The area of a circle is 49π cm^2. Find the circumference of the circle. Leave your answer in exact form, no decimals, and include units (Note: make sure you are showing the formulas you use to answer the question and how the numbers fit into the formulas).

[tex]\frac{79}{10}[/tex], which is a complex fraction, can be written as a mixed number resulting in [tex]7\frac{9}{10}[/tex].

A mixed number is a combination of a whole number, a numerator and a denominator.

The numerator is always less than the denominator in a mixed number because it has been converted from a complex fraction to its current status as a mixed number.

Mixed numbers are complex fractions, like [tex]\frac{79}{10}[/tex].  Before the conversion, complex fractions are fractions where the numerator is greater than the denominator.

Thus [tex]\frac{79}{10}[/tex] written as a mixed number is [tex]7\frac{9}{10}[/tex].

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Answer:

-3

Step-by-step explanation:

to find the scale factor dividex^1 by x (so old shape to new shape)

Step-by-step explanation:

9x2= 3 • 3 • x2

6x= 3 • 2 • x

12x= 2 • 2 • 3 • x

8= 2 • 2 • 2

Answer:

1) D

2) A, D, F

3) 3.5 mph

4) equation in explanation $15

Step-by-step explanation:

4) equation: 27.50-12.50

Question

During one waiters shift he delivered 13 appetizers, 17 entrées, and 10 desserts what percentage of the dishes he delivered were: A. Desserts B. Appetizers  C. entrees

Answer:

A)Desserts = 25 %

B)Appetizers = 32.5 %

C)Entrées =  32.5 %

Step-by-step explanation:

Given:

Number of appetisers = 13

Number of entrees =   17

Number of  desserts = 10

Solution:

Total number  of dishes = 13 + 17 + 10 = 40

percentage of the dishes he delivered were Desserts is   =  [tex]\frac{10}{40} \times 100 = 0.25 \times 100 = 25%[/tex]

percentage of the dishes he delivered were Appetizers is  =[tex]\frac{13}{40}\times 100 = 0.325 \times 100[/tex]  = 32.5%

percentage of the dishes he delivered were Entrées is = [tex]\frac{17}{40} \times 100 = 0.425 \times 100[/tex]=  42.5 %

To find the percentage of each type of dish a waiter has delivered, add up the total number of dishes, then divide the number of each type of dish by this total and multiply by 100.

The subject question requires us to determine what the percentage is of the various types of dishes a waiter delivers during his shift. We're given that the waiter delivered 13 appetizers, 17 entrees, and 10 desserts. We can solve this by doing some basic calculations:

First, we need to figure out the total number of dishes the waiter delivered. We do this by adding together the appetizers, entrees, and desserts he delivered: 13 appetizers + 17 entrees + 10 desserts = 40 dishes in total.

Next, to find the percentage of each type of dish, we divide the number of that type of dish by the total number of dishes, and then multiply the result by 100. For example, for appetizers: (13 appetizers / 40 total dishes) * 100 = 32.5%.

You can do the same calculations for entrees and desserts to find their percentages. These basic calculations are useful not only in a restaurant setting, but also in allocation of tasks in modern businesses and in many other real-world scenarios.

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Answer:   x-4, 2x-8, 8x-32

Step-by-step explanation:

Answer:

1) The polynomial [tex]8x^3+1[/tex] represents a sum of cubes

2) The polynomial [tex]49x^2-25[/tex] represents a difference of squares

Step-by-step explanation:

1) To find the polynomials represents a sum of cubes :

[tex]8x^3+1[/tex] represents a sum of cubes

For [tex]8x^3+1[/tex]

[tex]=2^3x^3+1^3[/tex]

[tex]=(2x)^3+1^3[/tex]

Therefore [tex]8x^3+1=(2x)^3+1^3[/tex]

Therefore [tex]8x^3+1[/tex] represents a sum of cubes

2)To find the polynomials represents a difference of squares :

[tex]49x^2-25[/tex] represents a difference of squares

For [tex]49x^2-25[/tex]

[tex]=7^2x^2-5^2[/tex]

[tex]=(7x)^2-5^2[/tex]

Therefore [tex]49x^2-25=(7x)^2-5^2[/tex]

Therefore [tex]49x^2-25[/tex] represents a difference of squares

Answer:

C i think..

Step-by-step explanation:

Answer:

15.666666666667=15.67 to the nearest hundredth or to two decimal places.

Step-by-step explanation:

We want to round 15.66666666667 to the nearest hundredth or to two decimal places.

We count two numbers after the decimal place to get:

15.66|6666666667

The next digit is 6

Since 6>5, we round up.

This means we add 1 to the number the hundredth place to get

15.67

Answer:

Step-by-step explanation:

30/5=6

Final answer:

Benjamin rides his scooter for a total of 6 miles over a period of 10 days, by multiplying the daily distance of 3/5 mile by 10 days.

Explanation:

To calculate the distance Benjamin rides his scooter over 10 days, we multiply the daily distance by the number of days. Benjamin rides 3/5 of a mile each day.

Distance per day = 3/5 mile
Number of days = 10 days

The total distance is:

3/5 mile/day × 10 days = 6 miles

Therefore, the correct answer is  Benjamin will have traveled a total of 6 miles over the course of 10 days.

Answer:

20

Step-by-step explanation:

Average =

sum of scores/number of score

= 14 + 17 + 22 + 27 / 4

= 80/4

= 20

Answer:

Total population = 200

Step-by-step explanation:

recaptured tagged/recaptured total ≈ tagged/total population

The best estimate for the total population of Robin's is 200.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given that,

Number of robins which are tagged = 20

Let x be the total population of robins.

Her catches some other robins.

Number of robins that he catched = 120

Number of robins he catched also is tagged = 12

We can write the expression as,

20 / x = 12 / 120

Cross multiplying, we get,

12x = 120 × 20

12x = 2400

x = 2400 / 12

x = 200

Hence the number of robins is 200.

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Answer:

infinite solutions

Step-by-step explanation:

6x + 18 = 2(3x + 9)

1. 6x + 18 = 6x + 18                      Distribute the 2

2. X can be any number since they are the same.

First, let's move combine like terms:

-5y + 8y = 6 + 2 -12.

3y = -4.

y = -4/3

Answer:

x = -3 + 2y

Step-by-step explanation:

I'm not sure if that's correct, sorry, dear~!

Answer:

The amount of a check issued for an 08/11 invoice, would depend on when the invoice is paid.  

If it's paid within 13 days, there's a 3% discount . which will be calculated as

648.50 x 3% = $19.455 discount

If it's paid within 11 - 15 days, there's a 2% discount.

648.50 x 2% = $12.97 discount

If it's paid within 16 - 30 days, there is no discount

If it's paid after 30 days, 5% APR is added to the bill

The check would be for the invoice amount of $648.50 plus a late fee of $2.67, totaling $651.17. The late fee is applied since the payment was made 3 days after the 30-day period from the invoice date and calculated using a daily rate derived from the 5% APR.

The invoice has specific payment terms: 3/10, 2/15, N30. These are discounts offered for early payment. The first part '3/10' means that the payer gets a 3% discount if they pay within 10 days. The second part '2/15' offers a 2% discount if the payer pays within 15 days. 'N30' means that the full amount due needs to be paid within 30 days from invoice date. Additionally, there is a 5% APR (annual percentage rate) charge for late payments.

The invoice was issued on 08/11, and the payment was made on 09/13, which is 33 days after the invoice date. Therefore, there aren't any discounts for the payment because it's not within the 10 or 15 days period. However, it's slightly over the 30 days, so there will be a late fee applied. The late fee is commonly calculated based on a daily rate. The daily rate is the APR divided by 365 (5%/365=0.0137%). Multiply the daily rate by the number of late days (33-30=3) and the invoice amount ($648.50).

So the late fee is 648.50*0.0137%*3=$2.67. The amount of the check would be the original invoice amount $648.50 plus late fee $2.67,  so the total is $651.17.

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Answer:

B) 1

Step-by-step explanation:

Answer:1

Step-by-step explanation:

Answer:

Since AC is perfectly equal to BD, 4x-60=30-x. If you solve for x, x=18. Then plug 18 into BD=30-x. Therefore, BD=12.

Answer:

12y and 6bc

Step-by-step explanation:

multiply by 2

The product of [tex]6y[/tex] and [tex]3bc[/tex] after doubling would be as follows:

[tex]36bcy[/tex]

Variable

Product of [tex]6y,3bc=18bcy[/tex]

Double the product of [tex]6y,3bc=2(18bcy)[/tex]

                                                [tex]=\textbf{36bcy}[/tex]

Thus, it is the correct answer.

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Answer:

625

Step-by-step explanation:

We have to find 125% of 500

 = [tex]\frac{125}{100} * 500 = 1 .25 * 500[/tex]  = 625 .

Here the solution (625) is greater than the original (500) because the percentage value is more than 100% . so the answer will come more than its original value.

Answer: Estimate means a close guess.

For example, when estimating with decimals, we would round them to the nearest whole number to estimate the answer.

Example: 3.6 + 1.2

1.2 is closest to 1

3.6 is closes to 4

4 + 1 = 5

A good estimate is 5

3.6 + 1.2 = 4.8

4.8 is very close to 5, so 5 is a very good estimate.

Final answer:

Estimating a math problem involves making an educated approximation of a quantity using prior knowledge and reasoning. It applies to various fields and helps to rule out unrealistic numbers, as well as develop important problem-solving skills.

Explanation:

To estimate a math problem means to find a rough approximation or a ballpark figure of the quantity in question, rather than calculating the exact number. Estimations are based on sound reasoning, prior experience, and a strong grasp of the relevant variables and physical principles. The process is not a wild guess but a calculated approximation that can be derived from formulas where the input quantities are known to a limited precision.

For example, to estimate the mean rent for a two-bedroom apartment in a town, you might calculate the average of several listed rents. Or, in physics, to estimate how large a current will be in a circuit when it is turned on, you would apply the relevant principles and any known quantities to arrive at an approximate value. The goal of estimation is to get within a reasonable range of accuracy without needing a precise computation.

The skills of estimation are vital in many fields, including physics, and they help in ruling out unrealistic results. Practicing these skills, getting familiar with units, and understanding relationships between variables all contribute to making better estimates. Moreover, after arriving at an estimate, it's important to do a sanity check to make sure the result seems reasonable within the context of what is known.

Answer:

$28

Step-by-step explanation:

Since each person got $14 and we know that there are 2 people receiving money, the total amount of money is equal to the amount of money John received, added to the amount of money his best friend got. Since both received $14, we can use the following equation:

Money found = $14 + $14 = $28

Answer:

112 candies

Step-by-step explanation:

Start from the end.

Joe gave 25% of the remaining candies to his sister and has 21 candies left. Then

[tex]21 \ candies - 75\%\\ \\x \ candies - 25\%[/tex]

Write a proportion:

[tex]\dfrac{21}{x}=\dfrac{75}{25}\\ \\75x=21\cdot 25\\ \\x=\dfrac{21}{3}=7[/tex]

Joe gave 7 candies to his sister, so before this he had 21 + 7 = 28 candies.

He gave 4/6 of what he had left to his brother when he went home, so 2/6 of all his candies left ot him. Hence,

[tex]28\ candies - \dfrac{2}{6}\\ \\x\ candies - \dfrac{4}{6}[/tex]

Write a proportion:

[tex]\dfrac{28}{x}=\dfrac{\frac{2}{6}}{\frac{4}{6}}\\ \\\dfrac{28}{x}=\dfrac{1}{2}\\ \\x=28\cdot 2=56[/tex]

Joe gave 56 candies to his brother, so Joe had 28 + 56 = 84 candies when he went home.

Joe gave 1/4 of his total candies to his classmates, so 3/4 of his candies left to him. So,

[tex]x\ candies - \dfrac{1}{4}\\ \\84\ candies - \dfrac{3}{4}[/tex]

Write a proportion:

[tex]\dfrac{x}{84}=\dfrac{\frac{1}{4}}{\frac{3}{4}}\\ \\\dfrac{x}{84}=\dfrac{1}{3}\\ \\3x=84\\ \\x=28[/tex]

Therefore, initially, Joe had 28 + 84 = 112 candies.

Answer:

10

Step-by-step explanation:

if you take 8 and divide it by 4 you get 2 meaning that each fifth is 2 pounds. if there are 5/5 that means there are 10 pounds

Answer:

There will be 13 songs in the final album.

Step-by-step explanation:

i) number of songs expected = 16 songs

ii) the band wrrites 62.5% more

   therefore the band writes [tex]16 \times ( 1 + 0.625) = 16 \times 1.625 = 26[/tex] songs

iii) During the editing process 50% of the songs are removed.

   Therefore there will be in the final album = [tex]( 1 - 0.5) \times 26 = 0.5 \times 26 = 13[/tex] songs.

Answer:

D

Step-by-step explanation:

Answer:

[tex]\left[\begin{array}{cc}0&2\\3&3\\6&4\\9&5\end{array}\right][/tex]

Step-by-step explanation:

+2 means that when c is at 0 w is at 2.

1/3c means that c moves up 3 at a time.

23-n > 33

- <--- that's a greater than or equal to sign

Answer:

23-n > 33

Step-by-step explanation:

Answer:

You'll need 18 cups of chicken broth!

Step-by-step explanation:

You are using a ratio of 1/4 cup (lentils) to 2 cup (broth). Therefore, you need to find the relationship between lentil and broth.

Therefore, 18 cups are needed :D

To make a soup with 2 1/4 cups of dried lentils, you would need 9 cups of chicken broth.

To find the number of cups of chicken broth needed, we need to multiply the given number of cups of dried lentils (2 1/4 cups) by the ratio of chicken broth to dried lentils. The ratio is 2 cups of chicken broth per 1/4 cup of dried lentils. So, for 2 1/4 cups of dried lentils, we would need:

2 1/4 cups × (2 cups/1/4 cup) = 9 cups of chicken broth

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