Mathematics College

Find the exact circumference of a circle with an area equal to 36 sq. in.


1) 12
2) 18
3) 324

Answers

Answer 1

Answer:

The answer would be option 1) 12

Answer 2

Answer:

The circumference is [tex]C=12\sqrt{\pi }\:in[/tex].

Step-by-step explanation:

The area of a circle when we know the circumference is

[tex]A=\frac{C^2}{4\pi }[/tex]

We know the area [tex]A=36 \:{in^2}[/tex], we plug this value into the above equation and we solve for C the circumference.

[tex]36=\frac{C^2}{4\pi }\\\frac{C^2}{4\pi }=36\\\frac{C^2\cdot \:4\pi }{4\pi }=36\cdot \:4\pi \\\\C^2=144\pi \\C=\sqrt{144\pi }\\C=12\sqrt{\pi }[/tex]

The circumference is [tex]C=12\sqrt{\pi }\:in[/tex].

Related Questions

what is the sum of (1-5q)+2(2.5q+8)

Answers

Answer:

17

Step-by-step explanation:

Eliminating parentheses, we have ...

... 1 - 5q +2·2.5q +2·8

... = 1 -5q +5q +16 . . . . . carry out the multiplication

... = q(-5+5) +(1 +16) . . . . group like terms

... = q·0 +17 . . . . . . . . . . . combine like terms

... = 17

Julianna works 32 hours each week. She earns $14.15 an hour. Which is closest to the amount of money Julianna will earn if she works for 46 weeks.(Please show work?)

A) $16,800
B) $18,000
C) $21,000
D) $22,500

Answers

32 hours * 46 weeks = 1,472 hours
1,472 * $14.15 = 20,828.8

Answer C is your answer
Final answer:

Julianna will earn $22,579.20 if she works for 46 weeks, which is closest to the option D) $22,500.

Explanation:

To calculate the amount of money Julianna will earn if she works for 46 weeks, we need to multiply the number of work hours per week (32) by the hourly wage ($14.15), and then multiply that result by the number of weeks worked (46). This can be calculated as follows:

Total earnings = (32 hours/week) × ($14.15/hour) × (46 weeks)

Total earnings = $22,579.20

Therefore, the closest amount of money Julianna will earn if she works for 46 weeks is $22,579.20, which is closest to option D) $22,500.

Learn more about Calculating Earnings here:

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Sam opened a savings account with an initial deposit of $2,000. Since then, he has never made any other deposits or withdrawals. His savings account earns 0.4% interest monthly and an annual bonus of 1.5% interest. Which equation gives the approximate amount, A(x), he has in his savings account as a function of x, the number of years since his initial deposit?


A(x) ≈ 2,000 + (1.059)x3

A(x) ≈ 2,000(1.019)x2

A(x) ≈ 2,000(1.065)x

A(x) ≈ 2,000(1.059)x2

Answers

Answer:

Third option:

[tex]A(x)\approx 2,000(1.065)^x[/tex]

Step-by-step explanation:

Notice if we invest 2,000 then the first month then after the first 0.4% interest is earned we will have in the account:

2,000(1+0.004) = 2,000(1.004)

I just applied the simple interest formula.

Then after the second month we will have:

[tex]2,000(1.004)(1.004) = 2,000(1.004)^2[/tex]

And so on each month.

So at the end of the first year (12 months) we have:

[tex]2,000(1.004)^{12}[/tex]

But we also earn an additional 1.5% in the year, so we will have:

[tex]2,000(1.004)^{12}(1.015)[/tex]

At the end of the second year we will have:

[tex]2,000[(1.004)^{12}(1.015)]^2[/tex]

At the end of the third year:

[tex]2,000[(1.004)^{12}(1.015)]^2[/tex]

And so on,

So if the number of years is denoted with x, at the end of x years we will have the following amount in the savings:

[tex]2,000[(1.004)^{12}(1.015)]^x[/tex]

We use our calculator to simplify that inside the brackets:

[tex](1.004)^{12}(1.015)=1.06481[/tex]

Rounding  to the third decimal place we get: 1.065

So notice the amount in the savings after x years will be:

[tex]2,000(1.065)^x[/tex]

Since they want it in function notation we just write the A(x) that denotes the amount in the savings:

[tex]A(x)\approx 2,000(1.065)^x[/tex]

Emma uses 5 ounces of milk to make a shake.she want to buy enough milk to make 7 shake and she want to buy the smallest size container ok milk that she can.should she buy a pint a quart or gallon of milk?justify your answer Help

Answers

Pint gallon because for gallon it is 0.352 of a gallon

write a word problem that can be solved by ordering three decimals to thousandths.

Answers

Angelo wants to grow the smallest pea which will be 2.6 times smaller than worlds smallest pea currently is 5 millimeters , what is 5 divided by 2.6? Given: smallest pea = 2.6 millimeters, worlds smallest pea = 5 millimeters

[Solution: 5 / 2.6 = 1.923076923076923 millimeters or approximately 1.923 millimeters]

differentiate please..

y= √x +6 ÷ √x-6

Answers

[tex]\bf y=\cfrac{\sqrt{x}+6}{\sqrt{x}-6}\implies \cfrac{dy}{dx}=\stackrel{quotient~rule}{\cfrac{\frac{1}{2}x^{-\frac{1}{2}}(\sqrt{x-6})~~-~~(\sqrt{x}+6)\frac{1}{2}x^{-\frac{1}{2}}}{(\sqrt{x}-6)^2}}[/tex]

[tex]\bf \cfrac{dy}{dx}=\cfrac{\frac{1}{2}x^{-\frac{1}{2}}~(\underline{\sqrt{x}}-6~-~\underline{\sqrt{x}}-6)}{(\sqrt{x}-6)^2}\implies \cfrac{dy}{dx}=\cfrac{\frac{1}{2}x^{-\frac{1}{2}}(-12)}{(\sqrt{x}-6)^2} \\\\\\ \cfrac{dy}{dx}=\cfrac{\frac{-12}{2\sqrt{x}}}{(\sqrt{x}-6)^2}\implies \cfrac{dy}{dx}=\cfrac{\frac{-6}{\sqrt{x}}}{(\sqrt{x}-6)^2}\implies \cfrac{dy}{dx}=\cfrac{-6}{\sqrt{x}(\sqrt{x}-6)^2}[/tex]

. Hot dogs come in packs of 8. Hot dog rolls come in packs of 12. What is the least number of packs of each Shawn should buy to have enough to serve 24 people and have none left over?

Answers

He should have at least 3 hot dog packs and 2 hot dog roll packs.
Because you know how many he should end up with of each its actually quite simple.
basically it simplifies down to 12x=24 and 8x=24
which means he should buy 2 packs of hot dog rolls and 3 packs of hot dogs

What is the 250th term of this sequence. Please explain. 4, 9,14,19,24

Answers

a1 = first term = 4
a2 = second term = a1+5 = 4+5 = 0
a3 = third term         a1 + 5 + 5 = a1 + 5(n-1), where n is the subscript that represents which term we're discussing.

an=4+5(n-1).

Is this correct?  Let's check it and find out.
What is your prediction for a2?  Here, n = 2.  Then a2 = 4+5(2-1), or 4+5, or 9.  That agrees with the given sequence rule.

Thus, the 250th term would be 4+5(250-1).  Evaluate this, please.

Which ordered pairs are solutions to the inequality y−4x≥−5 ?

Select each correct answer.



(−2, 1)

(−4, 2)

(4, 0)

(5, −2)

(1, −1)

Answers

The given inequality is
y - 4x ≥ - 5

To find the correct answer, we should test each answer as shown below.
Test (-2. 1): 
y - 4x = 1 - 4(-2) = 9
It is ≥ -5.
CORRECT

Test (-4, 2)
y - 4x = 2 - 4(-4) = 18
It is ≥ -5
CORRECT

Test (4,0)
y - 4x = 0 - 4(4) = -16
It is < -5
INCORRECT

Test (5,-2)
y - 4x = -2 - 4(5) = -22
It is < -5
INCORRECT

Test (1,-1)
y - 4x = -1 - 4(1) = -5
It is ≥ -5.
CORRECT

Answer: The correct answers are
(-2,1)
(-4,2)
(1,-1)

Answer:

The correct answers are

(-2,1)

(-4,2)

(1,-1)

Step-by-step explanation:

hope dis help u guys, habe a good rest of ya day!

Mark earns $135 for selling a $1500 refrigerator. Which sale listed has the same commission rate? $36 commission on a $400 dryer or B) $40 commission on a $500 dryer sale C) $210 commission on $1400 oven sale d) $30 commission on a $600 freezer sale?
salelisted has the same commssion rate. ?

Answers

The answer is A

36/400 * 3.8 = 136.6/1520
40/500 * 3 = 120/1500
210/1400 (not even close)
30/600 * 3 = 90/1800 (not even close)

so the two answer choices that are close are A and B, A has the closest numbers to the original commission rate.

Answer:

Option A is the correct choice.

Step-by-step explanation:

We have been given that Mark earns $135 for selling a $1500 refrigerator.

Since proportions states that two fractions are equal , so we will use proportions to find the same commission rate with the listed price from our given choices.

We can set proportion for commission and listed price as:

[tex]\frac{\text{Commission}}{\text{Listed price}}=\frac{135}{1500}[/tex]

Let us compare our given choices one by one.

A. $36 commission on a $400 dryer.

[tex]\frac{36}{400}=\frac{135}{1500}[/tex]

Upon simplifying our proportion we will get,

[tex]\frac{9}{100}=\frac{9}{100}[/tex]

[tex]0.09=0.09[/tex]

We can see that commission rates for both items are equal, therefore, option A is the correct choice.

B. $40 commission on a $500 dryer sale.

[tex]\frac{40}{500}=\frac{135}{1500}[/tex]

Upon simplifying our proportion we will get,

[tex]\frac{2}{25}=\frac{9}{100}[/tex]

[tex]0.08\neq 0.09[/tex]

We can see that both commission rates are different, therefore, option B is not a correct choice.

C. $210 commission on $1400 oven sale.

[tex]\frac{210}{1400}=\frac{135}{1500}[/tex]

Upon simplifying our proportion we will get,

[tex]\frac{3}{20}=\frac{9}{100}[/tex]

[tex]0.15\neq 0.09[/tex]  

Since the commission rates are different, therefore, option C is not a correct choice.

D.  $30 commission on a $600 freezer sale.

[tex]\frac{30}{1400}=\frac{135}{1500}[/tex]

Upon simplifying our proportion we will get,

[tex]\frac{3}{140}=\frac{9}{100}[/tex]

[tex]0.0214\neq 0.09[/tex]  

Since the commission rates are different, therefore, option D is not a correct choice.

Alice leaves her house and walks to school. She walks 45 meters south and 336 meters east. How far is Alice from her house?

Answers

she is 381 meters away from her house
The way to figure this out is to first set it up on an x/y graph. it also looks like a compass, which tells you which direction east and south is. So first draw a point where 45 would be (also south). Now draw a point around 336 east. You are now going to use the Pythagorean Theorem (Asquared +Bsquared =Csquared) to figure it out. 336 squared, + 45 squared. When you get that answer, square it, giving you your distance. Answer = 339

208,000,478 in expanded form

Answers

200,000,000+8,000,000+400+70+8

What is the value of x?

Answers

The value of x is 35°

Jane has a 5 × 7-inch photograph that she wants enlarged to a 10 × 14-inch photograph.

What is the scale factor from the original photograph to the enlarged photograph?

Answers

compare the 5 and 10 dimension then the 7 and 14 dimensions

10/5 =2

14/7 =2

 they both are the same ratio/factor

 the factor is 2


Answer:

2:1

Step-by-step explanation:

it asks for the scale since 5 x 2 = 10 and 7 x 2 = 14

the scale is 2 : 1


A person made an estimate for a three–minute interval. the estimate was 241.5 seconds. what was the error of this estimate?

Answers

We know a minute is 60 seconds.  So 3 minutes would be 60X3=180.  4 minutes would be 60X4=240.  The error was the person rounded to 4 minutes instead of 3 minutes.

Billy wants to live in the area defined by y < 3x − 6. Explain how you can identify the houses in which Billy is interested in living. (2 points)

Answers

check the picture below.

to graph an inequality, you pretty much first off, need to graph the "equality" or equation, so for y < 3x − 6, first off, graph the line y = 3x − 6.

and then you do a "true" or "false" check.

now, if you look at the line below, it splits the grid in two sections, so, let's check a point in either section, if one is false, the other is true and the other way around.

so, let's check the region on the left-hand-side, hmmmm say point 0,0, the origin.

y < 3x - 6

y = 0,  x = 0  thus

0 < 3(0) - 6

0 < -6   <--- now, is that really true? is 0 lesser than -6? not quite, is false.

recall that on the negative side, the closer to 0, the larger the value, so -1 is much larger than -1,000,000.

because the point 0,0 yielded a false inequality, that region is the "false region" and thus not shaded, therefore, the other side must be the "true region", and thus we shade that then.

we can run a quick check on that btw, say on point 4,4

y =4,   x = 4  thus

4 < 3(4) - 6

4 < 12 - 6

4 < 8    <---- yeap, is true, 4 is lesser/smaller than 8.

hmm ohh yes, the line needs to be dashed for a < or >, because it "has that boundary but it does not include it", unlike ⩽ and ⩾, which is a solid line, because it has that boundary and it includes it too.

Daniel dives into a swimming pool. The height of his head is represented by the function h(t) = -8t(squared) - 28t + 60, where t is the time in seconds and h(t) is the height of his head, in inches. How many seconds will it take for Daniel's head to reach the surface of the pool?

Answers

When Daniel's head reaches the surface, h(t) = 0
Therefore:
-8t² - 28t + 60 = 0             To simplify, divide both sides by -4
2t² + 7t - 15 = 0               
Consider the trinomial ax² + bx + c
To factor by grouping, we must find two numbers that multiply to equal AC (-30) and add up to B (7)
Two numbers that satisfy this are 10 and -3:
2t² + 10t - 3t - 15 = 0        Rewrite the equation using 10t and -3t
2t (t + 5) -3 (t +5) = 0        Regroup, then rewrite
(2t -3) (t+5) = 0 

2t-3 = 0 
2t = 3
t = 3/2
OR
t + 5 = 0
t = -5

We know t cannot be a negative number, so the answer is:
t = 3/2, or 1 and a half seconds
It should take him 1.5 sec to get to the top :)

One canned juice drink is 25% orange juice; another is 10% orange juice. How many liters of each should be mixed together in order to get 15L that is 17% orange juice

Answers

let's say we use "x" of the 25% OJ... ok... well, how much juice is really in that "x" liters?  well, 25% of it is OJ, the rest is water, how much is 25% of x? well, (25/100) * x,  or 0.25x.

likewise, we'll use "y" of the 10% OJ, and it will end up with (10/100) *y or 0.10y of juice in it.

whatever "x" and "y" are, they must add up to 15 Liters, and the juice concentration on that mixture, must also be the sum of their sum concentration.

[tex]\bf \begin{array}{lccclll} &\stackrel{liters}{amount}&\stackrel{juice~\%}{quantity}&\stackrel{juice}{quantity}\\ &------&------&------\\ \textit{25\% juice}&x&0.25&0.25x\\ \textit{10\% juice}&y&0.10&0.10y\\ ------&------&------&------\\ mixture&15&0.17&2.55 \end{array} \\\\\\ \begin{cases} x+y=15\implies \boxed{y}=15-x\\ 0.25x+0.10y=2.55\\ ----------\\ 0.25x+0.10\left(\boxed{15-x} \right)=2.55 \end{cases} \\\\\\ 0.25x-0.10x+1.5=2.55\implies 0.15x=1.05\implies x=\cfrac{1.05}{0.15} \\\\\\ x=7[/tex]

how much will be it of the 10% juice?  well, y = 15 - x.

x3-27i=0 solve for the root equation

Answers

Okay this should be simple...I remeber learning about this in class I just hope I did it right.

Add 27i to both sides

x * 3 - 27i + 27i = 0 + 27i

Then simplify

The form x * 3 = 27i

Divide both sides by 3

x * 3       27i
____ =  ____
  3           3

And now simplify to get your final answer

x = 9i
[tex]\bf x^3-27i\qquad \boxed{27=3^3}\qquad x^3=27i\implies x=\sqrt[3]{27i}\implies x=\sqrt[3]{3^3i} \\\\\\ x=3\sqrt[3]{i}[/tex]

write the equation of the line MN, which is formed by the points M(-3,5) and N(2,0)

Answers

The equation is y = -x + 2

Step 1

Find the slope of the given line

Let

[tex]M(-3,5)\ N(2,0)[/tex]

we know that

the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute the values

[tex]m=\frac{0-5}{2+3}[/tex]

[tex]m=\frac{-5}{5}[/tex]

[tex]m=-1[/tex]

Step 2

Find the equation of the line

we know that

the equation of the line into point-slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have  

[tex]m=-1[/tex]

point N [tex](2,0)[/tex]

substitute the values

[tex]y-0=-1(x-2)[/tex]

[tex]y=-x+2[/tex]

therefore

the answer is

[tex]y=-x+2[/tex]

Which of the following statements must be true about a rectangle? Choose all answers that apply: Choose all answers that apply: A It has four sides of equal length. B It has four right angles. C It has two pairs of parallel opposite sides.

Answers

c
because a rectangle has not the same exact side lengths like a square

Answer:

The correct answers are options B and C.                            

Step-by-step explanation:                      

B It has four right angles.

C It has two pairs of parallel opposite sides.

All angles are right angles by definition of a rectangle. The rectangle has 2 pairs of parallel opposite sides.              

Option A is wrong as its a square whose all 4 sides have equal length.

A seafood company sold 9,125 pounds of fish last month. If 6 seafood companies sold the same amount of fish, how much fish did the 6 companies sell last month in all ?

Answers

The 6 seafood companies sold 54,750 pounds of fish

kalen's truck has a 60 gallon fuel tank The fuel gauge points to 1/4 how much fuel does he need to buy to fill the tank show Your work

Answers

He should need 45 more gallons. 60/4=15 15gallons for every 1/4 of the tank. 60-15=45

What are 2 ways three people can share fifths?

Answers

if you have 5 pieces of something you split it up into 2 for each and then slip the last one into two.

Final answer:

Three people can share fifths by dividing one pie into five slices and each taking three, or dividing three pies into fifteen slices and each person getting one slice from each pie. Both methods ensure each person receives three-fifths of a pie.

Explanation:

Two ways that three people can share fifths involve division and allocation of pie (or any other divisible whole). One way is to take a single pie, divide it into five equal slices, and each person takes three slices. However, since we need to divide these among three people and a pie has only five slices, we'll end up with a fraction of a slice per person. The second way is to start with three pies, divide them so that there are a total of fifteen slices (five slices per pie), and then each person gets one slice from each pie, totaling three slices per person.

Here are two arithmetic representations of the scenarios:

First method: (3 slices/person) / 5 slices = 3/5 per personSecond method: 1 slice from each of 3 pies / 5 slices per pie = 3/5 per person

Whether we are dealing with one pie or three, each person ends up with the same fraction of the total available pie: three-fifths.

Find the point on the plane 2x+5y+z=8 that is nearest to​ (2,0,1).

Answers

Answer:

(2.2, 0.5, 1.1)

Step-by-step explanation:

The parametric equation of the line normal to the plane and through point (2, 0, 1) can be written ...

... L = (2, 0, 1) + t(2, 5, 1)

We want to find the value of t (and the corresponding point) that makes L satisfy the equation of the plane.

... 2(2+2t) +5(0 +5t) +1(1+t) = 8 . . . . . put values from L in for x, y, z in plane

... 5 + 30t = 8 . . . . . simplify

... t = (8 -5)/30 = 0.1 . . . . solve for t (subtract 5, divide by 30)

For this value of t, L is ...

... (2, 0, 1) + 0.1(2, 5, 1) = (2.2, 0.5, 1.1)

Select all numbers that are irrational. 1049−−√ 3.14 π 0.5

Answers

The answer would be 10/49 and π which are irrational numbers from the definition of the irrational number.

What is an irrational number?

It is defined as the numbers in all real numbers which cannot be represented as rational numbers, in other words, the irrational number cannot be expressed in the form of p/q form.

A rational number is a sort of real number that has the form p/q and does not equal zero.

It is given that:

The numbers are:

10/49,  3.14,  π,  0.5

As we know, from the definition of the irrational, the numbers which cannot be represented as rational numbers, in other words, the irrational number cannot be expressed in the form of p/q form.

The numbers 10/49 and π are irrational numbers.

Thus, the answer would be 10/49 and π which are irrational numbers from the definition of the irrational number.

Learn more about the irrational number here:

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At an automobile factory, 1849 parts are made in 4 hours. What is the average rate at which parts are made per hour?

Answers

Just divide "1849 parts" by "4 hours:"  the average rate is 1849/4 parts/hour,

or 1849 parts/ 4 hours, or 462.25 parts/hour, or (rounded off) 462 parts/hour.

Answer:

462.25

Step-by-step explanation:

At an automobile factory, the number of parts are made in 4 hours = 1849.

We have to calculate the average rate of production per hour.

We will divide the production of parts in 4 hours by 4 to get the number of parts made per hour.

The average rate of production in one hour = [tex]\frac{1849}{4}[/tex]

                                                                         = 462.25/hour

462.25 parts are made per hour.

What produces a graph in a straight line

Answers

Linear equations in one variables shows always graph in straight line,

For ex: x = 3, y = 4, x = -1.5, y = -2/3

Also two variables linear equations with degree of 0 or 1 (Each term) shows always graph in straight line,

For ex: x + y = 5, 2x - 4y = 7 etc.

What is the volume of a sugar cube that measure 1cm on each side? what is the cross-sectional area of the cube? the total surface area?

Answers

These are important and common formulas; better learn them!

The volume of a cube of side length x is x^3.
The cross-sectional area is x^2.
The total surface area is A = 6x^2.

-20,480 , -5,120 , -1280 , -320 what goes next

Answers

- 80, -20 and so on
- 1280/4 = -320
- 320/4 = - 80
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