The cargo bed of a commercial truck is shaped like a rectangular prism. The dimensions are shown. Billy has 80 cubic meters of mulch to take to his house. How many trips will he have to make until all the mulch is at his house?

The four different conic sections are the circle, ellipse, parabola, and hyperbola. They are called conic sections because they are formed by the intersection of a plane and a cone.

Circle: A circle is formed when the plane intersects the cone at an angle perpendicular to its axis. The circle has an eccentricity of 0, which means the distance between any point on the circle and its center is always the same.

Ellipse: An ellipse is formed when the plane intersects the cone at an angle that is not perpendicular to its axis. The ellipse has an eccentricity between 0 and 1, which means the distance between the two foci and any point on the ellipse is constant.

Parabola: A parabola is formed when the plane intersects the cone parallel to one of its sides. The parabola has an eccentricity of 1, which means it has a single focus point.

Hyperbola: A hyperbola is formed when the plane intersects the cone at an angle that is greater than the angle formed by the cone's side and its axis. The hyperbola has an eccentricity greater than 1, which means the distance between the two foci and any point on the hyperbola is constant.

In summary, the eccentricity of a conic section describes how stretched or elongated the shape is. A circle has an eccentricity of 0, an ellipse has an eccentricity between 0 and 1, a parabola has an eccentricity of 1, and a hyperbola has an eccentricity greater than 1.

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Part A:  The cost of bowling will be the same at both centers if 4 games are bowled. Part B:  It will cost $10 to bowl at both Fannin Lanes and Fun Time Lanes for 4 games.

The cost of bowling games can vary depending on a number of factors, including the location, time of day, and day of the week. Generally, bowling alleys charge per game or per hour, with additional fees for shoe rentals and any other amenities or services.

The cost per game can range from a few dollars to upwards of $10 or more, depending on the location and other factors. Some bowling alleys also offer discounted rates for children, seniors, or members of certain groups.

Part A:

Let's assume that the number of games to be bowled is 'x'. The total cost of bowling at Fannin Lanes is 2.5x + 2, and at Fun Time Lanes it is 2x + 4. We need to find the number of games where the cost of bowling at both centers is the same.

2.5x + 2 = 2x + 4

0.5x = 2

x = 4

Therefore, the cost of bowling will be the same at both centers if 4 games are bowled.

Part B:

Using the value of 'x' found in Part A, we can find the cost of bowling at both centers.

At Fannin Lanes: 2.5(4) + 2 = 10

At Fun Time Lanes: 2(4) + 4 = 12

Therefore, it will cost $10 to bowl at both Fannin Lanes and Fun Time Lanes for 4 games.

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The complete question is:

Answer:

m = -3/2

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Points (4, − 6) and (− 2, 3)

We see the y increase by 9 and the x decrease by 6, so the slope is

m = - 9/6 = -3/2

So, the slope of the line is -3/2

For 0 miles cost is 3 dollars, for 4 miles cost is 7 dollars, for 6 miles cost is 9 dollars, for 8 miles cost is 11 dollars.

Distance refers to the measurement of the space or length between two points, objects, or locations.  In mathematics, the distance between two points in a coordinate plane can be calculated using the distance formula, which is derived from the Pythagorean theorem. The distance formula is:

d = √[(x2 - x1)² + (y2 - y1)²]

In physics, distance is an important concept in understanding motion and energy. For example, the distance traveled by an object can be used to calculate its speed and acceleration, and the distance between two objects can affect the strength of their gravitational attraction.

In everyday life, distance is often used to describe physical space between objects, such as the distance between two buildings, the distance between two cities, or the distance between two people. It is also used in the context of travel, such as the distance between two destinations and the time it takes to travel that distance.

C = 3 + m

Distance in miles (m)              Cost in dollars (c)

0                                               3

4                                               7

6                                               9

8                                               11

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The complete question is:

The answer is 6a+5.

Distribute the negative sign to the second polynomial:
(9a+6)-(3a+1) = (9a+6)+(-3a-1)

Combine like terms:
(9a+6)+(-3a-1) = (9a-3a)+(6-1) = 6a+5

Therefore, the answer is 6a+5.

So, the subtraction of the polynomials (9a+6)-(3a+1) is 6a+5.

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The area of the circle which is drawn by tracing around the edge of the quarter on a sheet of paper is 0.78 in.²

All points in a plane that are at a specific distance from a specific point, the centre, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

Each of the four equally sized pieces that make up a circle is known as a quarter of a circle. The quadrant of the circle is the name given to each quarter. One-fourth of the total area of the circle is represented by the area of a quarter circle.

Given,

the diameter of the quarter  = 1 in.

When we trace around the edge of the quarter on a sheet of paper, we get a circle of diameter 1 in.

So the radius of the circle r = 1/2 = 0.5 inches

Area of the circle on the paper = πr² = 3.14 × 0.5² = 0.78 in.²

Therefore the area of the circle which is drawn by tracing around the edge of the quarter on a sheet of paper is 0.78 in.²

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To further analyze the function f(x)=1.3x^(4)-5.7x^(2)+3.71 on the interval [-4,4,-8,14], we can find the critical points, relative extrema, and inflection points of the function.

First, let's find the critical points by taking the derivative of the function and setting it equal to zero:
f'(x)=5.2x^(3)-11.4x
0=5.2x^(3)-11.4x
0=x(5.2x^(2)-11.4)
x=0, x=±√(11.4/5.2)
So the critical points are x=0, x=±1.4656

Next, let's find the relative extrema by using the second derivative test:
f''(x)=15.6x^(2)-11.4
f''(0)=-11.4<0, so x=0 is a relative maximum
f''(1.4656)=11.4>0, so x=1.4656 is a relative minimum
f''(-1.4656)=11.4>0, so x=-1.4656 is a relative minimum

Finally, let's find the inflection points by setting the second derivative equal to zero:
0=15.6x^(2)-11.4
x=±√(11.4/15.6)
x=±0.8544

So the inflection points are x=±0.8544

Overall, the function f(x)=1.3x^(4)-5.7x^(2)+3.71 has a relative maximum at x=0, relative minimums at x=±1.4656, and inflection points at x=±0.8544 on the interval [-4,4,-8,14].

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Answer:

In the exponential function y = C(a)^x, the value of a is the base of the exponent, which determines how fast the function grows or decays. If a were equal to zero, then any value of x would result in y being equal to zero, which would make the function flat and unchanging. Therefore, a cannot be equal to zero in an exponential function, as this would result in an undefined or meaningless expression. Additionally, any number raised to the power of zero is equal to 1, so an exponential function with a base of zero would also violate this mathematical rule.

The sales tax that Bobbi paid was 10 dollars. Below, you will learn how to solve the problem.

To find the sales tax, we can simply subtract the cost of the text books from the total amount paid:

Sales tax = Total amount paid - Cost of text books

Sales tax = 130 dollars - 120 dollars
Sales tax = 10 dollars

Therefore, the sales tax that Bobbi paid was 10 dollars.

In mathematics, subtraction (also called subtraction) is an arithmetic operation that removes quantities from any kind of operation.

After subtracting, we will always have a smaller value than the one we had before.

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The domain of the function is: {(x, y, z) | x ≠ 0, y ≠ -3x, z ≠ -2x, 2x + z ≠ -2xy/3}.

To find the domain of the function, we need to identify any values of x, y, or z that would make the denominator(s) of the function equal to zero. Division by zero is undefined, so any such values must be excluded from the domain.

For the first term, the denominator is z + 2x, which is equal to zero when z = -2x.

Therefore, we must exclude this value from the domain.

For the second term, the denominator is 3x + y, which is equal to zero when y = -3x.

Therefore, we must exclude this value from the domain as well.

For the third term, the denominator is 6x² + 3xz + 2xy. Factoring out 3x from the second and third terms in the denominator gives:

6x² + 3xz + 2xy = 3x(2x + z) + 2xy

This expression is equal to zero when either 3x = 0 (i.e., x = 0) or 2x + z = -2xy/3.

Therefore, we must exclude x = 0 and any values of z that satisfy the equation 2x + z = -2xy/3.

Putting it all together, the domain of the function is:

{(x, y, z) | x ≠ 0, y ≠ -3x, z ≠ -2x, 2x + z ≠ -2xy/3}

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Answer:

B, D, E

Step-by-step explanation:

52= -4(2n+1)

= -8n-4

52= -8n-4

8n= -4-52

8n= -56

n= -7

-8n= 52+4

= 56

Dijkstra's algorithm is a useful tool for finding the length of the shortest path between two vertices in a weighted graph.

To solve this problem, we can start by creating a distinguished vertex set Q that contains all of the vertices in the graph, and assigning a distance of ∞ to each vertex in the set. Then, we can assign the starting vertex, a, a distance of 0.

Next, we can choose the vertex in Q with the shortest distance from the source vertex, a. This vertex is then removed from the set Q, and all of its adjacent vertices are evaluated and added to the set Q if they are not already in it. We then assign each adjacent vertex the distance of the selected vertex, plus the weight of the edge connecting it to the selected vertex.

Finally, we continue this process until the destination vertex, z, is removed from the set Q. At this point, the length of the shortest path between vertices a and z can be found by looking at the distance of the destination vertex.

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The owner have 33 fewer customer per day for $45 per oil change.

The owner of a quick oil-change business should charge $45$45 per oil change in order to maximize income from the business.

To solve this, we need to consider the number of customers per day and how much money is made from each oil change.

The owner currently charges $36$36 per oil change and has 6060 customers per day. With each increase of $3$3, the number of customers decreases by 33.

This means that the owner should continue to increase the price until the decrease in customers is greater than the increase in price.

At $45$45 per oil change, the owner will have 33 fewer customers per day, but will make an additional $9$9 per oil change, resulting in an increase in total income. This is the price the owner should charge to maximize income.

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Answer:The father's position relative to the surface of the water is 4.2 meters below the surface of the water.

Step-by-step explanation:

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The height relative to the water surface is calculated as:-

Height from iceberg to water surface = 0.5 meters

The height from iceberg to deep inside the water is = 4.7 meters

Father's height relative to the water surface is,

H= 4.7 - 0.5 = 4.2 meters.

The image of the condition is also attached with the answer below.

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The function y=10x(x+1) is already in factored form, with a=10, r=0, and s=-1.

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The set X is termed the domain of the function and the set Y is called the codomain of the function. Initially, functions represented the idealized relationship between varied quantities and other variables.

To see this, we can rewrite the function as f(x)=10(x-0)(x-(-1)), which matches the form f(x)=a(x-r)(x-s). Therefore, the values of a, r, and s are:

a = 10
r = 0
s = -1

It is important to note that the values of r and s are the x-intercepts of the function, or the values of x that make the function equal to zero. In this case, the x-intercepts are 0 and -1, which correspond to the values of r and s.

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The solution for the inequality x² + 36 > 12x is {x| x € R and x ≠ 6) . Option D

From the information given, we have the inequality;

x² + 36 > 12x

Now, a quadratic expression;

x² - 12x + 36

Solve the quadratic expression by multiplying the coefficient of x squared by the constant value 36.

Then, find the pair factors of the product that would add up to give the coefficient of x, -12.

Substitute the factors, we have ;

x² - 6x - 6x + 36

Group in pairs, we have;

(x² - 6x) - (6x + 36)

factor the common terms

x(x - 6) - 6( x - 6)

Then, we have;

x - 6> 0

x > 6

And, x -6 > 0

x > 6

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Earl works 5 days a week, which is 50percentage of Monday through Friday. He works in the Tutoring center one day, cleans bathrooms one day, and has another day for unspecified work.

Earl works 5 days a week. He works in the Tutoring center one day, cleans bathrooms one day, and has another day for unspecified work. This means that he is working 50% of Monday through Friday. On Saturday and Sunday, he has no work. His work schedule is a great example of how one can balance work with free time. It also shows how one can make the most out of their working hours by doing different activities each day. It provides variety and prevents boredom from setting in. The days off also give Earl time to rest and relax, allowing him to be productive the other days. His weekly schedule is a great example of how one can efficiently manage their time.

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It would not be possible to construct a triangle with those given measurements.

What is triangle ?

Triangle can be defined which it consists of three sides, three angles and sum of three angles is always 180 degrees.

The conditions that will result in the construction of a unique triangle are:

C) side lengths: 2 in., 7 in., 8 in.

D) side lengths: 5 ft., 6 ft., 12 ft.

E) side lengths: 11 cm, 15 cm, 17 cm.

In each of these cases, the side lengths satisfy the triangle inequality, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This ensures that the three sides can be connected to form a unique triangle.

The other options do not satisfy the triangle inequality, and

Therefore, it would not be possible to construct a triangle with those given measurements.

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Answer:

  2 m

Step-by-step explanation:

You want the height of the triangular base of a triangular prism that has a volume of 12.6 m³. The base of the triangle is 2.8 m, and the height of the prism is 4.5 m.

The volume formula for the triangular prism is ...

  V = Bh . . . . the product of the triangle area and the base–base distance

  12.6 = B·4.5

  2.8 = B . . . . . . . area of the triangular base

The area of the triangular base is given by ...

  A = 1/2bh

The area is shown above to be 2.8 m², and the base of the triangle is given as 2.8 m, so we have ...

  2.8 = 1/2(2.8)h

  2 = h . . . . . . . . . . . . divide by 1.4, the coefficient of h

The center height of the tent is 2 meters.

__

Additional comment

If you combine the formulas, you see that a triangular prism has half the volume of a rectangular prism with the same overall dimensions.

  V = 1/2LWH

  12.6 = 1/2(4.5)(2.8)h = 6.3h

  2 = h . . . . meters

The distance from the top of the cliff to the ship at C 373.4 m.

The angle of depression from the top of the cliff to the ship at C is 20.4 degrees

The distance BC = 200.2m

the distance is given as

[tex]\sqrt{130^{2} +350^{2} }[/tex]

= 373.4 m

The distance of the top of the cliff to the ship at c is 373.4 m

angle of depression is tan ∅ = 130 / 350

∅ = tan⁻¹  130 / 350

= 20.4 degrees

b. The distance BC

tan 33 = 130 / AB

AB = 130 / tan 33

= 200.2 m

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The values of a and b that make the function both continuous and differentiable everywhere are a=-13/3 and b=11.

To make the function both continuous and differentiable everywhere, we need to find the values of a and b that make the two parts of the piecewise function equal at x=-1. This will ensure that there are no jumps or breaks in the function at x=-1, making it continuous and differentiable.

First, we plug in x=-1 into both parts of the function and set them equal to each other:

3−3(-1) = -2/3(-1)^2 + a(-1) + b

Simplifying both sides gives us:

6 = -2/3 + a + b

Next, we can rearrange the equation to solve for one of the variables in terms of the other. Let's solve for b in terms of a:

b = 20/3 - a

Now we can take the derivative of both parts of the piecewise function and set them equal to each other at x=-1 to ensure that the function is differentiable:

-3 = -4/3x + a

Plugging in x=-1 gives us:

-3 = 4/3 + a

Rearranging to solve for a gives us:

a = -13/3

Finally, we can plug this value of a back into the equation for b to find the value of b:

b = 20/3 - (-13/3) = 33/3 = 11

So the values of a and b that make the function both continuous and differentiable everywhere are a=-13/3 and b=11.

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If a model a rocket is used to test materials that will be used to build the body of the actual rocket. The limitation of this model is: D. It is smaller than the actual rocket.

A model rocket is a scaled-down version of an actual rocket, which means it is smaller than the actual rocket. While a model rocket can be used to test materials that will be used to build the body of the actual rocket, there are limitations to using a model rocket for this purpose.

One of the main limitations is that the smaller size of the model rocket may not accurately represent the effects of a full-scale rocket launch on the materials.

In addition, there may be other differences between the model rocket and the actual rocket, such as the types of engines used, the payload carried, and the environmental conditions during the launch, which can also limit the applicability of the results obtained from testing the materials on the model rocket to the actual rocket.

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Jean-Luc's account will be worth approximately $740.55 after 5 years of continuous  at a compounding annual interest rate of 1.6%.

Compound interest is the addition of interest to the principal amount of a loan or investment. In other words, it is the interest earned on both the principal amount and any accumulated interest from previous periods.

Interest rate is the amount charged by a lender to a borrower for the use of money or the amount earned by an investor for lending money or investing in an asset. It is usually expressed as a percentage of the principal amount and is typically calculated on an annual basis.

In the given question,

The formula for continuous compounding is:

A = Pe^(rt)

where A is the amount of money in the account after t years, P is the principal amount (the initial deposit), r is the annual interest rate (as a decimal), and e is the mathematical constant approximately equal to 2.71828.

Plugging in the given values, we get:

A = 625 * e^(0.016*5)

Simplifying this expression, we get:

A = 625 * e^(0.08)

Using a calculator, we can evaluate this expression to get:

A ≈ $740.55

Therefore, Jean-Luc's account will be worth approximately $740.55 after 5 years of continuous compounding at an annual interest rate of 1.6%.

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Answer:

55

Step-by-step explanation:

First, we need to divide 44 by 8 to find what to times 10 by.

44/8= 5.5.

After, we need to times 10 by 5.5 to get the answer

5.5x10=55

Answer: She can plant 55 plants within 44 feet.

Step-by-step explanation:

First; We must divide 8 by 44 receiving the result 5.5

( 8 ÷ 44 = 5.5 )

Second; We must multiply 5.5 with 10, giving the final result of 55.

( 5.5 x 10 = 55 )

(\mathrm{A}_{4}\) is larger than \(\mathrm{B}_{2}\)

Yes, \(\mathrm{A}_{4}\) is larger than \(\mathrm{B}_{2}\). To show this, we can use the following equation:

\[\mathrm{A}_{4} = a \cdot c \cdot \mathrm{H}\]

and

\[\mathrm{B}_{2} = b_{1} \cdot c_{1}\]

Given that \(a = 34\), \(c = 45\), \(\mathrm{H} = 194\), \(b_{1} = 7\), and \(c_{1} = 3\), then \(\mathrm{A}_{4} = 34 \cdot 45 \cdot 194 = 291930\) and \(\mathrm{B}_{2} = 7 \cdot 3 = 21\). As \(291930 > 21\), \(\mathrm{A}_{4}\) is larger than \(\mathrm{B}_{2}\).

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The height of the trapezoid is 2.84ft.

What is area ?

In mathematics, area is the measure of the amount of space inside a two-dimensional shape or surface. It is usually expressed in square units, such as square inches, square meters, or square feet.

The formula for the area of a trapezoid is:

A = (1/2)h(b1 + b2)

where A is the area, h is the height, b1 and b2 are the lengths of the two parallel bases.

We can rearrange this formula to solve for the height:

h = 2A / (b1 + b2)

We are given that the area of the trapezoid is 25.5ft. However, we also need to know the  of the two parallel bases in order to find the height.

Assuming that you have a diagram or other information that provides the lengths of the two bases, you can plug in the values for A, b1, and b2 and solve for h using the formula above.

For example, if we assume that the trapezoid has bases of length 4ft and 7ft, we can plug these values into the formula to get:

h = 2(25.5) / (4 + 7) = 2.84ft

Therefore, the height of the trapezoid is 2.84ft.

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Accοrding tο the given infοrmatiοn, nοne οf the expressiοns a), b), c), οr d) are equivalent tο (2-³.24) 2.

An algebraic expressiοn is a mathematical phrase that can cοntain numbers, variables, and mathematical οperatiοns such as additiοn, subtractiοn, multiplicatiοn, and divisiοn. Algebraic expressiοns are used tο represent quantities οr values that can vary, depending οn the values assigned tο the variables in the expressiοn. Algebraic expressiοns can be simple οr cοmplex, and they can have οne οr mοre variables.

We can simplify the expressiοn (2-³.24) 2 as fοllοws:

(2-³.24) 2 = (2-0.24) 2 = (1.76) 2 = 3.52

The expressiοn (2-³.24) 2 is equivalent tο 3.52.

Therefοre, nοne οf the expressiοns a), b), c), οr d) are equivalent tο (2-³.24) 2.

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The final answer is 2x^(2)-6x+21 with a remainder of -123. In polynomial division notation, this can be written as (2x^(2)-6x+21)-123/(x+5).

The polynomial division that Tiana is told to carry out is (2x^(3)+4x^(2)-9x-18)-:(x+5). To carry out this division, we can use long division.

Divide the first term of the dividend, 2x^(3), by the first term of the divisor, x. This gives us 2x^(2), which we write above the division symbol.
Multiply the divisor, x+5, by the first term of the quotient, 2x^(2), to get 2x^(3)+10x^(2).
Subtract this result from the dividend to get -6x^(2)-9x-18.
Repeat the process with the new dividend, -6x^(2)-9x-18. Divide the first term, -6x^(2), by the first term of the divisor, x, to get -6x, which we write above the division symbol next to 2x^(2).
Multiply the divisor, x+5, by the new term in the quotient, -6x, to get -6x^(2)-30x.
Subtract this result from the new dividend to get 21x-18.
Repeat the process with the new dividend, 21x-18. Divide the first term, 21x, by the first term of the divisor, x, to get 21, which we write above the division symbol next to 2x^(2)-6x.
Multiply the divisor, x+5, by the new term in the quotient, 21, to get 21x+105.
Subtract this result from the new dividend to get -123, which is our remainder.

So, the final answer is 2x^(2)-6x+21 with a remainder of -123. In polynomial division notation, this can be written as (2x^(2)-6x+21)-123/(x+5).

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The graph of the sin function 5sin(pi/2 x-pi) +3 is given as follows.

A function's graph is stretched or compressed vertically in proportion to the graph of the original function when we multiply it by a positive constant. We obtain a vertical stretch if the constant is bigger than 1, and a vertical compression if the constant is between 0 and 1. Figure 3-13 illustrates the vertical stretch and compression that follow from multiplying a function by constant factors 2 and 0.5. Graph of a function illustrating vertical expansion and contraction.

Given function is:

5sin(pi/2 x-pi) +3

The graph of the sin function is shifted by 3 and is compressed by 5.

Thus, the graph is as follows.

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