A lemonade recipe calls for the juice of 5 lemons, 2 cups of water, and 2 tablespoons of honey.
Invent four new versions of this lemonade recipe:
1: One that would make more lemonade but tastes the same as the original recipe.
2: One that would make less lemonade but taste the same as the original recipe.
3: One that would have a stronger lemon taste than the original recipe
4: One that would have a weaker lemon taste than the original recipe.
Since the lemonade recipe calls for the juice of 5 lemons, 2 cups of water, and 2 tablespoons of honey we can use mathematical operations to make different lemonades with the following recipes:
1) To make more lemonade taste the same as the original, we can use the multiplication operation on the above recipe as follows:
Lemons = 10
Cups of water = 4
Tablespoons of honey = 4
2) To make less lemonade taste the same as the original recipe, we can use the division operation as follows:
Lemons = 2.5
Cups of water = 1
Tablespoons of honey = 1
3) To make lemonade that has a stronger lemon taste than the original recipe, we can use the subtraction operation as follows:
Lemons = 4
Cups of water 1
Tablespoons of honey
4) To make lemonade that has a weaker lemon taste than the original recipe, we can use the addition operation as follows:
Lemons = 6
Cups of water 3
Tablespoons of honey = 3
Original Lemonade Recipe:Lemons = 5
Cups of water = 2
Tablespoons of honey = 2
1) Using the multiplication operation to make more lemonade taste the same as the original:
Lemons = 10 (5 x 2)
Cups of water = 4 (2 x 2)
Tablespoons of honey = 4 (2 x 2)
2) Using the division operation to make less lemonade taste the same as the original recipe:
Lemons = 2.5 (5 ÷ 2)
Cups of water = 1 (2 ÷ 2)
Tablespoons of honey = 1 (2 ÷ 2)
3) Using the subtraction operation to make lemonade that has a stronger lemon taste than the original recipe:
Lemons = 4 (5 - 1)
Cups of water 1 (2 - 1)
Tablespoons of honey = 1 (2 - 1)
4) Using the addition operation to make lemonade that has a weaker lemon taste than the original recipe:
Lemons = 6 (5 + 1)
Cups of water 3 (2 + 1)
Tablespoons of honey = 3 (2 + 1)
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Picture is the question
The months when the temperature will be 0 °C are May and August.
What is a trigonometric function?A trigonometric function is a function that has the trigonometric ratios.
What is temperature?Temperature is the degree of hotness or coldess of a body.
How to find the months in which the temperature is zero degrees?Since the average monthly temperature of a particular city is T(m) = 10cos(πm/6) + 5 where m = number of months of year and January begins at m = 0.
To find the number of months in which the temperature would be 0°C. This means T(m) = 0.
So, T(m) = 10cos(πm/6) + 5
0 = 10cos(πm/6) + 5
-10cos(πm/6) = 5
cos(πm/6) = 5/10
cos(πm/6) = -0.5
cos⁻¹cos(πm/6) = cos⁻¹(-0.5)
(πm/6) = π - π/6 or (πm/6) = 3π/2 - π/6 (since cos is negative int he second and third quadrant respectively)
πm/6 = 5π/6 or πm/6 = 8π/6
⇒ m = 5π/6 × 6/π or m = 8π/6 × 6/π
⇒ m = 5 or m = 8
Since m = 5 is May and m = 8 is August,
The months when the temperature will be 0 °C are May and August.
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Aiman has 6 pizzas to share at a party. If each person will eat 3 8 of a pizza, how many people can share the pizzas?
HINT: Use division!
Answer: 16
Step-by-step explanation: 16 people can share the pizzas.
Solve the equation: x^2-13/2 x+15/2=0
Answer:
Step-by-step explanation:
199/4
Look at photo for problem
Just need chart filled out
6. y=(x-2)(x-4)
On solving the given equation y=(x-2)(x-4) the point on the graph are as follows:
(4,0), (2,0), (5,3), (3,-1) &(0,8)
What is a graph?
A relation is a specific instance of a function graph. A function is truly equivalent to its graph in set theory and the current mathematical underpinnings.
It is frequently more helpful to think about functions as mappings, which include the sets that constitute the domain and the codomain in addition to the relationship between input and output. For instance, the codomain should be considered while determining if a function is onto (surjective) or not. The codomain of a function is not determined by the graph alone.
It is typical to use the phrases function and graph of a function interchangeably since, although referring to the same thing, they suggest distinct ways of looking at it.
1)
let y=0
0=(x-2)(x-4)
i.e. x = 4 and 2
2)
Let x =0
y=(0-2)(0-4)
y=8
3)
Let x = 3
y=(3-2)(3-4)
y=-1
4)
Let x = 5
y=(5-2)(5-4)
y=3
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Dominique throws a softball from the outfield. After 1 second, the ball is 15 feet high. After 4 seconds, the ball reaches its maximum height of 42 feet. After 7 seconds, it returns to a height of 15 feet. What is the equation of the quadratic function that models the height of the ball h(t) at time t? h(t) = −2(t − 4)2 + 42 h(t) = 2(t + 4)2 + 42 h(t) = −3(t − 4)2 + 42 h(t) = 3(t + 4)2 + 42
The equation of the quadratic function that models the height of the ball h(t) at time t is h(t) = −3(t − 4)² + 42
How to determine the equation of the height function?From the question, we have the following parameters that can be used in our computation:
Height after 1 second = 15 feetHeight after 7 seconds = 15 feetMaximum height = 42 feetThe above parameters mean that
h(1) = 15
h(7) = 15
h max = 42
This also means that the leading coefficient of the function is negative
So, the possible equations from the options are
h(t) = −2(t − 4)² + 42
h(t) = −3(t − 4)² + 42
Calculate h(1) and h(7)
h(t) = −2(t − 4)² + 42
h(1) = −2(1 − 4)² + 42 = 24
h(7) = −2(7 − 4)² + 42 = 24
h(t) = −3(t − 4)² + 42
h(1) = −3(1 − 4)² + 42 = 15
h(7) = −3(7 − 4)² + 42 = 15
Hence, the function is h(t) = −3(t − 4)² + 42
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Answer: Answer is C
Step-by-step explanation:
I took the test and it gave me credit for this question
As part of the training for the cross-country team, you must run a total of 20 miles per week. You ran 5.6 miles in the first two days of the week. If you run the same amount each day for the remaining five days, how many miles must you run per day to complete the 20 miles?
Write and solve an equation to determine the number of miles, m, you must run per day.
5m + 2(5.6) = 20; m = 1.76
5m + 5.6 = 20; m = 2.88
5m − 5.6 = 20; m = 5.12
m + 5(5.6) = 20; m = 8
pls help
The equation to determine the number of miles, m, you must run per day is B. 5m + 5.6 = 20; m = 2.88
How to illustrate the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. An equation is not the same as a mathematical expression. The equal (=) operator is always used to join two mathematical expressions in an equation.
In mathematics, an equation is a relationship between two expressions that is expressed as an equality on either side of the equal to sign. An equation would be 3y = 16, for instance. Equations can be categorized into one of the following three categories depending on their degree:
linear formulaquadratic formulaCubic problemIn this scenario, the person must run a total of 20 miles per week and ran 5.6 miles in the first two days of the week.
Let the number of miles for the remaining 5 days be m.
This will be:
5m + 5.6 = 20;
Solving for m = will give 2.88.
In conclusion, the correct option is B.
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10 points and brainliest.
two people need to answer or i won't be able to give brainliest
Fifteen students completed 80 puzzles. How many puzzles would 1 student complete? Round the answer to the nearest tenth.
1.6
0.2
5.3
15.0
5.3
80/15=5.3
which means each person completed 5.3 puzzles
In the last ten games, Jamal made 7/9 of his free throws and Brian made 5/8of his free throws. Which player has the better record? Explain.
By using the concept of fraction, it can be calculated that
Jamal has the better record
What is a fraction?
Suppose there is a collection of objects and a part of the collection has to be taken. The part which is taken is called fraction. In other words, part of a whole is called fraction.
The upper part of the fraction is called numerator and the lower part of the fraction is called denominator.
This is a word problem on fraction
Portion of free throws Jamal made in the last ten games = [tex]\frac{7}{9}[/tex]
Portion of free throws Brian made in the last ten games = [tex]\frac{5}{8}[/tex]
To compare between [tex]\frac{7}{9}[/tex] and [tex]\frac{5}{8}[/tex]
LCM of 9 and 8 = 72
[tex]\frac{7}{9} = \frac{7 \times 8}{9 \times 8} = \frac{63}{72}[/tex]
[tex]\frac{5}{8} = \frac{5 \times 9}{8 \times 9} = \frac{45}{72}[/tex]
As [tex]\frac{63}{72} > \frac{45}{72},[/tex]
So [tex]\frac{7}{9} > \frac{5}{8}[/tex]
So, Jamal has the better record
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The law of large numbers and the central limit theorem tell us how standard deviations behave as medians increase.
a. true
b. false
The law for all large numbers with the central limit-theorem will tell us about how standard deviations doesn't as increase with medians. So b). false is correct.
The Law for all Large Number states that once pattern length has a tendency to infinity, the pattern imply equals to populace imply. The statements aren't contradictory. The Central Limit Theorem inform us that because the pattern length has a tendency to infinity, the of the distribution of pattern method methods the ordinary distribution.
The regulation of huge numbers has a completely vital position in possibility and statistics. It states that in case you repeat an test independently a huge variety of instances and common the result, what you got must be near the predicted value.
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The force “F” (in pounds) needed on a wrench handle to loosen a certain bolt varies inversely with the length “L” (in inches) of the handle. A force of 35 pounds is needed when the handle is 6 inches long. If a person needs 25 pounds of force to loosen the bolt, estimate the length of the wrench handle. Round answer to two decimal places if necessary.
______ inches.
The length of the wrench handle 8.4 inches.
What is length?
Distance is measured in length. Length has the dimension of distance in the International System of Quantities. The majority of measurement systems choose a base unit for length from which all other units are derived. The metre serves as the foundational unit of length in the International System of Units.
f = k/l
35 = k/6
k = 210
f = 210/l
25 =210/l
l = 8.4 inches
The length "L" (in inches) of a wrench handle has an inverse relationship with the force "F" (in pounds) required to remove a certain bolt. In the case of a handle that is 6 inches long, 35 pounds of power is required. The length of the wrench handle if the bolt needs to be loosened with 25 pounds of force is 8.4 .
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What is the slope of a line parallel to the line whose equation is 3x-2y=14
Answer: 3/2
Step-by-step explanation:
3x - 2y = 14
-2y = 14-3x
y = 3/2x-7 divide both sides by -2
what is the average rate of change of the function on the interval from x=1 to x=2? f(x) = 10(5.5)^x
Answer: 246.7
Step-by-step explanation:
Which lists all the real zeros of the polynomial p(x)=x(x2−9)
The zero's of the polynomial p(x) = x(x² - 9) are -3, 0 and 3.
How to find zero's of a polynomial?The zero's of a polynomial p(x) are all the x-values that make the polynomial equal to zero.
In other words, zeros of a polynomial can be defined as the points where the polynomial becomes zero as a whole.
Therefore, let's find the zero's of the polynomial .
p(x) = x(x² - 9)
p(x) = x³ - 9x
0 = x³ - 9x
x³ = 9x
x² = 9
x = √9
Therefore, x = -3 or 3
x = 0
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There were 500 sweets in a box and Mrs. Miller has given out 35% as prizes. How many are left in
the box?
The number of sweets left in the box after giving 35% is 325.
How to find the sweet left in the box?There were 500 sweets in a box and Mrs. Miller has given out 35% as prizes. The number of sweets left in the box can be calculated as follows:
Therefore, the number of sweet left in the box = 500 - 35% of 500
number of sweet left in the box = 500 - 35 / 100 × 500
number of sweet left in the box = 500 - 17500 / 100
number of sweets left in the box = 500 - 175
= 325
Therefore, the number of sweets left in the box will be 325
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Write the statement "the sum of a number and 10.7 is at most −3.2" as an inequality.
The given statement:
"the sum of a number and 10.7 is at most −3.2"
Is equivalent to the following inequality:
x + 10.7 ≤ -3.2
How to write the inequality?Here we have the following statement:
"the sum of a number and 10.7 is at most −3.2"
So let's define the variable "x" as "the number", we know that the sum between x and 10.7 is at most -3.2, we can say that the sum is equal to or smaller than -3.2
In that case, the symbol we need to use is: ≤
Then the inequality is:
sum ≤ -3.2
x + 10.7 ≤ -3.2
That is the statement written as an inequality.
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Find the reciprocals of the following numbers.
a, if a ≠ 0
The Reciprocal of a (if a ≠ 0) is...
Reciprocal of a = [tex]\frac{1}{a}[/tex]
What is Reciprocal ?
In Mathematics , reciprocal is simply defined as the inverse of a value or a number. If n is a real number, then its reciprocal will be 1/n.
What are real numbers ?
In mathematics, a real number is a quantity that may be represented by an endless number of decimal expansions .
According to the given information
a ≠ 0
a is a real number
By the definition of reciprocal
Reciprocal of a will be the inverse of a = [tex]\frac{1}{a}[/tex]
Reciprocal of a = [tex]\frac{1}{a}[/tex]
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Which of the following is equivalent to 5(x+6)-6(3x+3)=10
Answer:
B
Step-by-step explanation:
5x + 30 - 18x - 18 = 10
-13x + 12 = 10
Help Please!!
Line q has an equation of y+7=9(x+4). Line r is perpendicular to line q and passes through (9,–10). What is the equation of line r?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
Answer:
Y= -1/9x-9 that's the answer, you're welcome
The equation of line which is perpendicular to the line q is given by
y = ( -1/9 )x - 9
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
The point is P ( 9 , -10 )
Let the equation of line q be y + 7 = 9 ( x + 4 )
Now , on simplifying the equation , we get
y + 7 = 9x + 36
Subtracting 7 on both sides of the equation , we get
y = 9x + 29
Now , the slope of the equation q is m₁ = 9
Now , since the line r is perpendicular to line q
The product of the slope is -1
So , m₁ x m₂ = -1
Substituting the values in the equation , we get
9 x m₂ = -1
Divide by 9 on both sides of the equation , we get
m₂ = -1/9
So , the slope of the line r m₂ = -1/9
The equation of line is given by y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - ( -10 ) = -1/9 ( x - 9 )
On simplifying the equation , we get
y + 10 = -1/9 ( x - 9 )
y + 10 = ( -1/9 )x + 1
Subtracting 10 on both sides of the equation , we get
y = ( -1/9 )x - 9
Therefore , the value of A is y = ( -1/9 )x - 9
Hence , the equation of line r is y = ( -1/9 )x - 9
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Can a triangle be formed with side lengths 15, 7, and 6? Explain
Answer:no
Step-by-step explanation:
There is a property with triangles that the sum of two sides of a triangle should always be greater than the 3rd side.
Here if we take the two smaller sides their sum is 7 + 8 = 15 which is equal to the third side.
So it is not possible to construct a triangle with sides 7, 8, and 15 respectively.
k h S Which of the following is a true proportion of the figure based on the triangle proportionality theorem?
The true proportion of the figure based on the triangle proportionality theorem is Option (A).
What is the basic proportionality theorem?
According to the Basic Proportionality Theorem (BPT), if a line is parallel to a triangle's side that divides the other sides into two separate points, the line will divide those sides proportionately.
Given that TU is parallel to QR, by the proportionality theorem, we get
[tex]\frac{ST}{TQ} = \frac{SU}{UR}[/tex]
or, [tex]\frac{k}{j} = \frac{h}{i}[/tex]
or, [tex]\frac{i}{j} = \frac{h}{k}[/tex]
Ans: [tex]\frac{i}{j} = \frac{h}{k}[/tex]
Hence, a true proportion of the figure based on the triangle proportionality theorem is (A) [tex]\frac{i}{j} = \frac{h}{k}[/tex]
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Use the commutative property to write an expression 8c-1.5
Answer:
Step-by-step explanation:
i need help on that too
suppose that we have collected information on how much a sample of households spend on clothing per year. if we are 90% confident that the true population mean will lie between $1,500 and $2,100, the chance that the population mean will either be less than $1,500 or above $2,100 is %.
10% of the time, the population mean will go below $1,500 or exceed $2,100.
Given that,
Assume that we have data on the annual spending on apparel of a sample of families. The probability that the population mean will fall below $1,500 or rise over $2,100 is ________% if we are 90% positive that the genuine population mean will be between $1,500 and $2,100.
We have to fill the blank.
We know that,
90% of the time, the real population mean will fall in the range of $1,500 and $2,100.
The genuine population mean will therefore most likely fall between $1,500 and $2,100, with a 90% probability.
So, the probability that it will fall outside of this range (i.e., be either less than $1,500 or beyond $2,100) is 100-90, or 10%.
Therefore, 10% of the time, the population mean will go below $1,500 or exceed $2,100.
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The area of the Sea of Japan is 1.007 × 106 km2. The area of the Southern Ocean is 2.0327 × 107 km2. Find the total area. Write the final answer in scientific notation with the correct number of significant digits.
2.1334 × 107 km2
3.0397 × 1013 km2
2.133 × 107 km2
3.040 × 1013 km2
The total area of the Sea of Japan and the Southern Ocean is 2.1334 × 10⁷ km². The correct option is the first option 2.1334 × 10⁷ km²
Calculating the total area of the Sea and OceanFrom the question, we are to calculate the total area of the sea and ocean
From the given information,
"The area of the Sea of Japan is 1.007 × 106 km²"
and
"The area of the Southern Ocean is 2.0327 × 107 km²"
Thus,
The total area of the sea and ocean = 1.007 × 10⁶ km² + 2.0327 × 10⁷ km²
The total area of the sea and ocean = 0.1007 × 10⁷ km² + 2.0327 × 10⁷ km²
The total area of the sea and ocean = 2.1334 × 10⁷ km²
Hence, the total area is 2.1334 × 10⁷ km²
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If f(x)=ex and the 4th degree Taylor polynomial of f(x) centered at 2, what is T4(2.4)?
Round your answer to four decimals.
The fourth degree Taylor polynomial of f(x) centered at 2 the [tex]T_4(2.4) = 11.0225[/tex].
What is Taylor polynomial?
The Taylor series or Taylor expansion of a function in mathematics is the infinite sum of terms expressed in terms of the function's derivatives at one particular point. The function and the sum of its Taylor series are roughly equal for the majority of common functions at this point.
Given:
[tex]f(x) = e^x[/tex] centered at 2.
[tex]f(2) = e^2[/tex]
[tex]f'(x) = \frac{d}{dx}e^x = e^x , f'(2) = e^2\\f"(x) = \frac{d^2}{dx}(e^x) = e^x, f"(2) = e^2\\ f^3(x) = \frac{d^3}{dx}(e^x) = e^x, f^3(2) = e^2\\ f^4(x) = \frac{d^4}{dx}(e^x) = e^x, f^4(2) = e^2[/tex]
Therefore,
[tex]T_4(x) = f(2) + \frac{f'(2)(x-2)}{1!} + \frac{f"(2)(x-2)^2}{2!} + \frac{f^3(2)(x-2)^3}{3!} + \frac{f^4(2)(x-2)^4}{4!} \\T_4(x) = e^2 [1 + (x - 2) + \frac{(x-2)^2}{2}+\frac{(x-2)^3}{6}+ \frac{(x-2)^4}{24} \\ T_4(2.4) = e^2[1 + (2.4-2) + \frac{(2.4-2)^2}{2}+ \frac{(2.4-2)^3}{6}+\frac{(2.4-2)^4}{24}]\\ T_4(2.4) = 11.0225[/tex]
Hence, the fourth degree Taylor polynomial of f(x) centered at 2 the [tex]T_4(2.4) = 11.0225[/tex].
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-8y² - 1 = -8y
Quadratic equation
Answer:
y = (2 + √2)/4 ; y = (2 - √2)/4
Step-by-step explanation:
-8y² + 8y - 1 = 0
8y² - 8y + 1 = 0
discriminant = 64 - 4(8) = 64 - 32 = 32 = 2^4 * 2
y = (8 + [tex]\sqrt{2^4 * 2}[/tex])/16
(8 + 2²√2)/16
(8 + 4 √2) / 16
4(2+√2)/16
(2+√2)/4
y = (8 - [tex]\sqrt{2^4 * 2}[/tex])/16
(8 - 4√2) / 16
4(2-√2)/16
(2-√2)/4
A garden table and a bench cost $703 combined. The garden table costs $47 less than the bench. What is the cost of the bench?
Answer:
375
Step-by-step explanation:
let a garben table cost x
a bench cost x+47
x+x+47=703
2x=703-47
2x=656
x=656÷2=328
bench: 328+47=375
Could Someone Let me know if I checked off the correct answer? And if not explain what I did wrong.
Answer:
See below ( you have it correct !)
Step-by-step explanation:
See image below....sometimes it is easier to see these things if you extend some lines a bit:
Pls help. Writing Linear equations from key information
1. goes through the points (-6,1) and (-3,2)
2. goes through the points (-3.2) and (8,2)
3. y-intercept = -1, goes through the point (3,8)
4. goes through the points (1,11) and (1,-2)
The linear functions in this problem are given as follows:
1. y = 1/3x + 3.
2. y = 2.
3. y = 3x - 1.
4. x = 1.
How to define the linear functions?The slope-intercept definition of a linear function is presented as follows:
y = mx + b.
In which the coefficients are given as follows:
m is the slope.b is the y-intercept.For item 1, the points are given as follows:
(-6, 1) and (-3,2).
When x increases by 3, increases by 1, hence the slope is given as follows:
m = 1/3.
Then:
y = 1/3x + b.
When x = -3, y = 2, then the intercept b is calculated as follows:
2 = 1/3(-3) + b
b = 3.
Thus the function is:
y = 1/3x + 3.
Then items 2 and 4 are given as follows:
2 -> horizontal line -> y = 2.4 -> vertical line -> x = 1.For item 3, we have an intercept of -1, hence:
y = mx - 1.
When x = 3, y = 8, hence the slope m is calculated as follows:
8 = 3m - 1
3m = 9
m = 3.
Hence the function is:
y = 3x - 1.
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. 3F furniture dealer has always sold its merchandise through 4 company-operated stores. Last year sales were birr 1million and net profit was 8% of sales. Fixed costs were birr 170,000. As a result of shifting population and increased competition, the four locations have become less desirable. 3F is considering eliminating its retail stores in favor of door-to-door selling. It is estimated that sales would increase by 25% and net profit by birr 30,000. Fixed costs would increase by birr 30,000 because operations would be moved to a low-rent warehouse. Required a) What was the break-even point under the old situation? b) What will be the break-even point under the proposed situation? c) What birr sales volume must be obtained under the proposed plan to make as much profit as last year?
a) The break-even point under the old situation is 680000.
b) The break-even point under the proposed situation is 806451.
c) Birr sales volume must be obtained under the proposed plan to make as much profit as last year is 1129032.
a) The break-even point under the old situation:
100000 * a - 170000 = 1000000 * 8%
a = 25% (Profit rate)
x.a = 170000
x = 680000
b) The break-even point under the proposed situation:
1250000 * b - 170000 -30000 = 80000 + 30000
b = 24.8%
x.b = 20000
x = 806451
c) Birr sales volume must be obtained under the proposed plan to make as much profit as last year :
x.b - 200000 = 80000
x.b = 28000
x = 1129032
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