A spinner used in a board game is divided into 8 equally sized sectors. Three of these sectors indicate that the player should move his token forward on the board, two of these sectors indicate that the player should move his token backward, and the remaining sectors award the player bonus points but do not move his token on the board. The total area of the sectors that do not allow the player to move his token is 35.9 inches squared. What is the radius of the spinner

Answers

Answer 1

Answer:

5.52 inch

Step-by-step explanation:

Recall :

Area of Sector : θ/ 360 * πr²

Sectors that do not allow movement : (8-3-2) = 3

Total sectors = 8

θ/ 360 = 3/8 ; Area = 35.9

Radius = r

35.9 = 3/8 * π * r²

35.9 / (3/8 * π) = r²

30.472866 = r²

r = √30.472866

r = 5.52 inch

Answer 2

The radius of the spinner is 5.520 inch whose  [tex]\frac{3}{8}[/tex]  sector area is 35.9 inches square.

It is given that the spinner used in a board game is divided into 8 equally sized sectors. three sectors indicate that the player should move his token forward on the board, two sectors indicate that the player should move his token backward, and the remaining sectors award the player bonus points but do not move his token on the board and its area of the sector is 35.9 inches square.

It is required to find the radius of the spinner.

What is the area of the sector?

The region enclosed by the two radii of a circle and the arc is known as a sector's area. In other words sector area is a portion of the circle's area.

We know the formula of sector area (A):

[tex]\rm A= \frac{\theta}{360 \°} \pi r^2[/tex]    Where 'r' is the radius of the circle and [tex]\rm \theta[/tex] is in degree

The remaining sectors = ( Total sectors - Three sectors - Two sectors)

= ( 8 - 3 - 2) ⇒ 3 sectors indicate the player do not move his token

Total sector = 8

[tex]\rm \frac{\theta }{360 \° } = \frac{3}{8} \ when \ A = 35.9 \ inches^2[/tex]

Putting these values in the above formula, we get:

[tex]\rm 35.9 = \frac{3}{8} \pi r^2\\\rm 35.9\times 8 = 3\pi r^2\\\rm 287.2 = 3\pi r^2\\\\\rm \frac{287.2}{3} = \pi r^2\\\\\rm 95.733= \pi r^2\\\rm 30.4728 = r^2[/tex]Where [tex]\rm \pi[/tex] = 3.14159

[tex]\sqrt{30.4728} = r\\\rm 5.520= r \\\rm or = 5.520 \ inch[/tex]

Thus, the radius of the spinner is 5.520 inch.

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Related Questions

Solve the system of equations below by graphing each line on the coordinate plane provided. Then place a point where the solution of the system occurs. 3x + 2y = 8 x + 2y = 4​

Answers

Point Form:
(2,1)
Equation Form:
x=2 y=1

i need help fast!! and i’m almost failing

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Answer:

well I would love to help-where is the pic...?

Solve for the variable x.
X=25
X=10
X=-25
X=11.66667

Answers

Answer:

Its 10 I think i could be wrong.

Step-by-step explanation:


The area of a rectangle is x^2-4/2x in.^2 and its length is (x+2)^2/2 in. What is the width in inches?

A. x(x+2)/x-2
B. x+2/x(x+2)
C. x-2/x(x-2)
D. x-2/x(x+2)

Answers

Is b I’m sure check

The money used in Tajikistan is called the Somoni. The exchange rate is $7 = 22 Somoni. Find how many dollars you would receive if you exchanged 66 Somoni.

A: $207.43
B: $21
C: $16
D: $18

Answers

Answer:

B: $21

Step-by-step explanation:

it’s 21$ because 66/22 = 3
and 7 x 3 = 21

The rectangular floor of a classroom is 20 feet in length and 32 feet in width. A scale
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i cant find the answer anywhere else lol

Answers

25.6 square inches

20 divided by 5 is 4

32 divied by 5 is 6.4

Multiply them and get 25.6

A doctor took a random sample of n=6n=6n, equals, 6 patients to see how long they each spent in the waiting room. She wants to construct a ttt interval for the mean waiting time with 99\%99%99, percent confidence. The times in the sample were roughly symmetric with a mean of \bar x=8.5 x ˉ =8.5x, with, \bar, on top, equals, 8, point, 5 minutes and a standard deviation of s_x=2.8s x ​ =2.8s, start subscript, x, end subscript, equals, 2, point, 8 minutes. What critical value t^*t ∗ t, start superscript, times, end superscript should she use? Choose 1 answer:

Answers

Answer:

4.032

Step-by-step explanation

Khan Academy

To find the critical value t^*t ∗t, start superscript, times, end superscript for a t-interval with 99% confidence and n=6, we need to use a t-distribution with degrees of freedom df=n−1=6−1=5.

What is t-distribution table?

A t-distribution table is a table that lists critical values for the t-distribution.

The t-distribution is a probability distribution that is used in hypothesis testing when the sample size is small or when the population standard deviation is unknown. The table lists critical values for various levels of significance and degrees of freedom.

Using a t-distribution table or calculator with 5 degrees of freedom and a 99% confidence level, we find the critical value t^*t ∗t to be approximately 4.032.

Therefore, the doctor should use t^*t ∗t = 4.032 for constructing the t-interval for the mean waiting time.

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1) how many 1/4's are in 2/3?
2) how many 5/12's are in 1/2?​

Answers

Answer:

1) how many 1/4's are in 2/3 = 8/3

2) how many 5/12's are in 1/2?=6/5

Step-by-step explanation:

The amount of money in a savings account is shown as a function of the number of days spent shopping. After 3 days of shopping how much money is left in the savings account.

A. 80$
B. 70$
C. 90$
D. None of the above ​

Answers

anwser is a

Step-by-step explanation:

i need HELP !!!!!!!!!!!!!!!!

Answers

Answer:

I think the solution is (p,q)=(-2,-5)

Find m 2x
(3x – 10)
D
E
B
mABC=
mZCBD-

Answers

Answer:

x--5

Step-by-step explanation:

2x+ x

9+10=?
A. 5
B. 14
C. 21
D. 19
Please help

Answers

Answer:

19

Step-by-step explanation:

is this a joke?

Option D. [tex]19.[/tex]

Step-by-step explanation:

[tex]10 + 9 = 19.[/tex]

Write a set of ordered pairs that is represented by the arrow diagram 49,13 69,32 18,22 78,57 28,57 the set of order pair is? 

Answers

Answer:

The mapping can also be represented as the set of ordered pairs: (4, 9) (5, 10) (6, 11) (7, 12). The ordered pair preserves the directional property of the relation. It is consistent with the order of points plotted on a Cartesian Plane represented by (",$). In the Arrow Diagram that follows.

Step-by-step explanation:

Dr. Porterfield a financial counselor guru informed Mr. Halpayne he needs $2,000,000 saved if he intends to retire with his wives (7 of them) and not be homeless in future. Calculate the present value Mr. Halpayne needs if he intends to retire in 20 years provided he invests in a financial plan that pays 5% interest compunded monthly.

Answers

9514 1404 393

Answer:

  $737,289

Step-by-step explanation:

The future value of an investment P invested at rate r per year compounded monthly for t years is ...

  FV = P(1 +r/12)^(12·t)

We want to find P for the given future value, so we can solve for that:

  P = FV/(1 +r/12)^(12·t) = FV(1 +r/12)^(-12·t)

  P = $2,000,000(1 +.05/12)^(-240) = $737,289

Mr. Halpayne needs a present value of $737,289 to support his retirement.

Answer this question to get marked as brainliest!!!

Answers

Answer:

22

Step-by-step explanation:

180 - 90 - 68

Answer:

22

Step-by-step explanation:


find the distance between (-1,-4) and (5,4)

Answers

Answer:

10 units

Step-by-step explanation:

√(-1-5)²+(-4-4)²

√(-6)²+(-8)

√36+64

√100

10 units

Answer:

Step-by-step explanation:

find the solution of given expression

[tex] \sqrt{365 \times 365} [/tex]

Answers

Answer:

√(365×365)=√365²=±365

HELP ! The angle measurements in the diagram are represented by the following expressions.
A= 6x – 2
B= 4x + 48
solve for x and then find the measure of a

Answers

Answer: 148

Step-by-step explanation:

Answer:

148

Step-by-step explanation:

khan

Evaluate the expression below when n = 4. If needed, answer as a fraction or a decimal.
6(n+8) - 5n

Answers

When n is equal to 4, the expression 6(n+8) - 5n evaluates to 52. This means that if we replace the variable n with 4, the expression simplifies to the constant value of 52.

To evaluate the expression 6(n+8) - 5n when n = 4, we substitute n with 4 and simplify step by step:

First, we substitute n with 4 in the expression:

6(4+8) - 5(4)

Next, we simplify the parentheses:

6(12) - 5(4)

Multiplying within the parentheses:

72 - 20

Finally, we subtract the two values:

52

As a result, the formula 6(n+8) - 5n evaluates to 52 when n is equal to 4. This indicates that the expression becomes simpler if we substitute the variable n with the number 4, which is 52.

for such more question on expression

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Customer Money Spent (in dollars) 1 $13 2 $46 3 $13 4 $87 5 $10 6 $5 7 $8 8 $16 9 $33 10 $57 A clothing store owner tracks the amount of money the last 10 customers spend in her store. The owner concludes that the typical amount spent by any customer is $28.80. The owner's conclusion A) is valid. The last 10 customers only bought sale items. B) is correct. This is the average amount spent by any customer. C) is invalid. This is not a good representation of all customers. Eliminate D) is unfair. The last ten people in the store may have been tired.

Answers

Answer:

Step-by-step explanation:

i think the anwer is c

Using the digits 1, 3, 5, 7 at most once, you can make many three-digit numbers. What is the maximum possible sum of two such distinct numbers?

Answers

Answer:

1504

Step-by-step explanation:

Given the digits :

1, 3, 5, 7

The maximum possible sum of two distinct three digit numbers formed from the digits above will be the sum of the the two hight possible three digit numbers that can be formed.

Highest three digit number = 753

Next highest = 751

The sum of these two. Values gives :

753 + 751 = 1504

Please help
-2x = x - 15

Answers

-2x-x=x-x-15 (subtract x on both sides)
-3x=-15
x=5

Hope this helps!! :)

Answer: x=5

Step-by-step explanation:

subtract x from both sides

-2x-x=x-15-x

-3x=15

then divide both sides by -3

-3x=-15

-3x   -3

x=5

hope this helps! please mark as brainliest! Thanks

what is the mean, median, mode and range of 7, 2, 1, 4, 1 (PLS DO NOT PUT ANY LINKS I AM USING THIS APP FOR HELP NOT FOR SCAM LINKS)

Answers

Answer:

Mean: 3

Median: 2

Mode: 1

Range: 6

Step-by-step explanation:

1.) The mean is the average of all the numbers. To find it, you add up all the numbers and then divide that by the amount of numbers. So, you would do:   7 + 2 + 1 + 4 + 1 = 15

15 ÷ 5 = 3

The mean is 3.

2.) The median is the middle number. In order to find it, you must put all the numbers in order:

1, 1, 2, 4, 7

The middle number is 2, so the median is 2.

3.) Mode is the number that appears the most often. Because 1 appears twice and the rest only appear once, the mode is 1.

4.) The range is the difference between the biggest and smallest numbers. Since 7 is the biggest number and 1 is the smallest, you would subtract them. 7-1 is 6, so the range would be 6.

An 8-foot roll of wrapping paper costs $9.60. What is the price per inch?An 8-foot roll of wrapping paper costs $9.60. What is the price per inch?An 8-foot roll of wrapping paper costs $9.60. What is the price per inch?

Answers

Answer:

$0.10

Step-by-step explanation:

STEPS TO ANSWERING THIS QUESTION

Convert the size of the wrapping paper to inches divide the total cost of the wrapping paper by the converted size

1 ft = 12 inches

8 feet = 8 x 12 = 96 inches

price per inch = total length of the wrapping paper in inches / total cost of the wrapping paper

$9.60 / 96 = $0.10

4×+5 ayudenme por favor ;)​

Answers

Answer:

There are no Like Terms.

Answer: 54=x

Step-by-step explanation:

Can someone please help me with this math question

Answers

Answer:

The answer would be D

Step-by-step explanation:

Most of the points are grouped together and can be define by a line or equation so there is a correlation between the outside temperatures and the heating cost so right away we can eliminate option A

There is no such thing as a constant correlation so we can eliminate answer choice C

As the temperatures rise ( or as the x values rise) the cost of heating decreases ( or the y values decrease) This is an example of negative correlation correlation because as one value increase the other value decreases.

this is also notable from looking at the graph .

Paul is buying packages of hot dogs for a camping trip. Each package is 30 oz. If he buys 4 packages, about how many pounds of hot dogs is he buying?
480 pounds
4 pounds
8 pounds
10 pounds

Answers

Answer:

8 pounds

Step-by-step explanation:

30 x 4 / 16 = 7.5  but abt 8

Answer:

8 pounds

Step-by-step explanation:

30 ounces = 1.875 pounds

1.875 * 4 = 7.5 rounded up = 8

Determine whether the equation is an identity or not an identity. Sin theta/cos theta + cos theta/sin theta = cos theta sin theta

Answers

Answer:

The equation is not an identity.

Step-by-step explanation:

Since we have Sin theta/cos theta + cos theta/sin theta = cos theta sin theta, we re-write as Sinθ/cosθ + cosθ/sinθ = cosθsinθ where theta = θ.

For the equation to be an identity, we need to show that L.H.S(left-hand-side)= R.H.S (right-hand-side)

So,

Sinθ/cosθ + cosθ/sinθ = (Sin²θ + cos²θ)/cosθsinθ (taking L.C.M = cosθsinθ)    

                                     = 1/cosθsinθ                         (Sin²θ + cos²θ = 1)

                                     ≠ cosθsinθ      

Since L.H.S = Sinθ/cosθ + cosθ/sinθ = 1/cosθsinθ ≠ R.H.S = cosθsinθ, the equation is not an identity.

These questions are very hard

Answers

They are not!
So put a point at 0,2 and then go down one and over four units. Keep doing that until you’re at the right. Then go back to the 0,2 and go up one and to the left 4 for every point.

the value of x varies directly with y and inversely with z. when x=4,and y=12, z=6. what is the value of k?
A. K=6
B. K=2
C. K=18
D. K=288

Answers

Answer:

B

Step-by-step explanation:

Given x varies directly with y and inversely with z then the equation relating them is

x = [tex]\frac{ky}{z}[/tex] ← k is the constant of variation

To find k use the condition when x = 4 and y = 12, z = 6 , then

4 = [tex]\frac{12k}{6}[/tex] ( multiply both sides by 6 )

24 = 12k ( divide both sides by 12 )

2 = k → B

The value of the constant 'k' will be 2. Then the correct option is C.

What are ratio and proportion?

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

The value of x varies directly with y and inversely with z. Then the proportionality is written as,

x ∝ y                 ...1

x ∝ 1 / z            ...2

Then the combined proportionality is given as,

x ∝ y / z

x = ky / z

At x = 4, y = 12, and z = 6, then the value of the constant 'k' will be given as,

4 = 12k / 6

Simplify the equation, then the value of the constant 'k' is calculated as,

4 = 12k / 6

4 = 2k

k = 4 / 2

k = 2

The worth of the steady 'k' will be 2. Then, at that point, the right choice is C.

More about the ratio and the proportion link is given below.

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