Brianno answers 5 questions for each chapter of a book she reads in English class,
Write an equation to represent the total number of questions, q, Brienne answers based on the number of chapters, o, in the book she reads,
.
Answers
Answer:
5o=q
Step-by-step explanation:
Related Questions
In the data set below, what is the mean absolute deviation?
8 4 2 3 6
If the answer is a decimal, round it to the nearest tenth.
mean absolute deviation (MAD):
Answers
The mean absolute deviation of the given data set is 1.6 (rounded to the nearest tenth).
We have,
In statistics, the mean (also known as the arithmetic mean or average) is a measure of central tendency that represents the sum of a set of numbers divided by the total number of numbers in the set.
To find the mean absolute deviation (MAD), we need to first calculate the mean of the given data set:
mean = (4 + 5 + 7 + 9 + 8) / 5 = 6.6
Next, we calculate the deviation of each data point from the mean:
|4 - 6.6| = 2.6
|5 - 6.6| = 1.6
|7 - 6.6| = 0.4
|9 - 6.6| = 2.4
|8 - 6.6| = 1.4
Then we find the average of these deviations, which gives us the mean absolute deviation:
MAD = (2.6 + 1.6 + 0.4 + 2.4 + 1.4) / 5 = 1.6
Therefore, the mean absolute deviation of the given data set is 1.6 (rounded to the nearest tenth).
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What is the radius of the circle if one point of the diameter touches the circle at (-3,1) and the other point touches the circle at (3,-7) ?
Answers
When one point of the diameter touches the circle at (-3,1) and the other point touches the circle at (3,-7) that is these are endpoints of diameter. Then the radius of this circle is equals to the 5 units.
Radius of a circle is defined as the distance from the center of the circle to any arbitrary point on it's circumference. It is generally represented by symbol 'R' or 'r'. When the diameter of a circle is known, the formula for Radius, R= Diameter/2. We have specified two endpoints, i.e., (-3,1),(3,-7) of a diameter of a circle. Let the radius of circle be 'r '. We have to determine the value of r that is radius of circle. From the above definition we can say that radius is half of length of diameter. So, first we calculate the length of diameter of circle. Using the distance formula, the distance between two points is written as, \(d = \sqrt{(x_2-x_1)²+(y_2-y_1)²}\)
So, the distance between two points (-3,1),(3,-7) is \(d = \sqrt{ ( 3-(-3))²+(-7 -1)²}\)
=> \(d = \sqrt{6²+8²} =\sqrt{ 36 + 64}\)
=> d = 10 units
so, length of diameter of circle is 10 units. Now, by definition of radius, the radius of circle is half of diameter. Thus, the required value of radius, r is 5 units (10/2).
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If Jodi eats 2 chocolates she will consume 72 calories how many calories will she consume if she eats 5 chocolates
Answers
Answer:
x = 180
Step-by-step explanation:
We can use ratios to solve
2 chocolates 5 chocolates
--------------------- = ------------------
72 calories x calories
Using cross products
2 *x = 5*72
2x = 360
Divide each side by 2
2x/2 = 360/2
x = 180
Set up a ratio 2/72 = 5/x.
Now use cross-products.
(2)(x) = (5)(72).
2x = 360.
Now divide both sides by 2.
This gives us x = 180.
So, Jodi consumes 180 chocolates when she eats 5 chocolates.
10. Which graph appears to show a proportional relationship between x
and y?
Answers
Answer:
A is proportional remember proportional is a graph that goes through the origin aka 0
Step-by-step explanation:
A woman can do a job in 9 days and her daughter can do the same job in 16 days. They start working together, but after 4 days the daughter leaves and the woman finishes the job alone. How many days did it take her to finish the job alone?
Answers
Step-by-step explanation:
ans...9days.......,........
A newspaper in Germany reported that the more semesters needed to complete an academic program at the university, the greater the starting salary in the first year of a job. The report was based on a study that used a random sample of 24 people who had recently completed an academic program. Information was collected on the number of semesters each person in the sample needed to complete the program and the starting salary, in thousands of euros, for the first year of a job. The data are shown in the scatterplot below. 70 65 60 55 Starting Salary (1.000 euros) 50 45 35 30 25 5 10 15 20 Number of Semesters (a) Does the scatterplot support the newspaper report about number of semesters and starting salary? Justify your answer. b) The coefficient of determination is 0.335. Interpret this value in the context of this problem. c) Determine the value of the correlation coefficient. Interpret this value in the context of this problem.
Answers
a) Yes, It does. The scatterplot support the newspaper report about number of semesters and starting salary.
b) The value is relatively low, indicating that there are other factors that also contribute to starting salary.
c) The correlation coefficient is a value between -1 and 1 that measures the strength and direction of the linear association between two variables.
The Correlation Coefficienta) The scatterplot appears to show a positive association between the number of semesters needed to complete an academic program and the starting salary in the first year of a job. As the number of semesters increases, the starting salary generally increases as well. Therefore, the scatterplot supports the newspaper report.
b) The coefficient of determination, or R-squared value, represents the proportion of the variation in the dependent variable (starting salary) that is explained by the independent variable (number of semesters). A value of 0.335 means that 33.5% of the variation in starting salary is explained by the number of semesters. This value is relatively low, indicating that there are other factors that also contribute to starting salary.
c) The correlation coefficient is a value between -1 and 1 that measures the strength and direction of the linear association between two variables. A value of 1 indicates a perfect positive correlation, a value of -1 indicates a perfect negative correlation, and a value of 0 indicates no correlation. The correlation coefficient for this data is not provided in the problem, so it is not possible to determine it. Without the correlation coefficient, it is not possible to interpret the strength and direction of the association between number of semesters and starting salary.
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Reuben made 3 identical necklaces each having beads and a pendant for all 3 necklaces was $15.60 if the beads cost $2.40 for each necklace how much did each pendant cost
Answers
Answer:
Each pendant costs $8.40
Step-by-step explanation:
Find the cost of the beads: 2.40 × 3 = 7.20
Subtract the cost of beads by the total amount spent: 15.60 - 7.20 = 8.40
Answer: Each pendant costs $ 8.40
Step-by-step explanation:
Find the cost of the beads: 2.40 × 3 = 7.20
Subtract the cost of beads by the total amount spent: 15.60 - 7.20 = 8.40
a jet airliner travels 1680 miles in 3 hours with a tail wind. the return trip, into the wind, takes 3.5 hours. write a system of equations whose solution is the ground speed of the airplane and the wind speed.
Answers
A system of equation is 1680mi3hr = p−w×600×2hr -p + w for a jet airliner travels 1680 miles in 3hours with a tail wind.
Let p be the speed of the jet airliner
and w be the speed of the tail wind
It takes the plane 3 hours to go 1680 miles when a jet airliner travels with a tail wind and and 3.5 hours to go 1680 miles against the wind.. So, using system of equations we get
1680mi3hr = p−w×600×2hr = p + w
Solving for the left sides we get:
200mph = p - w
300mph = p + w
Now solve for one variable in either equation, we use
200mph = p - w
Add w to both sides:
p = 200mph + w
Using the value of x, we can found the value of w using system of equations.
300mph = (200mph + w) + w
Combine like terms:
300mph = 200mph + 2w
Subtract 200mph on both sides:
100mph = 2w
On dividing by 2:
50mph = w
So the speed of the tail wind is 50mph.
Therefore, 200mph = p - 50mph
Add 50mph on both sides:
250mph = p
Hence, speed of jet airliner is 250mph.
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Which combination of hours can keitaro walk and run in a month to reach his goal? 2 hours walking; 12 hours running 4 hours walking; 3 hours running 9 hours walking; 12 hours running 12 hours walking; 10 hours running
Answers
Option 1 is correct. i.e 2 hours walking; 12 hours running keitaro walk and run in a month to reach his goal
We are given the equations
3w + 6r ≥ 36
3w + 6r ≤ 90
We will check which of the option satisfy the above equations.
1) 2 hours walking; 12 hours running
w = 2 and r =12
3w + 6r ≥ 36
3(2) + 6(12) ≥ 36
6+72 ≥ 36
78 ≥ 36
3w + 6r ≤ 90
3(2) + 6(12) ≤ 90
6+72 ≤ 90
78 ≤ 90
Both equations are satisfied. Option 1 is correct.
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The coach took all the tennis balls and split them up among 6 tennis courts. You found
24 tennis balls on each court, what is the total amount of balls?
Answers
Answer:
144
Step-by-step explanation:
bc 6 tennis courts x 24 equals 144 sorry if it's wrong
Please help me with number 5.
Answers
Answer:
D
Step-by-step explanation:
multiply the packs with the amount of bottles in each one. then subtract the number you got when you multiplied 4x8. I'm not good at explaining but hope this helps
Here ya go my lovely SkySkyWest <3
50 points as an early Christmas gift
(Whats 45÷9+66?)
Answers
Answer:
71
Step-by-step explanation:
three circles are drawn, so that each circle is externally tangent to the other two circles. each circle has a radius of a triangle is then constructed such that each side of the triangle is tangent to two circles, as shown below. find the perimeter of the triangle.
Answers
To find the perimeter of triangle formed by the tangents to the circles, find radii of circles and side lengths of triangle. The perimeter of triangle formed by the tangents to the circles is 12 times the radius of each circle.
Let's denote the radius of each circle as r. Since the circles are externally tangent to each other, the distance between their centers is equal to the sum of their radii, which is 2r.
When a triangle is formed by connecting the points of tangency on each circle, it creates three isosceles triangles. Each of these isosceles triangles has two congruent sides, which are the radii of the circles.By drawing the triangle, we can observe that the base of each isosceles triangle is equal to 2r, which corresponds to the diameter of one of the circles. The height of each isosceles triangle is equal to r, which is the radius of the circle.
Therefore, each side of the triangle formed by the tangents has a length of 4r.Since the triangle has three equal sides, its perimeter is given by 3 times the length of one side, which is 3 * 4r = 12r.The perimeter of the triangle formed by the tangents to the circles is 12 times the radius of each circle.
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The values in the table represent a function.
f(x)
8
X
-6
7
4
3
-5
3
-5
-2
12
Use the drop-down menus to complete the
statements.
The ordered pair given in the first row of the table can
be written using function notation as
f(3) is
◊
f(x) = -5 when x is
Done
Answers
The ordered pair given in the first row of the table can be written as (8, f(8)).
f(3) is equal to 7.
f(x) = -5 when x is -6 or -2.
The table represents a function where the input values (x) correspond to the output values (f(x)). Let's analyze the given information to complete the statements:
The ordered pair given in the first row of the table can be written using function notation as (x, f(x)) = (8, f(8)). This means that when x is equal to 8, the corresponding function value is f(8).
To find f(3), we look for the row in the table where x is equal to 3. From the given table, we can see that when x is 3, the corresponding function value f(x) is 7. Therefore, f(3) is equal to 7.
Similarly, to find when f(x) is equal to -5, we look for the rows in the table where the function value is -5. From the table, we can see that when x is equal to -6 and -2, the function value f(x) is -5. Therefore, we can say that f(x) = -5 when x is -6 or -2.
In summary:
The ordered pair given in the first row of the table can be written as (8, f(8)).
f(3) is equal to 7.
f(x) = -5 when x is -6 or -2.
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Find the mean for the data set. 6, 14, 7, 4, 12, 8, 13, 4, 18, 14
Answers
Answer:
Concept:
Mean is just another name for average. To find the mean of a data set, add all the values together and divide by the number of values in the set. The result is your mean!
The values are given below as
\(6,14,7,4,12,8,13,4,18,14\)The image below shows how to calculate the mean
By substituting values, we will have
\(\begin{gathered} \bar{x}=\frac{\sum ^{}_{n\mathop=0}x}{n} \\ n=10 \end{gathered}\)\(\begin{gathered} \bar{x}=\frac{6+14+7+4+12+8+13+4+18+14}{10} \\ \bar{x}=\frac{100}{10} \\ \bar{x}=10 \end{gathered}\)Hence,
The mean = 10
To calculate the variance, we will use the formula below
\(^{}\sigma^2=\frac{\sum ^{\infty}_{n\mathop=0}(x-\bar{x})^2}{n}\)\(\begin{gathered} \sigma^2=\frac{\sum ^{\infty}_{n\mathop{=}0}(x-\bar{x})^2}{n} \\ (x-\bar{x})^2=(6-10)^2+(14-10)^2+(7-10)^2+(4-10)^2+(12-10)^2+(8-10)^2+(13-10)^2+(4-10)^2+(18-10)^2+(14-10)^2 \\ (x-\bar{x})^2=16+16+9+36+4+4+9+36+64+16 \\ (x-\bar{x})^2=210 \end{gathered}\)\(\begin{gathered} \sigma^2=\frac{\sum ^{\infty}_{n\mathop{=}0}(x-\bar{x})^2}{n} \\ \sigma^2=\frac{210}{10} \\ \sigma^2=\frac{210}{10} \\ \sigma^2=21 \end{gathered}\)Hence
The variance = 21
To calculate the standard deviation,
\(\begin{gathered} \sigma=\sqrt[]{variance} \\ \sigma=\sqrt[]{21} \\ \sigma=4.58 \end{gathered}\)Hence,
The standard deviation is = 4.58
Someone give me the answer to this
Answers
The equation of the line from the given graph is y = 3x + 1.
What is equation of line?With the aid of the line's slope and a point on the line, the equation of a line may be created. For a better understanding of how a line's equation is created, let's learn more about the line's slope and the necessary point on the line. The slope of a line is the angle that the line makes with the positive x-axis and can be stated as a numerical integer, fraction, or as the tangent of that angle. The term "point" refers to a coordinate system point with the x and y coordinates.
From the given graph we observe the two coordinates of the line are (0, 1) and (3, 10).
The slope of the line is given as:
m = y2 - y1 / x2 - x1
m = (10 - 1) / (3 - 0)
m = 9/3 = 3
The point-slope intercept is given as:
y - y1 = m (x - x1)
Substituting the values:
y - 1 = 3 (x - 0)
y - 1 = 3x
y = 3x + 1
Hence, the equation of the line is y = 3x + 1.
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what is the price of a $90 mobile phone after a 30% discount
Answers
Answer:
$ 63
Step-by-step explanation:
Let the new price ( price after the discount ) be x.
Old price Discount New price
100 30 70
90 30 x
Now we can make an expression like this to solve this
100 ⇒ 70
90 ⇒ x
Use cross multiplication to solve for x.
100x = 70 × 90
100x = 6300
Divide both sides by 100.
x = $ 63
Answer:
Discount: $27.00
Final Price: $63.00
Step-by-step explanation:
Discount = Original Price x Discount %/100
Discount = 90 × 30/100
Discount = 90 x 0.3
You save = $27.00
Final Price = Original Price - Discount
Final Price = 90 - 27
Final Price = $63.00
Sam is baking cakes at her parents' bakery. She gets paid $20 a week in addition to $4 for every cake she bakes. She made $60 this week. Write an equation to show how many cakes Sam baked this week
Answers
An equation is formed of two equal expressions. The number of cakes that are made by Sam this week is $10.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Sam gets paid $20 a week in addition to $4 for every cake she bakes. Let y be the total amount that is made by Sam this week, while x represents the number of cakes she bakes. Therefore, the equation for the total amount made by sam in a week can be written as,
y = 20 + 4x
Since her total income for this week is $60, therefore, we can write,
60 = 20 + 4x
40 = 4x
x = 10
Hence, the number of cakes that are made by Sam this week is $10.
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Find the value of , and in the identity
+ 5 − + 4 ≡ 2 2 + − 10
Find the value of and in the identity
4 3 + + 5 + ≡ 22 + 28
Answers
y = 10x + 8 in the second identity. Substituting this into the equation:4(3x + 5) + 10x + 8 ≡ 22x + 28. Simplifying: 22x + 28 ≡ 22x + 28.
This equation is true for all values of x, so there are infinite solutions.
What is an equation?A mathematical statement that affirms the equality of two expressions, usually separated by an equal sign, is recognized as an equation. In other words, an equation is a statement that two expressions are the same.
Equations can be used to solve problems, find unknown values, or describe relationships between quantities.
To find the values of x and y in the first identity:
x + 5 − y + 4 ≡ 2(2x + y) − 10
Simplifying the left-hand side:
x + 5 − y + 4 = x + y + 9
Substituting this into the original equation:
x + y + 9 ≡ 2(2x + y) − 10
Expanding the right-hand side:
x + y + 9 ≡ 4x + 2y - 10
Simplifying the right-hand side:
x + y + 9 = 4x + 2y - 10
Solving for x:
3x = -19
x = -19/3
Substituting this into the original equation and solving for y:
-19/3 + y + 9 - y + 4 ≡ 2(2(-19/3) + y) − 10
-5/3 ≡ -38/3 + 2y - 10
-5/3 ≡ -48/3 + 2y
43/3 ≡ 2y
y = 43/6
Therefore, x = -19/3 and y = 43/6 in the first identity.
To find the values of x and y in the second identity:
4(3x + 5) + y ≡ 22x + 28
Expanding the left-hand side:
12x + 20 + y ≡ 22x + 28
Simplifying:
y - 10x ≡ 8
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intersecting lines r, s, and t are shown below. s t 23° r 106° x° what is the value of x ?
Answers
To find the value of x, we need to use the fact that when two lines intersect, the sum of the adjacent angles formed is equal to 180 degrees.
In this case, the angle formed between lines s and t is 23 degrees, and the angle formed between lines r and s is 106 degrees. Let's denote the angle between lines t and r as x.
Using the information given, we can set up the equation:
(106 degrees) + (23 degrees) + x = 180 degrees
Combine the known values:
129 degrees + x = 180 degrees
To isolate x, subtract 129 degrees from both sides of the equation:
x = 180 degrees - 129 degrees
x = 51 degrees
Therefore, the value of x is 51 degrees.
In conclusion, the value of x, the adjacent angles formed between intersecting lines t and r, is 51 degrees.
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For which of these numbers would you most likely count rather than subitize?
A. 0
B. 1
C. 3
D. 5
Answers
A and B are typically subitized, which means that they can be immediately recognized without counting. C and D are more likely to be counted.
Counting is the process of determining the number of items in a set by successively adding one. Subitizing, on the other hand, is the ability to immediately recognize the number of items in a small set without counting. The capacity for subitizing is limited to small sets typically ranging from 1 to 5 items, depending on the individual's age and mathematical ability. The answer to this question would be option C, 3. For most individuals, recognizing the number of items in a set of 3 would require counting rather than subitizing, as 3 is at the upper limit of the typical range for subitizing.
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You roll a die with the sample space S=(1,2,3,4,5,6]. You define A as (1,2,4),B as [1,2,4,5,6],C as [5,6) and D as [2,3,6) Determine which of the following events are exhaustive and/or mutually exclusive
Answers
- Events A, B, C, and D are exhaustive.
- Events A and B, B and D are not mutually exclusive.
- Events A and C, C and D, A and D are mutually exclusive.
To determine whether the events are exhaustive or mutually exclusive, we need to understand the definitions of these terms:
1. Exhaustive events: Events are considered exhaustive if the union of all the events covers the entire sample space S. In other words, there are no outcomes in the sample space that are not included in any of the events.
2. Mutually exclusive events: Events are considered mutually exclusive if they have no outcomes in common. In other words, the events cannot occur simultaneously.
Now let's analyze the given events:
A = {1, 2, 4}
B = {1, 2, 4, 5, 6}
C = {5, 6}
D = {2, 3, 6}
To determine if the events are exhaustive, we need to check if their union covers the entire sample space S.
The union of A, B, C, and D is {1, 2, 3, 4, 5, 6}, which covers the entire sample space S. Therefore, the events A, B, C, and D are exhaustive.
To determine if the events are mutually exclusive, we need to check if any outcomes are shared between the events.
The outcomes 1, 2, and 4 are shared between events A and B. Therefore, events A and B are not mutually exclusive.
The outcomes 2 and 6 are shared between events B and D. Therefore, events B and D are not mutually exclusive.
No outcomes are shared between events A and C, C and D, or A and D. Therefore, events A and C, C and D, and A and D are mutually exclusive.
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A rectangular plot of land is represented on a map by the vertices (10,10), (10, 90), (70.5, 90), and (70.5, 10), where the x- and y-coordinates are measured in yards. What is the area of the plot of land?
Answers
Answer:
Area of the plot of the land is 4840 square units.
Step-by-step explanation:
Let's draw the rectangle approximately on an x y plane. That would help us to find the length and width of the rectangle.
Answer: 4,480yd^2
Step-by-step explanation:
You have the x and y coordinates of the vertices (10, 10), (10,90), (70.5,90), and (70.5, 10) you have the coordinates: x and y as the first two which are the ones in bold. From that you do 70.5-10= 60.5.
Then you subtract the x and y coordinates again, which are underlined. From that do 90-10=80
Last you do 60.5x80=4,840 yards squared
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Find the equation of a line parallel to y = 2x + 4 that goes through the point (2,5)
Answers
Answer:
y= 2x+1
Step-by-step explanation:
Line parallel to y = 2x + 4
And that goes through the point (2,5)
-----------
Parallel lines have equal slope, so it will be in the form of y= 2x+b
Let's find the value of y-intercept (b) by using the given point:
5= 2*2+bb= 5-4b= 1So the line is: y= 2x+1
Out of 493 applicants for a job, 217 have over 5 years of experience and 52 have over 5 years of experience and have a graduate degree. Step 1 of 2 : What is the probability that a randomly chosen applicant has a graduate degree, given that they have over 5 years of experience
Answers
The probability that a randomly chosen applicant has a graduate degree, given that they have over 5 years of experience, is 52/217.
To find the probability that a randomly chosen applicant has a graduate degree, given that they have over 5 years of experience, we can use conditional probability.
Let's define the following events:
A: Applicant has a graduate degree
B: Applicant has over 5 years of experience
We are given:
P(B) = 217/493 (probability of having over 5 years of experience)
P(A ∩ B) = 52/493 (probability of having over 5 years of experience and a graduate degree)
The probability that a randomly chosen applicant has a graduate degree, given that they have over 5 years of experience can be calculated using the formula for conditional probability:
P(A | B) = P(A ∩ B) / P(B)
Plugging in the values:
P(A | B) = (52/493) / (217/493)
P(A | B) = 52/217
Therefore, the probability that a randomly chosen applicant has a graduate degree, given that they have over 5 years of experience, is 52/217.
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what is the area of a sector of a circle with a radius of 8 inches and formed by a cetnral angle that measures 60
Answers
The area of the sector is 16π square inches.
To find the area of a sector of a circle, we need to use the formula:
Area of sector = (central angle/360) x \(\pi r^2\)
where r is the radius of the circle.
In this case, the radius is given as 8 inches.
We are also given that the central angle measures from 60 to 150 degrees. To calculate the area of the sector, we need to find the size of the central angle first.
To do this, we subtract the smaller angle from the larger angle:
150 - 60 = 90 degrees
So, the central angle is 90 degrees.
Now, we can substitute the values into the formula:
Area of sector = (90/360) x \(\pi 8^2\)
Area of sector = (1/4) x π(64)
Area of sector = 16π square inches
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The slope (m) and the y-intercept (b) of the line 2x + 3y = 12 is:
Answers
Step-by-step explanation:
\(2x + 3y = 12 \\ 3y = - 2x + 12 \\ y = - \frac{2}{3} x + 4\)
slope is -2/3
y intercept is 4
Answer:
The slope is -2/3 and the y intercept is 4
Step-by-step explanation:
2x + 3y = 12
Slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
2x + 3y = 12
Subtract 2x from each side
2x-2x+3y = -2x+12
3y = -2x+12
Divide by 3
3y/3 = -2x/3 +12/3
y = -2/3 x +4
The slope is -2/3 and the y intercept is 4
Mom said Joe and Jane could equally share the change in her purse. They found 2X 50c pieces and 2X 20c pieces and a 10c pieces. How much did they get each?
Answers
Hello
total = 2 x 50c + 2 x 20c + 10c = 150c
150c/2 = 75c
they get each 75c.
can someone please help me
Answers
Answer:
Step-by-step explanation:
Apples are prepared in a process with two resources. The first resource has a capacity of 2.1 apples per hour. The capacity of the second resource is 4.4 apples per hour. The first resource has 1 worker and the second resource has 4 workers. Demand for this process is 1.6 apples per hour. Wages are $8 per hour.
What is the cost of direct labor (in $)?per unit
Answers
The cost of direct labor per unit is $5.628 per apple.
To calculate the cost of direct labor per unit, we need to determine the total labor hours required to produce one unit of output and then multiply it by the wage rate.
Let's denote the labor hours required for the first resource as "L₁" and the labor hours required for the second resource as "L₂".
The first resource has a capacity of 2.1 apples per hour, and the demand is 1.6 apples per hour. Therefore, the labor hours required for the first resource per unit of output are:
L₁ = 1 apple / (2.1 apples/hour) = 0.4762 hours/apple (rounded to 4 decimal places)
The second resource has a capacity of 4.4 apples per hour, and the demand is 1.6 apples per hour. Therefore, the labor hours required for the second resource per unit of output are:
L₂ = 1 apple / (4.4 apples/hour) = 0.2273 hours/apple (rounded to 4 decimal places)
Now, let's calculate the total labor hours required per unit:
Total labor hours per unit = L₁ (first resource) + L₂ (second resource)
= 0.4762 hours/apple + 0.2273 hours/apple
= 0.7035 hours/apple (rounded to 4 decimal places)
Finally, to calculate the cost of direct labor per unit, we multiply the total labor hours per unit by the wage rate:
Cost of direct labor per unit = Total labor hours per unit * Wage rate
= 0.7035 hours/apple * $8/hour
= $5.628 per apple (rounded to 3 decimal places)
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