A right rectangular prism measures 12 cm tall, 3 cm long, and 10 cm wide. A manufacturer would like to double the surface area of this prism. What should be the height of the new prism so that its surface area is doubled? Enter your answer, to the nearest tenth, in the box.
The height of the new prism so that its surface area is doubled will be 26.31 cm.
What is the surface area of the rectangular prism?Let the prism with a length of L, a width of W, and a height of H. Then the surface area of the prism is given as
SA = 2(LW + WH + HL)
A right rectangular prism measures 12 cm tall, 3 cm long, and 10 cm wide. A manufacturer would like to double the surface area of this prism.
Then the height of the new prism so that its surface area is doubled will be given as,
2 x 2 x (12 x 3 + 3 x 10 + 10 x 12) = 2(3h + 3 x 10 + 10h)
2(36 + 30 + 120) = 13h + 30
372 = 13h + 30
13h = 342
h = 26.31 cm
The height of the new prism so that its surface area is doubled will be 26.31 cm.
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In this figure, 12. 2% of the area is painted blue. How much of the area is painted blue? 1. 22 cm² 3. 05 cm² 4. 27 cm² 5. 49 cm² A square with side lengths of 5 cm. A triangle attached to one side has a perpendicular line indicating a height of 4 cm
12.2 % of the area painted blue of the figure representing a square with attached triangle on one side with perpendicular height 4cm is equal to 4.27 cm² .
Figure having square attached with triangle on one side.
Side length of the square = 5 cm
Area of the square = ( side-length )²
= 5²
= 25 cm²
Triangle attached on one side of the square with height = 4cm
Area of the triangle = ( 1/2) × base × height
= ( 1/2) × 5 × 4
= 10 cm²
Total area of the figure = 25 + 10
= 35 cm²
Percent of area painted blue = 12.2% of total area
= ( 12.2 / 100 ) × 35
= 4.27 cm²
Therefore, for the given figure made up of square and triangle area to be painted blue is equal to 4.27 cm².
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Determine whether the pairs of triangles are congruent.
Answer:
1. yes
2. No
Step-by-step explanation:
1. The triangles are congruent
2. It's not matching
12.2 Apples and Oranges
At the corner produce market, apples cost $1 each and oranges cost $2 each.
1. Find the cost of:
a. 6 apples and 3 oranges
b. 4 apples and 4 oranges
c. 5 apples and 4 oranges
d. 8 apples and 2 oranges
Unit 3: Linear Relationships
Lesson 12: Solutions to Linear Equations
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The total cost of 6 apples and 3 oranges is $6 + $6 = $12.
The total cost of 4 apples and 4 oranges is $4 + $8 = $12.
The total cost of 5 apples and 4 oranges is $5 + $8 = $13.
The total cost of 8 apples and 2 oranges is $8 + $4 = $12.
What is linear equation and the total cost of given terms?a). 6 apples at $1 each = $63 oranges at $2 each = $6The total cost of 6 apples and 3 oranges is $6 + $6 = $12.b). 4 apples at $1 each = $44 oranges at $2 each = $8The total cost of 4 apples and 4 oranges is $4 + $8 = $12.c). 5 apples at $1 each = $54 oranges at $2 each = $8The total cost of 5 apples and 4 oranges is $5 + $8 = $13.d). 8 apples at $1 each = $82 oranges at $2 each = $4The total cost of 8 apples and 2 oranges is $8 + $4 = $12.In all the above examples, we simply multiplied the number of apples by the cost per apple and the number of oranges by the cost per orange. Then we added the two amounts to find the total cost.To learn more about linear equation refer:
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Write a value for n that would make the inequality true. ⁿ⁄₉ > ½ n = _____________________
The value for n that would make the inequality true is 4.5
What is an inequality?You should understand that a statement of an order relationship with greater than, greater than or equal to, less than, or less than or equal to between two numbers or algebraic expressions is inequality.
The given inequality is ⁿ⁄₉ > ½
This implies that 2(n) > 1(9)
Opening the brackets to have
2n > 9
Making n the subject of the relation by dividing both sides by 2
2n/2 > 9/2
Therefore n = 4.5
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a factory (f) is producing smoke that causes damage of $80 per month to a local residents laundry (l). the damage can be eliminated in one of two ways:
The following two methods can be used for eliminating the damage to the laundry (l).
Factory (f) can install a scrubber at a cost of $500 to reduce the smoke, thereby eliminating the damage to the laundry (l).Local resident (l) can purchase and install a clothesline at a cost of $100, thereby eliminating the damage to their laundry.The factory and the local resident must decide whether to install the scrubber or the clothesline, depending on which option will result in the lowest cost. The best option for each party depends on their own willingness to pay for the damage reduction and their ability to pay for the solution.
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a bag contains 16 black balls and 14 white balls. two balls are drawn at random from the bag, one after the other without replacement. what is the joint probability the first ball drawn was black and the second ball drawn was also black?
Answer:
Step-by-step explanation:
a. three times the total number of adults was 17 less than the number of children who visited the petting zoo. write an equation to model this relationship.
If the 3 times of total number of adults was 17 less than number of children who visited the petting zoo , then the equation to model this relationship is written as c = 3a + 17 ;
let the number of children in the petting zoo be = c ;
and the number of adults in the petting zoo is = a ;
given that the the number of children are 3 times the number of adults ;
that means ⇒ c = 3a ;
and also given that the difference between the number of children and number of adults is 17 .
This situation can be represented as :
⇒ c - 3a = 17 ;
⇒ c = 3a + 17 .
Therefore , the equation to model this relationship is "c = 3a + 17" .
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The growth rate of a bacterial culture is 150% each hour. Initially, there are 10 bacteria. Describe the error in finding the number of bacteria in the culture after 8 hours. Correct the error and find, to the nearest whole number, the number of bacteria in the culture after 8 hours. The exponential function is b(t)=. After 8 hours, there are about bacteria in the culture
If the growth rate of bacterial culture is 150% each hour , then the correct exponential function is b(t) = 10(2.5)^t instead of b(t) = 10(1.5)^t , and after 8 hours there are about 15259 bacteria in culture .
The percent growth in the bacterial culture is = 150% = 1.5 ;
the initial amount of bacteria present is = 10 ;
the exponential function used to denote this situation is written as :
⇒ b(t) = 10(1 + 1.5)^t
⇒ b(t) = 10(2.5)^t
to find number of bacteria after 8 hours ,
we substitute t = 8 in b(t) ;
we get ;
⇒ b(8) = 10(2.5)⁸ ;
⇒ b(8) = 15258.789 ≈ 15259
Therefore , there will be 15259 bacteria present after 8 hours .
The given question is incomplete , the complete question is
The growth rate of a bacterial culture is 150% each hour. Initially, there are 10 bacteria. Describe the error in the data below, in finding the number of bacteria in the culture after 8 hours. Correct the error and find, to the nearest whole number,
"The number of bacteria in the culture after 8 hours. The exponential function is b(t) = 10(1.5)^t , b(8) = 10(1.5)⁸ . After 8 hours, there are about 256 bacteria in the culture ."
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7. Segment MN has endpoints at M(-12,-5) and N(8, 10). A third point Q is located on MN such that MQ:ON=2:3. Answer the following questions. (a) Find the coordinates of Q. Show how you arrived at your answer.
Answer:
To find the coordinates of Q, we can use the concept of proportional division of line segments.
Given that MQ:ON = 2:3, it means that the ratio of the length of MQ to ON is 2:3.
Let's first find the vector that represents the direction of MN, which is the vector pointing from M to N. We can find this by subtracting the coordinates of M from the coordinates of N:
(8,10) - (-12,-5) = (20, 15)
This is the vector <20,15>
Now, we can find the point Q, which is located two thirds of the way from M to N, by multiplying the vector <20,15> by 2/5 and adding the result to the coordinates of M:
Q = M + (2/5) * <20,15>
= (-12,-5) + (2/5) * <20,15>
= (-12,-5) + <8,6>
= (8,1)
So, the coordinates of Q are (8,1)
free bilirubin is transported by the blood to the liver. TRUE OR FALSE
True, free bilirubin is transported by the blood to the liver.
Macrophages begin the disposal of hemoglobin by separating the heme from the globin. They hydrolyze the globin into free amino acids, which can be used for energy-releasing catabolism or recycled for protein synthesis.
Bilirubin
Bilirubin is a red-orange compound that occurs in the normal catabolic pathway that breaks down heme in vertebrates. This catabolism is a necessary process in the body's clearance of waste products that arise from the destruction of aged or abnormal red blood cells.
Hemoglobin
Hemoglobin is a protein in your red blood cells that carries oxygen to your body's organs and tissues and transports carbon dioxide from your organs and tissues back to your lungs.
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Deepak is a landscaper who charges $30 for each job he does plus an additional $15 for each hour he works. He only accepts jobs if he will earn at least $90 per job. He writes this inequality to determine x, the number of hours he must work during each job in order to accomplish this.
30 + 15 x greater-than-or-equal-to 90
Which best describes the restrictions on the jobs Deepak will accept?
Answer:
He only accepts jobs that last 4 or more hours.
Step-by-step explanation:
He only accepts jobs that last 4 or more hours.
He only accepts jobs that last 5 or more hours.
He only accepts jobs that last 8 or more hours.
He only accepts jobs that last 9 or more hours.
30 + 15x ≥ 90
15x ≥ 60
x ≥ 4
Answer: He only accepts jobs that last 4 or more hours.
We want to know how a tudent’ level of education and their gender impact both their annual income and amount of tudent loan debt. However, we want to account for the annual income of the tudent’ parent a well. So which Statitical Tet are you going to ue?
The best statistical test to be used is multiple linear regression analysis.
Multiple linear regression is a statistical method that allows you to examine the relationship between two or more independent variables (in this case, level of education, gender, and annual income of the student's parents) and one dependent variable (annual income and student loan debt).
It will help you determine how much of the variation in the dependent variable is explained by the independent variables, and the strength and direction of the relationships between the variables.
In this case, this test will allow us to determine the impact of a student's level of education, gender, and the annual income of their parents on their annual income and student loan debt while accounting for the possible confounding effect of the annual income of their parents on these variables.
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jane spent 2 hours exploring a mountain with a dirt bike. when she rode the 40 miles uphill, she went 5 mph slower than when she reached the peak and rode for 12 miles along the summit. what was her rate along the summit?
The time to calculate her rate along the summit Rate = 1.5 mph
Rate = Distance / Time
To solve this problem, we will first need to calculate the time it took Jane to reach the peak. Since she rode 40 miles uphill, we can use the rate of 5 mph slower than when she reached the peak to calculate this time.
Time = Distance / Rate
Time = 40 miles / (Rate - 5 mph)
Time = 40 miles / (Rate - 5 mph)
Time = 40 miles / (Rate - 5)
Time = 8 hours
Since Jane spent 2 hours exploring the mountain, the total time it took her to reach the peak was 8 hours. We can now use this time to calculate her rate along the summit.
Rate = Distance / Time
Rate = 12 miles / 8 hours
Rate = 1.5 mph
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can someone help me out
answers
2 units
3 units
5 units
7 units
The length of PT is 3 units. The solution has been obtained using the concept of transformation.
What is transformation?
A transformation is an operation that moves a polygon or other two-dimensional object on a plane or coordinate system.
The term "pre-image" or "inverse image" refers to the shape in two dimensions prior to any modification. The image is the shape after transformation.
Transformation can be done by translation, rotation, reflection and dilation.
We are given two rectangles ABCD and PRQT
AB = DC = 3 units
AD = BC = 10 units
It can be observed that the rectangles PRQT and ABCD are same but PRQT is rotated.
Since, they are same so,
AB = PT = 3 units
Hence, the length of PT is 3 units.
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what is the answer to this question
Answer:82 cm squared
Step-by-step explanation:
Just draw imaginary lines on the shape to turn it into a bunch of squares and rectangles, then find the area of those and add them together.
Kinda hard to explain since there are multiple ways to do it, but I hope that this still helps!
Label each item as factor by grouping or factor using substitution.
To factor a trinomial of the form
a x 2 + bx + c, multiply the trinomial
by a. Rewrite the first two terms
using ax. Substitute a single variable
for ax. Factor the trinomial. Substitute ax
back in for the variable. Divide by a.
Step-by-step explanation:
I Don't even know what the answer is
Can someone help me please?
Answer:
Part A.) 153 Boxes
Part B.) 394 Boxes (395 if rounding up)
Step-by-step explanation:
The inequality used in this situation would be:
3.74x + 25 < 600
3.74 is the price of each box
x is the number of boxes
25 is that deposit
and < 600 is not making $600 in sales
What we need to do is get X alone. First we will subtract 25 from both sides since that's the opposite of +25.
Doing that will get you
3.74x = 575
Next step is to divide 3.74 on both sides since 3.74 is being multiplied by x and division is the opposite.
That will give you X = 153.74. We round down to stay under and we end up with 153.
For part B, we would do the same process, but instead of < 600, we would do >= 1500. Just typing the same steps out.
3.74x >= 1475 since we subtract 25 from both sides
x = 394.38 since we divide 3.74 on both sides. Rounding would get us 394
Week 23-Practice 19: Surface Area (PA.GM.2.1 & PA.GM.2
A cylinder has a surface area of 48 cm² and a radius of 2 cm. What is the height of the cylinder?
O 8 cm
O 10 cm
O 12 cm
O 14 cm
The lateral surface area of the cylinder is 51.22 cm2.
What is surface area?
Surface area is a two-dimensional measure that refers to the total area of a surface, such as the area of a two-dimensional shape, a three-dimensional solid, or a combination of both. It is the sum of the areas of all the faces of a solid object. It is also referred to as the area of the boundary of a three-dimensional object. It can be used to calculate the volume of an object, and is also used in other calculations like area of the base of a triangle, area of a circle, and more.
The cylinder shown below has a diameter of 5.2 cm on the base and a height of 7.1 cm. The diameter of the base is referred to as 'd' and the height of the cylinder is referred to as 'h'. The lateral surface area of the cylinder can be found by using the formula LSA = 2πrh, where 'r' is the radius of the base. The radius of the base of this cylinder is half of the diameter, or 2.6 cm. Therefore, the lateral surface area of the cylinder is: 2π x 2.6 x 7.1 = 51.22 cm2.
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An investor has an account with stock from two different companies. Last year, his stock in Company A was worth $3300 and his stock in Company B was worth $4140. The stock in Company A has increased 4% since last year and the stock in Company B has increased 5%. What was the total percentage increase in the investor's stock account? Round your answer to the nearest tenth Answers fast!
The total percentage increase in the investor's stock account was of 4.55%.
The values of the stocks of Company A and Company B, after the increase are given, respectively, by:
Company A: 3300 x 1.04 = $3432.
Company B: 4140 x 1.05 = $4347.
The total values are given as follows:
Before the increase: 3300 + 4140 = 7440.
After the increase: 3432 + 4347 = 7779.
The percent increase is given by the increase divided by the initial value and multiplied by 100%, hence:
P = (7779 - 7440)/7440 x 100% = 4.55%.
The total percentage increase in the investor's stock account was of 4.55%.
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Evaluate the expression for the given value of the variables.
0.5c−2.3d
c=15, d=3
DUE IN 20 MIN
Answer:
I got 0.6
Step-by-step explanation:
plug in c and d
0.5(15) - 2.3(3)
multiply them
7.5 - 6.9 = 0.6
HELPP GEOMETRY HOMEWORK
All of the angles in an acute triangle are less than 90 degrees. Triangles are referred to as right triangles when one of their angles is 90 degrees.
What is called triangle?The three vertices of a triangle make it a three-sided polygon. The angles of the triangle are formed by the three sides' end-to-end connections at a point. 180 degrees is the sum of the triangle's three angles. With three sides and three vertices, triangles are a particular kind of polygon in geometry.
It has three straight sides and is a two-dimensional figure. As a 3-sided polygon, a triangle is included. Three triangle angles added together equal 180 degrees. In one plane, the triangle is contained. When three straight lines cross, a triangle is the result. There are always three sides and three corners to a triangle (angles). A triangle's vertex is the location at which two of its sides meet.
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Suppose that the height H of a Ferris wheel can be modeled by the function H(t) = -12cos(πt/45) + 18, where t is the time in seconds. What is the maximum height of a cabin? Use 3. 14 for π.
For the given function H(t) = -12cos( πt/45 ) + 18 the maximum height is 30 units.
Function to modeled the height 'H' of the Ferries wheel is given by:
H(t) = -12cos( πt/45 ) + 18
Where 't' represents the time in seconds.
For cosine trigonometric function,
-1 ≤ cosα ≤ 1
Here cos function lies between two values -1 and 1.
Substitute cos( πt/45 ) = 1 or -1
When cos( πt/45 ) = 1
H(t) = -12(1) + 18
⇒H(t) = 6 units
When cos( πt/45 ) = -1
H(t) = -12(-1) + 18
⇒H(t) = 30 units
Maximum height of a required cabin is equals to 30 units.
Therefore, the maximum height of given cabin represented by the function
H(t) = -12cos( πt/45 ) + 18 is equal to 30 units.
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how many 9-digit integers contain exactly 5 zeroes? (recall that the leading digit is never zero! you may enter a formula or an exact numerical value.)
Considering that the leading digit is never zero , then the number of 9 digit integers that can contain exactly 5 zeroes are 367416 numbers .
the number of digits in the number is = 9 digits ;
the number should have exactly five zeroes ,
the number of ways to pick five of the digit positions for the zeroes, since the first digit can’t be zero is = ⁸C₅ ,
There are 9 possible digits for each of other 4 positions as other positions are occupied by 0 ,
So, the total number of possibilities is = ⁸C₅ × 9⁹⁻⁵
Simplifying further ,
we have ,
= ⁸C₅ × 9⁴
= 56 × 6561
= 367416 numbers .
Therefore , there can be 367416 numbers of 9 digits having 5 zeros .
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Macy made a 220 grooming dogs one day in her mobile grooming business she charges 60 per appointment and 40 earned in tips write an equation to represent the situation and solve the equation to determine how many appointments Messi had part B Logan made a profit of 300 as a mobile groomer he charge $70 per appointment and received $50 in tips but he had to pay a rental fee for the truck of $20 per appointment write an equation to represent the situation and solve the situation to determine how many appointments Logan had
Macy had 3 appointments.
Logan had 5 appointments.
What is the quadratic equation?
A quadratic equation is a type of polynomial equation of degree 2, which is written in the form of "ax^2 + bx + c = 0", where x is the variable and a, b, and c are constants. The solutions to a quadratic equation can be found using the quadratic formula: x = (-b ± √(b^2 - 4ac))/2a.
Part A:
Let x be the number of appointments Macy had.
We know that the total income (60x + 40) must equal 220.
Therefore, the equation representing the situation is:
60x + 40 = 220
To solve for x, we can subtract 40 from both sides:
60x = 180
Finally, we divide both sides by 60 to get:
x = 3
Macy had 3 appointments.
Part B:
Let y be the number of appointments Logan had.
We know that the total profit (70y + 50 - 20y) must equal 300.
Therefore, the equation representing the situation is:
50y + 50 = 300
To solve for y, we can subtract 50 from both sides:
50y = 250
Finally, we divide both sides by 50 to get:
y = 5
Logan had 5 appointments.
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Jacob has 6. 15 meters of rope. He is going to use 1. 2 meters of rope to tie up his boat. How many centimeters of rope does he have left?
The remaining rope he left is 495cm
Now, According to the question:
Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.
Jacob has 6. 15 meters of rope.
He is going to use 1. 2 meters of rope to tie up his boat.
When you do the subtraction, whatever is left (the decimal part) is the length in cm when multiplied by 100.
Remaining rope = starting length - what was used.
Remaining rope = 6.15 - 1.2
Remaining rope = 4.95 meters
Hence, The remaining rope he left = 4.95 × 100 = 495 cm
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5. while performing a starch test on several different cookie brands, four tests result in the typical black color of starch presence, but the fifth gives a yellow-brown color. how might you interpret this result?
Starch and protein levels are checked for In order to present the idea of chemical compound variety, it is necessary to test for the presence of starches and protein macromolecules.
Hypothesis: It is a negative result if the biuret reagent remains blue after a test for protein since the reagent itself is blue. The test for protein is positive if a solution is pinkish purple or purple. The starch test solution is a yellowish brown color. We utilized iodine to test for starch in some solutions if any ingredient produced a mixture that was yellowish brown in color. Polysaccharides, monosaccharides, and disaccharides are separated from starch by iodine. Iodine interacts with molecules, changing the color of the molecules, while starch is a coiled polymer of glucose.
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Refer to the initial crosstabulations. For those players with low handicaps (better players), which group (male or female) shows the highest percentage saying the greens are too fast? For the low handicappers, the men have a higher percentage who think the greens are too fast. Refer to the initial crosstabulations. For those players with higher handicaps, which group (male or female) shows the highest percentage saying the greens are too fast? For the high handicappers, the women have a higher percentage who think the greens are too fast. At each handicap level, how does the percentage of women who think the greens are too fast compare to the percentage of men who feel the same? Select When the crosstabulations are aggregated across handicap level, do you still conclude the same thing when comparing the percentage of women who complain that the greens are too fast with the percentage of the men who feel the same? Select Note: This exercise is an example of Simpson's Paradox
As per the given parentage, the highest percentage saying the greens are too fast is females.
In math the term percentage is defined as the number or ratio that can be expressed as a fraction of 100.
Here we have know that the number male players are
Male Golfers Greens Condition
Handicap Too fast Fine
Under 15 10 40
15 or more 25 25
And the female players are,
Male Golfers Greens Condition
Handicap Too fast Fine
Under 15 1 9
15 or more 39 51
Then the total value of them is calculated as,
Too fast Fine Total
Male 35 65 100
Female 40 60 100
So, the group with the highest percentage of too fast is the females.
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Create a proportion for each set of similar triangles, that can be used to find the missing side lengths indicated. Then solve the proportion.
The values of x from the given figures are 3 √29 and 24 respectively.
What is triangle ?
Triangle can be defined in which it has three sides , three angles and sum of three angles is always 180 degrees.
Given
In the figure,
The two given triangles are similar ,
So, in the first figure it is given that they are similar ,
√29 / 5 = x / 15
x = √29 * 15 / 5
x =√29 * 3
x = 3 √29
And in the second figure , here also they gave they are similar
so we get,
12 / 13 = x / 26
x = 12 * 26 / 13
x = 12 * 2
x = 24
Hence, The values of x from the given similar triangles are 3 √29 and 24 respectively.
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Assuming all the workers employed at the beanbag factory are of equal ability,
what might the beanbag factory do to address the diminishing marginal returns it
experiences after the hire of its third worker?
A. Fire the manager.
B. Invest in more equipment.
C. Hire more workers.
D. Wait for its workers to improve.
Assuming all the workers employed at the beanbag factory are of equal ability, the beanbag factory invest in more equipment to address the diminishing marginal returns it experiences after the hire of its third worker. So the option B is correct.
It is assumed that all of the factory's employed employees have the same level of skill. Additionally, it must follow that if they are working to their maximum ability, they will be able to accomplish the same amount of work as before.
Since the third man was hired, the quantity of work the three of them have completed has decreased, making it clear that he is to blame for the diminishing returns.
Therefore, it seems sense to fire the individual since he is either not performing to his full capacity or encouraging other employees to do the same.
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