Marcus and his dad were going camping. When they went into the garage to get their tent they
noticed it was ripped. Marcus's dad said he could fix the tent. He would buy some new material to
cover the one rectangular side that ripped.

Every year, 1800 units crossover point. The process focus is less expensive for volumes over 1800.

When all tax credits have been used up by a limited partnership and the limited partners are left with a tax burden, that moment is known as the crossover point.

When both projects have positive values, the crossover point is formed by the intersection of two IRR curves.

The weighted average cost of capital, also known as the crossover rate, is the rate of return at which the net present values (NPV) of two projects are equal.

The rate of return at which the net present value profiles of two projects cross each other is what this term denotes.

So, annual crossover sales are 1800 units.

Process emphasis is less expensive and less important for volumes under 1800 units; repeated manufacturing concentration is less expensive and less important for volumes exceeding 1800 units.

Fixed cost ÷ variable cost

$90000÷50 =$1800

$9,000÷5=$1800

Therefore, every year, 1800 units cross over. The process focus is less expensive for volumes over 1800.

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Correct question:

A product is currently made in a process-focused shop, where fixed costs are $9,000 per year and variable costs are $50 per unit. The firm is considering a fundamental shift in process, to repetitive manufacturing. The new process would have fixed costs of $90,000, and variable costs of $5. The cross over is at 1800 units annually. for volumes over 1800, the process focus is cheaper.

The value of arc x is solved to be 120 degrees

The Arc x is solved using the knowledge of linear pair

A linear pair of angles forms a straight line, and the two angles are said to be "linear" because they are next to each other and their measures add up to 180 degrees.

Applying this we have that

60 + x = 180

x = 180 - 60

x = 120 degrees

hence we can say that x is 120 degrees

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The expression which can be used to represent the given using the fewest possible terms is 2x + 2

The correct answer choice is option B.

(−5x − 12) + (14 + 7x)

open parenthesis

-5x - 12 + 14 + 7x

collect like terms

-5x + 7x - 12 + 14

2x + 2

In conclusion, 2x + 2 is the expression which represents the fewest possible terms of (−5x − 12) + (14 + 7x)

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Answer:

its C

Step-by-step explanation:

other guy wasn't reasonable and chose the actual shortest one possible instead of the one that made sense

The number of solutions that the system has is

One Solution

To solve the system algebraically, we can substitute the first equation into the second equation to eliminate one of the variables. We'll use y:

x=2y-5

7x-14y=10

Substitute x=2y-5 into 7x-14y=10:

7(2y-5)-14y=10

Expand the left side:

14y-35-14y=10

Combine like terms:

-35=10

Solve for y:

y = -7.5

Substitute y = -7.5 back into x=2y-5:

x = 2(-7.5) - 5

Solve for x:

x = -10

So the solution to the system of equations is (x, y) = (-10, -7.5).

Since there is one unique solution, the system has One Solution.

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Work is defined as the product of force and distance, and can be calculated using the equation W = F * d, where W is work, F is force, and d is distance.

When lifting the whole log, the force required is equal to the weight of the log, and the distance over which the force is applied is the distance from the ground to the height of the shoulder.

When lifting one end of the log, the force required is still equal to the weight of the log, but the distance over which the force is applied is reduced. This is because the lever arm (the distance from the axis of rotation, which is the shoulder joint, to the point where the force is applied, which is the end of the log) is reduced.

So the equation for work done in lifting the whole log would be  W = m * g * h, where m is the mass of the log, g is the acceleration due to gravity, and h is the height from the ground to the shoulder. The equation for work done in lifting one end of the log would be W = (m/2) * g * h', where h' is the reduced height.

It can be seen that the work done in lifting one end of the log is equal to half the work done in lifting the whole log, because the force applied is the same, but the distance over which it is applied is reduced.

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The correct options of the solution of the equation 2x+7y=-5 is (a) -6,1 and (c) 8,-3.

In mathematics, two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign.

In  order to determine whether an ordered pair is a solution, all we have to do is plug in the values of x and y and see if we end up with a true statement.

(a) for (-6, 1)

put the value of 1 for y and -6 for x:

2(-6)+7(1)=-5

-12+7=-5

-5=-5

Yes! Here we have a true statement. Therefore, this ordered pair is a solution.

(b) for (9, 2)

put the value of 2 for y and 9 for x:

2(9)+7(2)=-5

18+14=-5

32≠-5

Well, we can see that we have a false statement, because ≠ means "not equal to". Therefore, this ordered pair is not a solution.

(c) for (8, -3)

put the value of -3 for y and 8 for x:

2(8)+7(-3)=-5

16-21=-5

-5=-5

Yes! Here we have a true statement. Therefore, this ordered pair is a solution.

Let's try the last option.

(d) for (-5, -4)

put the value of -4 for y and -5 for x:

2(-5)+7(-4)=-5

-10-28=-5

-38≠-5

Well, we can see that we have a false statement, because ≠ means "not equal to". Therefore, this ordered pair is not a solution.

Hence, the correct options of the solution of the equation 2x+7y=-5 is (a) -6,1 and (c) 8,-3.

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The closest answer to the increase in the distance of the Olympic marathon is 1.50 miles. Hence the correct answer is option C.

In order to find the increase in the distance of the Olympic marathon, we will find the difference between the old distance (40 km) and the new distance (42 km) and then convert it to miles.

40 km - 42 km = -2 km

Converting -2 km to miles, we get:

-2 km x 1.6 miles/km = -3.2 miles

However, since the marathon was lengthened, the actual increase in the distance is:

-3.2 miles = 3.2 miles

Rounding to the nearest 0.25 miles, we get,

3.2 miles = 3.25 miles ≈ 3.25 miles

So the closest answer to the increase in the distance of the Olympic marathon is 1.50 miles.

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The complete question is -

In the 1908 Olympic Games, the Olympic marathon was lengthened from 40 kilometers to approximately 42 kilometers. Of the following, which is closest to the increase in the distance of the Olympic marathon, in miles? (1 mile is approximately 1.6 kilometers.)

A) 1.00

B) 1.25

C) 1.50

D) 1.75

Answer: $6000

Step-by-step explanation:

The initial value will be what the person deposits before the interest. Because Liam deposited $6000 the initial value would be $6000.

Hope this helps!

The order of the numbers from least to greatest is as follows:

7, 31/4,7¹⁹/₂₅,7.765,8.44

A decimal number is a number that consists of a whole number and a fractional part separated by a point. For example – 3.5, 6.79, 78.32, etc.

Given here: The numbers containing fractions and decimal numbers.

To get a clarity on the magnitude of the numbers, let's convert every fraction to decimal numbers

Thus 7¹⁹/₂₅=7.76

31/4=7.75

Hence, The order of the numbers from least to greatest is as follows:

7, 31/4,7¹⁹/₂₅,7.765,8.44

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The cardinalities:

n(A) = 3

n (B) = 1.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Let sets A and B be defined as follows.

A is the set of integers greater than or equal to -9 and less than or equal to - 3

Set A can be expressed as,

A = {n ≥ -9 or n ≤ -3}

And set B is given,

B = {1-29, -26, -23, 30}

Simplifying,

B = {-28, -26, -23, 30}

The cardinalities:

n(A) = 3

n (B) = 1.

Therefore, n(A) = 3 and n (B) = 1.

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The slope-intercept form of the line containing the point (5, −3) and is parallel to y = − 2/5x − 3/4 is y = -2/5x - 1.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given,  line containing the point (5, −3) and is parallel to: y = − 2/5x − 3/4

The slope-intercept form of the equation of a line

y=mx+b,

where m is the slope

b is the y-intercept

In our case Line is parallel to the Line y = − 2/5x − 3/4,

So the slope would be the same.

m = -2/5

Thus, the equation of the line:

y = -2/5x + b

Since the line passes through the point (5, -3)

-3 = -2/5 * 5 + b

b = -1

Thus the final equation of a line:

y = -2/5x - 1

Therefore, The slope-intercept form of the line containing the point (5, −3) and is parallel to y = − 2/5x − 3/4 is y = -2/5x - 1.

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If one of the three machines breaks down before starting the service, it would take the remaining two machines longer to meet the demand. If each machine can produce the same amount of material, it would take each machine 24 hours / 3 machines = 8 hours to perform the entire service.

So, with two machines working, it would take each machine 8 hours / 2 machines = 4 hours to complete the job. Thus, the total time to meet the demand would be 4 hours * 2 machines = 8 hours.

In 30 minutes, the woman will travel 12.5 miles.

This is due to the fact that the rate (25 mph) times the time equals the distance traveled. Mathematically, this can be expressed as d = rt, where d represents the distance, r represents the rate (speed), and t represents the time. In this instance, the distance can be calculated as d = 12.5 miles by multiplying d = 25 mph by 30 minutes/60 minutes.

The distance between two points is measured in distance. The rate, or the amount of distance traveled per unit of time, is the speed at which a person or vehicle travels. The woman in the car is traveling at a rate of 25 miles per hour (mph).

In this instance, the time is. The formula d = rt can be used to determine the distance traveled by multiplying her rate by the time. Given the rate and duration of travel, this formula can be used to determine the distance traveled by any object or person.

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Answer:

Answer is in attached photo.

Step-by-step explanation:

The solution is in the attached photo, do note that this question requires the concept on Pythagoras' Theorem.

The amount of the bottle that is filled with sand is; The whole bottle is full of sand

When talking about fraction word problems we are simply referring to fraction parameters being represented in the form of word problems.

The parameters given are;

Fraction with pink sand = 1/6

Fraction with red sand = 3/6

Fraction with white sand = 2/6

Thus;

Total sand = 1/6 + 2/6 + 3/6

= 6/6 = 1

Thus, the bottle will be full

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Based on each given quadrilateral, we know that:

Rectangle ABCD has:

Rhombus FGHJ:

Square LMNO:

Let's discuss each quadrilateral we have:

ABCD is a rectangle; then:

DC = AB = 12

BD² = BC² + CD²

13² = BC² + 12²

169 = BC² + 144

BC² = 25

BC = 5

DE = 1/2 BD

DE = 1/2 (13)

DE = 6.5

∠DBA and ∠BDC are alternate interior angles and congruent, then:

∠DBA = ∠BDC = 35°

∠DBA = ∠BAC because triangle BAE is isosceles triangle.

∠BAC is the alternate interior angle of ∠DCA; then:

∠BAC = ∠DCA = 35°

∠DAB = ∠DAC + ∠BAC

90° = ∠DAC + 35°

∠DAC = 55°

Focus on triangle DEC:

∠DEC + ∠EDC + ∠ECD = 180°

∠DEC + 35° + 35° = 180°

∠DEC = 110°

Focus on triangle CEB:

∠CEB + ∠EBC + ∠CBE = 180°

∠CEB + 55° + 55° = 180°

∠CEB = 70°

FGHJ is a rhombus; then:

∠JGH = ∠FJH = 2∠FJG

∠JGH = ∠FJH = 2(60)

∠JGH = ∠FJH = 120°

Since FGHJ is a rhombus, then:

∠JGH + ∠JHG + ∠FGH + ∠JFG = 360°

120° + ∠JHG + 120° + ∠JGH = 360°

240° + 2∠JHG = 360°

2∠JHG = 120°

∠JHG = 60°

∠KFG = 1/2∠JHG

∠KFG = 1/2 (60)

∠KFG = 30°

GH = FG = 10

To find KG, we need to focus on triangle F.KG. Under the Sines Law:

KG / sin 30 = FG / sin 90 = F.K / sin 60

KG / √3/2 = 10 / 1 = F.K / 1/2

KG = 5

F.K = 5√3

FH = 2F.K

FH = 2(5√3)

FH = 10√3

LMNO is a square, then:

∠OMN = 45°

Please focus on triangle MNP. Under the Sines Law:

PM / sin 45 = MN / sin 90

PM / √2/2 = 8√2 / 1

PM = 8

LN = 2PM

LN = 2(8)

LN = 16

∠OPL = 90°

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Answer:

B

Step-by-step explanation:

10*10*10 =1000

5*5 =25

2*2 =4

1000+25+4 =1029

Answer:

Below

Step-by-step explanation:

Value will be original value * ( 1 + i)^n      i = decimal annual interest

                                                                      n = years

  Value = 300 ( 1 + .07)^10 = 590.15  (dollars ?)

If p represents the total profit in dollars and cents when the store buys any number of sweaters, s, then the  proportional equation for p in terms of s is, p = $21 x s

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Let's call the selling price of each sweater "sp".

The store buys 15 sweaters for $90, so each sweater must cost

=$90 / 15

= $6

The store sells each sweater for

= $405 / 15

= $27,

so sp = $27

The total profit is equal to the selling price minus the buying price, so the equation for the total profit, p, in terms of the number of sweaters sold, s, is:

p = sp x s - $6 x s

We can simplify this equation to:

p = ($27 - $6) x s

p = $21 x s

So, the proportional equation for the total profit in dollars and cents when the store buys any number of sweaters, s, is:

p = $21 x s

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72 cm²  

3 * ( 6+2+2) + 2 * (2 * 6) + 6 * 3

If  ∆AFD, m ∠F = 90° AD = 14, m ∠D = 30° .The  Area of ∆AFD is 49 square units.

To find the area of triangle AFD, we can use the formula for the area of a triangle given its base and height. In this case, the base is AD, and the height can be found by constructing an altitude from F to AD.

First, we will find the length of FD. Since m ∠D = 30°, we can use the trigonometric  function sine to find the length of FD. Using the sine formula:

FD = AD * sin(∠D) = 14 * sin(30°) = 14 * 1/2 = 7

Next, we will find the length of A.F. Since m ∠F = 90°, FD is the height of the triangle. So, the area of triangle AFD is given by:

Area = (AD * FD) / 2 = (14 * 7) / 2 = 49 square units

Therefore the area of ∆AFD is 49 square units.

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The measure of the supplementary angles is:

∠X = 117°

∠Y = 63°

Here we know that angles ∠X and ∠Y are supplementary angles. Remember that two angles are supplementary if their measures add up to 180°.

Here we know that the measures are:

∠X = 3n − 18

∠Y = 2n − 27

We can write:

∠X + ∠Y = 180°

(3n - 18) + (2n - 27) = 180

Then we can solve that for n.

3n + 2n - 18 - 27 = 180

5n = 180 + 45

n = 225/5 = 45

Then the measures of tha angles are:

∠X = 3n − 18 = 3*45 - 18 = 117°

∠Y = 2n − 27 = 2*45 - 27 = 63°

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There will be left 7.5 grams of the radioactive kind of neodymium after 44 days, with half life of 11 days.

Half-life is the time required for a quantity to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable atoms survive. The term is also used more generally to characterize any type of exponential decay.

Given that, a radioactive kind of neodymium have the half-life is 11 days, and with 120 grams

We need to find the remaining after 44 days,

The formula to calculate half life =

[tex]N(t) = N(1/2)^\frac{t}{t_{1/2} }[/tex]

N(t) = quantity of the substance remaining

N = initial quantity of the substance

t = time elapsed

t{1/2} = half life of the substance

N(t) = 120(1/2)⁴⁴/₁₁

= 120(1/2)⁴

= 120(1/16)

= 7.5

Hence, there will be left 7.5 grams of the radioactive kind of neodymium after 44 days, with half life of 11 days.

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The parametric equations of a line can be determined using a point on the line and a direction vector. To find the parametric equation of a line that passes through a point A and is parallel to a direction vector b, we can use the following formula:

x = x0 + tbx

y = y0 + tby

z = z0 + tbz

where (x0, y0, z0) is the position vector of point A, (bx, by, bz) is the direction vector, and t is the parameter that varies along the line.

An algebraic equation, also known as a polynomial equation, is a mathematical equation of the form P=0, where P is a polynomial with coefficients in some field, most commonly the field of rational numbers. An algebraic equation is a mathematical statement that sets two expressions equal to each other. An algebraic equation is typically made up of a variable, coefficients, and constants.

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The difference 120.45-116.9 is 3.55.

Subtraction is a mathematic operation. Which is used to remove terms or objects in an expression.

Given:

The two decimal numbers,

120.45 and 116.9.

Applying subtraction operation,

the difference 120.45-116.9.

By adding on strategy,

116.9 is 3.55 left to the number 120.45 on the number line.

That means,

116.9 + 3.55 = 120.45.

Therefore, the difference is 3.55.

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Answer:

x=105

Step-by-step explanation:

The angles of a triangle add up to 180 degrees.

[tex]180 = 30 +45+x[/tex]

[tex]x=105[/tex]

The amounts of bacteria are given as follows:

The exponential function y = 8^x is graphed by the image presented at the end of the answer.

An exponential function is defined as follows:

y = ab^x.

In which:

The parameters for this problem are given as follows:

Hence the function is defined as follows:

y = 8^x.

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The new volume of the cylinder is 39.94cm³

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder.

The volume of a cylinder is expressed as V = πr²h

The volume of the original cylinder = 10cm³

The radius and height of the new cylinder = 4r and 4h

10 = 3.14 × r²h

V 2= 3.14 × 4r²4h

V2 = 3.14× 4( r²h)

10=3.14 × r²h

r²h = 10/3.14

r²h = 3.18

from

V2 = 3.14 × 4(r²h)

represent 3.18 by r²h in the equation

V2 = 3.14 × 4 ( 3.18)

V2 = 39.94cm³

therefore the volume of the new cylinder is 39.94 cm³

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The independent quantity is the number of days into the monitoring and the dependent quantity is the number of mole rats counted.

The independent quantity refers to a variable that is not influenced by any other factor and can be changed freely in an experiment or study.

In this case, the number of days into the monitoring is the independent quantity because it can be varied at the discretion of the zoo keeper.

The dependent quantity, on the other hand, is a variable that depends on the independent quantity and is affected by changes in it.

In this case, the number of mole rats counted is the dependent quantity because it is determined by the number of days into the monitoring. The zoo keeper counts a different number of mole rats based on how many days have passed, which is determined by the independent quantity.

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A zoo keeper thinks there is a problem with the Mole-Rat population at the zoo. He starts keeping track of the animals in the tunnels. 7 days into his monitoring he counts 120 mole rats, 13 days in he counts 108.

what information is provided?