Multiply. State any restrictions on the variable. (x^(2)+5x-36)/(x^(2)+4x-32)*(4x+32)/(x+6)

Answer:

90 cm²

Step-by-step explanation:

Let the greater side be the length L and the smaller side the width W

Given L : W = 5 : 2

we can rewrite this as a fraction

[tex]\dfrac{L}{W} = \dfrac{5}{2}[/tex]

Cross-multiplying we get
2L = 5W

The perimeter of a rectangle
= 2(L + W)
= 2L + 2W
and we are told it is 42 cm

Therefore
2L + 2W = 42

Substitute 5W for 2L to get

5W + 2W = 42
7W = 42

or

W = 42/6 = 6

Given 2L + 2W = 42, substitute 6 for W to get

2L + 2(6) = 42

2L + 12 = 42

2L = 42 - 12= 30

L = 30/2 = 15

So length  L = 15

Just to check
L/W = 15/6 = 5/2  by dividing both numerator and denominator by 3

Area of the rectangle
= L x W

= 15 x 6

= 90 cm²

The minimum number of people in the group should be 3.

In a group more than 1/2 are boys but there are less than 2/3 of the group.

Let the number of people in the group be x.

Therefore, the number of boys in the group is greater than 1/2 × x or x/2.

The number of people in the group is less than 2/3 × x or 2x/3.

As per the question, x > x/2 and x < 2x/3

multiply both sides by 2,

so we get:

2x > x and 2x < 4x/3.

Now, simplify the above equations as follows:

2x > x ⇒ x > 0 and

2x < 4x/3 ⇒ 6x < 4x ⇒ 0 < -2x ⇒ x < 0

Thus, it is not possible to have a group of 4 people as the number of people in the group is greater than 0.

Therefore, the minimum number of people in the group should be 3.

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From the given data in the question, the circumference of a circle is 31.42 centimeters then the area of the circle is 78.5 cm².

To find the area of a circle with a given circumference, we need to use the formula:

Circumference = 2πr

where π is the mathematical constant pi (approximately 3.14) and r is the radius of the circle. In this case, the circumference is given as 31.42 centimeters. So we can write:

31.42 = 2πr

To solve for r, we can divide both sides by 2π:

r = 31.42 / (2π)

r = 5

So the radius of the circle is 5 centimeters.

Now, to find the area of the circle, we can use the formula:

Area = πr²

Substituting the value of r, we get:

Area = π(5²)

Area = 25π

Area = 78.5 square centimeters

Therefore, the area of the circle with a circumference of 31.42 centimeters is approximately 78.5 square centimeters.

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Answer:

34m

Step-by-step explanation:

To find:-

Answer:-

We are here given that Elizabeth climbed up the mountain vertically 30m , and the distance between frank and the bottom of the mountain is 30m .

We are interested in finding out the distance between frank and Elizabeth. For that we will have to use Pythagoras theorem , in which;

[tex]\rm\implies a^2+b^2 = h^2 \\[/tex]

Where h is the longest side of the triangle and a and b are two other sides. here we need to find out the longest side ( see attachment) .

So on substituting the respective values, we have;

[tex]\rm\implies h^2 = (16m)^2+(30m)^2 \\[/tex]

[tex]\rm\implies h^2 = 256m^2 + 900m^2 \\[/tex]

[tex]\rm\implies h^2 = 1156m^2\\[/tex]

[tex]\rm\implies h =\sqrt{1156 \ m^2} \\[/tex]

[tex]\rm\implies \red{h = 34 m} \\[/tex]

Hence the distance between Elizabeth and Frank is 34m .

Using the speed formula, the coordinates to plot on the graph are (0, 0), (1, 60), (2, 120), (3, 180), and (4, 240).

What is the speed?

Speed is defined as the distance traveled per unit of time. It is the slope of the distance vs time graph. The formula for speed is:

Speed = Distance / Time

Where:

Speed is the speed of the object, usually expressed in units such as meters per second (m/s)

Distance is the distance traveled by the object, usually expressed in units such as meters

Time is the duration of travel, usually expressed in units such as seconds

To graph the relationship between the time and the distance traveled by the car, we can use the following formula:

Distance Traveled = Rate x Time

In this case, the rate (or speed) of the car is 60 miles per hour, and the distance traveled is a function of time.

So we can write the equation as:

Distance Traveled = 60 x Time

To graph this equation, we can plot a series of points using different values of time. For example:

At 0 hours, the distance traveled is 0 miles. Coordinate: (0, 0)

At 1 hour, the distance traveled is 60 miles. Coordinate: (1, 60)

At 2 hours, the distance traveled is 120 miles. Coordinate: (2, 120)

At 3 hours, the distance traveled is 180 miles. Coordinate: (3, 180)

At 4 hours, the distance traveled is 240 miles. Coordinate: (4, 240)

These points can be plotted on a graph with time on the x-axis and distance traveled on the y-axis. The resulting graph would be a straight line with a slope of 60 (which represents the rate or speed of the car) and passing through the origin (0, 0).

So the coordinates to plot on the graph are:

(0, 0), (1, 60), (2, 120), (3, 180), (4, 240)

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25 bottles every minute are filled using a filling and capping machine in [tex]11700[/tex]

Even though both pressures and movements are involved in a machine's functioning, one of its principal functions can either be force amplification or motion modification. A lever essentially adds force, but a gearbox often acts as a speed reducer.

A machine diagram represents a function operation on a variable x to create a variable output y diagrammatically. If x falls inside the scope of the f(x, the machine will accept x as an input and output y in accordance with the function's rules.

[tex]25 bottles/minute * 20 minutes = 500 bottles.[/tex]

During the remaining [tex]280[/tex] minutes, both machines are running and together they fill

[tex]25 bottles/minute + 15 bottles/minute = 40 bottles/minute[/tex]

So, the total number of bottles filled during this period is

[tex]40 bottles/minute * 280 minutes = 11,200 bottles.[/tex]

[tex]500+ 11,200= 11,700[/tex]

None of the given options represents this equation.

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Answer:

Ill help you figure out how to graph.

Step-by-step explanation:

The value in front of x (like 2x or 7x) is the slope (rise over run) rise is how much the line goes up, and run is how much it goes to the side. the second number (in the bottom left graph, it is -5) is the y intercept. it is where the line crosses the y axis. (in this case on -5) Here is an example. (of the problem y=x-5)

The expressions that represent the perimeter and area of the cornfield are: Perimeter = 14y + 12x,Area = 42xy

What is Area of rectangle ?

Area of rectangle can be defined as product of length and breadth of a rectangle.

The given expression represents the dimensions of a rectangular cornfield, where one side measures 7y units and the other side measures 6x units.

The perimeter of a rectangle is the sum of the lengths of all its sides. Therefore, the perimeter of this cornfield is:

P = 2(7y) + 2(6x) = 14y + 12x

To find the area of a rectangle, we multiply its length by its width. Therefore, the area of this cornfield is:

A = (7y) (6x) = 42xy

Therefore, the expressions that represent the perimeter and area of the cornfield are: Perimeter = 14y + 12x,Area = 42xy

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Answer : 6 Dollars

Explanation :  4.00 × 20/100 = 0.8 + 4 = 4.8 * 25/100 = 6

Answer : 6 doolarz                ThanK me

Answer: 7.4

Step-by-step explanation:

The value at the 60th percentile is 72°F. According to the given question.

What is whisker plot?

A whisker plot, also known as a box and whisker plot, is a graphical representation of a dataset that shows the distribution of values. It is often used to summarize and compare datasets, and to identify outliers or extreme values.

The plot is constructed using a rectangular box that represents the middle 50% of the data (the interquartile range or IQR). The box extends from the lower quartile (the value below which 25% of the data falls) to the upper quartile (the value below which 75% of the data falls). A line inside the box represents the median (the value below which 50% of the data falls).

Part A:

Here is a box and whisker plot representing the given data:

   |                   +                       |

75 -+                          +            |

   |                    |                       |

70 -+                |                       |

   |                    |                       |

65 -+-------------+-------------------+

   |  S  M  T  W |  T  F  S           |

The plot is divided into four sections: the lowest 25% of the data (the lower quartile), the next 25% of the data (the second quartile or median), the next 25% of the data (the third quartile), and the highest 25% of the data (the upper quartile). The box represents the middle 50% of the data, and the whiskers extend to the lowest and highest values that are not outliers.

Part B:

To determine which value is at a given percentile, we need to sort the data in ascending order and count how many values are less than or equal to the percentile we are interested in. Then we find the corresponding value in the sorted list.

For example, to find the value at the 60th percentile, we first calculate 60% of the total number of values, which is:

0.60 * 7 = 4.2

Since we cannot have a fraction of a value, we round up to the next integer, which is 5. This means that the value at the 60th percentile is the fifth value in the sorted list:

65, 66, 68, 70, 72, 74, 75

Therefore, the value at the 60th percentile is 72°F.

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Operating a 100-watt lamp for a week when the power utility rate is 16 cents/k

Wh can be calculated as follows:

Power of the lamp = 100 watts

Time of usage = 1 week = 7 days

Power utility rate = 16 cents/kWh

1 kW = 1000 watts

Power consumed by lamp = 100 watts

Total time of usage in hours = 7 days x 24 hours/day = 168 hours

Energy consumed = Power x Time= 100 watts x 168 hours= 16,800

watt-hours (Wh) = 16.8 kWh

Cost of operating the lamp = Energy consumed x Power utility rate= 16.8 kWh x 16 cents/k

Wh= 2.688 dollars= $2.7 (approx)

Therefore, the cost of operating a 100-watt lamp continuously for 1 week when the power utility rate is 16 cents/kWh is approximately $2.7 using two significant figures.

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The answer is B hope it helps

Answer:

Two objects are similar if they have the same shape.

(1): Two objects are similar if they have the same shape.

(2): Two objects are congruent if they have the same shape and size.

(3): Two objects are congruent if they have the same shape and size.

(4): Two objects are congruent if they have different shapes and sizes.

Hope this helps! I'm sorry if it's wrong. If you need more help, ask me! :]

After addressing the issue at hand, we can state that by function  Katherine now has 28 quarters.

Mathematicians investigate numbers and their varieties, equations and adjacent tissues, shapes but instead their locations, and potential locations for these things. The term "function" refers to the relationship here between set of inputs, each with its own output. A function is a relationship of both inputs and outputs in which each input results in a single, distinct production. Each function has its own domain, codomain, or scope. The letter f is commonly used to denote functions (x). An x represents entry. On functions, each capabilities, so several capabilities, in capabilities, and on operations are the four major types of accessible functions.

Let's represent the unknown quantities with variables.

Let d be the number of dimes Katherine possesses.

Let q represent Katherine's number of quarters.

We can deduce from the problem:

Equation 1: Total dimes and quarters value = $8.60 0.10d + 0.25q = 8.60

Number of quarters = Number of dimes + 12 q = d + 12 Equation 2:

Now we can plug equation 2 into equation 1 to eliminate q and find d:

0.10d + 0.25(d + 12) = 8.60

Katherine now has 16 dimes.

We can use equation 2 to calculate the number of quarters:

q = d + 12 = 16 + 12 = 28

Katherine now has 28 quarters.

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Antonio painted about 27% of the wall with melon color, 33% with green color, and 40% with white color.

Antonio painted a wall with an area of 15 square meters. He painted 4 square meters with melon color, 5 square meters with green color, and 6 square meters with white color.

To find the fraction of the wall that Antonio painted with each color, we need to divide the area painted with each color by the total area of the wall:

Fraction painted with melon color = 4 / 15 = 0.2666... ≈ 0.27

Fraction painted with green color = 5 / 15 = 0.3333... ≈ 0.33

Fraction painted with white color = 6 / 15 = 0.4

So Antonio painted about 27% of the wall with melon color, 33% with green color, and 40% with white color.

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Complete Question:

Antonio is participating in the restoration of the communal room. He paints a wall of 15m² in the following way: 4m² of melon color, 5m² of green color, and 6m² of white color. What fraction of the wall does he paint with each color? EXPRESS EACH OF THE FRACTIONS IN THE EXERCISE IN DECIMAL NOTATION.

Norris living room table is a trapezoid shape with a bottom length of 613.5 inches, a top length of 11.3 inches, and a height of 12 inches.

To find the area of the tabletop, we need to calculate the average of the lengths of the top and bottom, and then multiply that by the height.

Average of lengths = (613.5 + 11.3)/2 = 312.4 inches

Area of table top = (312.4) x 12 = 3748.8 square inches

Since one can of paint covers 12 square inches, we can find the number of cans of paint needed by dividing the area of the table top by the coverage per can:

Number of cans of paint = 3748.8/12 = 312.4 cans

However, we need to round up to the nearest whole can, so Norris needs to buy 313 cans of paint to cover the entire table top.

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Answer:

[tex]\boxed{ \$600}[/tex]

Step-by-[tex]\boxed{/$600}[/tex]step explanation:

El enunciado nos dice que toda la tienda cuenta con 20% de descuento, así que por cada artículo paga el 80% de su valor (100%-20%).

Una forma rápida de resolver el ejercicio es con regla de 3.

[tex]\$750 \Rightarrow 100 \% \newline x \Rightarrow 80\%[/tex]

para encontrar [tex]x[/tex]:

[tex]x=\frac{80*750}{100} \\x=\$600[/tex]

Por lo que la cantidad que termina pagando por el vestido es de $600.00

[tex]\text{-B$\mathfrak{randon}$VN}[/tex]

Trigonometry is a branch of mathematics that deals with the relationships and properties of triangles, particularly the relationships between their sides and angles.

1) sin 30 = 10/u

u = 10/sin 30

u = 20

Cos 30 = v/20

v = 20cos 30

v = 17

2) cos 30 = 4√3/m

m = 4√3/√3/2

m = 4√3 * 2/√3

m = 8

Sin 30 = n/8

n = 8 sin 30

n = 4

3) sin 60 = x/7

x = 7 sin 60

x = 6

Cos 60 = y/7

y = 7 Cos 60

y = 3.5

4) Tan 30 = v/10√3

v = 10√3 * 1/√3

v = 10

Cos 30 = 10√3/u

u = 10√3/Cos 30

u = 10√3/√3/2

u = 10√3 * 2/√3

u = 20

5)  Sin 60 = x/6√3

x = 6√3Sin 60

x = 6√3 * √3/2

x = 3

Cos 60 = y/6√3

y = Cos 60 * 6√3

y = 6√3 * 1/2

y = 3√3

6) Sin 60 = x/4√2

x = Sin 60 * 4√2

x = 4√2 * √3/2

x = 2√6

Cos 60 = y/4√2

y = Cos60 * 4√2

y = 1/2 * 4√2

y = 2√2

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The Bianca will contribute 14.6 works of art, and Claire will contribute 8.7 works of art.

a. In order to find each person's optimal number of art works, one must solve for the point at which the marginal benefit and the marginal cost intersect. For Alice, that point is when N = 7 and MBA = MCA, resulting in an optimal number of works of art of 7. For Bianca, the intersection point is when N = 14 and MBB = MCB, resulting in an optimal number of works of art of 14. For Claire, the intersection point is when N = 8.3 and MBC = MCC, resulting in an optimal number of works of art of 8.3.

b. Without considering altruism, Alice will contribute 7 works of art, Bianca will contribute 14 works of art, and Claire will contribute 8.3 works of art.

c. With altruism, the optimal number of art works for each individual can be calculated in the same way as without altruism, but with the warm-glow benefit added to their respective total marginal benefits. For Alice, that point is when N = 7.3 and TMBA = MCA, resulting in an optimal number of works of art of 7.3. For Bianca, the intersection point is when N = 14.6 and TMBB = MCB, resulting in an optimal number of works of art of 14.6. For Claire, the intersection point is when N = 8.7 and TMBC = MCC, resulting in an optimal number of works of art of 8.7.

d. With altruism, Alice will contribute 7.3 works of art, Bianca will contribute 14.6 works of art, and Claire will contribute 8.7 works of art.

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Answer:

Step-by-step explanation:

To see which bag is the better buy, calculate how much each pound of rice would cost.

To do that divide the price by the amount of costs for each then compare those numbers

$2.25/3 = $0.75 per pound

$6.66/9 = $0.74 per pound

So the 9 pound bag of rice would cost 1 cent less per pound making it the better buy.

The quantity of  shrink wrap that will be used to wrap ten game cubes is 540 square inches

To calculate the amount of shrink wrap needed to wrap ten game cubes, we need to first find the surface area of one game cube, and then multiply it by 10.

The surface area of a cube can be found by multiplying the length of one side by itself, and then multiplying that by 6 (since there are six faces on a cube). In this case, the length of one side is 3 inches, so the surface area of one cube is:

Surface area of one cube = 3 x 3 x 6 = 54 square inches

To wrap ten cubes, we need to multiply the surface area of one cube by 10:

Surface area of ten cubes = 54 x 10 = 540 square inches

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Answer: 51.2 pounds

Step-by-step explanation: The problem states that 20% of the total cost is taken when you purchase more than 20 bottles.

We start by finding the total cost without the 20% off

Multiply the unit price by the number of bottles

[tex]1.60*40 = 64 pound[/tex]

Next use the discount, since we are getting 20% off we only have to pay 80% of it and 80/100 simplifies to 4/5 so we can just multiply 64 by that.

[tex]64*4/5 = 51.2[/tex]

The cost of buying 40 bottles of orange juice, with a 20% discount, is £51.20.

percentage, a relative value indicating hundredth parts of any quantity.

The cost of one bottle of orange juice is £1.60.

To find the cost of 40 bottles of orange juice

40 bottles x 1.60 per bottle = £64

The total cost without the discount would be £64.

To calculate the discount, we can multiply the total cost by 20% or 0.20:

Discount = 20% x £64 = £12.80

The discount on 40 bottles of orange juice is £12.80.

To find the final cost, we need to subtract the discount from the total cost:

Final cost = Total cost - Discount

= £64 - £12.80

= £51.20

Therefore, the cost of buying 40 bottles of orange juice, with a 20% discount, is £51.20.

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Therefore , the solution of the given problem of angle comes out to be  x = 30°.

In Euclidean geometry, the barrier's centre and top separate two spherical faces, which make both of the sides of a tilt. Two rays may combine to create an angle where they collide. Another result of two things interacting is an angle. They most closely resemble dihedral shape. Two line beams can be arranged in different ways at their extremities to form a two-dimensional curve.

Here,

Given : a line making angle with x axis:

We have to find the angle with x axis.

So,

=> tan x = p/b

=> tanx  = 1/√3

=> x = tan⁻¹(1/√3)

=> x = 30°

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Answer:

32:9

Step-by-step explanation:

64 :18

32: 9

So 32: 9 is its simplest form.

Answer:

32:9

Step-by-step explanation:

64 : 18

Divide both sides by a common number 2

32 : 9

This cannot be further divided

The area of the sector is equal to 40.89 cm².

Mathematically, the area of a sector can be calculated by using this formula:

Area of sector = θπr²/360

Where:

Substituting the given parameters into the area of a sector formula, we have the following;

Area of sector = θπr²/360

Area of sector = 30(3.14/360) × (12.5)²

Area of sector = 0.2617 × 156.25

Area of sector = 40.89 cm²

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If the demand and supply curves are given by y=10-3x³ and y=4+x²+2x, the equilibrium quantity is approximately 1.477 units, and the equilibrium price is approximately $5.44 per unit.

To find the equilibrium price and quantity, we need to find the point where the demand curve intersects the supply curve. At this point, the quantity demanded by consumers is equal to the quantity supplied by producers, which means that the market is in equilibrium.

We can set the two equations equal to each other to find the equilibrium quantity:

10 - 3x³ = 4 + x² + 2x

Simplifying the equation, we get:

3x³ + x² - 2x - 6 = 0

We can solve for x using algebraic methods or by using a graphing calculator. Either method will yield three roots for x, but only one of them will be positive and realistic in the context of the problem.

The positive root for x is approximately 1.477, which means that the equilibrium quantity is approximately 1.477 units.

To find the equilibrium price, we can substitute the equilibrium quantity into either the demand or supply equation. Let's use the demand equation:

y = 10 - 3(1.477)³

Solving for y, we get:

y ≈ 5.44

Therefore, the equilibrium price is approximately $5.44 per unit.

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The maximum value of the objective function is 33, which occurs at the corner point (3, 3)

According to the question we have to maximize 6x+5y (OBJ)Subject tox+y≤6 (1)2x+y≤8 (2)y≤5 (3).Linear programming is a mathematical method that aims to maximize or minimize an objective function subject to a set of linear constraints. In this problem, we are asked to maximize the objective function 6x + 5y subject to the constraints given by the inequalities 1, 2, and 3.

The inequalities 1, 2, and 3 define a feasible region in the xy-plane, which is a region that satisfies all the constraints. The feasible region can be found by graphing the three inequalities and shading in the region that satisfies all of them.
In this case, the feasible region is a triangle with vertices (0, 0), (3, 3), and (4, 1), as shown below:

The objective function 6x + 5y is evaluated at each corner point as follows:
At (0, 0), 6(0) + 5(0) = 0,  At (3, 3), 6(3) + 5(3) = 33, At (4, 1),  6(4) + 5(1) = 29. Thus, the optimal solution is x = 3 and y = 3, and the maximum value of the objective function is 33.

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Therefore, the terminal point is 0.26 radii to the right of the circle's center and 0.67 cm to the right of the circle's center.

The angle in question has an initial ray pointing in the 3-o'clock direction and measures 2.8 radians. It is centered at the vertex of a circle with a radius of 2.6 cm. To calculate the number of radii and the number of cm the terminal point is to the right of the circle's center, we need to use the formula for arc length. Arc length is equal to the circumference of the circle multiplied by the central angle's measurement, divided by 2π.

So, the arc length of this angle is equal to 2.6 cm times 2.8 radians divided by 2π, or[tex]2.6 x 2.8 / 6.28 = 0.67 cm.[/tex] The terminal point is 0.67 cm to the right of the circle's center, which is equal to [tex]0.67/2.6 = 0.26 radii.[/tex]

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