If the circumference of a circle is 24, and the angle measure of an arc is 120o, which is the length of the arc?

Answers

Answer 1

The best way to solve this problem is to use proportions. That said, a circle's given arc length is proportional to the angle measure of that arc. So, 120degrees out of 360degrees total is one third (1/3) of the circle. Therefore, the arc length will be one third of the circle's circumference (24 • 1/3) which is 8.

The arc length is 8.

Related Questions

The tides around Cherokee Bay range between a low of one foot to a high of 5 feet. The tide is at its lowest point when time, t, is 0 and completes a full cycle over a 24 hour period. What is the amplitude, period, and midline of a function that would model this periodic phenomenon

A. Amplitude = 4 feet; period = 24 hours; midline: y = 3

B. Amplitude = 2 feet; period = 12 hours; midline: y = 2

C. Amplitude = 2 feet; period = 24 hours; midline: y = 3

D. Amplitude = 4 feet; period = 24 hours; midline: y = 2

Answers

Answer:

its C

Step-by-step explanation:

A flat-screen television has a rectangular screen that is 29 inches high and 32 inches wide. What is the surface area of the screen?

A. 120 sq. in.
B. 60 sq. in.
C. 784 sq. in.
D. 928 sq. in.

Answers

multiply height by width

29 x 32 = 928 sq in

How to calculate ten percent of something?

Answers

convert it to a decimal, for an example say you had to find 10% of 50.
you do .10 * 50 to get 5.

A)7/25
B)24/25
C)25/7
D)25/24
PLEASE HELP ME !!

Answers

It's B since sin is opposite divided by hypotenuse, so find the hypotenuse by using pythag therom and you will get 25, divide opposite of angle C which is 24 by hypotenuse which is 25

list the sides of triangle WXY in order from smallest to largest

Answers

The answer is c. WX, XY, YW because yw is obviously the longest side because the angle is opposite is the biggest. Then the next longest is XY because the angle opposite is 51 which is larger than the other angle which would be 49.

The sides of triangle WXY can be listed from smallest to largest as YW, WX, XY, by matching the side lengths to a set of Pythagorean triplets (5, 12, and 13 cm). This corresponds to option A of the provided choices.

To list the sides of triangle WXY in order from smallest to largest, we can use the Pythagorean theorem which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

According to the given information, we have two right triangles with sides 5 cm, 12 cm, and 13 cm.

Recognizing these are Pythagorean triplets, where 5 and 12 are the legs and 13 is the hypotenuse, it indicates that the side measures 13 cm is the longest side, followed by the 12 cm side, and then the 5 cm side is the shortest.

Therefore, if we match these lengths to the sides of triangle WXY, we can list the sides from smallest to largest based on their corresponding lengths, with the assumption XY matches the 13 cm side (as it is not specified and must be inferred).

The correct listing of triangle sides from smallest to largest would be: YW, WX, XY. This correlates to option A in your list.

The probable question may be:

list the sides of triangle WXY in order from smallest to largest

A. YW, WX, XY

B. XY, YW,WX

C. WX,XY,YW

D. XY, WX,YW

In triangle $abc$, the measure of $\angle a$ is $86$ degrees. the measure of $\angle b$ is $22$ degrees more than three times the measure of $\angle c$. what is the measure, in degrees, of $\angle c$?

Answers

Given:
m∠A = 86°

Because the measure of angle B is 22 degrees more than three times the measure of angle C, therefore
m∠B = 3*m∠C + 22 (1)

The sum of the angles should be 180°, therefore
m∠A + m∠B + m∠C = 180 (2)

Note that m∠A = 86°
Substitute equation (1) for m∠B in equation (2) to obtain.
86 + (3*m∠C + 22) + m∠C = 180
86 + 3*m∠C + 22 + m∠C = 180
4*m∠C = 180 - 86 - 22 = 72
m∠C = 72/4 = 18°

Answer: m∠C = 18°

The graph of f(x) = x^2 has been shifted into the form f(x) = (x − h)^2 + k

What is the value of h?

Answers

[tex]\bf \qquad \qquad \qquad \qquad \textit{function transformations} \\ \quad \\\\ % left side templates \begin{array}{llll} f(x)=&{{ A}}({{ B}}x+{{ C}})+{{ D}} \\ \quad \\ y=&{{ A}}({{ B}}x+{{ C}})+{{ D}} \\ \quad \\ f(x)=&{{ A}}\sqrt{{{ B}}x+{{ C}}}+{{ D}} \\ \quad \\ f(x)=&{{ A}}(\mathbb{R})^{{{ B}}x+{{ C}}}+{{ D}} \\ \quad \\ f(x)=&{{ A}} sin\left({{ B }}x+{{ C}} \right)+{{ D}} \end{array}\\\\ --------------------\\\\[/tex]

[tex]\bf \bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\ \bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the y-axis}[/tex]

[tex]\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by }{{ D}}\\ \left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\ \left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{{{ B}}}[/tex]

with that template in mind, let's see, it went to the right 2 units, and then up 3 units.

that simply means, C = -2, D = 3.

Answer: h=2

hope this helps

A company is about to launch a new cell phone model. In the past, 40% of its cell phones have launched successfully. Before any cell phone is launched, the company conducts market research and receives a report predicting favorable or unfavorable sales. In the past, 70% of successful cell phones and 20% of unsuccessful cell phones received favorable reports. What is the probability that the new cell phone will receive a favorable report, given that the cell phone launch is successful?

Answers

There is a 70% chance that te phone will receive a favorable report.

Answer:

The required probability is 0.70.

Step-by-step explanation:

Let A represents the event of launching successfully, B represents the event of receiving favourable reports,

Given,

Probability of successful launching,

[tex]P(A)=40\%=\frac{40}{100}=0.40[/tex]

Also, 70% of successful cell phones are received favorable reports.

[tex]\implies P(A\cap B)=70\%\text{ of P(A)}=\frac{70\times 0.40}{100}=0.28[/tex]

Thus, by the conditional property,

The probability that the new cell phone will receive a favorable report, given that the cell phone launch is successful,

[tex]P(\frac{B}{A})=\frac{P(A\cap B)}{P(A)}=\frac{0.28}{0.40}=0.70[/tex]

How to find the distance between two points using pythagorean theorem?

Answers

a^2 + b^2 = c^2
c is the hypotenuse and is always the longest side of a triangle
a and b can be any side that isn't the hypotenuse

If one coin is flipped and then a second coin is flipped, what is the probability that both coins turn up tails? question 18 options:

Answers

first you find the probability of each coin turning up tails, then you multiply the two probabilities together:
1/2 x 1/2 = 1/4

A certain forest covers an area of 2500 km2. Suppose that each year this area decreases by 5.25%. What will the area be after 15 years?

Use the calculator provided and round your answer to the nearest square kilometer.

Answers

The area will be
2500(1-5.25/100)^15
=1113km2 (nearest square kilometer)

3y = 2x-6
x + y =8
Solve algebraically.

Answers

3y = 2x - 6 Solve one equation for a variable. I'll solve the second one for x + y = 8 y.

x + y = 8 Subtract x from both sides
y = 8 - x

Now, substitute this y value (8 - x) into the other given equation and solve for x.

3y = 2x - 6 Replace y with 8 - x
3(8 - x) = 2x - 6 Multiply 3 (8 - x)
24 - 3x = 2x - 6 Add 3x to both sides
24 = 5x - 6 Add 6 to both sides
30 = 5x Divide both sides by 5
6 = x Flip the equation to make it easier to read
x = 6

Now, use the x + y = 8 equation, replace the x with 6, and solve for y.

x + y = 8 Substitute x for 6
6 + y = 8 Subtract 6 from both sides
y = 2

Check your answers in both equations.

3y = 2x - 6 Replace x and y with 6 and 2
3(2) = 2(6) - 6 Simplify 3(2)
6 = 2(6) - 6 Simplify 2(6)
6 = 12 - 6 Subtract
6 = 6

x + y = 8 Replace x and y with 6 and 2
6 + 2 = 8 Add
8 = 8

So, the answers to your system of equations are x = 6 and y = 2 .

Which number can each term of the equation be multiplied by to eliminate the fractions before solving? 6 –3/4x +1/3 =1/2 x + 5

Answers

They can all be multiplied to have 12 as the denominator. So you would have 6 - 9/12x + 4/12 = 6/12x + 5
This works as the fractions are the same value, they are just bigger numbers.

Answer:

The number is 12.

Step-by-step explanation:

Given: [tex]6-\dfrac{3}{4}x+\dfrac{1}{3}=\dfrac{1}{2}x+5[/tex]

We need to find a number multiply to each term to get rid of fraction.

We will find LCD of denominator.

First we see the numbers at denominator

Denominators are 4,3,2

Now, we will find the LCD of 2,3, and 4

Factor of 2: 2x1

Factor of 3: 3x1

Factor of 4: 2x2x1

LCD = 2x2x3 = 12

If we multiply by 12 to each term to eliminate the fraction.

Simplest equation:

[tex]12\cdot 6-12\cdot \dfrac{3}{4}x+12\cdot \dfrac{1}{3}=12\cdot \dfrac{1}{2}x+12\cdot 5[/tex]

[tex]72-9x+4=6x+60[/tex]

Hence, The number is 12.

The regular price of a child's entry ticket to a water park is $6 less than that for an adult's. The park offers half off all entry tickets during the off-peak season. The Sandlers paid a total of $78 for 1 adult ticket and 2 child's tickets to the water park during the off-peak season. The following equation represents this situation, where x represents the regular price of an adult ticket: 78 = one-half x + (x − 6)

Answers

let the price of adult's ticket be [tex]x[/tex]
the expression for the child's ticket is [tex]x-6[/tex]

The price of adult's ticket during off-peak season is [tex] \frac{1}{2}x [/tex]
The price of child's ticket during off-peak season is [tex] \frac{1}{2}(x-6) [/tex]

The total cost paid by The Sandlers is $78
The equation is [tex]78= \frac{1}{2}x- \frac{1}{2}(2(x-6)) [/tex] = [tex] \frac{1}{2}x+(x-6) [/tex]

rearranging to solve the equation
[tex]78= \frac{1}{2}x+x-6 [/tex]
[tex]78= \frac{3x}{2} -6[/tex]
[tex]78+6= \frac{3x}{2} [/tex]
[tex](84)(2)=3x[/tex]
[tex] \frac{168}{3} =x[/tex]
[tex]x=56[/tex]

The price of one adult's ticket is $56 (normal price) and the price of one child's ticket is $50

What is the value of x in the isosceles trapezoid below

Answers

Opposite angles of an isosceles trapezoid add up to 180.
(That graphic is very blurry. I hope I can read it correctly.)
14x + 3x + 10 = 180
17x = 170
x = 10

Answer:

X=10

Step-by-step explanation:

In order to solve this problem you just have to remember that in rectangles and trapezoids opposite angles are suplemmentary, in this case you can equal those to 180º, your equation would be:

[tex]14x+3x+10=180\\17x+10=180\\17x=180-10\\[/tex]

[tex]17x=170[/tex]

[tex]x=\frac{170}{17}[/tex]

[tex]x=10[/tex]

So the answer is X equals to 10.

How many boys are in a class of thirty-five student if the girls outnumber boys by five

Answers

15 Boys because 35-5 is 30 then divide 30 by 2 to get 15

There are total 35 students in the classroom. If the number of girls is 5 more than the number of boys, then the number of boys in the class is 15.

What is fraction?

An object or total number of some objects can be fractionated into two more fractions where the sum of these fractions equals to the total number. Let s be the total number of pearls in a glass. Let x be the number of white pearls and y be that of black pearls in it.

then s = x +y.

It is given that, the total number of students in the class is 35. The number of girls outnumber boys by 5. Let the number of boys be x then the number of girls will be x +5.

Now, the total number of students is the sum of number of boys and girls.

x + (x +5) = 35

2x + 5 = 35

2x = 35 - 5 = 30

x = 30/2 = 15.

Therefore, the number of boys is 15 and the number of girls is 20.

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The total cost to rent a row boat is $16 times the number of hours the boat is used. write an equation to model this situation if c = total cost and h = number of hours.answers

Answers

The equation is as follows

c = 16h

Last year Jill was 5.1 feet tall she grew 8% taller in 1 year how tall is she know

Answers

.051x8 which is .408 +5.1 = 5.508

You have to figure out what 8% of 5.1 is. 8% has to be written as .08, the word "of" means to multiply, and the word "is" means equals. So "what is 8% of 5.1" can be written in equation form like this: x = .08(5.1). This will tell you how much she grew; add it to the 5.1 she was originally and you'll find out how tall she is now. x = .408 Add that to 5.1 to see that she is 5.508 feet tall now.

If 20 is 20% of 20% of an integer what is that integer

Answers

n(20/100)(20/100)=20

400n/10000=20

400n=200000

n=500

the integer is 500 because 20 % of 500 is 100 and 20% of 100 is 20

what percentage is $7,360 of $78,000

Answers

I'd say 7.360 / 78.000 * 100 = 9,4359 %

divide 7360 by 78000

7360/78000 = 0.943589

= 9.44%

Write the product as a trinomial.(k – 1)(k – 4)

Answers

(k - 1)(k - 4)

Use FOIL to solve this.

First
k * k
Outer
k * -4
Inner
-1 * k
Last
-1 * -4

k^2 - 4k - 1k + 4

k^2 - 5k + 4 is the trinomial.

Every minute, the first letter of each word is moved to the other end of the word. After how many minutes will the original sentence first reappear?

Answers

Well you didn't give me a sentence, but if you'd like to find out how to get the answer, just find the least common multiple of the words, meaning however many letters there are in a word count those, do that for the whole sentence and you get your answer.

Final answer:

To find the time it takes for the original sentence to reappear, we need to find the least common multiple (LCM) of the cycle counts of each word. The LCM of the cycle counts gives us the number of minutes for the original sentence to reappear.

Explanation:

To find the number of minutes it takes for the original sentence to reappear, we need to analyze the pattern of the letters in a word. Let's take an example sentence: 'The quick brown fox jumps over the lazy dog.' After the first minute, the sentence becomes 'ehT uickq norwb foxp smuj revo eht yzal god.' Notice that each word has its first letter moved to the end. So, each word becomes a cyclic permutation of itself, with a period equal to the number of letters in the word.

Now, let's count the number of cycles for each word in the original sentence. 'The' has one cycle, 'quick' has five cycles, 'brown' has five cycles, 'fox' has three cycles, 'jumps' has five cycles, 'over' has four cycles, 'the' has one cycle, 'lazy' has four cycles, and 'dog' has three cycles. To find the time it takes for the original sentence to reappear, we need to find the least common multiple (LCM) of these cycle counts. The LCM of 1, 5, 5, 3, 5, 4, 1, 4, and 3 is 60.

Therefore, it will take 60 minutes for the original sentence to first reappear.

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5. Reflection: Marissa wants to describe the relationship between the scale factor and perimeter of an image and its pre-image and between the scale factor and area of an image and its pre-image. What should she say about the relationship between the scale factor and perimeter of an image and its pre-image? What should she say about the relationship between the scale factor and area of an image and its pre-image? Support her statements using scale factors of 5 and 6.

Answers

Relationship between the scale factor and perimeter of an image and its pre-image?

Scale factor = k

Pre-image lengths: a, b => perimeter = 2a + 2b

Image lenghts: ka, kb => perimeter = 2ka + 2 kb = k (2a + 2b) = 2 * preimage permeter.

=> She has to say that the perimeter of the image is the perimeter of the preimage times the same scale factor.

What should she say about the relationship between the scale factor and area of an image and its pre-image?

area of the pre-image = ab

are of the image = (ka)(kb) = k^2 (ab)

=> The area of the image is the area of the preimage times the square of the scale factor.

Support her statements using scale factors of 5 and 6.

Scale factor 5

length of the pre-image = 3 x 4 => perimeter = 2 (3 + 4) = 2(7) = 14

length of the image = 3*5 x 4*5 = 15 x 20 => perimeter = 2 (15 + 20) = 2 (35) = 70

=> 14 * 5 = 70 which shows the prediction

area of the pre-image = 3 * 4 = 12

area of the image = 15 * 20 = 300

12 * (5^2) = 12*25 = 300 which is the value predicted.

Now you can do the same using scale factor 6.

The blueprint for landscaping a yard has a scale of 1/2" to 1 foot. If the blueprint is a rectangle 18 inches by22 inches, what are the dimensions of the yard? If u find the answer please explain how you got it that would be very helpful

Answers

Set it up as a ratio with bp on top for blueprint and actual on the bottom for the actual measurements of the yard. I'll do 2 of them since there are 2 dimensions they are looking for. Set it up like this:
[tex] \frac{bp}{actual} : \frac{.5"}{1ft} = \frac{18"}{xft} [/tex]
Now cross multiply to get the first dimension: .5x = 18 and x = 36. Do the same with the other dimension of the yard:
[tex] \frac{bp}{actual}: \frac{.5"}{1ft} = \frac{22"}{xft} [/tex]
and cross multiply to solve for that dimension: .5x = 22 and x = 44. So the dimensions of the actual yard are 36x44 ft

Sam studied guinea pigs for his science fair project. He found that the amount of weight the guinea pigs gained varied directly with the number of calories they consumed. The guinea pigs gained 1 ounce for every additional 218 calories in their diet. How many additional ounces would they gain if their diet was increased by 1,090 calories? Let W represent the weight in ounces, and let C represent the number of calories.

Answers

From the given above, we can formulate the equation:

W = C / 218

By substituting the given values:

W = 1090 calories / (218 calories / 1 ounce)

W = 5 ounce

Therefore the guinea pigs will gain additional 5 ounce if the diet was increased by 1090 calories.

In how many ways can we seat 6 people around a round table if Fred and Gwen insist on sitting opposite each other? (Two seatings are considered equivalent if one is a rotation of the other.)

Answers

Make a picture of the problem.

Fred and Gwen are seated opposite each other, and we name the 4 remaining seats 1, 2, 3, 4, starting from the right of Fred.

There are 4 options for seat 1,

then 3 for the seat 2, after one is seated in the 1.st seat

2 options for the seat 3,

and 1 for the seat 4.

That is, the 4 friends can sit in 4*3*2*1=24 different ways.

Answer: 24

Answer:

Step-by-step explanation:

Find the 3rd term of (a-3b)^6

Answers

The answer for this question would be: -540a^3 b^3

Duncan shares 20 percent of all of his sales commissions with his personal assistant. If Duncan earns x dollars in commissions and gives his assistant y dollars, which equation correctly models this situation? mc011-1.jpg

Answers

x*0.2=y
if x = the total commissions, and 20% goes to his assistant, you would need to multiply your total sales commissions by 0.2 to find 20%, and that would be the total given to the assistant.
Hope this helps

Answer:

X * (0.2)y

Step-by-step explanation:

PLEASE HELP IM IN A HURRY

Answers

It's 48 cube feet I can show you how, just ask

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 4 - 3 sin θ

Answers

see picture, it is symmetrical about the Y axis

Answer:

Symmetry about y-axis

Step-by-step explanation:

We are given that

[tex]r=4-3sin\theta[/tex]

When the graph is symmetric about x- axis then the point (x,y) change in to (x,-y) and the function remain same.

The point[tex] (r,\theta,)[/tex] is replaced by [tex]( r,-\theta)[/tex]

Substitute the value then we get

[tex]r=4-3 sin(-\theta) [/tex]

[tex]r=4+3sin\theta[/tex] ([tex]sin(-\theta)=-sin\theta)[/tex]

The value of function changes .Hence , the function is not symmetric about x- axis.

When the function is symmetric about y-axis then the point [tex](r,\theta) [/tex] change into point [tex](r,\pi-\theta)[/tex] and function remain same

Substitute the value

[tex]r=4-3sin(\pi-\theta)[/tex]

[tex]r=4-3 sin\theta[/tex] ([tex]sin(\pi-\theta)=sin\theta[/tex])

The value of function does not change when point change ,Hence, the function is symmetric about y- axis.

When the graph is symmetric about origin then the point [tex](\theta,r)[/tex] change into point[tex](r,\pi+\theta)[/tex] and the value of function remain same.

Substitute the value then we get

[tex]r=4-3sin(\pi+\theta)[/tex]

[tex]r=4+3sin\theta [/tex]

Hence, the graph has symmetry about y-axis .

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Joyce is trying to solve the equation y = x2 8x + 7 using the quadratic formula. She has made an error in one of the steps below. Find the step where Joyce went wrong. (1 point)Step 1: x equals negative 8 plus or minus the square root of the quantity eight squared minus four times one times seven, end quantity, all over two times one.Step 2: x equals negative 8 plus or minus the square root of sixty-four minus twenty-eight all over two times one.Step 3: x equals negative 8 plus or minus the square root of thirty-six all over two times one.Step 4: x equals negative 8 plus or minus six all over two.Step 1Step 2Step 3Step 4 When an aqueous solution of lead(ii) nitrate is mixed with an aqueous solution of sodium iodide, an aqueous solution of sodium nitrate and a yellow solid, lead iodide, are formed? what are the six purposes of the American system of government Read the sentence.The waiter placated the angry customer by taking his meal off the bill and bringing him a free dessert.What does placated mean?Frustratedcalmed downEnragedAmazed How many known species of vertebrates are there? Use the Distributive Property to simplify each expression: 6(a + 10)(5 + w)514(4f - 8)2.1(5w -15)0(3.7x - 4.21)-(-m + n + 1) -10-2v Suppose the line of best fit is being found for some data points that have an r-value of 0.657. If the standard deviation of the x-coordinates is 2.445, and the standard deviation of the y-coordinates is 9.902, what is the slope of the line to three decimal places? "the conception and planning of an offense by an officer, and his procurement of its commission by one who would not have perpetrated it except for the trickery, persuasion, or fraud of the officer" best describes which term? Which of these civilizations laid the culture foundation for the civilizations in the Andes region A) Olmec B) Zapotec C)teotihuacan D)chavin If f(x)=2x^2sqrt(x-2), complete the following statement f(6) Imagine that you're standing in a large room when a loud noise is made. You begin hearing a series of echoes. Which characteristic of sound best explains what just happened? Susan invests 2times as much money at 8%as she does at 4%. If her total interest after 1year is $800, how much does she have invested at each rate? C: -5/2 D: 5/2 help please With the louisiana purchase:a. the country was bankrupted.b. louisiana entered the union as the eighteenth state.c. france gained control of new orleans.d. the size of the nation was doubled. Please help me ASAP. David had a coupon for the grocery store. He graphed on the x-axis what his total bill would be if he didnt use the coupon and graphed on the y-axis what his total bill would be if he used the coupon.Based on the information in the graph, if Davids bill came to $66 after the coupon was applied, how much would his bill have been if he hadnt used the coupon?a.$64b. $65c. $67d. $68 What is the meaning of "Room to haggle" in negotiation?I only know just what haggle means. but it is a phrases A pudding recipe makes 4 1/2 cups of pudding. How many 1/3 cup servings does this equal? Which scientific development has shown that some persons sentenced to death actually did not commit the crime? Consider a line l with positive x- and y- intercepts. Suppose l makes an angle of with the positive x- axis. What is the slope of l in terms of theta? Steam Workshop Downloader