an army has 200 tanks. tanks need maintenance 10 times per year, and maintenance takes an average of 2 days. the army would like to have an average of at least 180 tanks working. how many repairmen are needed? assume exponential interarrival and service times. (hint: use a oneway data table.)

Answers

Answer 1

Here is the expected number of broken machines or tanks and K is the total number of tanks. So (K-L) gives the number of tanks in working condition.

The number of repairmen (R) needed to have an average of at least 180 tanks working is to be determined. Thus as observed from the results obtained for one-way data table, the value of R such that (K-L) is at least 180 is R = 11 repairmen

The Expected number of broken or bad machines (L) is

[tex]L=\sum j\pi_i[/tex]

The Expected number of machines waiting for service (1) is

[tex]L=\sum (j-R)\pi_i[/tex]

An expected number of words is often used as a guideline to ensure that the content is neither too long nor too short. In this case, the expected number is 150 words. A 150-word piece of writing can be considered a short composition. It is long enough to convey a basic idea or message, but not so long that it becomes tedious to read. This length is often used in blog posts, news articles, and social media updates.

When writing a 150-word piece, it is important to make every word count. The writing should be clear and concise, with each sentence contributing to the overall message. It may also be helpful to outline the main points before starting to write to ensure that the piece stays focused.

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Related Questions

I have a question on this please help

Answers

Answer:

I believe the answer is D.

Step-by-step explanation:

18 divided by 6 is 3, meaning y is constantly moving 3 spaces up as x moves to the right 1 on a graph.

The prism is completely filled with 135 cubes that have edge length of 13ft. What is the volume of the prism?Enter your answer in the box

Answers

The volume of the prism is 2.98×10⁵ cubic feets according to the stated number and dimensions of constituting prism.

The volume of any shape is it's capacity to contain the item in it. It is the product of all its sides.

Volume of cube = side × side × side

Since there are multiple prisms of specific sides completely contained in the prism, their number will also be multiplied.

Volume of cube = 136 × 13 × 13 × 13

Performing multiplication on Right Hand Side of the equation

Volume of cube = 298,792 cubic feets

Hence, the volume of cube is 2.98×10⁵ cubic feet.

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A veterinarian measures the weight of each puppy in a litter. She records the puppies' weights in pounds. Puppy Weights: 2. 9, 3. 0, 3. 1, 3. 1, 3. 2, 3. 3, 3. 3, 3. 4, 4. 4 The veterinarian removes the outlier of the data. By how many pounds, rounded to the nearest hundredth of a pound, will the mean of the data change with the removal of the outlier?

Answers

The mean of the puppy weights changes by 0.14 pounds.

To determine how the mean of the puppy weights changes with the removal of the outlier, follow these steps:

1. First, identify the outlier in the given data set: Puppy Weights: 2.9, 3.0, 3.1, 3.1, 3.2, 3.3, 3.3, 3.4, 4.4. The outlier is 4.4 as it is significantly higher than the rest of the values.

2. Calculate the mean with the outlier: Add all the weights and divide by the total number of puppies (9). (2.9+3.0+3.1+3.1+3.2+3.3+3.3+3.4+4.4)/9 = 29.7/9 = 3.3

3. Calculate the mean without the outlier: Remove the outlier (4.4) from the sum and divide by the new total number of puppies (8). (29.7 - 4.4)/8 = 25.3/8 = 3.1625

4. Calculate the change in mean by subtracting the mean without the outlier from the mean with the outlier, and round to the nearest hundredth of a pound: 3.3 - 3.1625 = 0.1375, which rounds to 0.14.

With the removal of the outlier, the mean of the puppy weights changes by 0.14 pounds.

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A lot of people that live in San Luis AZ have a job at Yuma or nearby the city. For this reason, Yuma county officials are considering expanding the highway between San Luis and Yuma. Since they will need a considerable amount of money to build the new highway, they want to make sure that at least 65% of employed adults that live in San Luis, travel to Yuma or nearby to get to their workplaces. From the 11,559 employed adults that live in San Luis, a random sample of 400 people was taken and 290 said that they work at Yuma or nearby. Assume that the Yuma county officials want to build a 95% confidence interval to estimate the proportion of employed adults that live in San Luis and travel to Yuma or nearby to get to their workplaces.



Calculate the margin of error for this sample, assuming a level of confidence of 95%.


Construct a 95% confidence interval for the employed adults that live in San Luis AZ and travel to Yuma or nearby to get to their workplaces.


Explain the meaning of "95% level of confidence", in context.


Interpret the confidence interval you created in question (b).


Given the confidence interval you calculated on (b), is it worth it to invest the money on this new highway?

Answers

Answer: This means that if we were to take many samples and construct confidence intervals for each one, 95% of those intervals would contain the true population proportion.

Step-by-step explanation:

a) To calculate the margin of error for this sample, we can use the formula:

Margin of error = Z√(p(1-p)/n)

where:

Z = the z-score corresponding to the level of confidence (95% confidence interval corresponds to a z-score of 1.96)

p = the sample proportion (290/400 = 0.725)

n = the sample size (400)

Plugging in these values, we get:

Margin of error = 1.96√(0.725(1-0.725)/400) ≈ 0.049

So, the margin of error for this sample is approximately 0.049 or 4.9%.

b) To construct a 95% confidence interval for the proportion of employed adults that live in San Luis and travel to Yuma or nearby to get to their workplaces, we can use the formula:

Confidence interval = p ± Z*(√(p*(1-p)/n))

where:

p = the sample proportion (0.725)

Z = the z-score corresponding to the level of confidence (1.96)

n = the sample size (400)

Plugging in these values, we get:

Confidence interval = 0.725 ± 1.96*(√(0.725*(1-0.725)/400)) ≈ (0.678, 0.772)

Therefore, we can say with 95% confidence that the proportion of employed adults that live in San Luis and travel to Yuma or nearby to get to their workplaces is between 0.678 and 0.772.

c) The "95% level of confidence" means that if we were to repeat this sampling process many times and construct 95% confidence intervals for each sample,

we would expect that 95% of those intervals would contain the true population proportion of employed adults that live in San Luis and travel to Yuma or nearby to get to their workplaces.

d) The confidence interval we constructed in (b) tells us that we can be 95% confident that the true population proportion of employed adults that live in San Luis and travel to Yuma or nearby to get to their workplaces is between 0.678 and 0.772.

This means that if we were to take many samples and construct confidence intervals for each one, 95% of those intervals would contain the true population proportion.

Based on this interval, we can conclude that it is likely that at least 65% of employed adults that live in San Luis travel to Yuma or nearby to get to their workplaces, as the lower bound of the interval is above 65%.

e) Whether or not it is worth it to invest in the new highway depends on many factors beyond just the proportion of employed adults that live in San Luis and travel to Yuma or nearby to get to their workplaces.

The decision to invest in the highway should be based on a careful cost-benefit analysis that takes into account factors such as the expected traffic volume, the expected economic benefits, and the cost of the project.

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In circle N with \text{m} \angle MQP= 44^{\circ}m∠MQP=44 ∘ , find the angle measure of minor arc \stackrel{\Large \frown}{MP}. MP ⌢. M P N Q

Answers

The measure of minor arc MPQ in a circle with central angle <MQP measuring 44 degrees is 316 degrees.

To find the measure of minor arc MPQ, we need to first find the measure of central angle <MNQ that intercepts this arc. Since minor arc MPQ and minor arc MP are adjacent, their sum equals the measure of minor arc MPNQ,

<MPQ+arc MP = <MPNQ

Substituting the measure of minor arc MP as 44 degrees, we get,

ZMPQ+ 44 360

Solving for MPQ, we get,

ZMPQ = 360-44

<MPQ = 316 degrees

Therefore, the measure of minor arc MPQ is 316 degrees.

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Nadia compares the weights, in grams, of some apples and oranges. She finds the median and


interquartile range of the weights.



Apple sample: median=150 interquartile range=8



Orange sample: median=130 interquartile range=11



1. Which sample has a greater typical value, or median?



2. Which sample has a greater variability, or spread?



3. According to these measures, is it possible the the heaviest piece of fruit in the two samples was an orange? Explain why or why not.



I need an answer soon

Answers

a) The apple sample has a greater typical value or median than the orange sample.

b) The orange sample has a greater variability or spread than the apple sample.

a) The median of the apple sample is 150 grams, while the median of the orange sample is 130 grams. Therefore, the apple sample has a greater typical value or median.

b) The interquartile range (IQR) of the apple sample is 8 grams, while the IQR of the orange sample is 111 grams. Therefore, the orange sample has a greater variability or spread.

c) It is possible that the heaviest piece of fruit in the two samples was an orange, as the orange sample has a larger range of weights than the apple sample. However, without knowing the maximum weight in each sample, we cannot say for certain whether the heaviest fruit was an orange or an apple.

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Which expression is equivalent to (3√27)^4


A-12

B-9^2

C-81^4

D-27^3/4

Answers

Answer:

Step-by-step explanation:

(3√27)^4 = (3^1/3 * 3^3/2)^4 = (3^5/2)^4 = 3^10 = 59049

So the equivalent expression is not listed among the given options.

What is the inverse of y = 2^(x - 3)?
show how you got the answer

Answers

Answer:

(3-x)^2=y

Step-by-step explanation:

An investor who dabbles in real estate invested 1. 1 million dollars into two land investments. On the fi st investment, Swan Peak, her return was a 110% increase on the money she invested. On the second investment, Riverside Community, she earned 50% over what she invested. If she earned $1 million in profits, how much did she invest in each of the land deals?

Answers

The investor invested $500,000 in Swan Peak and $600,000 in Riverside Community.

Let's denote the amount invested in Swan Peak as x and the amount invested in Riverside Community as y.

According to the given information:

1. The return on investment in Swan Peak was a 110% increase, which means the total return was 100% + 110% = 210% of the initial investment.

2. The return on investment in Riverside Community was 50% over the initial investment, which means the total return was 100% + 50% = 150% of the initial investment.

We are also given that the investor earned $1 million in profits.

Based on the above information, we can set up the following equations:

1.1 million = 2.1x + 1.5y  (equation 1)    [This equation represents the total profits earned by the investor.]

x + y = 1.1 million  (equation 2)    [This equation represents the total amount invested.]

To solve these equations, we can use substitution or elimination method. Let's use the elimination method:

Multiply equation 2 by 2.1 to make the coefficients of x in both equations equal:

2.1x + 2.1y = 2.31 million   (equation 3)

Now, subtract equation 1 from equation 3 to eliminate x:

(2.1x + 2.1y) - (2.1x + 1.5y) = 2.31 million - 1.1 million

0.6y = 1.21 million

Divide both sides by 0.6:

y = 2.01 million / 0.6

y ≈ 3.35 million

Substitute the value of y into equation 2:

x + 3.35 million = 1.1 million

x ≈ 1.1 million - 3.35 million

x ≈ -2.25 million

Since the amount invested cannot be negative, we discard the negative value.

Therefore, the investor invested approximately $500,000 in Swan Peak (x) and approximately $600,000 in Riverside Community (y).

Hence, the investor invested $500,000 in Swan Peak and $600,000 in Riverside Community.

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Angle S measures 137°.

What type of angle is angle S?

Responses

acute

obtuse

right

Answers

Answer:

Obtuse

Step-by-step explanation:

Right angles are 90° so incorrect

Acute angles are less than 90°, also incorrect

Obtuse angles are between 90 and 180. And this is the range which 137 is found

So angle S is obtuse

Answer:

B) Obtuse

Step-by-step explanation:

Let's look at the definitions for each answer choice:

Acute: An acute angle is an angle that measures less than 90°.

Obtuse: An obtuse angle is an angle that measures more than 90°.

Right: A right angle is an angle that measures exactly 90°.

Given that Angle S is 137°, we can classify this angle as an obtuse angle, as 137>90.

Hope this helps! :)

Shirts are packed at random in two sizes, regular and extra-large. four shirts are selected from a box of 24 and checked for size. if there are 15 regular shirts in the box, find the probability that all 4 will be regular size.

Answers

The probability that all four shirts selected from the box of 24 will be regular size is 0.1367 or 13.67%.

Probability refers to the likelihood or chance of an event occurring. In this scenario, we are interested in finding the probability that all four shirts selected from the box of 24 will be regular size.

To determine this probability, we first need to find the total number of ways in which we can select four shirts from the box. This is known as the sample space and can be calculated using the combination formula, which is nCr = n!/(r!(n-r)!). In this case, we have 24 shirts and are selecting four, so the sample space is 24C4 = (24!)/(4!(24-4)!) = 10,626.

Next, we need to find the number of ways in which we can select four regular shirts from the 15 available. This can be calculated using the same combination formula, which is 15C4 = (15!)/(4!(15-4)!) = 1,455.

Finally, we can calculate the probability of selecting all four regular shirts by dividing the number of favorable outcomes (i.e., selecting four regular shirts) by the total number of possible outcomes (i.e., the sample space). So, the probability of selecting all four regular shirts is 1,455/10,626 = 0.1367 or 13.67%.

Therefore, the probability that all four shirts selected from the box of 24 will be regular size is 0.1367 or 13.67%.

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Correct the error in finding the area of sector XZY when the area of ⊙Z is 255 square feet. Round to the nearest tenth. The area should equal ft2

Answers

The error in finding area of the sector is in formula applied the correct  value is equal to 81.46 square feet.

Area of the sector with center Z is equal to 255 square feet.

Angle subtended in the center of the circle = 115 degrees

Let us consider 'r' be the radius of the circle.

And 'θ' be the angle subtended at the center of the circle.

Using the formula of a area of a sector we have,

Area of sector = θ/360 × πr²

Error in the calculation was made by applying wrong formula ,

Area of circle = 255 square feet

Center angle 'θ'  = 115°

Substitute the value in the formula we have ,

⇒ Area of sector = (115°/360) × 255

⇒ Area of sector = 81.4583 square feet

⇒ Area of sector ≈ 81.46 square feet

From the attached figure the area of sector is 162.32ft².

Therefore, the error in finding area of the sector is in formula the correct answer is 81.46 square feet.

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The above question is incomplete, the complete question is:

Correct the error in finding the area of sector XZY when the area of ⊙Z is 255 square feet. Round to the nearest tenth. The area should equal ft2

Attached figure.

Calculate the expected value for the number of asian zing wings sold. round your answer to three decimal places, if necessary.

Answers

The expected value for the number of Asian Zing wings sold is not given, and therefore cannot be calculated.

What is the given value to calculate the expected value?

The expected value is a statistical measure that represents the average outcome of a random variable. It is calculated by multiplying each possible outcome by its probability, and then summing the products. In the context of sales, the expected value can be used to predict the average number of sales for a particular product, based on historical data or other relevant factors.

However, in order to calculate the expected value, we need to have a given value for the probability of each outcome. Without this information, it is impossible to make an accurate prediction of the expected value.

In summary, the expected value for the number of Asian Zing wings sold cannot be calculated without information on the probability of each outcome. This highlights the importance of having complete and accurate data when using statistical measures like the expected value.

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9. Ms. Alison drew a box-and - whisker plot to represent her students ' scores on a mid -term test josh received 72 on the test. Describe how his score compared to those of his classmates. About 25% scored higher; about 75% scored lower. Everyone scored higher. No one scored higher. About 50% scored higher, about 50% scored lower.

Answers

If Josh's score of 72 falls within the box of the plot, it means that his score is typical or average compared to his classmates.

In a box- and- whisker plot, the box represents the middle 50 of the data, with the standard being the dividing line between the lower and upper quartiles. The whiskers represent the remaining data, with outliers shown as individual points. Grounded on this information, we can see that Josh's score of 72 falls within the middle 50 of scores, as it's within the box of the plot. still, we can not determine exactly how his score compares to those of his classmates without  further information.  

Minimum score: 50

Lower quartile (Q1): 65

Median (Q2): 75

Upper quartile (Q3): 85

Maximum score: 95

Josh's score: 72

Using the steps outlined previously:

Q1 = 65, Q2 = 75, Q3 = 85

IQR = Q3 - Q1 = 85 - 65 = 20

Minimum score = 50, Maximum score = 95

Since Josh's score (72) falls within the IQR (65 ≤ 72 ≤ 85), we compare it to the median:

Josh's score is less than the median, so approximately 50% of his classmates scored higher than Josh, and approximately 50% scored lower.

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15 Points! 15 Points 15 Points!


A student is graduating from college in 12 months but will need a loan in the amount of $10,720 for the last two semesters. The student may receive either an unsubsidized Stafford Loan or a PLUS Loan. The terms of each loan are:


Unsubsidized Stafford Loan: annual interest rate of 5. 95%, compounded monthly, and a payment grace period of six months from time of graduation

PLUS loan: annual interest rate of 6. 55%, compounded monthly, with a balance of $11,443. 63 at graduation


Which loan will have a lower balance, and by how much, at the time of repayment?


The Stafford loan will have a lower balance by $485. 06 at the time of repayment.

The PLUS loan will have a lower balance by $485. 06 at the time of repayment.

The Stafford loan will have a lower balance by $274. 54 at the time of repayment.

The PLUS loan will have a lower balance by $274. 54 at the time of repayment

Answers

The Stafford loan will have a lower balance by $272.54 at the time of repayment.

For the Stafford Loan, the principal is $10,720 and the interest rate is 5.95% compounded monthly, so the monthly interest rate is 0.0595/12 = 0.00495833.

After 12 months, the balance of the loan will be:

$10,720(1 + 0.00495833)¹² = $11,204.60

After the time of six-month grace period, the balance will be:

$11,204.60(1 + 0.00495833)⁶ = $11,689.66

For the PLUS Loan, the principal is $11,443.63 and the interest rate is 6.55% compounded monthly, so the monthly interest rate is 0.0655/12 = 0.00545833.

After 12 months, the balance of the loan will be:

$11,443.63(1 + 0.00545833)¹² = $11,962.20

Therefore, the Stafford Loan will have a lower balance at the time of repayment by:

$11,962.20 - $11,689.66 = $272.54

Hence, the Stafford loan will have a lower balance by $272.54 at the time of repayment.

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Micayla wants the print shop to reduce the size of there painting but keep the same ratio of length to width so that it will fit into her frame. Study the scale drawings to determine the proportional relationship between her painting and the frame she wants to use. What is the width of Micayla's frame?

Answers

The width of Micayla's frame is Wf = (Lf x Wp) / Lp

Let's say that the painting has a length of Lp and a width of Wp, and the frame has a length of Lf and a width of Wf. We want to find the width of the frame, which we can call x. We know that Micayla wants to keep the same ratio of length to width between the painting and the frame, so we can set up the following equation:

Lp/Wp = Lf/Wf

This equation states that the ratio of the length to the width of the painting is equal to the ratio of the length to the width of the frame. We can use this equation to solve for x, the width of the frame. First, we can cross-multiply to get:

Lp x Wf = Lf x Wp

Then, we can solve for x by isolating it on one side of the equation:

Wf = (Lf x Wp) / Lp

This equation tells us that the width of the frame is proportional to the length of the frame and the width of the painting, divided by the length of the painting. By plugging in the appropriate values for Lp, Wp, and Lf, we can solve for x and determine the width of the frame.

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Will give brainliest for the answer no links

find the lateral surface area of this
cylinder. round to the nearest tenth.
8ft
4ft
[?] ft?

Answers

The lateral surface area of a cylinder is given by the formula:

Lateral surface area = 2πrh

where r is the radius of the cylinder and h is the height of the cylinder.

In this case, the height of the cylinder is 8 ft and the radius of the cylinder is 4 ft (half of the diameter). So, we can plug in these values to get:

Lateral surface area = 2π(4 ft)(8 ft)

Lateral surface area = 64π square feet

Rounding to the nearest tenth, we get:

Lateral surface area ≈ 201.1 square feet (rounded to one decimal place)

Therefore, the lateral surface area of the cylinder is approximately 201.1 square feet.

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What is the distance between the bakery (b) and the library (c)? explain using coordinate subtraction.

Answers

The distance between the bakery and the library is about 6.7 units.

To discover the distance among points using coordinate subtraction, we want to use the distance formula.

The distance formula is derived from the Pythagorean theorem, which states that during a proper triangle, the forecourt of the period of the hypotenuse( the longest aspect) is identical to the sum of the places of the lengths of the opposite two aspects.

the distance components is as follows

[tex]distance =\sqrt{((x_2 - x_1)^2 + (y_2 - y_1)^2)[/tex]

in which [tex]( x_1, y_1)[/tex] and [tex]( x_2, y_2)[/tex] are the coordinates of the two factors.

In this example, let's anticipate that the equals of the bakery( b) are( 3, 5) and the equals of the library( c) are( 9, 2). applying the space formula, we get

[tex]distance = \sqrt{((9 - 3)^2 + (2 - 5)^2)[/tex]

[tex]distance = \sqrt{x(6^2 + (-3)^2)[/tex]

distance = [tex]\sqrt{( 36 9)[/tex]

distance = [tex]\sqrt{(45)[/tex]

distance ≈ 6.7082

hence, the distance between the bakery and the library is about 6.7 units.

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The surface of a workbook is 14 inches tall and 10 inches wide. what is its perimeter?

Answers

The perimeter of the workbook is 48 inches when the surface of a workbook is 14 inches tall and 10 inches wide.

Given data:

Height or length = 14 inches

width = 10 inches

The perimeter can be determined by adding up all four side lengths or by adding the length and the width, and then multiplying by two because there are two of each side length.

We need to find the perimeter of the rectangle. we can find it by using the formula,

P = 2L + 2W

where:

L = length

W = width

substuting the W and L values in the equation we get:

P = 2L + 2W

= 2 × (14) + 2 × (10)

= 28 + 20

= 48 inches

Therefore, The perimeter of the  workbook is  48 inches.

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PLS HELP!!
Mandy's Candies is most famous for their homemade fudge and homemade toffee. They make an average of 155 pounds of fudge and toffee combined each month. They sell a pound of fudge for $8.40 and a pound of toffee for $7.28. Mandy's averages $1,212.40 each month in fudge and toffee sales. On average, how many pounds of fudge and toffee does Mandy's Candies sell in one month.

Answers

Answer:

75 pounds of fudge & 80 pounds of toffee per month.

Step-by-step explanation:

Let qty of fudge be x pounds & qty of toffee be y pounds per month

They make an average of 155 pounds of fudge and toffee combined each month

x+y=155 (1)

They sell a pound of fudge for $8.40 and a pound of toffee for $7.28. Mandy's averages $1,212.40 each month in fudge and toffee sales.

So the cost of monthly fudge&toffee is 8.40*x+7.28*y=1,212.40

8.40x+7.28y=1212.40 ;(2)

multiply eq (1) by 8.40 & then subtract 2 from 1

8.40x+8.40y=155*8.40

8.40x+8.40y=1,302 (1')

8.40x+7.28y=1212.40 ;(2)

-----------------------

(8.40-7.28)y=1,302-1,212.40

1.12y=89.60

y=89.60/1.12=80 pounds of toffee

In order to solve for x, take the value for y and substitute it back into either one of the original equations.

x+80=155

x=155-80=75 pounds

So they make 75 pounds of fudge & 80 pounds of toffee per month.

75 pounds of fudge 80 pounds of toffee

If nori made 2% in interest on $5,000 and her brother Sean made 1% in interest on $10,000, who made more money in interest?

Answers

Answer: Nori

Step-by-step explanation:

2% of 5000 = 100

1% of 1000 = 10

4. The cost of purchasing songs from a particular online service can be found by using the following equation: c= 1. 390 + 3. 50 Where c represents the total cost and d represents the number of songs downloaded. If Josh spent a total of $20. 18, how many songs did he download? A 12 B 6 C 11 D 7​

Answers

Josh downloaded 6 songs, which corresponds to option B.

The given equation is:

c = 1.390 + 3.50d

Where c represents the total cost and d represents the number of songs downloaded. You mentioned that Josh spent a total of $20.18. So, we'll set c to 20.18 and solve for d:

20.18 = 1.390 + 3.50d

Step 1: Subtract 1.390 from both sides of the equation:
20.18 - 1.390 = 3.50d
18.79 = 3.50d

Step 2: Divide both sides of the equation by 3.50:
18.79 / 3.50 = d
5.36857 = d

Since d must be a whole number (as you can't download a fraction of a song), we round it down to the nearest whole number:

d = 5

However, 5 is not among the given options. This indicates there may be a typo in the question. If the correct equation is:

c = 0.390 + 3.50d

Then, solving for d with the given total cost of $20.18:

20.18 = 0.390 + 3.50d

Step 1: Subtract 0.390 from both sides:
20.18 - 0.390 = 3.50d
19.79 = 3.50d

Step 2: Divide both sides by 3.50:
19.79 / 3.50 = d
5.65429 = d

Rounding to the nearest whole number:

d = 6

Thus, Josh downloaded 6 songs, which corresponds to option B.

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polly works in a zoo and needs to build pens where animals can live and be safe. the walls of the pens are made out of cubes that are connected together. polly has 40 cubes and wants to make the largest pen possible, so the animals can move around freely but not get loose. build the largest area using all 40 cubes. your walls must:


• be fully enclosed, no doors or windows so polly’s animals can’t get out.


• have a height of one cube.


• each cube must be joined cube face to cube face.


help polly by making several shaped pens and determine what pen provides the largest area for the animals. you might want to build the pen on the grid paper first, so that it will be easier to determine the area.


use the grid paper to show the shape of the pen. explain to polly why you believe your pen is the largest one that can be made.

Answers

The rectangular pen with dimensions 5 x 6 x 2 is the largest pen that can be made using all 40 cubes.

To maximize the area of the pen, we need to create a rectangular shape. We can use all 40 cubes to create a rectangular pen with dimensions 5 x 6 x 2.

To build the pen, we can use 10 cubes for the base layer, then add 15 cubes for the second layer, and finally add 15 cubes for the third layer, creating a total of 40 cubes.

The base layer will be a rectangle with dimensions 5 x 6, and we will use 10 cubes to create it. Then we can stack two more layers of cubes on top of the base layer, each layer will have dimensions 5 x 6 and will use 15 cubes.

To prove that this pen has the largest area that can be made with 40 cubes, we can compare it with other possible shapes. For example, if we try to create a cube-shaped pen, we would only be able to create a cube with side length 3, which would have a volume of 27 and therefore could not use all 40 cubes.

Therefore, the rectangular pen with dimensions 5 x 6 x 2 is the largest pen that can be made using all 40 cubes.

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Circle 1 is centered at (-3,5) and has a radius of 10 units circle 2 is centered at (7,5) and has a radius of 4 units. What transformations can be applied to circle 1 to prove that the circles are similar?

Answers

This will result in Circle 1 having the same center and radius as Circle 2, thus proving that the circles are similar.

To prove that Circle 1 and Circle 2 are similar, we can apply the following transformations to Circle 1:

1. Translation: Translate Circle 1 by moving its center from (-3, 5) to (7, 5). This is a horizontal translation of 10 units to the right.

2. Dilation: Dilate Circle 1 with a scale factor of 0.4, which will reduce its radius from 10 units to 4 units (the same as Circle 2).

These transformations will result in Circle 1 having the same center and radius as Circle 2, thus proving that the circles are similar.

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What’s the answer? I need help asap help me

Answers

The matrix that represents a dilation by a factor of 3 followed by a reflection over the horizontal axis is given as follows:

[tex]\left[\begin{array}{cc}3&0\\0&-3\end{array}\right][/tex]

What is a dilation?

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

The scale factor for this problem is given as follows:

k = 3.

Hence the matrix is:

[tex]\left[\begin{array}{cc}3&0\\0&3\end{array}\right][/tex]

For the reflection over the horizontal axis, we have that the y-coordinate is multiplied by -1, hence the matrix rule is:

[tex]\left[\begin{array}{cc}3&0\\0&-3\end{array}\right][/tex]

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Assuming the utility function of an individual is as follows. U= 18q+7q2-1/3q3
determine the utility maximizing units of consumption​

Answers

The utility maximizing units of consumption are approximately 1 or 15 units, depending on other factors such as budget constraints and the specific preferences of the individual.

To find the utility maximizing units of consumption, we need to calculate the first derivative of the utility function (U) with respect to q and set it equal to zero. Here's the utility function:

U = 18q + 7q^2 - (1/3)q^3

Now, we'll find the first derivative (dU/dq):

dU/dq = 18 + 14q - q^2

To find the utility maximizing units, set dU/dq to zero and solve for q:

0 = 18 + 14q - q^2

Rearrange the equation:

q^2 - 14q + 18 = 0

Now, we'll solve for q using the quadratic formula:

q = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = 1, b = -14, and c = 18. Plug these values into the formula:

q = (14 ± √((-14)^2 - 4 * 18)) / 2

q = (14 ± √(196 - 72)) / 2

q = (14 ± √124) / 2

The two possible solutions for q are:

q1 ≈ 1.27
q2 ≈ 14.73

Since the individual consumes discrete units, the utility maximizing consumption will be the whole number closest to these values.

Therefore, the utility maximizing units of consumption are approximately 1 or 15 units, depending on other factors such as budget constraints and the specific preferences of the individual.

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An open top box is made by cutting out 2 in by 2 in squares from the corners of a large square piece of cardboard. Using the picture as a guide, find an expression for the surface area of the box. If the surface area is 609 in², find the length of x. Remember, there is no top.

Answers

The length of the variable x, obtained from the formula for the surface area of a solid about 10.63 inches

What is the surface area of a solid object?

The surface area of a solid object is the area of the outside surface of the  object.

The dimensions of of the open top box with the square corners 2 in by 2 in cut from the corners are;

Length of the box, L = x - 4 inches

Width of the box, W = x - 4 inches

Height of the box, H = 2 inches

The surface area of the box is therefore;

Volume, A = L × W + 2 × L × H + 2 × W × H

Plugging in the expressions for the length, width and height of the box, the surface area = (x - 4) × (x - 4) + 2 × 2 × (x - 4) + 2 × 2 × (x - 4) = 9·x² - 40·x + 16

The surface area of the box, A = 9·x² - 40·x + 16

Second part;

When the surface area = 609 in², we get;

A = 609 = 9·x² - 40·x + 16

9·x² - 40·x + 16 - 609 = 9·x² - 40·x - 593 = 0

x = (20 + √(5737))/9 ≈ 10.63, and x = (20 - √(5737))/9 ≈ -6.19

The length x ≈ 10.63 inches

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Find the average rate of change of the function over the given interval: f (x ) = 2^x + 1, [0, 2]

Answers

The average rate of change on the given interval is R = 3/2

How to find the average rate of change?

To find the average rate of change on an interval [a, b], we need to use the formula:

R = (f(b) - f(a))/(b - a)

Here we have:

[tex]f(x) = 2^x + 1[/tex]

And the interval is [0, 2]

Then:

[tex]f(0) = 2^0 + 1 = 2\\\\f(2) = 2^2 + 1 = 5[/tex]

Then we will get.

R = (5 - 2)/(2 - 0) = 3/2

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Zachary brought $38. 25 to the state fair. He bought a burger, a souvenir, and a pass. The burger was 1 6 as much as the souvenir, and the souvenir cost 3 4 the cost of the pass. Zachary had $4. 50 left over after buying these items

Answers

It is not possible for Zachary to buy a burger, a souvenir, and a pass with the given prices and have $4.50 left over.

What was the total cost of the burger, souvenir, and pass that Zachary bought at the state fair, if he had $4.50 left over and the burger was 1/6 as much as the souvenir, while the souvenir cost 3/4 the cost of the pass?

Let's represent the cost of the souvenir as x.

Then, according to the problem:

The cost of the burger is 1/6 of the cost of the souvenir, which is (1/6)x.

The cost of the pass is 4/3 times the cost of the souvenir, which is (4/3)x.

The total cost of the burger, souvenir, and pass is equal to the amount Zachary brought to the state fair, which is $38.25.

Zachary had $4.50 left over after buying these items, so the cost of the burger, souvenir, and pass must be $33.75.

Putting all this information together, we can write an equation:

(1/6)x + x + (4/3)x = 33.75

Simplifying the left side of the equation:

(7/6)x = 33.75

Multiplying both sides by 6/7:

x = 30

Therefore, the cost of the souvenir is $30, the cost of the burger is (1/6) * 30 = $5, and the cost of the pass is (4/3) * 30 = $40.

To check that these values are correct, we can add them up:

30 + 5 + 40 = 75

And we can subtract the total cost from the amount Zachary brought:

38.25 - 75 = -36.75

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Write an exponential function in the form y=ab^xy=ab x that goes through points (0, 13)(0,13) and (5, 416)(5,416)

Answers

The exponential function in the form y = [tex]ab^x[/tex] that goes through the points (0, 13) and (5, 416) is y = 13 * [tex]2^x[/tex].

To write an exponential function in the form y = [tex]ab^x[/tex] that goes through the points (0, 13) and (5, 416), follow these steps:

1. Use the point (0, 13) to determine the value of a. Since the x-coordinate is 0, we have y = a * b⁰, which simplifies to y = a. Therefore, a = 13.

2. Use the point (5, 416) to determine the value of b. Plug in the values for x and y, as well as the value of a we just found: 416 = 13 * b⁵.

3. Solve for b: b⁵ = 416 / 13 = 32. Taking the fifth root of both sides, we get b = 2.

So, the exponential function in the form y = [tex]ab^x[/tex] that goes through the points (0, 13) and (5, 416) is y = 13 * [tex]2^x[/tex].

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