A fashion store is planning its end–of–season sale. It sells 40 of its signature jeans every week at $175 per pair. Last year, the store's sales increased to 60 pairs per week when the price was dropped by $25. By what amount should the store discount the price this year to maximize its revenue?

A. $112.50
B. $103.50
C. $62.50
D. $71.50

The rate at which the water flow from the given volume is 21.72 in³/sec

To find the rate at which water is being drained from the container, we first need to find the rate at which the water level is falling and then use that to calculate the volume of water being drained per unit of time.

We know that the surface level is falling at a rate of 0.9 inches per second and that the container has the shape of an inverted right circular cone. The volume of a cone is given by the formula:

V = (1/3) * π * r^2 * h

Where V is the volume, π is pi (approximately 3.14), r is the radius of the base, and h is the height of the cone.

We can use this formula to find the volume of the container when the water level is 8 inches. The radius at this point is 6 * (8/10) = 4.8 inches and the height is 8 inches.

V = (1/3) * π * (4.8 inches)^2 * 8 inches = 193.02 inches³

Now that we know the volume of the container when the water level is 8 inches, we can use the rate at which the water level is falling (0.9 inches per second) to find the rate at which the water is being drained.

The rate at which water is being drained = rate of change of volume / rate of change of height = dV/dt = dV/dh * dh/dt = -dV/dh * dH/dt

Where dV/dh is the derivative of volume with respect to height, dH/dt is the rate of change of height.

-dV/dh = -(1/3) * π * (4.8 inches)^2 = -24.13 in³

dH/dt = -0.9 inches/sec

The rate at which water is being drained = -dV/dh * dH/dt = -24.13 * -0.9 inches/sec = 21.72 in³/sec

So the rate at which water is being drained from the container is 21.72 in³/sec

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The equation when making x the subject is X = -2 - 6y

To do this, we would have to take the values that are in the left hand side to the right hand side. When we do this, the signs on the left hand side would have to change

X+6y=-2

we have to take +6y to the right hand side.

When the positive sign crosses the equal sign it becomes negative

X = -2 - 6y

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X+6y=-2 show ur work make x the subject

If the sun is 69° above the horizon, the length of the shadow cast by a building 91 ft tall

You should understand that the length of the shadow is the distance between a point to the foot of the tenth

This makes an angle of depression, with 69 degrees

Remember that the angle on top of the tenth is 90-69 = 21 degrees

therefore, using the trigonometrical ratio

We have Tan∅ = opposite of adjacent

Tan 21⁰ = x/9

x= 9*tan 21⁰

x = 9*0.3839

The distance is 3.45

Therefore the length of the shadow cast by a building is approximately 3.5 feet long

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Answer: To find the price of the 3-year old car, we need to determine how much less it is than the new car, which is 23% of the price of the new car.

We can start by finding the value of 23% of the price of the new car, which is: $12,400 x 0.23 = $2,832

Now we know that the price of the 3-year old car is $2,832 less than the price of the new car. To find the price of the 3-year old car, we subtract $2,832 from the price of the new car: $12,400 - $2,832 = $9,568

So the price of the 3-year old car is $9,568.

Step-by-step explanation:

The additional fact that would prove that

EFGH is a square is D) IFLEH ~ LFGH.

A quadrilateral is a plane figure with four edges and four corners, also known as vertices. The quadrilateral's four vertices or corners all have angles.

If a quadrilateral is a rhombus, that means opposite sides are congruent, but it does not mean that all angles are congruent. In order to prove that EFGH is a square, we need to show that all angles are congruent. The statement "IFLEH ~ LFGH" implies that all angles in the quadrilateral are congruent, since it states that opposite angles are congruent, which is one of the defining characteristics of a square. Therefore, statement D is the correct answer.

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Answer:

Step-by-step explanation:

36

(

x

+

3

)

2

(

x

−

3

)

2

Answer:

59.036

Step-by-step explanation:

tanΘ = opposite/adjacent

Θ =tan⁻¹(opposite/adjacent)

tan⁻¹(10/6) - 59.03624347

Using the quadratic equation the distance of point B from the ground level is D. 3 units

An equation is a mathematical function that shows the relationship between two variables.

Since an archway is modeled by the equation y = -2x² + 8x.

A rod is to be placed across the archway at an angle defined by the equation x − 2.23y + 10.34 = 0.

If the rod is attached to the archway at points A and B, such that point B is at a higher level than point A, we desire to find the distance of point be from the ground. To do this , we proceed as follows.

Since we have the equations

Substituting y into the second equation, we have

x - 2.23y + 10.34 = 0

x - 2.23(-2x² + 8x) + 10.34 = 0

x + 4.46x² - 17.84x + 10.34 = 0

4.46x² - 16.84x + 10.34 = 0

To find the points a and B, we solve for x where both equations intersect.

So, using the quadratic formula, we solve for x

[tex]x = \frac{-b +/-\sqrt{b^{2} - 4ac} }{2a}[/tex] where a = 4.46, b = -16.84 and c = 10.34

So, substituting the values of the variablers into the equation, we have that

[tex]x = \frac{-(-16.84) +/-\sqrt{(-16.84)^{2} - 4\times4.46\times10.34} }{2\times4.46}\\= \frac{16.84 +/-\sqrt{283.5856 - 184.4656} }{8.92}\\= \frac{16.84 +/-\sqrt{99.12} }{8.92}\\= \frac{16.84 +/-9.96 }{8.92}\\x = \frac{16.84 + 9.96 }{8.92} or x = \frac{16.84 - 9.96 }{8.92}\\x = \frac{26.8}{8.92} or x = \frac{6.88}{8.92}\\x = 3.004 or x = 0.771[/tex]

Since B is higher, we take the higher value x = 3.

So, the distance of point B from the ground level is D. 3 units

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Using the quadratic equation the distance of point B from the ground level is D. 3 units

An equation is a mathematical function that shows the relationship between two variables.

Since an archway is modeled by the equation y = -2x² + 8x.

A rod is to be placed across the archway at an angle defined by the equation x − 2.23y + 10.34 = 0.

If the rod is attached to the archway at points A and B, such that point B is at a higher level than point A, we desire to find the distance of point be from the ground. To do this , we proceed as follows.

Since we have the equations

Substituting y into the second equation, we have

x - 2.23y + 10.34 = 0

x - 2.23(-2x² + 8x) + 10.34 = 0

x + 4.46x² - 17.84x + 10.34 = 0

4.46x² - 16.84x + 10.34 = 0

To find the points a and B, we solve for x where both equations intersect.

So, using the quadratic formula, we solve for x

[tex]x = \frac{-b +/-\sqrt{b^{2} - 4ac} }{2a}[/tex] where a = 4.46, b = -16.84 and c = 10.34

So, substituting the values of the variablers into the equation, we have that

[tex]x = \frac{-(-16.84) +/-\sqrt{(-16.84)^{2} - 4\times4.46\times10.34} }{2\times4.46}\\= \frac{16.84 +/-\sqrt{283.5856 - 184.4656} }{8.92}\\= \frac{16.84 +/-\sqrt{99.12} }{8.92}\\= \frac{16.84 +/-9.96 }{8.92}\\x = \frac{16.84 + 9.96 }{8.92} or x = \frac{16.84 - 9.96 }{8.92}\\x = \frac{26.8}{8.92} or x = \frac{6.88}{8.92}\\x = 3.004 or x = 0.771[/tex]

Since B is higher, we take the higher value x = 3.

So, the distance of point B from the ground level is D. 3 units

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The movie theater will have 50 shows in 6 days

To find the total number of shows in 6 days, we need to calculate the number of shows for each type of day (4 days per week with 7 shows per day and 2 days per week with 11 shows per day) and then add them together.

First, let's calculate the number of shows for the 4 days per week with 7 shows per day:

4 days per week x 7 shows per day = 28 shows per week

Next, let's calculate the number of shows for the 2 days per week with 11 shows per day:

2 days per week x 11 shows per day = 22 shows per week

Now, we can add the number of shows for each type of day together to find the total number of shows in 6 days:

28 shows per week + 22 shows per week = 50 shows in 6 days

We used multiplication to calculate the number of shows per week for each type of day (by multiplying the number of days by the number of shows per day) and then added the two results together to find the total number of shows in 6 days.

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Diya could earn 72 marks out of 80 after getting the extra credits.

Teachers employ extra credit for a variety of reasons. For example, it may be felt that students who are highly capable may benefit from an additional challenge that might not be suitable as required work for all students. Extra credit may also be used as a way to allow a student to improve their grade after a weak performance earlier in a course. In both of these cases, extra credit can promote differentiated instruction by factoring in optional work in the assessment of student performance.

Given here: Diya scores 36 out of 80 on a test.

Also, her teacher gives her extra credit with which she could double her marks.

If Diya doubles her marks then her total marks would be 72

Therefore the increase in her marks is 72-36=36

She could earn another 36 credits.

Thus her score after the extra credit is equal to 72

Hence, Diya could earn 72 marks out of 80 after getting the extra credits.

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A two-sample z-interval for a population proportion. This method is used to create an estimate of the percentage of trees in a large forest that are infested with a certain beetle by taking a random sample of trees to inspect.

A two-sample z-interval for a population proportion is the most appropriate method for creating an estimate of the percent of trees in a large forest that are infested with a certain beetle. This method involves taking a random sample of trees from the forest and inspecting them to determine the proportion of infested trees. The sample size chosen should be large enough to provide a reliable estimate of the proportion of trees in the population that are infested. A two-sample z-interval is then used to calculate a confidence interval for the population proportion, which can be used to estimate the overall percent of trees in the forest that are infested with the beetle. This method can provide a reliable estimate of the percent of trees in the forest that are infested with the beetle, allowing environmentalists to make informed decisions regarding management of the forest.

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Equivalent equations are algebraic equations that are having identical roots or solutions

Equations in algebra with the same roots or solutions are said to be equivalent. An analogous equation is one that is created by adding or removing the identical number, symbol, or expression from both sides of an equation. We can also get an equivalent equation by multiplying or dividing both sides of an equation by the same nonzero value.

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

To determine which complex expression is the simple expression's equivalence:

Give any coefficients a distribution:

a(bx±c)=abx±ac

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After 180 miles both the cars' tanks contain same amount of gas.

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.

Given that, Ann and Leila are driving separate cars to New York. They begin the trip with full gas tanks.

From the given  graph,

After 360 miles Ann's car has 2 gallons of gas.

After 180 miles both the cars' tanks contain same amount of gas.

When they travelled less than 180 miles, Leila's car has more gas.

Therefore, after 180 miles both the cars' tanks contain same amount of gas.

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Answer:

Step-by-step explanation:

[tex]\sf 8-3(4-4)+2*4*6[/tex]

[tex]\sf 8-(3)(0)+(2)(4)(6)[/tex]

[tex]\sf 8-0+(2)(4)(6)[/tex]

[tex]\sf 8+(2)(4)(6)[/tex]

[tex]\sf 8+(8)(6)[/tex]

[tex]\sf 8+48[/tex]

[tex]\sf 56[/tex]

In a plane, intersecting lines are any two or more lines that cross each other. The point of intersection is the common point shared by all intersecting lines.

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Answer:

7/12 of salt.

1/4 + 1/3 =

1/3 + 1/4 =

4/12 + 3/12 = 7/12.

Step-by-step explanation:

Hope it helps! =D

Answer:

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Step-by-step explanation:

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728 kilograms of sugar is used in this month.

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

Given that a bakery used 30% more sugar this month than last month.

Let us convert 30% to decimal.

Divide 30 by 100

30/100=0.3

the bakery used 560 kilograms of sugar last month we have to find the amount of sugar used this month.

Now multiply 30% of 560

0.3×560

168.

So now 560+168=728 is the amount of sugar used this month.

Hence, 728 kilograms of sugar is used in this month.

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Answer:

y = 1/3x +2

Step-by-step explanation:

when x =o, y=2

when x= -6, y=0

so slope is always the difference between the Ys divided by diff b/w the Xs

so the slope is (2-0)/(0-(-6)) =  1/3

the intercept by definition is when x=0, so it's 2

so Y = 1/3 X +2

Since the longest side cannot be longer than the total of the other two sides, the third side's potential lengths range from 8 to 44.

A triangle's third side must be longer than the difference between the other two sides' lengths and shorter than the total length of the other two sides. The two side lengths in this situation are 18 and 26. The third side must be greater than 8 because the difference between them is 8. The third side must be less than 44 because the total length of the first two sides equals 44. Therefore, the third side length might be any side length between 8 and 44.Since the longest side cannot be longer than the total of the other two sides, the third side's potential lengths range from 8 to 44.

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The complete question is

a triangle has one side length of 26 and another side length of 18. select all of the possible lengths of the third side potential lengths range from 8 to 44?

The ratios equivalent to 7:6 can be expressed as a) 14 : 12

The concept that will be used here is ratio. The proportion is an equation that demonstrates how two ratios are equivalent, but the notion of ratio defines us to compare two quantities.

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

From the  ratios equivalent to 7:6 which can be written as 7/6

Then we consider option A , 14/12 = 7/6 ( divide the denominator and numerator by factor of 2.

Option B; 2 : 18 = 2/18 = 1/9

option C : 28 : 26 = 16/ 13

option D : 30 : 25 = 6/5

Therefore, option A is correct.

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Missing options:

a) 14 : 12

b) 2 : 18

c) 28 : 26

d) 30 : 25

Answer:

1.44

Step-by-step explanation:

11.52/8=1.44

Sarah's profit, given the shirts sold, the cost of the shirts, and the shirts returned, can be found to be $ 126

First, find Sarah's cost :

= Cost to buy the shirts + cost to return the shirts

= ( 37 x 9 ) + ( 7 x 3)

= 333 + 21

= $ 354

The revenue made from selling the shirts was :

= 30 x 16 per shirts

= $ 480

Sarah's profit is therefore:

= 480 - 354

= $ 126

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Answer:

You are correct

Step-by-step explanation:

You are correct sir. They want the answer in feet, so everything on that triangle has to be converted into feet.

There are 12 inches in a foot. If we do 108/12 we get 9 feet.

The volume of the solid is equal to 96 cubic units.

V= Integral (from x=2 to x=-4) of (8-x^2-2x)^2 dx = ∫(8-x^2-2x)^2 dx

= 1/3*∫(24-6x^2-12x)dx

= 1/3*[24x-2x^3-6x^2] from x=2 to x=-4

= 1/3*[(-6)-(-140)-(-136)]

= 1/3*(288)

= 96 cubic units

Set up an integral to compute the volume of the solid.

V= Integral (from x=2 to x=-4) of (8-x^2-2x)^2 dx

Rewrite the integral with a function of x in terms of a single power of x.

V= Integral (from x=2 to x=-4) of (8-x^2-2x)^2 dx = ∫(8-x^2-2x)^2 dx

= 1/3*∫(24-6x^2-12x)dx

Integrate the function.

= 1/3*[24x-2x^3-6x^2] from x=2 to x=-4

Evaluate the integral to find the volume of the solid.

= 1/3*[(-6)-(-140)-(-136)]

= 1/3*(288)

= 96 cubic units

The volume of the solid is equal to 96 cubic units.

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Answer:

As a whole, the piece first measured 38 inches. No matter how many times you cut it, all of the pieces will still add up to 38 inches. You know that 19 inches is the length of one of the two pieces, so all you need to find is the other unknown piece. Add the two together, with m being the unknown length.

19+m=38

If you want to solve the equation, just subtract 19 from both sides.

19+m=38

m=19

The roof of the barn measures 4701 square feet. (This is equivalent to saying that the barn has a roofing area of 4701 square feet.)

What is integration ?

Integration is a fundamental concept in calculus. It refers to the process of finding the integral of a function, which gives the total amount of change of a quantity over a given interval. The process of integration is the reverse of differentiation, which is the process of finding the rate of change of a quantity. The symbol for integration is ∫.

A barn is 100 feet long and 40 feet wide.

Find the first derivative of the given function:

dy/dx = -10[1/20e^x/20 - 1/20 e^-x/20]

1 + (dy/dx)^2 = 1/4[e^x/20 - e^-x/20]^2

The arc length:

= ∫ √1/4[e^x/20 - e^-x/20]^2 dx

After solving the above integration:

= 20(e - 1/e)

The roofing = 100(20(e - 1/e))

= 4701 square feet,

The roof of the barn measures 4701 square feet. (This is equivalent to saying that the barn has a roofing area of 4701 square feet.)

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