A rectangle has a length of x + 4 cm and a width of 2x − 7 cm.
(a) If the perimeter is 36cm, what is the value of x?
(b) What is the area of this rectangle

6 inches will be the length of the patio.

According to the scale, 1 inch on the plan corresponds to 3.5 feet in real life.

We must convert the patio's real length of 21 feet to inches using the scale in order to determine how long it would look on the blueprint:

3.5 feet to one inch

21 feet in x inches

If we cross-multiply, we obtain:

1 inch/3.5 feet * 21 feet

= x inches

= 6 inches.

As a result, the length of the patio will be indicated on the blueprint as 6 inches.

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The work done in stretching the spring from 10 cm to 40 cm is 10,837.5 J.

The work done in stretching a spring is given by the formula:

W = (1/2)k[tex]x^{2}[/tex]

where W is the work done, k is the spring constant, and x is the displacement of the spring from its original position.

To find the spring constant k, we can use the given information:

F = kx

where F is the force applied to the spring. Rearranging this equation, we get:

k = F/x

Substituting the given values, we get:

k = 350 N / 30 cm = 11.67 N/cm

Now, we can find the work done in stretching the spring from 10 cm to 40 cm:

W = (1/2)k([tex](x_{2})^{2} -(x_{1} )^{2}[/tex])

where [tex]x_{1}[/tex] is the initial displacement of the spring (10 cm) and [tex]x_{2}[/tex] is the final displacement (40 cm).

Substituting the values, we get:

W = (1/2) * 11.67 N/cm * ([tex](40 cm)^{2} - (10 cm)^{2}[/tex])

W = (1/2) * 11.67 N/cm * (1600  [tex]cm^{2}[/tex] - 100  [tex]cm^{2}[/tex])

W = (1/2) * 11.67 N/cm * 1500 [tex]cm^{2}[/tex]

W = 10,837.5 joules (J)

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The scale factοr is οne-half. The perimeter οf the mοdel is the prοduct οf the scale factοr and the perimeter οf the οriginal rectangle. The area οf the reduced figure is (1/2)² = 1/4 times the area οf the οriginal figure

The ratiο between cοmparable measurements οf an οbject and a representatiοn οf that οbject is knοwn as a scale factοr in mathematics.

Here,

We have tο cοmpare the perimeter and area οf the οriginal figure tο the perimeter and area οf the reduced figure using the scale factοr.

The ratiο οf the length οf the οriginal rectangle tο that οf the reduced rectangle is 6 tο 3 οr a factοr οf 1/2.

The ratiο οf the width οf the οriginal rectangle tο that οf the reduced rectangle is 2 tο 1, οr, again, a factοr οf 1/2. Sο, because this ratiο οf 1/2 is cοnstant, we knοw the tοtal scale factοr is 1/2, making B cοrrect.

16 ×(1/2) = 8, which means that the perimeter οf the scale-factοred, reduced rectangle is "the prοduct οf the scale factοr and the perimeter οf the οriginal rectangle". Sο, C is cοrrect.

Hence,  The scale factοr is οne-half.

The perimeter οf the mοdel is the prοduct οf the scale factοr and the perimeter οf the οriginal rectangle.

The area οf the reduced figure is (1/2)² = 1/4 times the area οf the οriginal figure.

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those attending the party ate 4 1/2 pounds of candy in total.

How to solve the question?

To solve this problem using an array model on graph paper, we can draw a rectangular array with 2 1/4 rows and 3 1/2 columns. Each cell in the array represents a 1/4 pound of candy. The total number of cells in the array will give us the total amount of candy eaten.

To start, we can divide each row into four equal parts to represent 1/4 pound of candy. We can also divide each column into two equal parts to represent 1/2 pound of candy. Then, we can shade in the cells that represent the amount of candy eaten.

Starting with the first row, we shade in two full rows and an additional half row, representing 2 1/2 bags of candy. Then, in the second row, we shade in two full columns and an additional half column, representing 2 1/4 bags of candy.

When we count the total number of shaded cells in the array, we see that there are 18 cells shaded. Each cell represents 1/4 pound of candy, so we can multiply 18 by 1/4 to get the total amount of candy eaten:

18 * 1/4 = 4 1/2 pounds

Therefore, those attending the party ate 4 1/2 pounds of candy in total.

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Thus, the volume of cylinder with the given height and diameter is found as 1413 ft³.

A cylinder is three-dimensional. It's not a flat thing. There are parallel circular bases in this shape. These bases have a curved face affixed to them. A cylinder in this instance has three faces. Along both end of a curved face, which rounds back to the face's origin, are two spherical bases.

Given that-

Volume of cylinder = πr²h

Volume of cylinder = 3.14 *5²*18

Volume of cylinder = 3.14*25*18

Volume of cylinder = 1413 ft³

Thus, the volume of cylinder with the given height and diameter is found as 1413 ft³.

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An equation which is true include the following: A. 4 × n × n × n × n = 4n⁴.

In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By applying the multiplication law of exponents for powers to each of the expressions, we have the following:

4 × n × n × n × n = 4n⁴

4 × n⁴ = 4n⁴

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If Laurel received a 1099 form from her bank for her savings account interest in the amount of $690 and a 1099 form from an employer that she did some consulting work for in the amount of $2,600, then Laurel's taxable income is calculated as  $98,580.

Taxable income refers to the base upon which an income tax system imposes tax.

We deduct the following;

Wages reported on W-2 =  $100,750

Interest income reported on 1099=  $690

Consulting income reported on 1099= $2,600

Therefore, her total income = $100,750 + $690 + $2,600 = $104,040

Laurel's allowable deductions include:

FSA contributions: $30 per week x 52 weeks = $1,560

Retirement plan contributions: $75 per week x 52 weeks = $3,900

Total deductions = $1,560 + $3,900 = $5,460

Laurel's taxable income  is found as

= Total income - Total deductions

= $104,040 - $5,460

= $98,580

In conclusion, Laurel's taxable income is $98,580.

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The surface area of the prism is 426 m²

A cuboid is a rectangular prism. And has all the properties related to a prism. The general formula for the surface area of a cuboid is ;

SA = 2B + ph

We can use net formula to find the surface area of a cuboid.

surface area of a cuboid is expressed as;

SA = 2( lb+lh +bh)

l = 12m , b = 5m and h = 9m

lb = 12×5 = 60m²

lh = 12 × 9 = 108m²

bh = 5×9 = 45m²

SA = 2(60+108+45)

= 2(213)

= 426 m²

therefore the surface area of the cuboid is 426m²

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The training wheel has an area approximately 286.34 square inches smaller than the regular wheel.

The area of a circle is given by the formula A = πr², where A is the area of the circle and r is the radius of the circle. Since we have the radii of both wheels, we can use this formula to find their respective areas.

The area of the training wheel is A₁ = π(3)² = 9π square inches.

The area of the regular wheel is A₂ = π(10)² = 100π square inches.

To find the difference in their areas, we can subtract A₁ from A₂:

A₂ - A₁ = 100π - 9π = 91π

So the difference in their areas is 91π square inches. To round to the nearest hundredth, we can use the approximation π ≈ 3.14:

91π ≈ 286.34 square inches

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If over what interval does f(x) = 2x increase faster than g (X): A. 1

To determine over what interval f(x) = 2x increases faster than g(x) = x^2, we need to compare their derivatives. The derivative of f(x) is 2, which is a constant, and the derivative of g(x) is 2x. Therefore, f(x) increases at a constant rate of 2, while g(x) increases at a rate that depends on x.

To find the interval where f(x) increases faster than g(x), we need to find where the derivative of g(x) is less than 2. Setting 2x < 2 and solving for x, we get x < 1.

So, over the interval x < 1, f(x) = 2x increases faster than g(x) = x^2.

Therefore, the answer is A. 1.

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There are 462 different possible lineups of 5 songs that can be composed from the given list of 11 songs.

We need to use the idea of combinations to figure out how many different lineups of musical entertainment can be made. A way to select objects from a larger set without regard to their order is called a combination.

In this problem, we have to choose five songs from an 11-song list. We would like to know how many different ways there are for us to select five songs from the eleven that are available, where the order of the songs in the lineup is irrelevant. We can use the combination formula to solve this.:

n choose k = n! / (k! * (n - k)!)

where n is the total number of items to choose from, k is the number of items to choose, and ! denotes factorial, which is the product of all positive integers up to and including that number.

In this case, we have 11 songs to choose from and we want to choose 5 songs. So we can plug these values into the formula:

11 choose 5 = 11! / (5! * (11 - 5)!)

= (11 * 10 * 9 * 8 * 7) / (5 * 4 * 3 * 2 * 1)

= 11,880 / 120

= 462

Consequently, there are 462 unique potential setups of 5 tunes that can be created from the given rundown of 11 melodies.

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To create a consistent and dependent system with the equation x - y = -2, we need to find another equation that has the same solution as this equation.

We can manipulate the equation x - y = -2 to get y = x + 2.

Now, we can substitute y = x + 2 into each of the given equations to see which one creates a dependent system:

6x + 2y = 15 becomes 6x + 2(x + 2) = 15, which simplifies to 8x = 11. This equation has no solution, so it does not pair with x - y = -2 to create a dependent system.

-3x + 3y = 6 becomes -3x + 3(x + 2) = 6, which simplifies to 0 = 0. This equation has infinitely many solutions and pairs with x - y = -2 to create a dependent system.

-8x - 3y = 2 becomes -8x - 3(x + 2) = 2, which simplifies to -11x = -8. This equation has a unique solution, so it does not pair with x - y = -2 to create a dependent system.

4x - 4y = 6 becomes 4x - 4(x + 2) = 6, which simplifies to -4 = 6. This equation has no solution, so it does not pair with x - y = -2 to create a dependent system.

Therefore, the equation -3x + 3y = 6 can pair with x - y = -2 to create a consistent and dependent system.

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We can compare and contrast the primary differences between the Job costing and Process costing processes as follows:

Job costing process:

Process costing:

We can classify the cost types by understanding their usage in the accounting industry. Process costing is used for calculating the costs for mass-produced materials while job costing is used for calculating the cost for customized products.

Process costing is used for accumulating costs and to ascertain the flow of costs through accounts. Job costing is the main document for tracking costs.

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In the formula, A is the amount after interest, P is the principal, r is interest rate in decimals, n is the amount of times the interest is compounded per year, and t is the amount of years.

a. Statistical question about vacation destinations: What percentage of people who traveled for vacation last year went to a beach destination?

Data that is descriptive but not numerical is considered qualitative data. It is frequently used to describe the qualities or traits of things, people, or occasions. Qualitative data examples include hues, textures, tastes, and perspectives.

On the other hand, quantitative data are numerical data that can be measured and statistically analysed. It is frequently used to describe numbers or amounts of different things. Measurements like height, weight, temperature, and test results are examples of quantitative data.

a. Statistical question about vacation destinations: What percentage of people who traveled for vacation last year went to a beach destination?

b. Statistical question about books: What is the average number of books read per month by individuals who report reading as a favorite hobby?

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Answer: PSD

Step-by-step explanation: perfectly symmetrical distribution

Hannon's maximum allowable production cost for the All-Body swimsuit is $80 if it wants to make a profit of $20 per unit.

Given data ,

a)

Using cost-plus pricing, the selling price is set 20% above the costs.

Selling price=Costs+(Costs x Markup)

Selling price=$100 + ($100x0.20)

Selling price=$100+$20

On simplifying the equation , we get

Selling price=$120

The price charged for the All-Body swimsuit would be$120.

Hannon might consider manufacturing the All-Body swimsuit under the cost-plus pricing approach if the market demand is strong enough to justify the selling price of $120 and if Hannon can efficiently produce and sell the swimsuit to generate profits.

(b)

Using target costing, the price charged by Hannon to the retailer is determined by subtracting the desired profit per unit from the target selling price.

Target selling price=$100 (given)

Desired profit per unit=$20 (given)

Price charged to retailer=Target selling price - Desired profit per unit

Price charged to retailer=$100-$20

On simplifying the equation , we get

Price charged to retailer=$80

The price that Hannon would charge the retailer for the All-Body swimsuit under target costing is$80.

(c)

To determine the highest acceptable manufacturing cost for the All-Body swimsuit under target costing, we subtract the desired profit per unit from the target selling price.

Target selling price=$100 (given)

Desired profit per unit=$20 (given)

Highest acceptable manufacturing cost=Target selling price-Desired profit per unit

Highest acceptable manufacturing cost=$100-$20

Highest acceptable manufacturing cost=$80

Hannon would be ready to spend up to $80 in manufacturing costs to develop the All-Body swimsuit if it wanted to make $20 each unit.

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The bearing of B from P is N24.65°E (or S24.65°W), and the ship is approximately 33.54 nautical miles from the port.

Since the ship travels at a constant speed, we can use the formula:

distance = speed × time

For the first hour, the ship travels at a bearing of S80°E, which is equivalent to a bearing of N10°E. Therefore, the ship travels 15 nautical miles in a direction N10°E. This gives us:

PA = distance = speed × time = 15 × 1 = 15 nautical miles

After the first hour, the ship turns 90° towards the North. This means that the ship is now heading due East. Therefore, for the next 2 hours, the ship travels 15 × 2 = 30 nautical miles in an easterly direction. This gives us:

AB = distance = speed × time = 15 × 2 = 30 nautical miles

Now, we can use the Pythagorean theorem to find the value of y:

y² = x² + (AB)²

y² = 15² + 30²

y² = 225 + 900

y² = 1125

y ≈ 33.54 nautical miles

To find the bearing of B from P, we can use trigonometry. The bearing is the angle between the line PA and due North. Let θ be this angle. Then we have:

tan(θ) = x / y

θ = tan^-1(x / y)

Using the values we have found, we get:

tan(θ) = 15 / 33.54

θ ≈ 24.65°

Therefore, the bearing of B from P is N24.65°E (or S24.65°W), and the ship is approximately 33.54 nautical miles from the port.

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Answer is down below!

Step-by-step explanation:

This is of the form h = a + b cos ct, where: a = 40 m. This is the height of the axle of the Ferris wheel. b = -30 m. The magnitude of this number is the radius of the wheel.

The total possible points in the course is approximately 470.

Let's assume that the total possible points in the course is "x".

Since you needed 90% of the course total for an A, that means you needed to earn 90% of "x" to get an A. This is equivalent to 0.90x.

You missed an A by only 8 points, so your actual earned points must be 90% of "x" minus 8. This can be expressed as 0.90x - 8.

Given that your actual earned points for the course is 415, we can set up an equation:

0.90x - 8 = 415

Now, we can solve for "x" to determine the total possible points in the course:

0.90x = 415 + 8

0.90x = 423

x = 423 / 0.90

x ≈ 470

So, the total possible points in the course is approximately 470.

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The vertical component of the particle's location, when its horizontal component is 2, is:

y = -1.25

To find the vertical component of the particle's location when its horizontal component is 2, we need to first find the value of t when x = 2.

Given the equation:

x = 3sin(t)

Substitute x with 2:

2 = 3sin(t)

Now, isolate t by dividing both sides by 3:

sin(t) = 2/3

Take the inverse sine (arcsin) of both sides:

t = arcsin(2/3)

Now, plug the value of t back into the y equation:

y = t - 4cos(t) + 1

y = arcsin(2/3) - 4cos(arcsin(2/3)) + 1

Using a calculator to find the approximate value of y, we get:

y ≈ -1.25

Therefore, the vertical component of the particle's location when its horizontal component is 2 is:

y = -1.25

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If prices are rising, I would choose to use the FIFO (first-in, first-out) cost flow assumption. This is because under FIFO, the earliest inventory items purchased are assumed to be sold first, leaving the more recently purchased, and therefore higher-priced, items in inventory. As a result, the cost of goods sold (COGS) will be based on the lower, earlier purchase prices, resulting in higher net income and, therefore, a higher year-end bonus.

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Answer:

The inequality v ≥ 3 can be satisfied by any number greater than or equal to 3, such as 4, 5, 6.7 etc. The smallest value that will make the inequality true is 3 itself. As long as the number chosen for v is greater than or equal to three then it will satisfy the given equation and make it true.

Step-by-step explanation:

The values that make the inequality v ≥ -3 make true are -3, -2.99, -2.9, and 0.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

We have the inequality v ≥ -3.

Here the inequality shows that the value is equal to greater than -3.

1. -11 < -3.

2. -8 < -3

3. -6 < -3

4. -4< -3

5. -3.1< 3

6. -3.01 < -3

7. -3.001 < -3

8. -3 = -3

9. -2.999 > -3

10. -2.99 > -3

11. -2.9 > -3

12. 0 > -3

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Answer:

  b 12, 14, 16

Step-by-step explanation:

You want the next three terms of a sequence that starts 6, 8, 10, ....

The rule seems to be "add 2." If we continue to add 2 to each term, we find the next terms to be ...

  10 +2 = 12

  12 +2 = 14

  14 +2 = 16

The next 3 terms are 12, 14, 16.

__

Additional comment

Without the figure, the idea of "add one column" is meaningless. Since answers are in terms of dot counts, it would be more meaningful to describe the pattern in terms of what happens to the dot count.

The features of function g if g(x) = -f(x)-1 include the following:

B. domain of (0, ∞).

C. vertical asymptote of x = 0.

D. x-intercept at (1/2, 0).

In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following key features:

Domain = (0, ∞)

Range = (-∞, ∞).

vertical asymptote, x = 0.

x-intercept = (1/2, 0).

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Answer:

B. (2, 2)

Step-by-step explanation:

(x, y)

3x = 8 - y

a) 3(3) = 8 - 1

9 = 8 - 1

9 = 7  False

b) 3(2) = 8 - 2

6 = 6  True

c) 3(8) = 8 - 0

24 = 8 False

Answer:

10y + 17

Step-by-step explanation:

1) (given): 3(6y+5) — 2(4y — 1)

2) (distributive property): 18y + 15 - 8y + 2

3) (combine like terms): 10y + 17

The values of b and c include the following:

c = 8

b = 4√3

In order to determine the length of b, we would apply the law of tangent because the given side lengths represent the adjacent side and opposite side of a right-angled triangle.

Tan(θ) = Opp/Adj

Where:

Therefore, we have the following tangent trigonometric function:

Tan(θ) = Opp/Adj

Tan(30°) = 4/b

√3/3 = 4/b.

b = 4√3

From Pythagorean Theorem, the length of c is given by;

c² = (4√3)² + 4²

c² = 48 + 16

c = √64

c = 8

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.