14. Calculate the x-intercepts of the equation by factoring:
8x²-16x = 0

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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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

The properties of isosceles trapezoid are

The lengths of the left and right sides of an isosceles trapezoid are equal or identical hence the base angles are likewise equal.

Because lengths of the left and right sides are equal and base angels are equal, the diagonals are equal

Other types of trapezoid include

generally all trapezoid have two sides that are parallel to each other

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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]

Answer:

yes

Step-by-step explanation:

9(b_5)

multiply 9 with everything in the bracket:

9×b=9b

9×5=45

:9(b-5)

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 solution for the expression is (35y - 22)/(5y-8)(10y+1). The solution has been obtained by solving the algebraic expression.

What is algebraic expression?

An algebraic expression is one that uses variables, constants, and algebraic operations (addition, subtraction, etc.).

The four primary categories of expressions are as follows:

We are given

⇒(2/5y -8)+ (3/10y+1)

⇒(2(10y+1) + 3(5y -8))/(5y-8)(10y+1)

⇒(20y + 2 + 15y - 24)/(5y-8)(10y+1)

⇒(35y - 22)/(5y-8)(10y+1)

Hence, the solution for the expression is (35y - 22)/(5y-8)(10y+1).

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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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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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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?

Answer: The marginal product is the change in total product that results from an additional unit of input. With the addition of the seventh unit of input, the marginal product can be calculated as follows:

Total product when 7 units of input is used: 58

Total product when 6 units of input is used: 55

Marginal product = Total product when 7 units of input is used - Total product when 6 units of input is used

Marginal product = 58 - 55 = 3

So with the addition of the seventh unit of input, the marginal product is 3 units.

Step-by-step explanation:

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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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 code chunk to add is summarize(mean(Rating)), and the mean rating is 3.185933 according to the ratings system, summarize(), and mean() functions.

Now, According to the question:

The full code should be trimmed flavors df%>% summarize(mean(Rating)) to determine the mean rating.

In order to present summary statistics, this code combines the summarize() and mean() functions to show the mean rating of your data.

The statistic that will be displayed due to the "mean()" method is the mean rating, which in this instance would be 3.185933.

The mean scale score represents the overall effectiveness of a group of students on a test. A mean scale score is calculated specifically by adding up the scores of each individual student and dividing that total by the number of scores. It is additionally known as an average.

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The length of the road after D days of construction (L) is equal to the original length of the road (10 miles) plus the number of miles added by the construction crew each day (1 mile/day) times the number of days the construction has been going on (D).

So the equation relating L to D is:

L = 10 + 1D

This equation can be graph on a Cartesian plane with D on the x-axis and L on the y-axis. The graph will be a straight line passing through the point (0,10) and having a slope of 1, meaning that for every one increase in D there is a one increase in L.

It will look like this:

graph{10+x [-12, 12, -6, 6]}

Where D=x and L=y.

Answer: L - 10 = D

Step-by-step explanation:

1 Day = 1 Mile
After 1 Day of construction a 1 Mile is added to the road
Original length is 10 miles
Length (e.g. 11 miles) - 10miles = Day 1
So:
L - 10 = D

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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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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The inequality that represents the situation in this problem is given as follows:

x + 3 < 16

The inequality symbols are given as follows:

In three years, your friend's age is given as follows:

x + 3.

To apply for the driver's license, an age of 16 is needed, and your friend will be younger than 16, as he/she cannot apply, hence the inequality is:

x + 3 < 16

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The order of rotational symmetry of a square about its center is 4.

Geometrically speaking, a shape has rotational symmetry when it retains its appearance following a small amount of rotation by a partial turn. The number of different orientations in which an object appears exactly the same for each rotation is known as the degree of rotational symmetry.

The number of times a square fits onto itself during a full rotation of 360 degrees determines a square's rotational symmetry. The square in the images above can be seen to fit four times on top of itself during a full 360-degree rotation.

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All of the trains scheduled to leave from the Concert Hall station are listed in Keiko's record for the population, and a random selection of 70 train records are listed in Keiko's record for the sample. As a result, statement II is true for the population, whereas statement I is true for the sample. The total population or all trains is regarded as a parameter, while the random group is regarded as a statistic.

In statistics, when we talk about population, we are talking about the entire population from which we want to draw a conclusion about. And when we talk about sample, we are talking about a particular or specific group from which we want to collect data from. So the size of sample will be less compared to the total size of the population.

a) In the given scenario, when we discuss population, we are referring to all of the trains that were scheduled to depart the Concert Hall station in the previous year. So statement II is correct.

And, when we discuss samples, we are referring to the random sample of 70 train records that Keiko audited. So statement I is correct.

b) When we talk about parameters, we are talking about the data of an entire population or all trains. And, when we are talking about statistics, we are talking about the sample data or random group.

The complete question is -

The records for all trains scheduled to depart from the Concert Hall train station last year showed that the average delay for these trains was 13.1 minutes, 18.6% of the trains had been delayed, and 12 trains had been canceled. Keiko is a traffic engineer helping the Concert Hall station improve its performance. She audited a random group of 70 records of trains scheduled to depart from the Concert Hall station last year. In her group the trains were late an average of 22.5 minutes, 30% of the trains had been delayed, and 4 trains had been canceled.

a. For Keiko's audit of train records, identify the population and the sample

Population:

I. The random group of 70 records of trains audited by Keiko.

II. The records of all the trains scheduled to depart from the Concert Hall station last year.

Sample:

I. The random group of 70 records of trains audited by Keiko.

II. The records of all the trains scheduled to depart from the Concert Hall station last year

b. Choose whether each number described below is a parameter or a statistic for Keiko's audit.

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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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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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The relationship between factors and multiples from the equation  6 x 7 = 42 are given below.

Factorization in mathematics is the process of dividing a large number into smaller ones that, when multiplied together, give you the original number. Factorization is the process of dividing a number into its components or divisors.

Given:

An equation,

6 x 7 = 42.

Multiples are what you receive after multiplying a factor, which is what you can multiply to produce a number.

1 x 42 = 42

2 x 21 = 42

3 x 14 = 42

6 x 7 = 42

So the factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42

The multiples of 42 are 1,2,3,4,5,6 etc.

Therefore, the relationship between factors and multiples are given

above.

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Answer:

$155.56

Step-by-step explanation:

S.I=(PRT)÷100

$144=(P×9×1)÷100

crossmultiply

$144×100=9P

P=$14400÷9

P=$155.56

The larger angle between the pair of supplementary angles is 126 degrees.

Supplementary angles are simply angles that sum up to 180 degrees.

Given the data in the question;

Since, they both form a supplementary angle, their sum gives a total of 180 degree.

Angle 1 + Angle 2 = 180

(4x+30) + (2x+6) = 180

Solve for x

4x + 2x + 30 + 6 = 180

6x + 36 = 180

6x = 180 - 36

6x = 144

x = 144 / 6

x = 24

Now, we determine the measure of the angles.

Angle 1 = (4x+30)

Angle 1 = 4(24) + 30

Angle 1 = 126 degrees

Angle 2 = (2x+6)

Angle 2 = 2(24) + 6

Angle 2 = 54 degrees.

Therefore, the larger angles measures 126 degree.

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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:

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

The expression of (9 * 10⁶)(8 * 10⁸) in scientific notation is; 72 * 10¹⁴

Scientific notation is defined as a way of writing very large or very small numbers. A number is usually written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. For example, 750,000,000 can be written in scientific notation as 7.5 * 10⁸.

We want to multiply the expression given as;

(9 * 10⁶)(8 * 10⁸)

Now, we can rewrite this as;

(9 * 8) * (10⁶ * 10⁸)

According to laws of exponents, x² × x³ = x²⁺³

Thus;

(9 * 8) * (10⁶ * 10⁸) = 72 * 10⁶⁺⁸

= 72 * 10¹⁴

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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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