Panamint Systems Corporation is estimating activity costs associated with producing disk drives, tapes drives, and wire drives. The indirect labor can be traced to five separate activity pools. The budgeted activity cost and activity base data by product are as follows: Line Item Description Activity Cost Activity Base Procurement $370,000 Number of purchase orders Scheduling 250,000 Number of production orders Materials handling 500,000 Number of moves Product development 730,000 Number of engineering changes Production 1,500,000 Machine hours Line Item Description Number of Purchase Orders Number of Production Orders Number of Moves Number of Engineering Changes Machine Hours Number of Units Disk drives 4,000 300 1,400 10 2,000 2,000 Tape drives 4,000 150 800 10 8,000 4,000 Wire drives 12,000 800 4,000 25 10,000 2,500 The activity-based cost (rounded to the nearest cent) for each tape drive unit is a.$97.73 b.$394.12 c.$232.69 d.$103.84

Answers

Answer 1

The activity-based cost (rounded to the nearest cent) for each tape drive unit is approximately $0.434.

Given the activity cost and activity base data, we can calculate the allocated costs for each activity as follows:

Procurement:

Allocated cost for tape drives = (Activity cost for procurement * Number of purchase orders for tape drives) / Total number of purchase orders

= ($370,000 * 4,000) / (4,000 + 300 + 1,400 + 10 + 2,000)

= $1,480,000 / 7,710 ≈ $192.11

Scheduling:

Allocated cost for tape drives = (Activity cost for scheduling * Number of production orders for tape drives) / Total number of production orders

= ($250,000 * 150) / (4,000 + 150 + 800 + 10 + 8,000)

= $37,500 / 12,960 ≈ $2.89

Materials handling:

Allocated cost for tape drives = (Activity cost for materials handling * Number of moves for tape drives) / Total number of moves

= ($500,000 * 800) / (4,000 + 300 + 1,400 + 10 + 2,000)

= $400,000 / 7,710 ≈ $51.83

Product development:

Allocated cost for tape drives = (Activity cost for product development * Number of engineering changes for tape drives) / Total number of engineering changes

= ($730,000 * 10) / (4,000 + 150 + 800 + 10 + 8,000)

= $7,300,000 / 12,960 ≈ $562.73

Production:

Allocated cost for tape drives = (Activity cost for production * Machine hours for tape drives) / Total machine hours

= ($1,500,000 * 8,000) / (4,000 + 150 + 800 + 10 + 8,000)

= $12,000,000 / 12,960 ≈ $925.93

Now, we can calculate the total allocated cost for tape drives by summing up the allocated costs for each activity:

Total allocated cost for tape drives = Allocated cost for procurement + Allocated cost for scheduling + Allocated cost for materials handling + Allocated cost for product development + Allocated cost for production

= $192.11 + $2.89 + $51.83 + $562.73 + $925.93

= $1,735.49

Finally, we can calculate the activity-based cost per unit for tape drives by dividing the total allocated cost by the number of tape drive units:

Activity-based cost per unit for tape drives = Total allocated cost for tape drives / Number of tape drive units

= $1,735.49 / 4,000

≈ $0.434

Therefore, the activity-based cost (rounded to the nearest cent) for each tape drive unit is approximately $0.434.

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Related Questions

Choose which sampling technique 1s used. (R) Random (STR) Stratined (CLS) Cluster
(CON) Convenience (SYS) Systematic

1. I ask everyone in my 5th period class who has more than one computer
at home in a study about all of my students for the year.

2. I collect data from every 15th student on my list of the entire school
population.

3. After using a random number table to generate two-digit numbers, I
decide on 10 people to choose from the population.

Answers

Answer:

1.  CON (convenience sampling) - This sampling technique involves selecting participants who are readily available and willing to participate. In this case, the researcher is only selecting from their 5th period class, which is not a representative sample of the entire student population.

2.  SYS (systematic sampling) - This sampling technique involves selecting every nth element from a population. In this case, the researcher is selecting every 15th student on their list of the entire school population.

3.  R (random sampling) - This sampling technique involves selecting participants at random from the population. In this case, the researcher is using a random number table to generate two-digit numbers and selecting 10 people from the population.

Hope this helps!

Answer:

1.  CON (convenience sampling) - This sampling technique involves selecting participants who are readily available and willing to participate. In this case, the researcher is only selecting from their 5th period class, which is not a representative sample of the entire student population.

2.  SYS (systematic sampling) - This sampling technique involves selecting every nth element from a population. In this case, the researcher is selecting every 15th student on their list of the entire school population.

3.  R (random sampling) - This sampling technique involves selecting participants at random from the population. In this case, the researcher is using a random number table to generate two-digit numbers and selecting 10 people from the population.

Hope this helps!

In a game of cards you win $1 if you draw a heart (except the ace), $5 if you draw an ace (including the ace of hearts), $10 if you draw the king of spades and $0 for any other card. Let W be the amount you win playing this game, what the probability distribution of W?​

Answers

There are four possible outcomes in this game: winning $1, winning $5, winning $10, or winning $0.

The probability of winning $1is the probability of drawing one of the 11 hearts that are not the ace of hearts. There are 52 cards in the deck, so the probability of drawing any one of them is 1/52. However, there are 11 hearts that win $1, so the probability of winning $1 is:

P(W = $1 ) = 11/52

The probability of winning $5 is the probability of drawing the ace of hearts, which is 1/52.

P(W = $5) = 1/52

The probability of winning $10 is the probability of drawing the king of spades, which is also 1/52.

P(W = $10) = 1/52

The probability of winning $0 is the probability of drawing any other card, which is 39/52.

P(W = $0) = 39/52

Find the sum of 10x² + 7x + 6 and 6x + 5.
Answer:
Submit Answer
M
DELL

Answers

10x² + 13x + 11 is the sum of linear equation .

What is a linear equation in mathematics?

The algebraic equation y=mx+b is known as a linear equation. All of its terms are constant, first-order linear ones. where m denotes the slope and b the y-intercept.

                             The aforementioned is occasionally referred to as a "linear equation in two variables" where y and x are variables. One or more variables may be present in a linear equation. The term "bivariate linear equation" refers to a linear equation with two variables.

two equations are  10x² + 7x + 6 and 6x + 5.

now add both equations

= (10x² + 7x + 6 )+ (6x + 5)

=  10x² + 7x + 6 + 6x + 5

= 10x² + 13x + 11

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Write an equation for the transformed logarithm shown below, that passes through (1,0) and (-3,3)

Answers

The equation of the transformed logarithmic function that passes through the points (1,0) and (-3,3) is f(x) = 4.366*log10(x+4)

To find the equation of the transformed logarithmic function that passes through the points (1,0) and (-3,3), we need to determine the values of a, b, h, and k.

First, we know that the function passes through (1,0), so we can substitute x=1 and y=0 in the general equation of the transformed logarithmic function to get:

0 = a x log b(1-h) + k

Since log b(1-h) = 0 for any base b and any value of h, we can simplify the equation to:

0 = k

Therefore, k=0 and the equation becomes:

f(x) = a x log b(x-h)

Now, we have two equations with two unknowns (a and h), which we can solve by substitution or elimination. For simplicity, we can substitute b=10 (base 10 logarithm) since it is a common base and the values of a and h do not depend on the base of the logarithm. We get:

10⁶/ᵃ = 3-h

Since h is the horizontal shift of the graph, we can choose any value of h that makes the expression inside the logarithm positive. For example, we can choose h=-4, which makes x-h=-3-(-4)=1, the same as the x-coordinate of the point (1,0).

Taking the logarithm of both sides with base 10, we get:

log(4) = (6/a)*log(10)

Solving for a, we get:

a = 6/(log(4)*log(10)) ≈ 4.366

Now, we can substitute the values of a and h in the equation of the transformed logarithmic function to get:

f(x) = 4.366*log10(x+4)

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what is the circumference i need a refresh of how to do it i kinda forgot sum1 give answer and explanation

Answers

Answer:

102

Step-by-step explanation:

34 is d so 34×3=102

pls correct me if im wrong

Help with this math please.

Answers

It should be 1,870

if 1cm = 110 m then, 4.5 cm = 495 m and 4cm = 440 m

so perimeter is equal to all the sides added up
495 + 440 + 495 + 440 which is equal to 1870

A room is 18 feet long and 12 feet wide. At $13.25 per square yard, what will be the cost for wall-to-wall
carpeting?

Answers

The cost for wall-to-wall carpeting is equal to $ 318.

How to compute the cost for wall-to-wall carpeting

In this problem we need to compute the cost for wall-to-wall carpeting, that is, the cost of covering the floor of the entire room. This can be done by using the following formula:

C = (1 / 9) · c · w · l

Where:

C - Cost, in monetary units. c - Unit cost, in monetary units per yard.w - Width, in feetl - Length, in feet

If we know that c = 13.25, w = 12 and l = 18, then the cost of the wall-to-wall carpeting is:

C = (1 / 9) · 13.12 · 12 · 18

C = 318

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(4a-ts)(2a+2ts) what is the solution

Answers

Answer:

8a^2 + 6ats - 2t^2s^2

Step-by-step explanation:

(4a-ts)(2a+2ts)

4a(2a+2ts) -ts(2a+2ts)

8a^2 + 8ats - 2ts - 2t^2s^2

= 8a^2 + 6ats - 2t^2s^2

A ribbon is 29 centimeters long. How many millimeters long is the ribbon?

2.9 millimeters
2,900 millimeters
290 millimeters
58 millimeters

Answers

Answer: The 290 millimeters long is the ribbon.

Step-by-step explanation:

To convert centimeters to millimeters

1 cm =10 millimeters

therefore,

29cm= 290 millimeters

Therefore, the ribbon is 290 millimeters long.

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I don’t understand how to do this ?

Answers

The value of the derivative of the composite function h(x) = f[g(x)] is equal to h'(3) = 2.

How to find the exact value of the derivative of a composite function

In this problem we find a function in the form of a composite function of the form h(x) = f[g(x)], whose derivative is defined by the chain rule:

h'(x) = f'(g) · g'(x)

If we know that g'(3) = 2 and f'(2) = 1, then the exact value of the derivative of the composite function is:

h'(3) = 2 · 1

h'(3) = 2

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please help asap!!!!!!!

Answers

As we have shown that both AE is congruent to CE and BE is congruent to DE.

Now, let's focus on the diagonals of the parallelogram, AC and BD. We are told that they intersect at point E.

To prove that AE is congruent to CE, we can use the fact that opposite sides of a parallelogram are congruent. Since AC is a diagonal of the parallelogram, it divides it into two congruent triangles, AEC and CED. This is because AE is parallel to CD (as they are opposite sides of the parallelogram), and EC is common to both triangles.

Therefore, by the Side-Angle-Side (SAS) congruence theorem, we can conclude that triangle AEC is congruent to triangle CED. In particular, this means that AE is congruent to CE.

Similarly, to prove that BE is congruent to DE, we can use the same reasoning. Since BD is a diagonal of the parallelogram, it divides it into two congruent triangles, AEB and DEC. This is because BE is parallel to AC (as they are opposite sides of the parallelogram), and ED is common to both triangles.

Therefore, by the SAS congruence theorem, we can conclude that triangle AEB is congruent to triangle DEC. In particular, this means that BE is congruent to DE.

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sine law vector method ​

Answers

Answer: Well that wouldn't work quite as well.

Step-by-step explanation:

La ley del seno en el método vectorial se utiliza para encontrar la magnitud y dirección de un vector desconocido en un sistema de coordenadas.

Para aplicar la ley del seno vectorial, se deben conocer los vectores conocidos y los ángulos entre ellos. A partir de esto, se pueden utilizar las propiedades del seno para encontrar la magnitud del vector desconocido y la dirección en la que apunta.

La ley del seno vectorial establece que la magnitud del vector desconocido es igual a la magnitud del vector conocido dividido por el seno del ángulo opuesto al vector desconocido. Además, la dirección del vector desconocido se puede encontrar utilizando la ley de los cosenos para encontrar el ángulo entre el vector desconocido y uno de los vectores conocidos.

En resumen, la ley del seno vectorial se utiliza para encontrar la magnitud y dirección de un vector desconocido a partir de los vectores conocidos y los ángulos entre ellos.

There have been many cases where long-standing issues that divided societies have been resolved, such as the reunification of Germany and the end
of apartheid in South Africa. Both of these benefitted society as whole, but one of the short-term results was an increase in crime. Why is this the case?
O A. Both experienced racially motivated crime.
OB.
O C.
O D.
Both involved a sudden reorganization of society.
Both came after a massive reform in public education.
Both are the result of implementing social service programs.

Answers

The increase in crime was caused by D. Both are the result of implementing social service programs.

What led to the increase in crime ?

Significant modifications made to a society's social and political structures can cause periods of instability and uncertainty, leading to a rise in crime rates. The daunting tasks of restructuring society that came with the abolishment of apartheid in South Africa and Germany's reunification represent examples of such changes.

When power structures, economic systems, and social norms abruptly shift, gaps in authority may arise, thereby presenting opportunities for criminal activity to escalate. Criminal elements can capitalize on these unexpected power vacuums.

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Find The volume of this 7th Grade Mathematical 3D Triangular Prism!!!!!!!!

Answers

The volume of the triangular base prism is  120 inches³.

How to find the volume of a triangular prism?

The prism above is a triangular base prism. The volume of the triangular base prism can be calculated as follows:

volume of the prism = base area × height

Therefore,

base area = 1 / 2 bh

base area = 1 / 2 × 8 × 10

base area = 80 / 2

base area = 40 inches²

Therefore,

volume of the prism = 40 × 3

volume of the prism = 120 inches³

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At Downtown Pizza, 4 of the last 6 pizzas sold had pepperoni. What is the experimental probability that the next pizza sold will have pepperoni?

Answers

The answer of the given question based on the experimental probability is the next pizza sold at Downtown Pizza will have pepperoni is 2/3 or approximately 0.67.

What is Experimental probability?

Experimental probability is  ratio of number of times  event occurs to the total number of trials or observations conducted in  experiment or real-life situation. It is based on actual observations or data and is also known as empirical probability.

Experimental probability is used when it is not possible or feasible to determine the theoretical probability of an event, or when the theoretical probability does not match the actual outcomes observed in a given situation. In such cases, experimental probability provides an estimate of the likelihood of an event occurring based on real-life data.

The experimental probability that the next pizza sold will have pepperoni is the ratio of the number of pepperoni pizzas sold to the total number of pizzas sold in the recent past.

According to the problem, 4 of the last 6 pizzas sold had pepperoni. So, the experimental probability of the next pizza sold having pepperoni is:

experimental probability = number of pepperoni pizzas sold / total number of pizzas sold

experimental probability = 4 / 6

experimental probability = 2 / 3

Therefore, the experimental probability that the next pizza sold at Downtown Pizza will have pepperoni is 2/3 or approximately 0.67.

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Which number line shows the solution set for |h-3| ≤5?​

Answers

Answer:

Second number line

Step-by-step explanation:

(h-3)^2 <= 25

h^2 - 6h + 9 <= 25

h^2 - 6h - 16 <= 0

(h-8)(h+2) <=0

Using the graph of (x-8)(x+2),

-2 <= h <= 8

Hence, the answer is the second one (as it has shaded circles)

Hope this helps and be sure to mark this as brainliest! :)

View photo below. This is timed.

Answers

Answer: ∠EFB, ∠DFE, and ∠CFB

Step-by-step explanation:

Starting Angle: ∠CFD

Since its in an X formation: ∠EFB, ∠DFE, and ∠CFB would all work.

Compound Inequalities

The manufacturers of Cheerios only ship boxes that weigh more than 13.98 and less than 14.02 oz.

a. Represent the weights of boxes that will ship in three forms.

b. Represent the weights of boxes that will not ship in three forms.

*In Symbolic/Inequality and number line*

Answers

An compound inequality that describes the acceptable weights for a 20 oz box is 19.25 ≤ x ≤ 20.75.

We have,

The absolute value of a number is defined as its magnitude irrespective of the sign of the number. To determine the absolute value of a real number, we consider only the number and remove the sign. It can only be a non-negative value.

We are Given that, cereal manufacturer has a tolerance of 0.75 oz for a box of cereal that is supposed to weigh 20 oz.

Let the weight of cereal box be; w

Now, the inequality is

20-0.75 ≤ x ≤ 20+0.75

Add 20 on both sides of an inequality, we get

19.25 ≤ x ≤ 20.75

Here, 19.25 ≤ x ≤ 20.75

Therefore, an absolute value inequality to find the range of acceptable weights is 19.25 ≤ x ≤ 20.75.

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In the diagram shown, ABC is equilateral. AD is an altitude.


10). ABD = _____.

11). ADB = _____.

12). BAD = _____.

13). CAD = _____.


Suppose AB = 6. Find:


14). BD

15). AD

16). Area of ABC

Answers

All the correct values are,

⇒ ∠ABD = 60°

⇒ ∠ADB = 90°

⇒ ∠BAD = 30°

⇒ ∠CAD = 30°

⇒ BD = 3

⇒ AD = √27

⇒ The value of area of triangle ABC is, 3√27

Given that;

In the diagram shown, ABC is equilateral. AD is an altitude.

Hence, We get;

All the angles of a equilateral triangle are,

⇒ 60°

Thus, We get;

⇒ ∠ABD = 60°

Since, AD is an altitude.

⇒ ∠ADB = 90°

And,

⇒ ∠BAD = 60 / 2 = 30°

⇒ ∠CAD = 60/2 = 30°

By Pythagoras theorem;

AB² = AD² + BD²

6² = AD² + 3²

36 = AD² + 9

AD² = 27

AD = √27

Thus, The value of area of triangle ABC is,

⇒ 1/2 × AD × BC

⇒ 1/2 × √27 × 6

⇒ 3√27

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Find the weighted mean. Round your answer to the nearest tenth.

Answers

The weighted mean of the deliveries each week can be found to be 5. 38 .

How to find the weighted mean ?

The weighted mean is a type of mean that takes into account, the weight of the various items in question.

First, find the total frequency :

= 1 + 5 + 4 + 3

= 13

The weighted mean would then be:

= ∑ ( weight of delivery x number of deliveries )

= ( 1 / 13 x 2 ) + ( 5 / 13 x 4 ) + ( 4 / 13 x 6 ) + ( 3 / 13 x 8 )

= 0. 15  + 1. 54 + 1. 84 + 1. 85

= 5. 38

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Triangle D has been dilated to create triangle D′. Use the image to answer the question.

image of a triangle labeled D with side lengths of 3.8, 4.8, 4.2 and a second triangle labeled D prime with side lengths of x, 2.4, 2.1

Determine the scale factor used.

one half
2
one fourth
3

Answers

Answer:

To determine the scale factor used, we need to find the ratio of corresponding side lengths in both triangles.

Let's compare the length of the first side in both triangles:

x/3.8 = 2/4.8

Cross-multiplying, we get:

4.8x = 7.6

Dividing both sides by 4.8, we get:

x = 1.58

Now, let's compare the length of the second side in both triangles:

2.4/4.2 = 0.57

Finally, let's compare the length of the third side in both triangles:

2.1/4.8 = 0.44

Since the scale factor is the same for all corresponding side lengths, we can take the average of the ratios:

(scale factor) = (1.58/3.8 + 0.57 + 0.44)/3

(scale factor) = 1.01

Therefore, the scale factor used is approximately 1.

The scale factor used to dilate triangle D to triangle D' is 1/2.

To see this, notice that the side lengths of triangle D' are half the length of the corresponding sides in triangle D. For example, the length of the shortest side in triangle D is 3.8, while the length of the shortest side in triangle D' is x. Since the length of the shortest side in triangle D' is half the length of the shortest side in triangle D, the scale factor is 1/2.

) Find the average gold medal winnings of those NOCs who have been
awarded fewer than ten bronze medals.
Count the number of those NOCs that have been awarded ten or more
silver medals.

This question requires the construction and interpretation of a pie chart based
on the data throughout this task.
a) Create a suitable and fully labelled pie chart to show the total medal
winnings of the Top 10 NOCs at the Beijing 2022 Winter Olympic games.
Interpret the pie chart produced in Question 8a). Discuss two probable
justifications for the behaviour of the data.

Answers

a. To create a pie chart to show the total medal winnings of the Top 10 NOCs at the Beijing 2022 Winter Olympic games:

Obtain the data for the medal winnings of the Top 10 NOCs

Find the average gold medal winnings of those NOCs who have beenawarded fewer than ten bronze medals.?

Calculate the total medal winnings for each NOC (i.e., the sum of gold, silver, and bronze medals)

Create a pie chart in Excel or any other software by selecting the data and choosing the pie chart option

Add a title and labels to the chart to show the NOCs and their corresponding medal winnings

b. The interpretation of the pie chart produced in Question 8a) depends on the shape and distribution of the chart. Two probable justifications for the behavior of the data are:

Dominance of certain NOCs: The pie chart may show that certain NOCs have a significantly higher share of medal winnings compared to others. This may be due to the dominance of these NOCs in specific sports or events, or due to their superior training and preparation.

Balanced distribution of medals: The pie chart may show a relatively balanced distribution of medal winnings among the Top 10 NOCs. This may indicate a high level of competitiveness and equal opportunities for success among the NOCs.

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A genetic experiment with peas resulted in one sample of offspring that consisted of 427 green peas and 154 yelow peas. a. Construct a 90% confidence interval to estimate of the percentage of yellow peas. b. Based on the confidence interval, do the results of the experiment appear to contradict the expectation that 25%, of the offspring peas would be yellow? a. Construct a 90% confidence interval. Express the percentages in decimal form. ​

Answers

a. To construct a 90% confidence interval, we can use the following formula:

CI = p ± z*sqrt((p*(1-p))/n)

where:
p = proportion of yellow peas = 154/(427+154) = 0.265
z = z-score for a 90% confidence level = 1.645 (from a standard normal distribution table)
n = sample size = 427+154 = 581

Substituting the values, we get:

CI = 0.265 ± 1.645*sqrt((0.265*(1-0.265))/581)
CI = 0.265 ± 0.042
CI = (0.223, 0.307)

Therefore, we can say with 90% confidence that the true proportion of yellow peas in the population lies between 0.223 and 0.307.

b. The expected proportion of yellow peas is 0.25. Since the confidence interval does not contain 0.25, the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow.

sketch the graphs y=|x|, y=|x|+2, y=|x|-1

Answers

The graph of y=|x| is a v-shaped graph that starts at the origin and continues infinitely in both the positive and negative x-directions. The graph of y=|x|+2 is the same v-shaped graph, but it has been shifted up two units so that it no longer intersects the x-axis. Finally, the graph of y=|x|-1 is a v-shaped graph that has been shifted down one unit so that it intersects the x-axis at (1,0) and (-1,0). All three graphs are symmetric with respect to the y-axis.

how do I do 75% of 200

Answers

You can use the part=percent(whole) method, which would produce X=75%(200), which is X=0.75(200), which is 150. 75% is 0.75 because 75% is really 75/100, which is 0.75. You can also use the proportion method, which is (percent)/100=(part)/whole. This would be 75/100=X/200. When cross multiplying and solving for X, you would once again get 150.

Answer:

150

Step-by-step explanation:

divide the percentage by 100 to make it decimal form,
75/100= .75

The multiple .75 by the total amount to find the 75%,

200 x .75 = 150

Which means 75% of 200 is 150

If the image is rotated about the x-axis, which of the following images best represents the result?
A. Y
B. Z
C. X
D. W

Answers

The images best represents the result is image W.

We have, the image is rotated about the x-axis.

Now, rotating around x axis can give the other half of the image.

Also, rotating about x axis gives the mirror image of the figure.

So, the rotation leads to a circle.

and, In three dimensional we can say that Sphere.

Thus, the required image is W.

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Use the graph to answer the question.

graph of polygon ABCD with vertices at 0 comma 0, 5 comma 2, 5 comma negative 5, 0 comma negative 3

Determine the coordinates of polygon A′B′C′D′ if polygon ABCD is rotated 90° counterclockwise.

A′(0, 0), B′(−2, 5), C′(5, 5), D′(3, 0)
A′(0, 0), B′(−2, −5), C′(−5, 5), D′(−3, 0)
A′(0, 0), B′(−5, −2), C′(5, −5), D′(3, 0)
A′(0, 0), B′(−5, −2), C′(−5, −5), D′(0, 3)

Answers

the Correct option of  coordinates of polygon A′B′C′D′ if polygon ABCD is rotated 90° counterclockwise is A

What is coordinate?

A coordinate is a set of numbers that represents the position of a point in space. It is often used to describe the location of a point on a graph or a map

According to given information

To determine the coordinates of polygon A′B′C′D′, we need to rotate each vertex of polygon ABCD 90° counterclockwise.

We can do this by using the following formulas for a 90° counterclockwise rotation of a point (x, y):

x' = -y

y' = x

Using these formulas, we can find the coordinates of each vertex of polygon A′B′C′D′ as follows:

A′(0, 0): Since (0, 0) is the origin, a 90° counterclockwise rotation will still result in (0, 0).

B′(-2, 5): To rotate the point (5, 2) 90° counterclockwise, we have x' = -y = -2 and y' = x = 5. So, B′ is (-2, 5).

C′(5, 5): To rotate the point (5, -5) 90° counterclockwise, we have x' = -y = 5 and y' = x = 5. So, C′ is (5, 5).

D′(3, 0): To rotate the point (0, -3) 90° counterclockwise, we have x' = -y = 0 and y' = x = 3. So, D′ is (3, 0).

Therefore, the coordinates of polygon A′B′C′D′ are A′(0, 0), B′(-2, 5), C′(5, 5), and D′(3, 0).

So, the answer is A) A′(0, 0), B′(−2, 5), C′(5, 5), D′(3, 0).

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For each of the following, place a decimal point in the number to make the sentence reasonable. a. The basketball player is 1950 cm tall. b. A new piece of chalk is about 8100 cm long. c. The speed limit in town is 400 km/hr.​

Answers

a. The basketball player is 19.50 cm tall. (Assuming you meant to write

195 cm instead of 1950 cm)

b. A new piece of chalk is about 81.00 cm long.

c. The speed limit in town is 40.0 km/hr. (Assuming you meant to write 40 km/hr instead of 400 km/hr).

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

By placing a decimal point in the appropriate location, we can make the numbers more reasonable.

a. The basketball player cannot be 1950 cm tall, as that is almost 20 meters or over 65 feet.

The average height of a basketball player in the NBA is around 6'7'' (or about 2 meters).

Therefore, we can assume that the correct height of the basketball player is 195 cm, or about 6'5''.

b. A piece of chalk that is 8100 cm long is over 80 meters long, which is clearly too long for a piece of chalk.

Therefore, we can assume that the correct length of the chalk is 81.00 cm or about 32 inches.

c. A speed limit of 400 km/hr is unreasonably high, as it is equivalent to over 248 miles per hour.

The highest speed limits in the world are typically around 80-85 mph (130-140 km/hr), so 400 km/hr is clearly incorrect.

Therefore, we can assume that the correct speed limit is 40.0 km/hr, which is a more reasonable speed limit for a town or residential area.

Hence,

a. The basketball player is 19.50 cm tall. (Assuming you meant to write

195 cm instead of 1950 cm)

b. A new piece of chalk is about 81.00 cm long.

c. The speed limit in town is 40.0 km/hr. (Assuming you meant to write 40 km/hr instead of 400 km/hr).

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What is the area of this figure?
20 mi
3 mi
11 mi
7 mi
3 mi
4 mi
3 mil
Write your answer using decimals, if necessary.
square miles
3 mi

Answers

The area of the figure composed of two rectangles is 99 mi²

How to solve an equation?

An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.

The area of a figure is the amount of space it occupies in its two dimensional state.

For the first rectangle:

Area = 11 mile * 5 mile = 55 mi²

For the second rectangle:

Area = 11 mile * 4 mile = 44 mi²

The area of figure = 55 mi² + 44 mi² = 99 mi²

The area of the figure is 99 mi²

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What’s the equation of the line shown above ? A y=2x+3 B y=2x+1/3 C y=3x+2 D y=1/3x+2

Answers

It should be noted that to find the equation of a line, two pieces of information are necessary: the slope and coordinates of a point on the line.

How to find the equation

Also, to acquire this, one can leverage either the point-slope form or the slope-intercept form to compose it.

If both the slope (m) and coordinates of the point  (x1, y1) on the line are known, then one can express the equation in its point-slope style as follows:

y - y1 = m(x - x1)

Or, if only the slope (m) and the y-intercept (b), which is the value of y where the line crosses the y-axis, are accessible, then the equation can be expressed via the slope-intercept form with: y = mx + b

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