted is one of them. Therefore, the theoretical probability of choosing Ted is:

Theoretical probability = 1 / 9

Simplifying, the theoretical probability of choosing the name Ted is approximately 0.1111 or about 11.11% (rounded to the nearest hundredth).

If the number of names in the hat were different, both the experimental and theoretical probabilities would change.

For the experimental probability, the number of times Ted is chosen would change based on the frequency of Ted in the new set of names. The total number of names chosen would also change.

For the theoretical probability, the total number of possible outcomes would change based on the number of names in the hat. If there were more names, the probability of choosing Ted would decrease. Conversely, if there were fewer names, the probability of choosing Ted would increase.

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The factorization of[tex]8(p-q)^3-(p+q)^3 is 8(p-q)^3 - (p+q)^3 is [p - 3q][7p^2 - 8pq + 3q^2].[/tex]

The given expression is[tex]8(p-q)^{3}-(p-q)^{3}[/tex]

To factorize this expression, we can use the identity for the difference of cubes, which states that [tex]a^3 - b^3 = (a - b)(a^2 + ab + b^2).[/tex]

Let's apply this identity to the given expression:

[tex]8(p-q)^3 - (p+q)^3 = [2(p-q)]^3 - (p+q)^3.[/tex]

Now we can see that we have a difference of cubes:[tex](2(p-q))^3 - (p+q)^3.[/tex]

Using the identity, we can factorize this expression as follows:

[tex][(2(p-q)) - (p+q)][(2(p-q))^2 + (2(p-q))(p+q) + (p+q)^2].[/tex]

Simplifying further:

[tex][2p - 2q - p - q][(2(p-q))^2 + (2(p-q))(p+q) + (p+q)^2].[/tex]

Combining like terms:

[tex][p - 3q][(2(p-q))^2 + 2(p-q)(p+q) + (p+q)^2].[/tex]

Expanding the squared term:

[tex][p - 3q][4(p^2 - 2pq + q^2) + 2(p^2 - q^2) + (p^2 + 2pq + q^2)].[/tex]

Simplifying:

[tex][p - 3q][4p^2 - 8pq + 4q^2 + 2p^2 - 2q^2 + p^2 + 2pq + q^2].[/tex]

Combining like terms again:

[tex][p - 3q][7p^2 - 8pq + 3q^2].[/tex]

Therefore, the factorization of [tex]8(p-q)^3 - (p+q)^3 is [p - 3q][7p^2 - 8pq + 3q^2].[/tex]

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There were 600 downloads of the standard version.

An equation means the formula that expresses the equality of two expressions by connecting them with the equals sign.

Let x represents the number of downloads of the standard version.

Given:

Size of the standard version = 2.4 MB

Size of the high-quality version = 4.2 MB

Total download size = 4716 MB

Total downloads = 1380

We will set up the following equation:

2.4x + 4.2(1380 - x) = 4716

2.4x + 5796 - 4.2x = 4716

-1.8x + 5796 = 4716

-1.8x  = 4716 - 5796

-1.8x = -1080

x = 600

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Let's denote crew A's work per week as A and crew B's work per week as B.

We are given that A = 58 ft per week and B = 59 ft per week.

We have to calculate how many weeks it will take both crews to complete the tunnel.

585 feet have already been dug from the south end. So, the total tunnel length that needs to be dug is 7605 - 585 = 7020.

Now, let's assume that both the crews continue to work at their respective rate of A = 58 ft/week and B = 59 ft/week.

Therefore, total tunnel length that needs to be dug in weeks = (7020 ft) / (A + B)

                       =  (7020 ft) / (58 ft/week + 59 ft/week)

                       =  120.20 weeks

Hence, it will take a total of 120.20 weeks for both crews to complete the tunnel.

The reason that is NOT typically used in a proof is two angles being congruent. Option C.

Among the options A, B, C, and D, the reason that is NOT typically used in a proof is option C: two angles being congruent.

Congruence is a fundamental concept in geometry that refers to the equality of shape and size. When two angles are congruent, it means they have the same measure. While congruence is an important concept used in geometric proofs, it is typically not used as a standalone reason in a proof.

In geometric proofs, various properties, theorems, and postulates are used to establish relationships and make deductions. Let's briefly discuss the other options:

A. Definition of supplementary angles: This is a valid reason that is commonly used in proofs involving supplementary angles. The definition states that if the sum of two angles is 180 degrees, they are considered supplementary.

B. Substitution property: The substitution property is a logical property used in algebraic proofs. It allows us to replace one expression with another expression that is equal to it. This property is often employed when simplifying equations or substituting known values.

D. Parallel lines: The concept of parallel lines is frequently utilized in geometric proofs, particularly in proving angles and angle relationships. Properties such as alternate interior angles, corresponding angles, and vertical angles are established based on the parallel lines. Option C is correct.

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For an item with a marked price of Rs. 26,600 and a 10% discount, the discount price is Rs. 2,660. Therefore, the customer will pay Rs. 23,940 after applying the discount.

To calculate the amount of discount on an item with a marked price of Rs. 26,600 and a discount percentage of 10%, we can follow a simple formula.

First, let's calculate the discount amount. The discount percentage is 10%, which means we can find the discount amount by multiplying the marked price by the discount percentage:

Discount amount = Marked price × Discount percentage

= Rs. 26,600 × 10/100

= Rs. 2,660

So, the discount amount for the item is Rs. 2,660.

Now, let's understand what this means. A discount is a reduction in the original price of an item. In this case, the discount amount of Rs. 2,660 is the amount by which the price of the item is reduced. Therefore, after applying the discount, the customer would only need to pay Rs. 26,600 - Rs. 2,660 = Rs. 23,940.

It's important to note that the discount amount is not the final price the customer pays. The final price is the marked price minus the discount amount. So, in this scenario, the customer will receive a discount of Rs. 2,660, and they will pay Rs. 23,940 for the item.

Understanding how discounts work can be helpful when making purchasing decisions or comparing prices. It allows customers to evaluate the value they are receiving and make informed choices based on their budget and preferences.

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Probable question:

What is the amount of the discount if the marked price of an item is Rs. 26,600 and the discount percentage is 10%?

Answer:

b) graph pass through origin for both.

c) mario would take 5minutes to have more balloons filled than tanesha

Answer:        -0.7

Step-by-step explanation:

Answer:Peggy will spend approximately $363.52 constructing the pond and patio in her backyard. The correct answer is not provided among the options given (A, B, C).

Step-by-step explanation:

To calculate the cost of constructing the pond and patio in Peggy's backyard, we need to determine the areas of the pond and patio and then multiply them by their respective costs per square foot.

From the given scale, we can convert the dimensions of the pond and patio from centimeters to feet. According to the scale, 1 cm represents 5 ft.

Patio dimensions:

Width: 2 cm (2 cm * 5 ft/cm = 10 ft)

Length: 2 cm (2 cm * 5 ft/cm = 10 ft)

Area of patio = Width * Length = 10 ft * 10 ft = 100 ft²

Pond dimensions:

Width: 4 cm (4 cm * 5 ft/cm = 20 ft)

Length: 4 cm (4 cm * 5 ft/cm = 20 ft)

Area of pond = π * (Width/2)² = π * (20 ft/2)² = π * 10 ft² ≈ 31.42 ft²

Cost calculation:

Cost of pond = Area of pond * Cost per square foot = 31.42 ft² * $6/ft² = $188.52

Cost of patio = Area of patio * Cost per square foot = 100 ft² * $1.75/ft² = $175.00

Total cost = Cost of pond + Cost of patio = $188.52 + $175.00 = $363.52

The value of x in the given figure is 8.

In the given figure there are two lines which are parallel.

We have to find the value of x.

In the straight line the sum of angles is 180 degrees.

8x+1+115=180

8x+116=180

Subtract 116 from both sides:

8x=180-116

8x=64

Divide both sides by 8:

x=64/8

x=8

Hence, the value of x in the given figure is 8.

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The volume of the cylinder is 98π cubic centimeters.

To find the volume of a cylinder, we use the formula:

Volume = π × [tex]r^2[/tex] × h

Given:

Radius (r) = 7 cm

Height (h) = 2 cm

Substituting the values into the formula, we have:

Volume = π × (7 [tex]cm)^2[/tex] × 2 cm

Calculating the values inside the parentheses:

Volume = π × 49 [tex]cm^2[/tex] × 2 cm

Multiplying the values:

Volume = 98π [tex]cm^3[/tex]

Therefore, the volume of the cylinder is 98π cubic centimeters.

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Collecting the like terms in the expression 5z - 7 - 13z + 35 gives -8z + 28

From the question, we have the following parameters that can be used in our computation:

5z - 7 - 13z + 35

Consider an expression given as

Ax + Bx

Where A and B are constants and x is a variable

The terms Ax and Bx are like terms

using the above as a guide, we have the following:

5z - 7 - 13z + 35 = 5z - 13z - 7 + 35

Evaluate the like terms

5z - 7 - 13z + 35 = -8z + 28

Hence, collecting the like terms gives -8z + 28

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Susan has 875 grams of grapes left.

1. Susan bought a 1 kilogram bag of grapes, which is equivalent to 1000 grams (since there are 1000 grams in a kilogram).

2. Susan ate 125 grams of the grapes on her way home.

3. To find out how many grams of grapes Susan has left, we need to subtract the amount she ate from the initial weight of the bag. Therefore, we subtract 125 grams from 1000 grams.

  1000 grams - 125 grams = 875 grams

4. Thus, Susan has 875 grams of grapes left.

measurement units:

In this problem, we used grams as the measurement unit. Grams are commonly used to measure the weight of small objects like grapes. Since the problem stated that Susan bought a 1 kilogram bag of grapes, it was necessary to convert the kilogram measurement to grams.

This conversion was done by multiplying the kilogram value by 1000 (1 kilogram = 1000 grams). By using the correct measurement units, we were able to accurately calculate the amount of grapes Susan had left after eating a portion.

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The cumulative frequency to be used in solving the 28th percentile is 16.

Cumulative frequency is described as  the total of a frequency and all frequencies in a frequency distribution until a certain defined class interval.

we add up the frequencies until we reach or exceed 28% of the total data set in order to find the cumulative frequency for the 28th percentile.

Total frequency = 4 + 9 + 16 + 10 + 9 + 2 = 50

28th percentile = (28/100) * Total frequency

28th percentile = (28/100) * 50 = 14

We start from the beginning of the distribution and add up the frequencies until we reach or exceed 14 so as to find the cumulative frequency.

In conclusion, and with reference to the given data set we notice that the cumulative frequency exceeds 14 at the 91-120 minute interval = 16.

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The volume of the prisms are:

1. 432 yd³

2. 36in³

3. 252 m³

4. 240 ft³

5. 576 mm³

6. 144 cm³

7. 343 m³

8. 120 yd³

9. 150 in³

The formula for calculating the volume of a rectangular prism is expressed as;

V = lwh

such that;

Now, substitute the value for each of the prisms, we have;

1. Volume = 6 × 6 ×12

Multiply

Volume = 432 yd³

2. Volume = 2 ×9 × 2

Multiply

Volume = 36in³

3. Volume = 9 × 4 × 7

Multiply

Volume = 252 m³

4. Volume = 10 × 8 × 3

Multiply

Volume = 240 ft³

5. Volume = 4 × 12 × 12

Multiply the values

Volume = 576 mm³

6. Volume = 6 × 8 × 3

Volume = 144 cm³

7. Volume = 7 × 7 ×7

Volume = 343 m³

8. Volume = 8 × 3 × 5

Volume = 120 yd³

9. Volume = 5 × 6 × 5

Volume = 150 in³

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