1). There are 5,245,786 different number combinations that could win. The likelihood of taking home the lottery's grand prize is 1 in 5,245,786 or roughly 0.000019%.
2). There are 42,467,328,000 different winning number combinations that a gambler can choose from.
What is combinations?Combinations are the various ways, independent of their sequence, in which a group of things or objects can be chosen.
The formula n! / (r! * (n-r)! can be used to determine the number of potential combinations of r items from a collection of n items, which is symbolised by the symbol C(n,r).
1. Six numbers are chosen at random from a pool of 42 numbers in a 6/42 lottery. The formula for combinations can be used to determine how many winning number combinations a gambler has the option of choosing:
C(42, 6) = 42! / (6! * (42-6)!)
= 5,245,786
2. The number of winning number combinations that a bettor may choose to select can be determined using the formula for permutations with repetition if the 6/42 Lottery permits repeat of numbers:
[tex]42^6[/tex] = 42 * 42 * 42 * 42 * 42 * 42 = 42,467,328,000
There are therefore 42,467,328,000 different ways to pick winning numbers. The odds of taking home the lottery's grand prize are 1 in 42,467,328,000, or roughly 0.000000002%.
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The size P of a certain insect population at time t (in days) obeys the function P = 700e0.03t, After how many days will the population reach 1500?
the population will reach 1500 after about 30.1 days.
After how many days will the population reach 1500?We can solve for the time t by setting P = 1500 and solving for t:
1500 = 700[tex]e^{(0.03t)}[/tex]
Divide both sides by 700:
2.14 = [tex]e^{(0.03t)}[/tex]
Take the natural logarithm of both sides:
ln(2.14) = ln([tex]e^{(0.03t)}[/tex])
Using the logarithm property that ln([tex]e^{x}[/tex]) = x, we can simplify to:
ln(2.14) = 0.03t
Divide both sides by 0.03:
t = ln(2.14)/0.03
Using a calculator, we get:
t ≈ 30.1 days
Therefore, the population will reach 1500 after about 30.1 days.
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the temperature at noon was 10degree Celsius above 0 . if it decreases at the rate 2 degree Celsius per hour till midnight , at time the temperature would be 8 degree Celsius below zero ? what would be the temperature at mid-night?
Answer:
Time at which temperature will be -8 degrees Celsius = 21 00 (24 hour clock) or 9pm (12 hour clock)
Temperature at midnight = - 14°C
Step-by-step explanation:
The pic
For the rotation -757°, find the coterminal angle from 0° ≤ 0 < 360°, the
quadrant, and the reference angle.
To find the coterminal angle for a rotation of -757°, we can add or subtract multiples of 360° until we find an angle between 0° and 360° that is coterminal with -757°.
Adding 360° multiple times:
-757° + 360° = -397° (not coterminal)
-397° + 360° = -37° (not coterminal)
-37° + 360° = 323°
Therefore, the coterminal angle for -757° is 323°.
To find the quadrant in which 323° lies, we can note that 323° is between 270° and 360°, which means it lies in the fourth quadrant.
To find the reference angle for 323°, we can subtract 360° from 323° until we get an angle between 0° and 90°:
323° - 360° = -37° (not in the correct range)
-37° + 360° = 323°
So the reference angle for 323° is 37°.
Math: please answer this question very important for me, I’ll give brainliest if it’s correct!!
Q2. The average depth of the water in a port on a tidal river is 4 m. At low tide, the depth of the water is 2 m. One cycle is completed approximately every 12h.
(a) [4 marks] Find an equation of the depth, d(t) meters, with respect to the average depth, as a function of the time, t hours, after low tide, which occurred at 15: 00.
(b) [2 marks] Draw a graph of the function for 48 h after low tide.
Need help will give brainliest and 5 stars!
Looking for x and y intercepts, the hole and vertical asymptote.
Check the picture below.
In settings where we can assume that each possible outcome is equally likely to occur we are
using theoretical probabilities. We do this when we expect a coin to have the same chance of
landing on heads as it does on tails. We also do this when we assume that if we roll a six sided
die each possible number has the same chance of landing up.
The statement on theoretical probabilities is True.
What is theoretical probability ?Theoretical probabilities, referred to as classical probabilities, are utilized when we can suppose that each conceivable result has an equal chance of happening.
Typically, this is observed in games of luck like tossing a coin or rolling dice, where the chances of every possible outcome are equivalent. Such scenarios permit one to use probability principles and determine the probability of each outcome transpiring.
For instance, with fair coins, it's reasonable to assert that there's an even likelihood for heads or tails, setting both probabilities at 1/2.
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Find the measure of
The measure of ∠LPN is 57°.
What is arc?An arc is a segment of a circle in geometry that is typically defined by two endpoints and the arc itself, which is the collection of all points on the circle that are situated between the two endpoints.
The subtendency of an arc can be measured by measuring its central angle.
Since angles inscribed in the same arc are congruent, we have:
m(arc LP) = m(arc NP) = 102° + 144° = 246°
Now, using the fact that the sum of the measures of the arcs of a circle is 360°, we have:
m(arc LM) + m(arc LP) + m(arc NP) + m(arc MN) = 360°
Substituting the known values, we get:
m(arc LM) + 246° + m(arc MN) = 360°
Simplifying, we have:
m(arc LM) + m(arc MN) = 114°
But angles inscribed in the same arc are congruent, so we have:
m(∠LPN) = (m(arc LM) + m(arc MN))/2
Substituting the value we found for m(arc LM) + m(arc MN), we get:
m(∠LPN) = 114°/2 = 57°
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Please help me
Decide the type of transformation and state the rule
The four translation rules are defined as follows:
Left a units: x -> x - a.Right a units: x -> x + a.Up a units: y -> y + a.Down a units: y -> y - a.Comparing the equivalent vertices, the translations are given as follows:
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Given that sin theta = 15/17 with theta quadrant 1 , find cos 2theta
[tex]\textit{Double Angle Identities} \\\\ \cos(2\theta)= \begin{cases} \cos^2(\theta)-\sin^2(\theta)\\ 1-2\sin^2(\theta)&\leftarrow \textit{we'll use this one}\\ 2\cos^2(\theta)-1 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ 1-2\sin^2(\theta)\implies 1-2\left( \cfrac{15}{17} \right)^2\implies 1-2\left( \cfrac{225}{289} \right) \\\\\\ 1-\cfrac{450}{289}\implies \cfrac{289-450}{289}\implies -\cfrac{161}{289}[/tex]
what is an equation of the image of the line after dilation
An equation of the image of the line after dilation is -30x - 20y = -8.
What is scale factor?In Mathematics and Geometry, a scale factor is the ratio of two corresponding side lengths or diameter in two similar geometric objects, which can be used to either vertically or horizontally enlarge (increase) or reduce (compress) a function representing their size.
Generally speaking, the transformation rule for the dilation of a geometric object based on a specific scale factor of 5 is given by this mathematical expression:
(x, y) → (kx, ky)
Where:
x and y represents the data points.k represents the scale factor.Therefore, the transformation rule for this dilation is given by;
(x, y) → (kx, ky)
(x, y) → (5(-6x), 5(-4y)) = -30x - 20y = -8.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
5. Shanequa graphed a triangle with the coordinates R(-2, 1), S(2, 1) and T(0, -3). She wanted to graph
a dilation of the figure with a scale factor of 2 centered at the origin so she graphed the points
R'(-2, 2), S'(2, 2) and T'(0, -6).
a. Is AR'S'T' a dilation of ARST? Why or why not?
b. If Shanequa was wrong, correct her answer by giving the correct coordinates for AR'S'T'.
c. Shanequa's teacher said Shanequa had made a common mistake. Explain her mistake.
a) No , it is not a dilation
b) The coordinates are R'(-2, 2), S'(2, 2), and T'(0, -6)
c) Shanequa's mistake is that she incorrectly applied the dilation transformation
Given data ,
a)
In ARST, the coordinates of the original triangle are given by R(-2, 1), S(2, 1), and T(0, -3), and in AR'S'T', the coordinates are R'(-2, 2), S'(2, 2), and T'(0, -6)
So , the dilated triangle is R'(-2, 2), S'(2, 2), and T'(0, -6)
b)
The coordinates for AR'S'T' can be calculated by multiplying the original coordinates of ARST by the scale factor of 2, centered at the origin.
R'(-4, 2), S'(4, 2), and T'(0, -6)
c)
The dilation transformation was applied wrongly by Shanequa. The coordinates of the original points in a dilation centred at the origin with a scale factor of two should be multiplied by the scale factor to obtain the coordinates of the dilated points.
Hence , the dilation is solved
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Plot the numbers -1 1/2 and 2 3/4 on the number line below.
For the second number 2 3/4 you will find the 2 points, to the right from 0. Now count three small points to the left to get the 3/4 part
How to solveTo locate the value of -1 1/2 on the number line, first locate the point denoting -1 to the left of 0. Progressing to the second minor point on the right immediately after -1 will indicate this position.
For the second figure of 2 3/4, identify the point at 2 by moving to the right from 0. An additional count of three minor points towards the left reveals where the fraction of 3/4 is located. The exact spot is depicted here.
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URGENT!! Please help
The correlation coefficient between the minutes the actor appeared shirtless in a film and the film's opening weekend gross is 0.75.
How to write the linear regression equation and determine the correlation coefficient?In this scenario, the minutes shirtless (x) would be plotted on the x-axis of the scatter plot while the open weekend gross (y) would be plotted on the x-axis of the scatter plot.
By critically observing the scatter plot (see attachment) which models the relationship between the minutes shirtless (x) and the open weekend gross (y), an equation for the linear regression is given by:
y = 10.83 + 0.86x
Correlation coefficient, r = 0.7488571925 ≈ 0.75
In conclusion, we can logically deduce that there is a strong correlation between the data because the correlation coefficient (r) is approximately greater than 0.7;
0.7＜|r| ≤ 1 (strong correlation)
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Correct
The owner of a new pizzeria in town wants to study the relationship between weekly revenue and advertising expenditures. All measures are recorded in thousands of
dollars. The summary output for the regression model is given below.
df
SS
Regression 1 16.54127801
Residual 6 5.641280047
Total 7
22.18255806
ANOVA
MS
F
16.54127801 17.59311136
0.94021334
Significance F
0.005721150
Step 1 of 3: What is the coefficient of determination for this model, R2? Round your answer to four decimal places.
Answer:
17.023413
Step-by-step explanation:17.023413
Solve the following system of linear equations 3x₁ + x₂ + 2x3= 6
4x₁ - 3x₂ + 5x3 = 8,
2x₁ + x₂ + 3x3 = 10
Okay, here are the steps to solve this system of linear equations:
3x1 + x2 + 2x3= 6
4x1 - 3x2 + 5x3 = 8,
2x1 + x2 + 3x3 = 10
1) Add 4 times the first equation to the second equation:
7x1 + 2x2 + 7x3 = 22
2) Add -2 times the first equation to the third equation:
5x1 - x2 + 5x3 = 12
3) Divide both sides by 5 to get:
x1 = 2
x2 = -2
x3 = 1
Therefore, the solution to the system is:
x1 = 2
x2 = -2
x3 = 1
Let me know if you have any other questions!
Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot 8(x2 + 2x + 1) = 3 + 1 8(x2 + 2x) = –3
Answer:
Step-by-step explanation:
Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartR…
✓ Answer:8(x2 + 2x) = –3 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRootStep-by-step explanation:S…
I am in need of this to be answered~
Transform this sentence into NNF:
~(~(P&~Q)v(R&~S))
Please answer, step by step to the answer.
Thank you!
~(~(P&~Q)v(R&~S)) transformation of this statment into NNF is ((~P v Q) & (~R v S))
How to transform the statement by using NNF?The transformations used to turn the given sentence into NNF:
Using the equivalence, remove the implication: p → q ≡ ~p ∨ q
≡ (((P&~Q)) & ~(R&~S))
Use De Morgan's law: ~(p ∨ q) ≡ ~p & ~q, and ~(p & q) ≡ ~p ∨ ~q
≡ ((~P v Q) & (~R v S))
Elimination by double negation:~~p ≡ p
≡ ((~P v Q) & (~R v S))
The resulting sentence, ~(~(P&~Q)v(R&~S)) is in NNF (Negation Normal Form), which limits negations to atomic propositions (P, Q, R, S) and logical connectives ¬, ∧, and ∨.
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Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
The three (3) true statements about the quadratic function and its graph include the following:
A. The value of f(–10) = 82
B. The graph of the function is a parabola.
D. The graph contains the point (20, –8).
How to determine the true statements about this quadratic function?Generally speaking, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. For this quadratic function, the graph is a upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero.
Next, we would determine the other true statements about the graph of this quadratic function:
At point (-10, 82), we have:
Quadratic function, f(x) = 1/5 x² – 5x + 12
Quadratic function, f(x) = x²/5 – 5x + 12
Quadratic function, f(-10) = -10²/5 – 5(-10) + 12
Quadratic function, f(-10) = 82
At point (20, -8), we have the following:
Quadratic function, f(x) = 1/5 x² – 5x + 12
Quadratic function, f(x) = x²/5 – 5x + 12
Quadratic function, f(20) = 20²/5 – 5(20) + 12
Quadratic function, f(20) = -8
In conclusion, we can logically deduce that the graph of this quadratic function does not contain the point (0, 0) as shown in the image attached below.
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Need to solve some questions can you Help me?
2nd Question
6 ÷ 2 ( 1 + 2 ) = ?
Answer:
Step-by-step explanation:
[tex]6/2 ( 1 + 2 ) = 3(3) = 9[/tex]
Pleaseeeee helppp meeee
Subtracting 8 times the first row to the second row we will get the matrix.
[tex]\left[\begin{array}{ccc}1&10&-23\\0&-83&249\end{array}\right][/tex]
How to get a zero in row 2, column 1?To get that, you will need to take row 2 and subtract 8 times row 1, then the values of each column will be:
Remember that the rows are the horizontal vectors and the columns are the vertical ones.
8 - 8*1 = 0
-3 - 8*10 = -83
65 - 8*-23 = 249
Then the new matrix will be:
[tex]\left[\begin{array}{ccc}1&10&-23\\0&-83&249\end{array}\right][/tex]
That is the matrix with a zero in row 2, column 1.
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The garment factory plans to make 690 sets of garments. It has been done for 5 days, with an average of 75 sets per day. The rest needs to be completed in 2.5 days, how many sets are done on average per day (step-by-step answer)
For the remaining set of garments, the average per day that they need to be completed would be = 126 sets/day.
How to calculate the average set made per day?The quantity of garments planned to be made by the factory = 690sets.
The rate of coverage for 5 days = 75sets/day.
That is for 5 days the number of garments covered = 75×5 = 375
The remaining sets = 690-375 = 315
The average per day to cover the remaining sets of garment = 315/2.5 = 126 sets/day
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Please help, ASAP! This is for a College Algebra Class, No wrong answer.
The value of x in the equation is 2.10.
How to solve exponential equation?The exponential equation above can be solved as follows:
[tex]8^{\frac{4}{x} } = 53[/tex]
Therefore, let's log both sides
log [tex]8^{\frac{4}{x} }[/tex] = log 53
Hence,
4 / x log 8 = log 53
divide both sides by log 8
4 / x = log 53 / log 8
4 / x = 1.7242758696 / 0.90308998699
4 / x = 1.9092439208
cross multiply
1.902x = 4
x = 4 / 1.902
x = 2.09511837419
Therefore,
x = 2.10
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For questions 4 – 7, find the value of x.
The values of x in the isosceles trapezoids x = 32, x = 10.9 and x = 41
Calculating the values of x in the figuresAn isosceles trapezoid is a four-sided geometric shape that has two parallel sides and two non-parallel sides that are of equal length.
The parallel sides are called the bases of the trapezoid, while the non-parallel sides are called the legs and the angles in the same base are equal in measure
Using the above as a guide, we have the following:
2x + 14 = 78
x = 32
2 * (6x +32 + 4x + 39) = 360
x = 10.9
4x = 164
x = 41
The last details are not clear
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reduce to lowest terms 4x^y^3/-8x^2y
Answer:
x^(y^3-1) / -2xy
Step-by-step explanation:
4x^y^3 = 4x^(y^3)
-8x^2y = -8x^2y^1
= 4x^(y^3) / -8x^2y^1
= (4x^(y^3) / 4xy) / (-8x^2y^1 / 4xy)
= x^(y^3-1) / -2xy
Answer:
Step-by-step explanation:
At a local college 29 of the male students are smokers and 262 are non smokers. Of the female students, 40 are smokers and 360 are non smokers. A male student and a female student from the college are randomly selected for a survey. What is the probability that both are smokers
The probability that both a male student and a female student from the college are smokers is 0.01 or 1%.
We have,
Let's first find the probability of selecting a male smoker and then the probability of selecting a female smoker.
P(Male smoker) = Number of male smokers / Total number of male students
P(Male smoker) = 29 / (29 + 262)
P(Male smoker) = 0.10
Similarly, the probability of selecting a female smoker is:
P(Female smoker) = Number of female smokers / Total number of female students
P(Female smoker) = 40 / (40 + 360)
P(Female smoker) = 0.10
Now, we can find the probability of selecting both a male smoker and a female smoker by multiplying the probabilities:
P(Both smokers) = P(Male smoker) x P(Female smoker)
P(Both smokers) = 0.10 x 0.10
P(Both smokers) = 0.01
Therefore,
The probability that both a male student and a female student from the college are smokers is 0.01 or 1%.
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PLEASE SOLVE THIS....I WILL GIVE BRAINLIEST!!!
Answer:
Give me a sec
Step-by-step explanation:
The price of an item has been reduced by 25%. The original price was $35
The winner of a contest will be blindfolded and then allowed to reach into a hat containing 29 $1 bills and 7 $100 bills. The winner can remove 4 bills from the hat and keep the money. Find the probability that the winner will pull out at least 1 $100 bill. (See Example 5 in this section. Round your answer to the nearest tenth of a percent.)
The probability that the winner will pull out at least one $100 bill is 7/36, or 19.4%.
What is probability?The probability of an event occurring is determined by the number of favorable outcomes divided by the total number of possible outcomes.
In this problem, the favorable outcome is that the winner will pull out at least one $100 bill, while the total number of possible outcomes is the number of ways to select 4 bills from the hat, which is 36.
Thus, the probability of the winner pulling out at least one $100 bill is calculated by dividing the favorable outcome by the total number of possible outcomes.
Since there are 7 $100 bills in the hat, the favorable outcome is 7. The total number of possible outcomes is 36, which is calculated by using the formula nCr, where n is the total number of objects and r is the number of objects selected.
In this case, n = 36 and r = 4, so the equation is 36C4.
Thus, the probability that the winner will pull out at least one $100 bill is 7/36, or 19.4%.
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answer and explain in detail
Answer:
The area of right-angled triangle is 30 cm².
Step-by-step explanation:
Given : Here we given that the base and hypotenuse of triangle 12 cm and 13 cm respectively.To Find : We have to find the area of right-angled triangle but before we will find the height of the triangle.Solution :By using Pythagoras Theorem we will find the hypotenuse of triangle :
[tex] \sf{\longrightarrow{{(Hypotenuse)}^{2} = {(Height)}^{2} + {(Base)}^{2}}}[/tex]
Substituting all the given values in the formula to find hypotenuse :
Hypotenuse = 13 cmBase = 12 cm[tex]\sf{\longrightarrow{{(Hypotenuse)}^{2} = {(Height)}^{2} + {(Base)}^{2}}}[/tex]
[tex]\sf{\longrightarrow{{(13)}^{2} = {(Height)}^{2} + {(12)}^{2}}}[/tex]
[tex]\sf{\longrightarrow{(13 \times 13) = {(Height)}^{2} + {(12 \times 12)}}}[/tex]
[tex]\sf{\longrightarrow{(169) = {(Height)}^{2} + {(144)}}}[/tex]
[tex]\sf{\longrightarrow{{(Height)}^{2} = 169 - 144}}[/tex]
[tex]\sf{\longrightarrow{{(Height)}^{2} = 25}}[/tex]
[tex]\sf{\longrightarrow{{(Height)} = \sqrt{25}}}[/tex]
[tex]\sf{\longrightarrow{\underline{\underline{\red{(Height) = 5 \: cm}}}}}[/tex]
Hence, the height of triangle is 5 cm.
[tex]\begin{gathered} \end{gathered}[/tex]
Now, calculating the area of right-angled triangle by substituting all the given values in the formula :
[tex]\dashrightarrow{\sf{Area_{(\triangle)} = \dfrac{1}{2}bh}}[/tex]
b (Base) = 12 cmh (Height) = 5 cm[tex]\dashrightarrow{\sf{Area_{(\triangle)} = \dfrac{1}{2}bh}}[/tex]
[tex]\dashrightarrow{\sf{Area_{(\triangle)} = \dfrac{1}{2} \times b \times h}}[/tex]
[tex]\dashrightarrow{\sf{Area_{(\triangle)} = \dfrac{1}{2} \times 12\times 5}}[/tex]
[tex]\dashrightarrow{\sf{Area_{(\triangle)} = 6\times 5}}[/tex]
[tex]\dashrightarrow{\sf{\underline{\underline{\pink{Area_{(\triangle)} =30 \: {cm}^{2}}}}}}[/tex]
Hence, the area of triangle is 30 cm².
—————————————————What is the unit sales of product A at the monthly break even point?
The unit sales of product A at the monthly break-even point is 193,750 units.
What is the unit sales of product A at the monthly break even point?To determine the unit sales of product A at the monthly break-even point, we need to calculate the total contribution margin that covers the monthly fixed costs of $387,500.
Given that the unit contribution margin for product A is $2 and the unit selling price for product A is $5, we can calculate the contribution margin ratio for product A as follows:
Contribution Margin Ratio for Product A:
= (Unit Contribution Margin for Product A) / (Unit Selling Price for Product A)
= $2 / $5
= 0.4
40%
Now, let's consider the sales ratios given in the problem statement. It states that the company sells two units of A for each unit of B, and three units of B for each unit of C. This means that the sales ratio for product A to product B is 2:1, and the sales ratio for product B to product C is 3:1.
Let's assume that the unit sales of product A at the monthly break-even point is "x". Then, the unit sales of product B would be "2x" (based on the sales ratio of 2:1 between A and B), and the unit sales of product C would be "6x" (based on the sales ratio of 3:1 between B and C).
The total contribution margin for product A at the monthly break-even point can be calculated as follows:
Total Contribution Margin for Product A = (Unit Contribution Margin for Product A) * (Unit Sales of Product A at Break-Even Point)
= $2 * x
Since the monthly fixed costs are $387,500, we can set up the equation for the break-even point as follows:
Total Contribution Margin for Product A = Monthly Fixed Costs
$2 * x = $387,500
Now we can solve for x, the unit sales of product A at the monthly break-even point:
$2 * x = $387,500
x = $387,500 / $2
x = 193,750
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