6) Carmen has several spools of embroidery floss in different colors that she uses to make
bracelets and necklaces. Suppose she selects a spool at random to make a friendship bracelet.
How much greater is the probability that she selects blue floss than orange floss? Express your
answer as a percent.
Color
black
brown
red
blue
orange
purple
pink
yellow
Number of Spools
8
5
7
10
3
6
4
7
The probability of selecting a blue spool is 14% greater than the probability of selecting an orange spool.
What is probability?Probability is a branch of mathematics that deals with the study of random events or phenomena. It involves the calculation of the likelihood or chance of an event occurring, based on the available information or data.
What is known by the term percent?Percent is a mathematical concept used to represent a part of a whole as a fraction of 100.
To calculate the probability of selecting a blue spool or an orange spool, we need to first find the total number of spools and the number of blue and orange spools.
The total number of spools is: 8+5+7+10+3+6+4+7 = 50
The number of blue spools is: 10
The number of orange spools is: 3
Therefore, the probability of selecting a blue spool is: 10/50 = 0.2 or 20%
The probability of selecting an orange spool is: 3/50 = 0.06 or 6%
The difference in probability is: 20% - 6% = 14%
Therefore, the probability of selecting a blue spool is 14% greater than the probability of selecting an orange spool.
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What is the area of a triangle where the base is 4m and the height is 5m
Answer:
10m²
Step-by-step explanation:
A=b×h/2=4×5/2=20/2=10m²
Hope this helps!
Consider the function g(x)x²+3x-4
Help me pls :/
Below is the graph of a trigonometric function. It has a minimum point at
(2,-0.9) and an amplitude of 3. What’s the midline?
The midline of the function is the horizontal line: y = -0.9
What is Graph ?
A graph is a visual representation of data or a mathematical function that shows the relationship between different variables. Graphs can take many forms, but some common types of graphs include line graphs, bar graphs, scatter plots, and pie charts.
The midline of a trigonometric function is the horizontal line that is equidistant from the maximum and minimum points of the function. For a sine or cosine function, the midline is given by the equation:
y = a
where a is the vertical displacement of the graph (i.e., the distance between the horizontal axis and the center of the graph).
In this case, the function has a minimum point at (2, -0.9) and an amplitude of 3. The amplitude is the distance between the maximum and minimum points of the function, which is equal to half the distance between the maximum and minimum y-values. Therefore, the maximum y-value is:
y_max = -0.9 + 3 = 2.1
Similarly, the minimum y-value is:
y_min = -0.9 - 3 = -3.9
The center of the graph is the average of the maximum and minimum y-values, which is:
a = (y_max + y_min) ÷ 2
a = (2.1 - 3.9)÷ 2
a = -0.9
Therefore, the midline of the function is the horizontal line: y = -0.9
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PLEASE LOO AT PCTURE
The five number summary, based on the given box plot would be:
Min - 1Q1 - 2Median - 7 Q3 - 9Max - 11.5How to find the five number summary on box plot ?Minimum value is the left-most point or the left end of the left whisker of the box plot. In the box plot, the minimum value is 1. Q1 is the left edge of the box. It represents the value below which 25% of the data falls.
Median is the line inside the box that divides it into two parts. It represents the value below which 50% of the data falls, or the 50th percentile. The median is 7. Q3 is the right edge of the box. It represents the value below which 75% of the data falls. In your given summary, Q3 is 9.
Maximum value is the right-most point or the right end of the right whisker of the box plot.
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The x y-coordinate plane is given. The curve labeled y = f ′(x) begins on the positive y-axis, goes down and right becoming more steep, crosses the x-axis at x = 1, goes down and right becoming less steep, changes direction at a point below x = 2, goes up and right becoming more steep, crosses the x-axis at x = 3, goes up and right becoming less steep, changes direction at a point above x = 4, goes down and right becoming more steep, crosses the x-axis at x = 5, goes down and right becoming less steep, and ends at a point below x = 6.
(a)
On what intervals is f increasing? (Enter your answer using interval notation.)
On what intervals is f decreasing? (Enter your answer using interval notation.)
b)
At what values of x does f have a local maximum or local minimum? (Enter your answers as a comma-separated list.)
The answer is: f has a local maximum at x = 2 and a local minimum at x = 4.
What is local minimum?A local minimum is a point on the graph of a function where the function takes on its smallest value in some small interval around the point. More formally, a point (x,y) is a local minimum if there exists some open interval (a,b) containing x such that for all values of x in (a,b), y is greater than or equal to f(x). Visually, a local minimum is a "valley" on the graph of the function where the function is lower than all nearby points, but may still be higher than points farther away.
In the given question,
(a)
The curve labeled y = f'(x) represents the derivative of a function f(x). Since f'(x) is positive when f(x) is increasing and negative when f(x) is decreasing, we can use the sign of f'(x) to determine the intervals of increase and decrease of f(x).
From the given information, we can sketch the graph of f'(x) as follows:
Based on this graph, we can see that f(x) is increasing on the intervals: [0, 1) and (3, 5).
Similarly, f(x) is decreasing on the intervals: (1, 3) and (5, 6).
Therefore, the answer is:
f is increasing on the intervals [0, 1) and (3, 5).
f is decreasing on the intervals (1, 3) and (5, 6).
(b)
From the given graph, we can see that f(x) has a local maximum at x = 2 and a local minimum at x = 4.
Therefore, the answer is: f has a local maximum at x = 2 and a local minimum at x = 4.
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what will be favored for the following search terms: Chevrolet and Corvette
Answer:
The pages that will be favored for the search terms Chevrolet AND Corvette are Pages that include Chevrolet Corvette.
Step-by-step explanation:
I hope it helps:)
The seventh term of an arithmetic sequence is 10.2 and the twelfth term is 17.7.
What is the common difference of the arithmetic sequence?
Therefore, the common difference of the arithmetic sequence is 1.5.
How to find common difference?To find the common difference of an arithmetic sequence, you need to know at least two consecutive terms of the sequence. The common difference is the constant amount by which each term increases or decreases from the previous term.
If you have the first term (a1) and the second term (a2) of an arithmetic sequence, you can find the common difference (d) using the formula:
[tex]d = a_2 - a_1[/tex]
For example, consider the arithmetic sequence: 3, 7, 11, 15, ...
Here, a1 = 3 and a2 = 7. Substituting these values in the formula, we get:
[tex]d = a_2 - a_1 = 7 - 3 = 4[/tex]
So, the common difference of this sequence is 4.
Let the first term of the arithmetic sequence be "a", and let the common difference be "d".
Then the seventh term would be:
[tex]a + 6d = 10.2[/tex]
And the twelfth term would be:
[tex]a + 11d = 17.7[/tex]
Now we have two equations with two variables. We can solve for "a" and "d" using these equations.
First, we can subtract the first equation from the second equation:
[tex](a + 11d) - (a + 6d) = 17.7 - 10.2[/tex]
Simplifying this equation, we get:
[tex]5d = 7.5[/tex]
Dividing both sides by 5, we get:
[tex]d = 1.5[/tex]
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Triangle NMO is drawn with vertices N(−4, −2), M(−1, −1), O(−4 , −5). Determine the image coordinates of N′M′O′ if the preimage is translated 5 units to the left.
N′(1, −2), M′(4, −1), O′(1, −5)
N′(−4, 3), M′(−1, 4), O′(−4, 0)
N′(−9, −2), M′(−6, −1), O′(−9, −5)
N′(−4, −7), M′(−1, −6), O′ (−4, −10)
The image coordinates of N'M'O' are (−9, −2), (−6, −1), and (−9, −5).
Translating the triangle 5 units leftTo translate the preimage 5 units to the left, we need to subtract 5 from the x-coordinates of all three vertices.
So the new coordinates of N', M', and O' will be:
N'((-4)-5, (-2)) = (−9, −2)
M'((-1)-5, (-1)) = (−6, −1)
O'((-4)-5, (-5)) = (−9, −5)
Therefore, the image coordinates of N'M'O' are (−9, −2), (−6, −1), and (−9, −5).
So the correct answer is N′(−9, −2), M′(−6, −1), O′(−9, −5).
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How much did Ashley make in overtime if her regular rate was $30.40 per hour ?
an employee's overtime rate is 1.5 times their regular rate, but this can vary depending on the company and jurisdiction. Once the overtime rate is known
what is regular rate?
Regular rate refers to the standard hourly wage that an employee receives for their regular, non-overtime work. This is the base rate of pay that an employer agrees to pay an employee for their normal working hours
In the given question,
In order to determine how much Ashley made in overtime, we would need to know her overtime rate and the number of overtime hours she worked. Without this information, it is not possible to calculate the amount she earned in overtime.
Typically, an employee's overtime rate is 1.5 times their regular rate, but this can vary depending on the company and jurisdiction. Once the overtime rate is known, we could multiply the overtime rate by the number of overtime hours worked to determine the amount earned in overtime.
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The diameter of a circle is 15 centimeters.
Using 3.14 as π
, enter the area of the circle, in square centimeters. Round your answer to the nearest HUNDREDTH.
Answer:
132.676072.67Step-by-step explanation:
the vertices of the rectangle lie on the circumference of the circle
We know that our diameter of the circle is equal to 13 cm, radius of the circle is half the diameter
the radius of the circle = 1/2 (13) = 6.5 cm
1. 3.14 × (6.5)² = 132.67 cm²
2. 12 × 5 = 60 cm²
3. 132.67 - 60 = 72.67 cm²
132.676072.67Assume that the line
A. ∠XAE and ∠EAY form a linear pair.
What is linear pair ?A linear pair refers to two adjacent angles formed when two lines intersect. The angles are said to be "linear" because they are positioned along the same line, and together they add up to 180 degree
Mathematically, we can express the relationship between the angles as:
∠A + ∠B = 180 degrees
As the ∠XAE + ∠EAY =180 degrees
so ∠XAE and ∠EAY form a linear pair.
What are complementary angles?Two angles are said to be complementary if their sum is equal to 90 degrees. In other words, if ∠A and ∠B are two angles, and ∠A + ∠B = 90°, then ∠A and ∠B are complementary angles.
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Show that 1216 can be written as
a cube number multiplied by a prime number between 10 and 20
Answer:
[tex]1216 = 64 \times 19[/tex]
64 is 4 cubed, and 19 is a prime number between 10 and 20.
Step-by-step explanation:
A polygon is convex when no line that contains a side of the polygon contains a point in the interior of the polygon. Consider a convex polygon with n sides.
a. Use the combinations formula to write an expression for the number of diagonals in an n-sided polygon.
b. Use your result from part (a) to write a formula for the number of diagonals of an n -sided convex polygon.
Answer:
a. To find the number of diagonals in an n-sided polygon, we need to count the number of pairs of vertices that can be connected by a diagonal, while excluding the sides of the polygon. Any pair of vertices that are adjacent or separated by only one vertex are already connected by a side of the polygon, so we need to consider pairs of vertices that are separated by at least two vertices.
We can choose two vertices out of n vertices in the polygon in nC2 ways. However, any pair of vertices that are separated by only one vertex defines a side of the polygon, so we need to subtract n from this count to exclude the n sides of the polygon. Therefore, the number of diagonals in an n-sided polygon is:
nC2 - n = (n * (n-1))/2 - n = (n^2 - 3n)/2
b. The above expression gives the number of diagonals for any polygon, not just a convex one. However, for a convex polygon, any pair of vertices separated by only one vertex defines a side of the polygon, so we need to exclude these diagonals as well.
For an n-sided convex polygon, there are n sides and n vertices, so we have to exclude n diagonals (one diagonal for each vertex). Therefore, the number of diagonals in an n-sided convex polygon is:
(n^2 - 3n)/2 - n = (n^2 - 5n)/2
Step-by-step explanation:
Each square in the grid is a 1 x 1 unit square. What is the area of the shape? square units
The area of the 2 by 2 unit square is 4 square units.
Calculating the area of the squareAssuming that the shape being referred to is a square with sides of length 2 units as shown in the figure, the area can be calculated as follows:
Area of a square = (side length)^2
In this case, the side length is 2 units, so we can substitute this value into the formula:
Area = (2 units)^2 = 4 square units
Therefore, the area of the 2 by 2 unit square is 4 square units.
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Julian and two of his friends are going to share 1/4 of a pizza how much will each person get
If Julian and two of his friends are going to share 1/4 of a pizza, then they will be sharing the pizza equally among three people. To find out how much each person will get, you need to divide the 1/4 of the pizza by 3, which gives:
1/4 ÷ 3 = 1/4 × 1/3 = 1/12
So each person will get 1/12 of the pizza.
In which quadrant would point (10, 15) be located?
Answer:Quadrant 1
Only in Quadrant 1, the both y and x-axis is positive. So (10, 15) is in quadrant 1.
Which equations can be used to find the lengths of the legs of the triangle? Select three options. 0.5(x)(x + 2) = 24 x(x + 2) = 24 x2 + 2x – 24 = 0 x2 + 2x – 48 = 0 x2 + (x + 2)2 = 100
The lengths of the legs of the triangle cannot be determined by
[tex]x^2 + (x + 2)^2 = 100[/tex]. Thus, option D is correct.
What is triangle ?Three vertices when joined with a straight line make up a triangle, a
three-sided polygon. The angles of triangle are formed by a point,
where each of the three sides are joined end to end.
The three angles add up to make a triangle, sum of angles is a total of 180 degrees. The equations that can be used to find the lengths of the legs of triangle are:
[tex]0.5 (x) (x + 2) = 24\\x(x + 2) = 24\\x^2 + 2x -24 = 0[/tex]
Therefore, 4, [tex]x^2 + (x + 2)^2 = 100[/tex], is not an equation to find the
lengths of the legs of a triangle. It is a different equation that involves
the value of x and y that satisfy the equation of a circle with a center
[tex](-2, 0)[/tex] and radius of [tex]10[/tex] .
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how do i find the area of this regular polygon when only given the apothem?
Yes, we can find the area of the regular polygon when only given the apothem. The given polygon area is 753.093 in²
what is a polygon?In a two-dimensional plane, a polygon is a closed object formed of line segments rather than curves. Polygon is a term that combines the words poly (which means numerous) and gon (which means sides).
To create a closed figure, a minimum of three line segments must be connected end to end. As a result, a polygon with at least three sides is known as a triangle and is also known as a 3-gon. An n-gon is a polygon with n sides.
what is apothem mean?Apothem is the distance of a perpendicular line from any side of the polygon to its center.
Area = [tex]Area =\frac{1}{2} (ap)\\Area=\frac{1}{2} (bh)*(n)[/tex]
n= no of sides of polygon
b= side of the polygon
h= height of polygon / (apothem)
Area= [tex]\frac{1}{2} (16.7354 * 15 * 6 )\\[/tex]
= 125.5155 * 6
= 753.093 in²
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Please help solve this problem
The given function is not one-to-one.
Determining the functionTo determine whether the function y = 2(x+1)²-4 is one-to-one, we need to check whether each unique value of x produces a unique value of y.
Let's begin by assuming that two different values of x, say x1 and x2, produce the same value of y, i.e., y(x1) = y(x2).
Then we have:
2(x1+1)²-4 = 2(x2+1)²-4
Simplifying this equation, we get:
(x1+1)² = (x2+1)²
Taking the square root of both sides, we get:
x1+1 = ±(x2+1)
We can now solve for x1 in terms of x2 as follows:
x1 = -(x2+1)±1
Since there are two possible values for x1 corresponding to a given value of x2, the function is not one-to-one.
Therefore, the given function is not one-to-one.
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In the past month, Kaitlin rented 6 video games and 1 DVD. The rental price for each video game was $3.30. The rental price for the DVD was $4.70. What is the total amount that Kaitlin spent on video game and DVD rentals in the past month?
Answer:
$24.5
Step-by-step explanation:
Given info:
Kaitlin bought 6 games which are $3.30 each and 1 DVD which cost $4.70
Now to find out the cost of all 6 games multiply 6 by the cost of each one, $3.30
$3.30*6 = $19.8
Now add the price of the DVD to it to find the total price
19.8+ 4.70= $24.5
So thus, the total cost of Kaitlin's items was $24.5
6. Choose the correct answer.
James bought an antique chair. Its value can be modeled with the function A(t) = 1,050(1.12). Which statement is true about this situation?
A. its value will increase by 1.12%.
B. its value will decrease by 1.12%.
C. Its value will decrease by 12%.
D. its value will increase by 12%.
stella is learning mathematics. her teacher wrote the following verbal sentence on the white board: " A variable is ten more than thrice another variable." which equation correctly represents this
Both of these equations correctly represent the verbal sentence "A variable is ten more than thrice another variable. "
What is variable?A variable is a symbol or a letter that represents a value that can change or vary. It is usually denoted by a letter from the alphabet, such as x, y, z, a, b, c, etc. Variables are used to represent unknown or unspecified values, as well as to express relationships between quantities.
For example, in the equation[tex]y = mx + b[/tex], x and y are variables, where x represents the input variable and y represents the output variable. The values of x and y can change depending on the specific problem being considered.
Variables can also be used in formulas, functions, and other mathematical expressions to represent a quantity that may vary or depend on other factors. In algebra, variables are commonly used to solve equations and express mathematical relationships.
Let's assume that the first variable is represented by x and the second variable is represented by y.
According to the verbal sentence, we know that:
The first variable is ten more than thrice the second variable, which can be written as:
[tex]x = 3y + 10[/tex]
Alternatively, we can also express the same equation as:
[tex]y = (x-10)/3[/tex]
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Which is the best statement for paying your credit card bill?
What are the x intercepts
The x-intercepts are (4,0)(5,0) of the following graph.
What is x-intercepts?In the context of a graph, an x-intercept is a point where a curve or line crosses the x-axis. It is the point at which the value of y is zero. In other words, the x-intercept is the value of x when the function or equation crosses the x-axis.
To find the x-intercepts of a function, you can set y equal to zero and solve for x. The resulting values of x will be the x-intercepts.
What is y-intercepts?In the context of a graph, a y-intercept is a point where a curve or line crosses the y-axis. It is the point at which the value of x is zero. In other words, the y-intercept is the value of y when the function or equation crosses the y-axis.
To find the y-intercept of a function, you can set x equal to zero and solve for y. The resulting value of y will be the y-intercept.
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The cost of building a storage house is $70 per square foot flooring. What will it cost to build a floor in a storage house 12 feet wide and 10 feet long and 8 feet high?
Therefore, it will cost $8400 to build a floor in the storage house with dimensions 12 feet wide, 10 feet long, and 8 feet high.
What are square feet?Square feet (often abbreviated as sq ft or ft²) is a unit of area commonly used in the United States and other countries that measures the area of a two-dimensional space. One square foot is equal to the area of a square with sides that are each one foot long. For example, a room that measures 10 feet by 12 feet has an area of 120 square feet (10 x 12 = 120). Square feet are commonly used to measure the size of houses, apartments, and commercial spaces, as well as outdoor areas such as yards or gardens.
To calculate the cost of building a floor in the storage house, we need to first determine the area of the floor.
The area of the floor is simply the product of the length and width of the storage house. Therefore:
[tex]Area of floor = Length * Width = 12 ft *10 ft = 120 sq ft[/tex]
To calculate the cost of building the floor, we can multiply the area of the floor by the cost per square foot:
Cost of building floor = Area of floor × Cost per square foot
[tex]Cost of building floor = 120 sq ft * $70/sq ft = $8400[/tex]
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I need help with this question
Where the daily growth factor is 1.15 and the starting height in inches is 7.
What is function?a. Given by, the function that calculates the height of the beanstalk in relation to the time since Gregory planted it.
[tex]f(t) = 7(1.15)^t[/tex]
where the daily growth factor is 1.15 and the starting height in inches is 7.
B). The following ratios can be calculated using the formula from section (a):
f(1)/f(0) = (71.15¹)/(71.15⁰) = 1.15
f(2)/f(1) = (71.15²)/(71.15¹ = 1.15
f(1)/f(1) = (71.15¹)/(71.15¹) = 1
[tex]f(9.56)/f(8.56) = (71.15^{9.56})/(71.15^{8.56})[/tex] ≈ 1.15
[tex]f(8.56)/f(8.55) = (71.15^{8.56})/(71.15^{8.55})[/tex] ≈ 1.15
c. For the any value of z, we have:
[tex]f(z+1)/f(z) = (71.15^{(z+1)})/(71.15^z)[/tex] = 1.15
and
[tex]f(z)/f(z-1) = (71.15^z)/(71.15^{(z-1)})[/tex] = 1.15
For question 6:
a. As a increases throughout the function's domain, f(z) [Select an answer]
Since the base of the exponential function is less than 1 (0.69 < 1), as x increases, f(x) will approach 0.
b. The 1-unit growth factor of f is
The 1-unit growth factor for f is 0.69, since f(x+1)/f(x) = 0.69.
c. The -unit growth factor of f is
The 1/2-unit growth factor for f is (0.69)¹/₂, since f(x+1/2)/f(x) = (0.69)¹/₂.
d. The 6-unit growth factor of f is
The 6-unit growth factor for f is (0.69)⁶, since f(x+6)/f(x) = (0.69)⁶.
e. The 6-unit percent change of f is
The 6-unit percent change for f is ((0.69)^6 - 1) * 100%, which is approximately -38.77%.
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Help pls i dont understand this
The percent change in the number of water bottles the company manufactured from February to April is 19.5%, to the nearest percent.
What is the percentage?A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.
The total number of water bottles the company manufactured in February, March, and April.
In February, the company manufactured 4,100 water bottles. In March, the company manufactured 7% more water bottles than in February, which is 7/100 * 4,100 = 287 water bottles.
Therefore, the total number of water bottles the company manufactured in March is 4,100 + 287 = 4,387 water bottles. In April, the company manufactured 500 more water bottles than in March, which is 4,387 + 500 = 4,887 water bottles.
This is calculated as (4,887 - 4,100) / 4,100 = 0.195 or 19.5%.
Therefore, the percent change in the number of water bottles the company manufactured from February to April is 19.5%, to the nearest percent.
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Which expression has a sum of 42?
Answer: Sorry meant to send this*
Step-by-step explanation:
Han Products manufactures 42,500 units of part S-6 each year for use on its production line. At this level of activity, the cost per unit for part S-6 is as follows: Direct materials $ 4.75 Direct labour 10.75 Variable overhead 3.75 Fixed overhead 9.75 Total cost per part $ 29.00 An outside supplier has offered to sell 37,500 units of part S-6 each year to Han Products for $25.75 per part. If Han Products accepts this offer, the facilities now being used to manufacture part S-6 could be rented to another company at an annual rental of $94,000. However, Han Products has determined that 30% of the fixed overhead being applied to part S-6 will be avoided if part S-6 is purchased from the outside supplier. Required: 1. What is the net dollar advantage or disadvantage of accepting the outside supplier’s offer?
The net dollar advantage or disadvantage of accepting the outside supplier's offer is a disadvantage of $50,937.50.
What is cost?
cost typically refers to the amount of resources, such as time, money, or effort, that is required to perform a particular task or to acquire a certain item or quantity. Cost can be represented numerically and is often expressed in terms of currency or other units of measurement. In some contexts, cost may also refer to the negative consequences or drawbacks associated with a particular action or decision.
To calculate the net dollar advantage or disadvantage of accepting the outside supplier's offer, we need to compare the total cost of producing 42,500 units of part S-6 with the cost of purchasing 37,500 units from the outside supplier and renting out the facilities.
Total cost of producing 42,500 units of part S-6:
Direct materials: $4.75 x 42,500 = $201,875
Direct labour: $10.75 x 42,500 = $457,375
Variable overhead: $3.75 x 42,500 = $159,375
Fixed overhead: $9.75 x 42,500 = $414,375
Total cost: $1,233,000
Cost per unit: $1,233,000 / 42,500 = $29.00
Total cost of purchasing 37,500 units from the outside supplier:
Cost per unit: $25.75 x 37,500 = $965,625
Cost of renting out the facilities: $94,000
Total cost: $965,625 + $94,000 = $1,059,625
Avoided fixed overhead: 30% x $414,375 = $124,312.50
Net dollar advantage or disadvantage: Total cost of producing - Total cost of purchasing - Avoided fixed overhead
= $1,233,000 - $1,059,625 - $124,312.50
= -$50,937.50
The net dollar advantage or disadvantage of accepting the outside supplier's offer is a disadvantage of $50,937.50.
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