A dollar bill is 6.14 inches long. If type laid ten million dollar bills end to end lengthwise, how many times around Cincinnati I-275 highway loop would the line of bills reach? The I-275 highway loop is approximately 84 miles long

The possible ways the 3 medals can be distributed is 132600

There are 658008 of such rankings

From the question, we have the following parameters

Athletes = 52

Positions = 3

From the question, we understand that:

There is no tie

This means that

So, we have

Ways = 52 * 51 * 50

Evaluate

Ways = 132600

Here, we have

Salespersons = 40

List = 5

The number of ways is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 40 and r = 5

Substitute the known values in the above equation

Total = ⁴⁰C₅

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 40!/35!5!

Evaluate

Total = 658008

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Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

The 108 decibel sound is 6.31 times more intense than a 100 decibel sound option (B) is correct.

It is another way to represent the power of numbers, and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.

\(\rm a^b = c\\log_ac =b\)

We have:

The loudness L of sound in decibels is given by

\(\rm L=10log(\dfrac{I}{I_0})\)

Here I is the intensity of the sound.

\(\rm I_0=10^{-12} \ W/m^2\)

Loudness for 108 decibel sound:

\(\rm 108=10log(\dfrac{I}{10^-^1^2})\)

I = 0.06309

Similarly, for:

100 decibel sound:

i = 0.01

I/i = 0.06309/0.01 = 6.31

I = 6.31i

Thus, the 108 decibel sound is 6.31 times more intense than a 100 decibel sound option (B) is correct.

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Answer:

Explanation:

First, let's review the definition of horizontal.

In the picture given, we can see that DE is the vertical line and CD is the horizontal line. I have uploaded a picture. To find the length of CD (horizontal line), simply count the red dots. After counting, there was a total of 8 dots.

Hence, the length of CD is 8 units.

Answer:

scientific notation

-6 * 10 ^ 1

Step-by-step explanation:

No Problem

In June, A.B.C company invested $20,000, purchased equipment, paid insurance premium, bought office supplies, billed students for tutorial services, received cash, paid for supplies, withdrew personal funds.

Accounting Cycles:

1. June 1:

  - A.B.C company invests $20,000 in the business.

  - Prepare the journal entry:

    - Debit: Cash ($20,000)

    - Credit: Capital ($20,000)

2. June 3:

  - Purchased equipment for $12,100.

  - Prepare the journal entry:

    - Debit: Equipment ($12,100)

    - Credit: Cash ($12,100)

3. June 4:

  - Paid $220 premium for an insurance policy.

  - Prepare the journal entry:

    - Debit: Insurance Expense ($220)

    - Credit: Cash ($220)

4. June 6:

  - Purchased office supplies on account for $140.

  - Prepare the journal entry:

    - Debit: Office Supplies ($140)

    - Credit: Accounts Payable ($140)

5. June 9:

  - Purchased a new computer for $9,000. Paid 40% in cash and agreed to pay the remainder later.

  - Prepare the journal entry for the cash payment:

    - Debit: Computer ($3,600) [40% of $9,000]

    - Credit: Cash ($3,600)

  - Prepare the journal entry for the remaining amount:

    - Debit: Computer ($5,400)

    - Credit: Accounts Payable ($5,400)

6. June 10:

  - Billed student Omar $58 for tutorial services performed.

  - Prepare the journal entry:

    - Debit: Accounts Receivable ($58)

    - Credit: Tutorial Services Revenue ($58)

7. June 14:

  - Paid for the supplies purchased on June 6th ($140).

  - Prepare the journal entry:

    - Debit: Accounts Payable ($140)

    - Credit: Cash ($140)

8. June 15:

  - The owner suggested purchasing a new building for the company for $22,000.

  - No journal entry is required at this point. It is a decision made by the owner.

9. June 25:

  - Received $85 cash from student Salim Ali for tutorial services performed.

  - Prepare the journal entry:

    - Debit: Cash ($85)

    - Credit: Accounts Receivable ($85)

10. June 30:

   - Student billed on June 10 pays the amount due ($58).

   - Prepare the journal entry:

     - Debit: Cash ($58)

     - Credit: Accounts Receivable ($58)

11. June 30:

   - A.B.C company withdraws $60 for personal use.

   - Prepare the journal entry:

     - Debit: Withdrawals ($60)

     - Credit: Cash ($60)

These transactions represent the accounting cycles for the given period.

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The price should be higher than the AVC and ATC in order to make a profit in the short term. Therefore, in order to achieve the requisite profit, the MR curve must rise above cost = 7.

When businesses in a cutthroat sector start making money, it opens the door for more businesses to enter the market, which leads to a shift to the right in the supply curve, a drop in price, and the return of all businesses to a state of no economic profit.

If the market price is lower than the average total cost, a company will experience positive economic profit in the short term.

In the short run, a monopolistically competitive firm optimises profits or avoids losses by producing the amount where marginal revenue equals marginal cost. If the average total cost is less than the market price, the company will make a profit.

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The equation of remaining chocolate C  in terms of t is C = 30 - 3t.

A mathematical statement called an equation demonstrates the balance or equality of two expressions. It contains of variables, integers, and mathematical operations and is denoted by the equal symbol (=). Equations may be solved to determine unknown values and are used to express relationships between various quantities. To solve for x in the equation 2x + 3 = 7, for instance, remove 3 from both sides, which gives 2x = 4, then divide both sides by 2, which gives x = 2.

Given that,

Initial number of chocolates in box = 30

Also given that after 8 nights, number of remaining chocolates = 6

Implies that,

In 8 nights, 24 chocolates were treated.

In 1 night, 3 chocolates were treated.

The equation of remaining chocolate C  in terms of t can be written as

C = 30 - 3t.

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Answer:

Step-by-step explanation:

When we are using percentages, what we are really saying is that the percentage is a fraction of 100. "Percent" means per hundred, and so 50% is the same as saying 50/100 or 5/10 in fraction form.

So, since our denominator in 1/7 is 7, we could adjust the fraction to make the denominator 100. To do that, we divide 100 by the denominator:

100 ÷ 7 = 14.285714285714

Once we have that, we can multiple both the numerator and denominator by this multiple:

1 x 14.285714285714/7 x 14.285714285714

= 14.285714285714100

Now we can see that our fraction is 14.285714285714/100, which means that 1/7 as a percentage is 14.2857%.

We can also work this out in a simpler way by first converting the fraction 1/7 to a decimal. To do that, we simply divide the numerator by the denominator:

1/7 = 0.14285714285714

Once we have the answer to that division, we can multiply the answer by 100 to make it a percentage:

0.14285714285714 x 100 = 14.2857%

And there you have it! Two different ways to convert 1/7 to a percentage. Both are pretty straightforward and easy to do, but I personally prefer the convert to decimal method as it takes less steps.

Given:

\(P=\$120,000\)

\(r=5.3\%\)

\(t=8\text{ years}\)

To find:

The value of the investment when the interest is compounded annually.

Solution:

The formula for amount is:

\(A=P\left(1+\dfrac{r}{n}\right)^{nt}\)

Where, P is the principal, r is the rate of interest in decimal, n is the number of time interest compounded in an years, and t is the number of years.

The interest is compounded annually. So, \(n=1\).

Substituting \(P=120000, r=0.053, n=1, t=8\) in the above formula, we get

\(A=120000\left(1+\dfrac{0.053}{1}\right)^{1(8)}\)

\(A=120000\left(1.053\right)^{8}\)

\(A=181387.85936\)

\(A\approx 181387.86\)

Therefore, the value of the investment after 8 years is $181,387.86.

Answer:

y=1x+1 is your answer

Step-by-step explanation:

you find the slope and y-int

Answer:

A

Step-by-step explanation:

The binomial factors of x³- 4x²+x+6​ are (x+2), (x+3), and (x-1).

Using the splitting and grouping the terms:

x³ + 4x² + x - 6

= x³ + 2x² + 2x² + x - 6  [Splitting 4x² = 2x² + 2x²]

= (x³ + 2x²) + (2x² + x - 6)

= x² (x + 2) + (2x² + 4x - 3x - 6)

= x² (x + 2) + [ 2x (x + 2) - 3 (x + 2)]

= x² (x + 2) + (x + 2) (2x - 3)

= (x + 2) ( x² + 2x - 3)

= (x + 2) ( x² + 3x - x - 3)

= (x + 2) [x (x + 3) - 1 (x + 3)]

= (x + 2) (x + 3) (x - 1)

Hence, the binomial factors are (x + 2), (x + 3) and (x - 1)

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Answer: To calculate the amount of canvas needed for one tent, we need to calculate the total surface area of the tent. The tent consists of two parts: the cylindrical lower part and the conical upper part.

The surface area of the cylindrical part can be calculated as follows:

The base area of the cylinder = π × r² = π × 2.8² ≈ 24.61 m²

The lateral area of the cylinder = 2 × π × r × h = 2 × π × 2.8 × 3.5 ≈ 54.99 m²

So, the total surface area of the cylindrical part is the sum of the base area and lateral area, which is:

Total surface area of cylindrical part = 24.61 + 54.99 ≈ 79.60 m²

The surface area of the conical part can be calculated as follows:

The slant height of the cone = √(r² + h²) = √(2.8² + 2.1²) ≈ 3.44 m

The lateral area of the cone = π × r × slant height = π × 2.8 × 3.44 ≈ 24.12 m²

So, the total surface area of the conical part is the sum of the base area and lateral area, which is:

Total surface area of conical part = 24.61 + 24.12 ≈ 48.73 m²

Therefore, the total surface area of one tent is:

Total surface area of one tent = 79.60 + 48.73 ≈ 128.33 m²

To make 1500 tents, the total amount of canvas required is:

Total amount of canvas required = 1500 × 128.33 ≈ 192,495 m²

The cost of the canvas is given as Rs 120 per m². Therefore, the total cost of the canvas required to make the tents is:

Total cost of canvas = 192,495 × 120 ≈ Rs 23,099,400

As 50 schools have decided to share the expenditure equally, the amount shared by each school will be:

Amount shared by each school = Total cost of canvas / 50

Amount shared by each school = 23,099,400 / 50

Amount shared by each school ≈ Rs 461,988

Therefore, each school will have to contribute approximately Rs 461,988 to set up the tents.

Step-by-step explanation:

The correct answer is A. a characteristic of the population.

A population parameter refers to a specific characteristic

A population parameter refers to a specific characteristic or numerical value that describes the entire population being studied. It is a fixed value that is typically unknown and estimated using sample data. Examples of population parameters include the population mean, population standard deviation, population proportion, etc.

Answer:c

Step-by-step explanation is va cuz when your multiply:

Answer:

\(\sqrt[6]{2}\left(\cos\left(\frac{3\pi}{4}\right)+i\sin\left(\frac{3\pi}{4}\right)\right)\)

Step-by-step explanation:

The analysis is as attached below.

We have the following equation from the line

We must remember that the equation of the line is expressed in the form y=mx+b, where a represents the slope of the line.

Since we are standing a line parallel to the line described in the previous equation, we must ensure that their slopes are exactly the same, so when identifying the slope of the equation, this same slope is used for a completely parallel line.

In conclusion, the slope of the line that is parallel to the line y = 2x + 5 is:

Answer:

n = 4

Step-by-step explanation:

4(3n + 3) = 60 ( divide both sides by 4 )

3n + 3 = 15 ( subtract 3 from both sides )

3n = 12 ( divide both sides by 3 )

n = 4

The value of n in 4(3n+ 3) = 60 that satisfies the equation is 4.

To solve for the variable n, we need to get n by itself on one side of the equation. We can do this by isolating n by performing the same operations on both sides of the equation.

First, we can simplify the left side of the equation by performing the operations inside the parentheses:

4(3n+ 3) = 4(3n) + 4(3) = 12n + 12

Then, we can subtract 12 from both sides of the equation to isolate n:

12n + 12 - 12 = 60 - 12

12n = 48

Finally, we can divide both sides of the equation by 12 to solve for n:

12n / 12 = 48 / 12

n = 4

Therefore, the value of n that satisfies the equation is 4.

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Answer:

3721

Step-by-step explanation:

6 by the power of 2= 36 and 5 by the power of 2= 25

so (36+25)²= 61²

61²=3721

Let's call the amount Susan invested in the fund that paid a 12% profit "x" and the amount she invested in the stock that suffered a 4% loss "y".

We know that Susan's overall net profit was $2,160, so the total amount of profit she earned from both investments was $2,160.

The profit from the investment in the fund that paid a 12% profit was 0.12x (since the profit rate was 12%). The loss from the investment in the stock that suffered a 4% loss was -0.04y (since the profit rate was negative 4%).

We can set up two equations based on this information:

The total amount invested was $22,000:

x + y = 22,000

The total profit was $2,160:

0.12x - 0.04y = 2,160

We can use the first equation to solve for one of the variables in terms of the other:

x = 22,000 - y

Now we can substitute this expression for "x" into the second equation:

0.12(22,000 - y) - 0.04y = 2,160

Simplifying:

2,640 - 0.12y - 0.04y = 2,160

Combining like terms:

2,640 - 0.16y = 2,160Subtracting 2,640 from both sides:

-0.16y = -480

Dividing both sides by -0.16:

y = 3,000

So Susan invested $3,000 in the stock that suffered a 4% loss.

To find the amount she invested in the fund that paid a 12% profit, we can substitute this value for "y" in one of the equations we set up earlier:

x + y = 22,000

x + 3,000 = 22,000

x = 19,000

So Susan invested $19,000 in the fund that paid a 12% profit.

Therefore, the amount invested at 12% was $19,000 and the amount invested in stock was $3,000.

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The amount invested in the in account that had an 12% profit is $19,000

The amount invested in the in account that had a 4% loss is $3,000.

\(\sf a + b = 22,000\) equation 1

\(\sf 0.12a - 0.04b = 2160\) equation 2

Where:

Multiply equation 1 by 0.12

\(\sf 0.12a + 0.12b = 2640\) equation 3

Subtract equation 2 from equation 3

\(\sf 0.16b = 480\)

Divide both sides of the equation by 0.16

\(\sf b = 3000\)

Subtract 3,000 from 22,000

\(\sf a = 22,000 - 3,000 = 19,000\)

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The mean, median, and mode of the number of units produced per day are 317.4, 390, and 390.

Measures of central tendency assist in the discovery of a data set's middle, or average. The mode, median, and mean are the three most popular metrics of central tendency.

Given the production of Arielle for Monday is 375 units; Tuesday is 22 units; Wednesday is 410 units; Thursday is 390 units, and Friday is 390 units. Therefore, the dataset is {375, 22, 410, 390, 390}.

A.) The the mean number of units produced per day is,

Mean = (375+22+410+390+390)/5 = 1587/5 = 317.4 units per day

B.)  The median number of units produced is 390.

C.) The mode number of units produced is 390.

Hence, the mean, median, and mode of the number of units produced per day are 317.4, 390, and 390.

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Answer:

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

Apply the Triangle Inequality Theorem.

It states that:

We'll take the sum of two shortest sides and compare with the longest:

It confirms the theorem, without testing the other two sides (which is obvious) so the answer is yes.

The matching answer choice is e).

Let's assume David's average speed is S km/h.

A) To find David's average speed, we can use the formula: Speed = Distance / Time.

David completed the race in 5 hours, so his speed is S km/h. Therefore, we have:

S = Distance / 5

B) Ken's average speed is 9.8 km/h less than David's average speed, which means Ken's average speed is (S - 9.8) km/h.

Ken took 7 hours to complete the race, so we have:

S - 9.8 = Distance / 7

Now, we can solve the system of equations to find the values of S and Distance.

From equation (1): S = Distance / 5

Substitute this into equation (2):

Distance / 5 - 9.8 = Distance / 7

Multiply both sides of the equation by 35 to eliminate the denominators:

7 * Distance - 35 * 9.8 = 5 * Distance

7 * Distance - 343 = 5 * Distance

Subtract 5 * Distance from both sides:

2 * Distance - 343 = 0

Add 343 to both sides:

2 * Distance = 343

Divide both sides by 2:

Distance = 343 / 2 = 171.5 km

Therefore, the distance of the cycling race is 171.5 kilometers.

To find David's average speed, substitute the distance into equation (1):

S = Distance / 5 = 171.5 / 5 = 34.3 km/h

So, David's average speed was 34.3 km/h.\(\)

Answer:

A) 34.3 km/h

B) 171.5 km

Step-by-step explanation:

Since Ken's average speed is said to be 9.8km/h less than David's average speed, and we know that Ken's average speed is dependent on him traveling for 7 hours, then we have our equation to get the distance of the cycling race:

\(\text{Ken's Avg. Speed}=\text{David's Avg. Speed}\,-\,9.8\\\\\frac{\text{Distance}}{7}=\frac{\text{Distance}}{5}-9.8\\\\\frac{5(\text{Distance})}{7}=\text{Distance}-49\\\\5(\text{Distance})=7(\text{Distance})-343\\\\-2(\text{Distance})=-343\\\\\text{Distance}=171.5\text{ km}\)

This distance for the cycling race can now be used to determine David's average speed:

\(\text{David's Avg. Speed}=\frac{\text{Distance}}{5}=\frac{171.5}{5}=34.3\text{ km/h}\)

Therefore, David's average speed was 34.3 km/h and the distance of the cycling race was 171.5 km.

Answer:

The test statistic for the hypothesis test is -1.202.

Step-by-step explanation:

We are given that a report on the nightly news broadcast stated that 10 out of 129 households with pet dogs were burglarized and 23 out of 197 without pet dogs were burglarized.

Let \(p_1\) = population proportion of households with pet dogs who were burglarized.

\(p_2\) = population proportion of households without pet dogs who were burglarized.

SO, Null Hypothesis, \(H_0\) : \(p_1=p_2\)     {means that both population proportions are equal}

Alternate Hypothesis, \(H_A\) : \(p_1\neq p_2\)     {means that both population proportions are not equal}

The test statistics that would be used here Two-sample z-test for proportions;

                           T.S. =  \(\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }\)  ~ N(0,1)

where, \(\hat p_1\) = sample proportion of households with pet dogs who were burglarized = \(\frac{10}{129}\) = 0.08

\(\hat p_2\) = sample proportion of households without pet dogs who were burglarized = \(\frac{23}{197}\) = 0.12

\(n_1\) = sample of households with pet dogs = 129

\(n_2\) = sample of households without pet dogs = 197

So, the test statistics  =  \(\frac{(0.08-0.12)-(0)}{\sqrt{\frac{0.08(1-0.08)}{129}+\frac{0.12(1-0.12)}{197} } }\) 

                                     =  -1.202

The value of z test statistics is -1.202.

Answer:

that isnt a question but good to know! :)

Step-by-step explanation: