The incremental profit is $175,000 and the new situation would obviously have less business risk than the old one.
Incremental profitFirst step
Profit $600,000
Add Fixed cost $3,000,000
Contribution $3,600,000
Variable Cost=Total Sales−Contribution
Variable Cost=$115,000×50-$3,600,000
Variable Cost=$2,150,000
Second step
Profit at revised cost
Sales $8,625,000
(75x $115,000)
Less: Variable cost $4,350,000
[75×($3,000,000+$500,000/50-$12,000)]
Contribution $4,275,000
Less Fixed cost $3,500,000
($3,000,000+$500,000)
Profit $775,000
Incremental profit=Profit at revised cost-Existing profit
Incremental profit=$775,000-$600,000
Incremental profit=$175,000
Expected rate of return=Incremental profit/Investment
Expected rate of return=$175,000/$4,000,000×100
Expected rate of return=$4.375%
2. Break-even point
Existing
Break-even point=Fixed cost/Contribution
Break-even point=$3,000,000/[($115,000-($3,000,000+$500,000/50)]
Break-even point=$3,000,000/[($115,000-$70,000)
Break-even point= 66.67
Revised
Break-even point=Fixed cost/Contribution
Break-even point=$3,500,000/[($110,000-($3,000,000/50)]
Break-even point=$3,000,000/[($110,000-$60,000)
Break-even point=60
II. The new situation would obviously have less business risk than the old one.
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A. In 2000, the population of a country was approximately 5.89 million and by 2050 it is projected to grow to 10 million.
Use the exponential growth model A = Ao ekt, in which t is the number of years after 2000 and Ao is in millions, to find
an exponential growth function that models the data.
B. By which year will the population be 11 million?
A. The exponential growth function that models the data is: [tex]A(t) = 5.89{0.0106t}[/tex]
B. Using the function, the population will be 11 million by 2059.
What is the exponential growth function for the population?The function is given by:
[tex]A(t) = A(0)e^{kt}[/tex]
In which:
A(0) is the population in 2000.k is the exponential growth rate, as a decimal.t is the number of years after 2000.Item a:
We have that:
A(0) = 5.89, A(50) = 10.
We use this to find k, hence:
[tex]A(t) = A(0)e^{kt}[/tex]
[tex]10 = 5.89e^{50k}[/tex]
[tex]e^{50k} = \frac{10}{5.89}[/tex]
[tex]\ln{e^{50k}} = \ln{\frac{10}{5.89}}[/tex]
[tex]50k = \ln{\frac{10}{5.89}}[/tex]
[tex]k = \frac{\ln{\frac{10}{5.89}}}{50}[/tex]
k = 0.0106.
Hence the equation is:
[tex]A(t) = 5.89{0.0106t}[/tex]
Item b:
We have to solve for t when A(t) = 11, hence:
[tex]A(t) = A(0)e^{kt}[/tex]
[tex]11 = 5.89e^{0.0106t}[/tex]
[tex]e^{0.0106t} = \frac{11}{5.89}[/tex]
[tex]\ln{e^{0.0106t}} = \ln{\frac{11}{5.89}}[/tex]
[tex]0.0106t = \ln{\frac{11}{5.89}}[/tex]
[tex]t = \frac{\ln{\frac{11}{5.89}}}{0.0106}[/tex]
t = 58.9
Rounding up, the population will be of 11 million in 2059.
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A supermarket purchases chickens wholesale from a farm for $4 each. The store then marks up the chickens 50%. After 10:00 p.m., the supermarket marks down the price of the chickens by 50% to make sure they all sell before the store closes. Which statements are true about the price of a chicken?
The true statements are:
The marked up price of chicken before 10pm is $6
The 50% mark down is taken off the marked up price
What are the true statements?Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred.
Price after the mark up= (1 + mark up) x initial price
1.50 x 4 = $6
Price after the mark down = (1 - percentage mark down) x price after mark up
0.50 x $6 = $3
Here are the options:
The marked up price of chicken before 10pm is 6
The 50% mark down is taken off the marked up price
The chickens sell for $4 after 10pm
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[tex] \sf{x {}^{2} + 6x + 7 = 0 }[/tex]
x² + 6x + 7 = 0
help please it's due today :(
[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\large{\textsf{\textbf{\underline{\underline{Answer : \:}}}}}}[/tex]
[tex] \bold{ \blue{Answer:} \sf{x = \sqrt{2} - 3, - \sqrt{2 } - 3 }}[/tex]
[tex]\bold{Step \: \: by \: \: step \: \: explanation }[/tex]
1: The expression x² + 6x + 7 fits the form a x²+ bx + c Let's complete the square, where:
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{a = 1} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf{ b = 6} \\ \sf{c = 7}[/tex]
2: Enter the constant k, which is 9 in our case.
[tex] \sf{x {}^{2} + 6x {}^{} + 9 - 9 + 7}[/tex]
3: Use Sum Square (a + b) ² = a² + 2ab + b².
[tex] \sf{(x + 3) {}^{2} - 9 + 7}[/tex]
4: Simplify
[tex] \sf{(x + 3) { }^{2} - 2}[/tex]
5: Substitute the above back into the original equation.
[tex] \sf{( x + 3) {}^{2} - 2 = 0}[/tex]
6: Add 22 to both sides.
[tex] \sf{(x + 3) {}^{2} = 2}[/tex]
7: Take the square root of both sides.
[tex] \sf{x + 3 = ± \sqrt{2}} [/tex]
8: Divide the problem into these 2 equations.
[tex]\sf{x + 3 = \sqrt{2} } \\ \: \: \: \: \: \sf{x + 3 = - \sqrt{2} }[/tex]
9: Solve the 1st equation:
[tex] \sf{ x + 3 = \sqrt{2} } \\ \sf{x = \sqrt{2} - 3 }[/tex]
10: Solve the 2nd equation.
[tex] \sf{ x + 3 = - \sqrt{2} } \\ \sf{x = - \sqrt{2} - 3 } [/tex]
11: Collect all the solutions.
[tex] \sf{x = \sqrt{2} - 3, - \sqrt{2} - 3 }[/tex]
I hope I've helped : )
Estimate the decimal 61.33 + 53.482 by first rounding each number to nearest whole number
Answer:
it's
answer
is
32.36
.
.
.
.
.
.
.
..
.
.
..
.
.
.
.
.
Write 4.714 as a mixed number
Answer:
47/14 is a mixed number i think
It's the computer seice can u help me
Answer:
I can help you, just tell me what it is.
Step-by-step explanation:
Step 1: Tell me the problem
Step 2: Wait for a response.
Answer:
yes it can help in some ways I think
Which of the following is a characteristic of all parallelograms?
A. All pairs of consecutive angles are complementary.
B. Both pairs of opposite sides are parallel.
C. The diagonals are congruent.
D. The diagonals are perpendicular.
IF THREE DIAGONALS ARE DRAWN INSIDE A HEXAGON WITH EACH ONE PASSING THROUGH THE CENTER POINT OF THE HEXAGON, HOW MANY TRIANGLES ARE FORMED?
Answer: 6 triangles
Step-by-step explanation:
hope this helps :)
Which graph represents this inequality? 3x + y ≤ 1
Answer:
Step-by-step explanation:
Tierra, Nico, and Alex had $ 865 altogether.
Tierra spent 2/5 of her money. Nico spent $40,
and Alex spent twice as much as Tierra. If the 3
friends had the same amount of money left, how
much money did Alex have in the beginning?
Alex had $444.231 in the beginning.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let, x = the money Tierra had in the beginning
y = the money Nico had in the beginning
z = the money Alex had in the beginning
Tierra, Nico and Alex had $865 altogether
x + y + z = 865
Tierra spent 2/5 of her money and now she has: x - (2/5)x = 3x/5 left
Nico spent $40 and now has y - 40 left
Alex spent twice as much as Tierra and now has z - 2(2/5)x = z - 4x/5 left
the three friends had the same amount of money left
3x/5 = y - 40
y - 40 = z - 4x/5
by solving the system of equations
x + y + x = 865
3x/5 = y - 40
y - 40 = z - 4x/5
we find
x= $317.308
y = $230.385
z = $444.231
Alex had $444.231 in the beginning.
Hence, Alex had $444.231 in the beginning.
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A farmer needs to mix 8 ounces of fertilizer for every 10 pounds of soil. How many pounds of fertilizer will the farmer need to make a mix that contains 80 pounds of soil? ( Remember- 16 ounces = 1 pound)
4 pounds of fertilizer is mixed to make a mix of 80 pounds of soil.
What is Ratio ?The relationship between two things is called Ratio. It is written in p:q form.
It is given that
For 10 pounds of soil , farmer mixes 8 ounces of fertilizer.
=8/16 = 0.5 pounds of fertiliser
The ratio is 10 : 0.5
Suppose he mixes x pounds of fertilizer for 80 pounds of soil
to determine x
The ratio is 80 : x
As they are in Proportion
10 / 0.5 = 80 /x
x = 80 * 0.5 /10
x = 4 pounds
Therefore 4 pounds of fertilizer is mixed to make a mix of 80 pounds of soil.
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Anderson's Solar Systems manufactures solar panels, and their business is growing. Last year,
they hired 90 new employees. This year, they hired 20% more new employees than they hired las
year. How many new employees were hired this year?
which of the following ordered pairs satisfies the following linear pairs? 3x+2y=-2 x+2y=2
Answer:
-2
Step-by-step explanation:
you will group the like terms and add and subtract the remaining digits
Determine the period.
Using it's concept, it is found that the period of the function is of 20 units.
What is the period of a function?The period of a function is given by the distance between it's repetitions.
Looking at the graph, the distance between the repetitions is of 20 units, which is the period of the function.
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A ferris wheel is 15 meters in diameter and boarded from a platform that is 4 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 2 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. Write an equation for h = f(t).
The equation for h = f(t) will be, [tex]\rm h(t)=7.5sin({\pi}t-\frac{\pi}{2})+12.5[/tex].
What is a function?A connection between independent variables and the dependent variable is defined by the function. Functions help to represent graphs and equations.
The given data in the problem is;
Ferris wheel diameter,d= 15 meters
The platform is 5 m above the ground.
The Ferris wheel function is;
h(t) = A sin(Bt + C) + D
Here,
A is Amplitude
D is the midline
B is period
C is a phase shift
t is the time
The amplitude of the function is half of the diameter;
A = d/2
A=15 m /2
A = 7.5 m
The value of the mid-line is found as;
Mid-line = amplitude + distance from the mid-line;
D= 7.5 + 5
D = 12.5
From the given data, the wheel completes 1 full revolution in 2 minutes
The period of the wheel is T.
B = 2
The phase shift is found as;
[tex]\rm \frac{C}{\pi}=\frac{-1}{2}\\\\ {C}=\frac{-\pi}{2}[/tex]
The Ferris wheel function is;
h(t) = A sin(Bt + C) + D
Substitute the obtained values we get;
[tex]\rm h(t)=7.5sin({\pi}t-\frac{\pi}{2})+12.5[/tex]
Hence, the equation for h = f(t) will be, [tex]\rm h(t)=7.5sin({\pi}t-\frac{\pi}{2})+12.5[/tex].
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What are the domain and
range of the function below?
Answer:
2nd answer option
Step-by-step explanation:
the domain is the interval or set of valid x values. the range is the same for valid y values.
so, what is the smallest x value we see in the functional graph ?
x = 0
there is no functional value for any x smaller than that.
and then the function goes on and on to the right in all eternity. that means it goes to infinity.
so, domain = [0, infinity)
please consider the round bracket at the end, because "infinity" is not a number.
now for the range and the y values.
in this case I start to ask for the largest y value.
y = 4
for no x value do we get a larger y value.
but it goes down and down in all eternity, going also to infinity, but -infinity (down is negative for y).
so, the range = (-infinity, 4]
"-infinity" is also not a number and therefore not included (hence the round bracket).
Which equation represents the standard form of the equation y= (x + 3)² - 4?
A. y=x² + 3x-4
B. y=x2² +6x+5
C. y=x² + 6x-4
D. y=x2²+3x+5
Answer:
The answer is B. [tex]y = x^2 + 6x + 5[/tex]
Step-by-step explanation:
Because [tex]y = (x + 3)^2 - 4 = x^2 + 6x + 9 - 4 = x^2 + 6x + 5[/tex]
So the answer in this question is B.
Math interest, I, P, R,T
I will give more points to you once questions are completed.
The interest based on the information given is $2564.
How to calculate the interest?From the information given, the following can be deduced:
Principal = $36900
Time = 178 days
Rate = 14.25%
The simple interest will be:
= (PRT)/100
= (36900 × 14.25 × 178/365)/100
= $2564
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A rectangular piece of metal is 30 in longer than it is wide. Squares with sides 6 in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 594 inch to the 3 in, what were the original dimensions of the piece of metal?
The original dimensions of the metal sheet are 22 inches by 52 inch
What is volume?The volume is defined as the space occupied by any object in three dimensions. For a rectangular box, the volume will be calculated by multiplying the length, width, and height of the object.
If the Width of the metal = x
The length is 30 inches longer than its width= x+30
If Squares with sides 6 in long are cut from the four corners and the flaps are folded.
The length of the pre-folded box =x+30-12=(x+18)inch
The width of the pre-folded box = (x-6-6)inch = (x-12) inch
The height of the flap= 6 inch
The volume of the box = 2400-inch cubed
Volume of a Cuboid = LWH
6(x-12)(x+18)=2400
6x²+36x-1296=2400
6x²+36x-1296-2400=0
6x²+36x-3696=0
6(x-22)(28+x)=0
x-22=0 or x+28=0
Therefore the original dimensions of the metal sheet are 22 inches by 52 inch
The complete question with correct data is given below:-
A rectangular piece of metal is 30 in longer than it is wide. Squares with sides 6 in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 2400 incubatedwhat were the original dimensions of the piece of metal?
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Elaine had StartFraction 5 Over 8 EndFraction of a pizza left after lunch. She told 5 of her friends that they could share the rest. What fraction of the pizza did each of her friends get if they split it evenly?
The fraction of pizza each of her friends get if they split it evenly is 1/8
Division of fractionQuantity of pizza Elaine has = 5/8Number of Elaine friends = 5Number of pizza each friend gets = Quantity of pizza Elaine has ÷ Number of Elaine friends
= 5/8 ÷ 5
= 5/8 × 1/5
= (5 × 1) / (8 × 5)
= 5/40
= 1/8
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HELP FAST PLEASEE
(05.05 MC)
What are the measures of Angles a, b, and c? Show your work and explain your answers.
(PLEASE EXPLAIN WELL)
Answer:
a=30,b=60,c=105
Step-by-step explanation:
a = 30 vertical angle therom
b = 180-120 = 60 using triangle sum therom
c = 180-75 = 105 because a line is always 180 degrees
A ball is dropped off a high cliff, and 2 s later another ball is thrown vertically downward with an initial speed of 30 ms¹. How long will it take the second ball to overtake the first?
helppppppp!!! pleaseeeeeeeee
Answer:
62,400 J
Step-by-step explanation:
As the problem statement tells you, the work done to lift the mass is the product of the force applied and the distance the mass is lifted. Here, the force decreases as the height of the mass increases.
SetupFor x meters of exposed cable, the force required to lift it is 3x newtons. The force required to lift the object is 1500 newtons, so the total force required to lift the masses an incremental distance (dx) is (3x +1500) newtons.
The work done lifting the mass that distance is the product of force and distance. The total work done is the integral of the incremental work over the total of distance lifted:
[tex]\displaystyle W = \int_0^{40}(3x+1500)\,dx[/tex]
SolutionThe value of the integral is ...
[tex]\displaystyle W=\left.\left(\dfrac{3}{2}x^2+1500x\right)\right|_{x=0}^{x=40}=40\left(\dfrac{1}{2}(3\cdot40)+1500\right)=62\,400\qquad\text{joules}[/tex]
The work done to lift the cable and weight is 62,400 joules.
__
Additional comment
One reason for writing the integral evaluation this way is to demonstrate that the total of work done is that required to lift the weight (1500 N, 40 m) and that required to lift the center of mass of the cable (120 N, 20 m).
This will generally be the case for "disappearing mass" or "increasing distance" problems. Pumping from a pool is a similar kind of problem with a similar kind of solution.
Effectively, you're doing work on the center of mass of the system, moving it from its initial position to the top of the building.
Edward Nigma is installing square tiles in his bathroom. The blueprint above is a scaled drawing of the tile pattern to be used. If the total area of the shaded region is 22 ft^2, what is the total floor area of the bathroom?
Answer:
H. 99 ft²
Step-by-step explanation:
Area is proportional to the number of tiles.
ProportionThe total area of the bathroom is 6×9 = 54 tiles. Of these, 12 are shaded. The proportion can be written as ...
total area / shaded area = total tiles / shaded tiles
total area / (22 ft²) = 54/12 . . . . . use given numbers
total area = (22 ft²)×(54/12) = 99 ft² . . . . . multiply by 22 ft²
The total floor area of the bathroom is 99 square feet.
If the Federal Reserve sets the reserve rate to 4%, what is the resulting money
multiplier?
Answer:
The money multiplier is the ratio of money supply to the money base. The money base is the sum of currency in circulation and reserves held by commercial banks.
The reserve rate is the percentage of deposits that commercial banks must hold in reserve.
If the reserve rate is 4%, the money multiplier is 10.
Step-by-step explanation:
Could someone help me out?
The values of the functions are f(4) = 47, f(k) = 2(k)^2 + 4(k) - 1 and f(x + h) = 2x^2 + 4hx + 2h^2 + 4x + 4h - 4
How to evaluate the expression?The function is given as:
f(x) = 2x^2 + 4x - 1
To calculate f(4), we have:
f(4) = 2(4)^2 + 4(4) - 1
Evaluate the expression
f(4) = 47
To calculate f(k), we have:
f(k) = 2(k)^2 + 4(k) - 1
To calculate f(x + h), we have:
f(x + h) = 2(x + h)^2 + 4(x + h) - 1
Expand
f(x + h) = 2(x^2 + 2hx + h^2) + 4x + 4h - 4
Expand
f(x + h) = 2x^2 + 4hx + 2h^2 + 4x + 4h - 4
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your family is driving from cincinnati to st louis. the graph relates your distance from st.louis d in miles and travel time h (in hours). The equation of the line is d=360-60h
The solution is about a distance-time graph. The interpretation of the graph is that it took the family 6 hours to travel a distance of 360 miles. Note that the distance is plotted on y-axis and time on the x-axis.
What is a distance-time graph?A distance time graph is a simple graph that shows the relationship between the time travelled the distance covered while doing do.
The slope-intercept form is
y= mx+b−⋯(1)
The y-intercept is 360
⇒b = 360; and m = −60
Substituting the value of m = −60
and b = 360
in (1) above,
⇒y = −60x +360
The x-intercept is
y = 0,
⇒0= −60x+360
hence, x=6
The y-intercept is
x=0
⇒y=−60(0)+360
⇒y=360
In conclusion, the x - intercept is the time in hours between Cincinnati and St. Loui: and
The y - intercept is the distance between Cincinnati and St. Louis.
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Suppose that a forest on a flat terrain has perimeter 200 kilometers, but there is no information on the shape of the forest. What shape will give the largest possible area for the forest? what is this area?
The largest possible area of the forest is 2500 km^2
How to determine the largest area?The perimeter is given as:
P = 200 km
The shape that will give the largest possible area for the forest is a square, and the area is calculated as:
A = (P/4)^2
This gives
A = (200/4)^2
Evaluate
A = 2500 km^2
Hence, the largest possible area of the forest is 2500 km^2
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What is the gradient of the graph shown?
Answer:
gradient: 1.5
Explanation:
Take two points from the graph: (2, 0), (0, -3)
[tex]\sf gradient : \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
So here given:
(x₁ , y₁) = (2, 0)(x₂ , y₂) = (0, -3)Inserting values
[tex]\rightarrow \sf gradient : \dfrac{-3-0}{0-2} = \dfrac{-3}{-2} = 1.5[/tex]
PLEASE HELP
Graph the following exponential function. Show work in how you find the y intercept, talk about the end behavior, and state if it is a growth or decay function. See image.
The y-intercept of the function is -9,25
How to graph the function?The function is given as:
[tex]y = -5(.8)^{x - 1} - 3[/tex]
See attachment for the graph of the function
From the graph, we have the following highlights:
y-intercept = -9,25As x increases, y approaches -3As x decreases, y approaches negative infinityRead more about exponential functions at:
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