if x=15 degrees and the measure of Arc YZ is 3 centimeters, what is the circumference of the circle?

A- 24
B- 45
C- 60
D- 72

Answers

Answer 1
An arc length is just a fraction of the circumference of the entire circle. So we need to find the fraction of the circle made by the central angle we know, then find the circumference of the total circle made by the radius we know. Then we just multiply them together. Let’s try an example where our central angle is 72° and our radius is 3 meters.

First, let’s find the fraction of the circle’s circumference our arc length is. The whole circle is 360°. Let’s say our part is 72°. We make a fraction by placing the part over the whole and we get 72360, which reduces to 15. So, our arc length will be one fifth of the total circumference. Now we just need to find that circumference.

The circumference can be found by the formula C = πd when we know the diameter and C = 2πr when we know the radius, as we do here. Plugging our radius of 3 into the formula, we get C = 6π meters or approximately 18.8495559 m.

Now we multiply that by 15 (or its decimal equivalent 0.2) to find our arc length, which is 3.769911 meters. Note that our units will always be a length.

How to Find the Sector Area

Just as every arc length is a fraction of the circumference of the whole circle, the sector area is simply a fraction of the area of the circle. So to find the sector area, we need to find the fraction of the circle made by the central angle we know, then find the area of the total circle made by the radius we know. Then we just multiply them together. Let’s try an example where our central angle is 72° and our radius is 3 meters.

First, let’s find the fraction of the circle’s area our sector takes up. The whole circle is 360°. Our part is 72°. We make a fraction by placing the part over the whole and we get 72360, which reduces to 15. So, our sector area will be one fifth of the total area of the circle. Now we just need to find that area.

The area can be found by the formula A = πr2. Plugging our radius of 3 into the formula we get A = 9π meters squared or approximately 28.27433388 m2.

Now we multiply that by 15 (or its decimal equivalent 0.2) to find our sector area, which is 5.654867 meters squared. Note that our answer will always be an area so the units will always be squared.

Answer 2

The circumference of the circle is 72cm.

Arc length formula

[tex]Arc length = 2\pi r(\frac{x}{360} )[/tex]

where

r is the radius of the circle

x is the central angle of the arc

Circumference of the circle

Circumference of the circle or perimeter of the circle is the measurement of the boundary of the circle. It is calculated as

circumference of the circle = 2πr

According to the given question we have

central angle of the arc, x = 15 degrees

Arc length = 3 cm

Let r be the radius of the given circle.

Then,

Arc length = 2πr[tex](\frac{15}{360} )[/tex]

⇒ 3 ×[tex]\frac{360}{15}[/tex]  = circumference of the circle   ( circumference or circle =2πr)

circumference of the circle = 72 cm

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Related Questions

How do I draw the circle correctly to solve the problem?

Answers

Answer:

2/4N

Step-by-step explanation:

I don't know if it's correct

-6/10-2/10 simply this equation

Answers

Answer: hii

The Answer is = -4/5

Step-by-step explanation:

Combine the fractions by finding a common denominator.

Hopefully this helps you

- Matthew

Of the marbles in a bag, 3 are yellow, 2 are red, and 2 are blue. Sandra will randomly choose one marble from the bag.The probability that Sandra will choose a blue marble at random is . It is that Sandra will randomly choose a blue marble.

Answers

Answer:

2/7 or 29%

Step-by-step explanation:

you add all the numbers than you put the blue marble on top and there it is.

Answer:

2/7

Step-by-step explanation:

Hello there.

1. First, you would add all the numbers up to get the total.

3 + 2 + 2 = 7 total marbles

2. Of those 7 marbles, 2 are blue. This would be 2/7 in fraction form.

Hence, there is a 2 in 7 chance that Sandra will choose a blue marble from the bag.

Hope this helps.

- Angelo

7 * as much as the sum of1/3+ 4/5

Answers

Answer:

First you add 1/3 and 4/5

To add 2 fractions, they need to have the same denominator. Since 3 and 5 don't have a common factor, so you multiply 1/3 by 5, and 4/5 by 3, so you get: 5/15 +12/15

Now, the two fractions got the same denominator, and you can add them by adding the numerators over the same denominator. (You don't add denominators in addition) so you get:

5+12/15 which is 17/15

That's the sum of 1/3 + 4/5.

Now, they want the sum of the 2 fractions 7 times. So you multiply 17/15 by 7. And as you know, 7 = 7/1. So you get:

In multiplication no need to have the same denominator. You multiply nominators by nominators and denominators by denominators. So you get:

17*7/15*1  and you get 119/5

Since 119 and 15 don't have a common factor, so they can't be simplified.

So, the answer is 119/15.

Scientific knowledge allows new technologies to be built, and those technologies, in turn, impact society at many levels.

options:
True
False

Answers

Answer:

true

Step-by-step explanation:

A small tank has a cylindrical shape. It has a radius of 15 inches and a height of 48 inches. A can of spray paint will cover 720 square inches. How many cans of paint must be bought to completely cover the tank with one coat of paint?

HELP FAST WILL GIVE LOTS OF POINTS

Answers

Answer:

c)  9

Step-by-step explanation:

[tex]\textsf{Surface area of a cylinder}=2\pi r^2+2\pi rh[/tex]

(where r is the radius and h is the height)

Given:

r = 15 inh = 48 in

Substitute given values into the equation to find the surface area:

[tex]\begin{aligned}\implies \textsf{Surface area} & =2\pi (15)^2+2\pi (15)(48)\\ & =1890 \pi\: \sf in^2\end{aligned}[/tex]

To calculate the number of cans of paint to be bought, divide the surface area by the area one can of paint will cover:

[tex]\implies \dfrac{1890 \pi}{720}=8.246680716...[/tex]

We need to round this number up, as rounding down will mean we will not have quite enough paint to cover the surface area of the cylinder.

Therefore, the numnber of cans of paint that must be bought to completely cover the tank with one coat of paint is 9.

Which graph represents 3x - 2y > 4?​

Answers

Answer:

It should somewhat look like the graph below...

Hope it helps!

26 × (-5 + 3)= step by step

Answers

Hello ~

My name is lrxdscent, and I will be answering your question today! :D

Let's go by step-by-step ~

→ Answer :-

[tex]\sf{= -52x}[/tex]

→  Explanation :-

[tex]\sf{26x \: (-5 \: + \: 3)[/tex]

[tex]\sf{Add \: the \: numbers: \: -5 \: + \: 3 = -2}[/tex]

[tex]\sf{= 26x \: (-2)[/tex]

[tex]\sf{Multiply \: the \: numbers: \: 26 \: (-2) \: = \: -52}[/tex]

[tex]\sf{= -52x}[/tex]

Hope It Helps! ~

~ Learn With Lrxdscent ~

[tex]\underline{Answer :}[/tex]

ɪ ʀ x ᴅ ꜱ ᴄ ᴇ ɴ ᴛ

-52x is the answer to the question

True or False
A solution to 8 = -x + 10 is 2

Answers

Answer:

[tex]\huge\underline{Answer - }[/tex]

[tex]\bold{8 = - x + 10} \\ \\ \bold{\implies \: - x = 8 - 10} \\ \\ \bold{\implies \: \cancel - x = \cancel - 2 }\\ \\ \bold{\implies x\: = 2}[/tex]

hence , the given statement is true !

hope helpful ~

Answer:

True

Step-by-step explanation:

So, Lets find out if the solution is true or not, So first let us find the value of x.

⇒ 8 = -x + 10

We can rewrite the equation as,

⇒ -x + 10 = 8

Subtracting 10 from both sides we get :

⇒ -x + 10 – 10 = 8 – 10

⇒ -x = -2

Multiplying both sides by (-1) :

⇒ -1(-x) = -1(-2)

x = 2

Therefore,

The statement "A solution to 8 = -x + 10 is 2" is true

A dance studio teaches students a contemporary dance form. it is observed that the probability of students from this studio becoming dance teachers is 0.69. an event management company wants to use this studio for a show. they decide to observe it for a year before making the deal. they enroll 120 students of their own in this studio and decide that once 75 of them get jobs as dance teachers, they will sign the contract with them. what is the probability that the event management company will sign the contract with the dance studio? a. 0.076 b. 0.053 c. 0.024 d. 0.924 e. 0.947

Answers

The probability that the event management company will sign the contract with the dance studio is; c. 0.024

How to solve binomial probability?

The general formula for binomial Probability is;

P(X = x) = ⁿCₓ * pˣ * (1 - p)⁽ⁿ ⁻ ˣ⁾

From the question, we want to find;

P(X = 75)

where;

Sample size; n = 120 and probability of success; p = 0.69

Thus, we have;

P(X = 75) = ¹²⁰C₇₅ * 0.69⁷⁵ * (1 - 0.69)⁽¹²⁰ ⁻ ⁷⁵⁾

P(X = 75) = 0.024

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What is the value of y in the relative frequency table? round the answer to the nearest percent. 12% 27% 46% 52%

Answers

The relative frequency table is a two way table, and the value of y in the relative frequency table is 27%

How to determine the value of y?

From the complete question, we have the following row

y    24%   51%

Express the row as an equation

y + 24% = 51%

Subtract 24% from both sides

y + 24% - 24%= 51% - 24%

Evaluate the difference

y = 27%

Hence, the value of y in the relative frequency table is 27%

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Solve this quadratic equation using the quadratic formula.

3x 2 + 5x + 1 = 0

Answers

Solution

x=\frac{-5 \pm \sqrt{13}}{6}

HELP PLEASE!!

Lowes sold garden gnomes for $28. 99 each a customer signed up for a free membership card and received a 5% discount off the price. Sales tax of 5% was applied after the discount what was the final price of the garden gnome

Answers

Answer:

$28.92

Step-by-step explanation:

Find the discount

28.99 × 0.05 = 1.4495

28.99-1.4495 = 27.5405

Calculate the tax of the discounted item

27.5405 x 0.05 = 1.377

27.5405 + 1.377 = 28.9175

what is the y-value of the solution to the system of equations shown below? 5x+4y=12 -5x-2y=-16
A. -4
B. -2
C. 2
D. 4​

Answers

Answer:

B. -2

Step-by-step explanation:

b. -2 i’m pretty sure but i don’t know

I don't understand how to do this section of this worksheet. Can someone help me understand how to get the answer? I have a test tomorrow and I can't fail it.

Answers

Answer:

see explanation

Step-by-step explanation:

There are 4 sections on the spinner so each option is 1/4

1) 4 Ds = 1/4 × 1/4 × 1/4 × 1/4 × 3/4 × 3/4 = 9/4096

the other two spins can be A, B, or C (3/4)

2) 2As = 1/4 × 1/4 × 3/4 × 3/4 × 3/4 × 3/4

the other two spins can be B, C, or D (3/4)

3) 2As = 1/4 × 1/4 = 1/16    OR means add

   3Bs = 1/4 × 1/4 × 1/4 = 1/64

1/16 + 1/64 = 5/64

4) at least 4 Cs = 1/4 × 1/4 × 1/4 × 1/4 =1/256

For the polyhedron, use Euler's Formula to find the missing number.
faces:
edges: 14
vertices: 9
The number of faces is

Answers

If the number of the edges of the polyhedron is 14 and the vertices are 9. Then the number of the faces of the polyhedron is 7.

What is a polyhedron?

A polyhedron is a solid made composed of polygons in three dimensions. It has vertices, flat faces, and straight edges.

We know the Euler's formula

F + V - E = 2,

where, F = number of faces, V = number of vertices, and E = number of edges

Edges: 14

Vertices: 9

F + 9 - 14 = 2

            F = 14 + 2 - 9

            F = 16 - 9

            F = 7

Then the number of the faces of the polyhedron is 7.

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100 points brainliest help asap
1 choice- left or right
2 choice- mean or median
3 choice- iqr or range the iqr
PICK ONE FROM EACH CHOICE

Answers

Answer: (not sure)

right

median

range the iqr

(x-2y)^5 using pascal triangle

Answers

Step-by-step explanation:

I edit this on computer, because I have class later

A rectangle is 4 times as long as it is wide. If the area of the rectangle is 1600cm^2, what are the dimensions?

Answers

Answer:

dimensions 20cm x80cm

Step-by-step explanation:

length is 4W of 1W,

LxW=area of 1600

4W x 1W = 1600cm2

divide both by 4 to isolate W

W=400cm2

square root of 400=20

replace W with 20 into equation 4Wx1W

4x20=80

1x20=20

80 is 4x the width of 20

7x+42 what is x
please i need help

Answers

Answer:

x = 6

Step-by-step explanation:

7x = 42

Divide both sides by 7

x = 6

Answer: 49x I am pretty sure

Step-by-step explanation: you take 7 + 42= 49 then you put the x there

Then your answer should be correct please dont be mad if its not correct!!

Tonja is a married taxpayer who claims 2 withholding allowances. She earns
$600 per week, and pays $150 per week in childcare expenses. How much will
she save in federal income and FICA taxes if she has her childcare expenses
deducted from her check before taxes?

Answers

The amount that Tonja will save in Federal Income and FICA Taxes if she has her childcare expenses deducted from her check before taxes is: $26.17

What is Federal Income Tax?

Federal Income Tax is a tax that is levied by the Federal Government and most states in the United States of America. It comprises of 7 tax rates.

What is FICA Tax?

FICA Tax is a Federal Insurance Contributions Act Tax. This tax is levied on every payroll of employees to fund Social Security and Medicare programs. This is divided into two parts:

Social Security Tax which is 6.2% and Medicare Tax which is 1.45%. The total is 7.65%

How to calculate Tonja's Tax before deduction

Federal Tax rate first level is 10% on 0$ - $19,900.

1) Hence, the first tax is 10% on $600, which is $60

2) The next tax is FICA. This is applied to the Gross Pay of $600.

Applying both taxed under FICA we have 7.65% * $600 = $45.9

Total Tax before a deduction is:

$60 + $45.9 = $105.6

The Tax Payable if childcare expenses is deducted first will be:

10% on $450     = $45

7.65% on $450 = $34.43

Total                   = $79.43

Hence the tax savings will be:

105.6 - 79.43 = $26.17

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Which block has a volume of 90 cm3?

Answers

Answer:

The volume of c. figure is equal to 90 cm³

Step-by-step explanation:

These are the cuboids

The volume of a cuboid = b×h

A. 2×6×5

=> 60 cm³

B. 8×2×4

=> 64 cm³

C. 5×6×3

=> 90 cm³

D. 3×7×2

=> 42 cm ³

so, the volume of c. cuboid is equal to 90 cm ³

who can please do my math iready!!!! im level E pls i need help. i don’t understand it.

Answers

Answer:

sure

Step-by-step explanation:

Simplify the expression:
10x+10x2+2x

Answers

Answer:

[tex]10x + 10x^{2} + 2x\\= 10x + 2x + 10x^{2}\\= 12x + 10x^{2}\\= \boxed{2x(6 + 5x)}[/tex]

Given Expression,

10x + 10x² + 2x

We can also write it as,

10x² + 10x + 2x

Now, Combining the like terms,

The like terms are 10x and 2x so,

10x² + 12x

We simplified the expression.

If you want it to factorise it,

⇒10x² + 12x

⇒ 2x(5x + 6)

This is required factorised expression

The distance formula will be a key component in this unit.
O True
O False

Answers

True, I use it all the time in algebra and geometry. I assume that’s what you’re taking.

Please help<3 due in 30 mins !!!!!!!!

Answers

Answer and Explanation:

Sara's sample is biased, she's only taking people that naturally would pull out their phones as they are waiting for a bus to arrive.

Sara's claim is not valid, the sample is too small and biased to be applied to her whole town.

The interior of a building is in the form of cylinder of diameter 10m and height 8m, surmounted by a cone whose vertical angle is a right angle.
Then what will be the area of the surface and the volume of the building?​

Answers

Answer:

Surface Area = 399.4 m²Volume = 1675.5 m³

Step-by-step explanation:

Lateral Surface Area of the Cylindrical Part

2πrh2 x π x 5 x 880 x π251.3 m²

Slant height of cone

√r² + h²√25 + 64√899.43 m

Surface Area of Conical Portion

πrlπ x 5 x 9.4347.15 x π148.1 m²

Total Surface Area :

251.3 + 148.1399.4 m²

Volume

V = πr²h + 1/3πr²hV = πr²h (1 + 1/3)V = π x 25 x 8 x (4/3)V = π x 1600/3V = 1675.5 m³

Hope it helps.

If you have any query, feel free to ask.

Please help!! Will mark brainlyest.

Answers

Answer:

(-7,-3)

Step-by-step explanation:

explained in graph :)

please help me !!!!!!!!

Answers

Answer:

the fourth option

Step-by-step explanation:

due to the range and median the range is 4 to 17 and the median is 10

A softball has a volume of 125/6 pie cubic inches. Find the radius of the softball

Answers

The radius of the softball is 2.5 inches

The volume of a sphere is given by

V = 4/3 pi r^3

We know the volume is 125/6 pi

Substituting in

125/6 pi = 4/3 pi r^3

Divide by pi on each side

125/6 pi/ pi = 4/3 pi/ pi r^3

125/6 = 4/3  r^3

Multiply by 3/4 on each side to isolate r

125/6 * 3/4 = 3/4 *4/3  r^3

125/8 = r^3

Take the cube root on each side

(125/8) ^ 1/3 = (r^3) ^ 1/3

5/2 = r

2.5 =r

The radius of the softball is 2.5 inches

Answer:

[tex]\huge\boxed{\sf r = 2.5 \ in.}[/tex]

Step-by-step explanation:

[tex]\sf Volume \ of \ sphere = \frac{4}{3} \pi r^3\\\\Where \ volume = \frac{125 \pi }{6 } \ in.^3\\\\Put \ in \ the \ above\ formula:\\\\\frac{125 \pi}{6} = \frac{4}{3} \pi r^3\\\\Cancel \ pi\\\\\frac{125}{6} = \frac{4}{3} r^3\\\\20.83 = 1.33 r^3\\\\Divide \ 1.33 \ to \ both \ sides\\\\20.83/1.33 = r^3\\\\15.625 =r^3\\\\Take \ cube \ root \ on \ both \ sides\\\\\sqrt[3]{15.625} = \sqrt[3]{r} \\\\2.5 = r\\\\[/tex]

[tex]\sf r = 2.5 \ in.\\\\\rule[225]{225}{2}[/tex]

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