When playing a board game, Leilani rolls a number cube twice to determine her next move. In her past 10 moves, she’s rolled two 5s once. How many times does she expect to again roll two 5s in her next 30 moves? Which statement compares this prediction to the theoretical probability of rolling two 5s.

Answers

Answer 1

Answer: Leilani has the probability of rolling two 5s three times on her next 30 moves.

Step-by-step explanation: If on average Leilani rolls once in 10, then we can predict that she will at least roll 3 in 30.


Related Questions

4. If the base of a parallelogram is 61 m and the area is 645 m2, what is the height of the parallelogram

Answers

Answer:

10.57 m

Step-by-step explanation:

Let the height of the parallelogram be x m

Area of the parallelogram = base*height

                                645    = (61 * x ) m

                                 x = 645/61

                                    = 10.57 m

Hope this helps

Height of parallelogram = 10.57m

Given,

Base of parallelogram = 61 m

Area of parallelogram = 645 m²

Now, according to formula

Area of parallelogram = Base × Height

Substitute the given values in the formula,

645 = 61 × height

Height = 10.57 m

Hence, the height of the parallelogram with area 645m² and base 61 m is 10.57 m  .

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Help...
The Japanese 5 yen coin has a hole in the middle. What are the possible ways to calculate the difference between the outer and inner circumference of the coin? Check all that apply.

Subtract the two diameters and multiply by 3107-11-05-20-05-task
Calculate the circumference of the coin.
Add the two diameters and multiply by 3107-11-05-20-05-task
Subtract the circumference of the hole from the circumference of the coin.
Calculate the radius of the hole.
P.S fr33 points, I know the answers ;)

Answers

Answer:

Subtract the two diameters and multiply by 3107-11-05-20-05-task

Calculate the circumference of the coin.

Subtract the circumference of the hole from the circumference of the coin.

Calculate the radius of the hole.

Step-by-step explanation:

Please help me out on this needed 20-30 mins

Answers

Answer:

x=+10

Step-by-step explanation:

I hope that helps I think it's the right answer if my calculations are correct it's +10

Answer : x = 10

In a triangle, the angles add up to 180 degrees. 46 + (8x-2) must be equal to 11x + 14, as angles on a straight line also equal to 180 and therefore 180 - (11x + 14) is the missing interior angle on the triangle. (angle ABC + angle BAC = angle BCD)
Using these substitutions, we can calculate x.

(8x - 2) + 46 = (11x + 14)
(80 - 2) + 46 = (110+14)

George solved the equation -103 = -2(-7x + 7) + 8x as follows:


-103 = -2(-7x + 7) + 8x

Step 1: -103 = 14x + 7 + 8x

Step 2: -103 = 22x + 7

Step 3: -110 = 22x

Step 4: -5 = x


At which step did he make an error?

Explain the error:

Answers

when multiplying -2 by 7 the answer will be -14 instead of 7 so the answer will be like this
-103 = -2(-7x + 7) + 8x
-103 = 14x - 14 + 8x
-103 = 22x - 14
-89 = 22x
x = -4
Step 1:-103=14x - 14 + 8x
Step 2: -103 = 22x - 14
Step 3: -117 = 22x
Step 4: -5.31818182 = x

The table shows the number of runs earned by two baseball players.


Player A Player B
2, 1, 3, 8, 2, 3, 4, 4, 1 1, 4, 5, 1, 2, 4, 5, 5, 10


Find the best measure of variability for the data and determine which player was more consistent.
Player A is the most consistent, with a range of 7.
Player B is the most consistent, with a range of 9.
Player A is the most consistent, with an IQR of 2.5.
Player B is the most consistent, with an IQR of 3.5.

Answers

To find the best measure of variability for the data and determine which player was more consistent, we can calculate the range and the interquartile range (IQR) for both players.

The range is calculated by subtracting the minimum value from the maximum value in a dataset. The IQR is a measure of dispersion that represents the range between the first quartile (Q1) and the third quartile (Q3) in a dataset.

Let's calculate the range and IQR for both players:

For Player A:

The data for Player A is: 2, 1, 3, 8, 2, 3, 4, 4, 1.

To calculate the range:

[tex]\text{Range} = \text{maximum value} - \text{minimum value}[/tex]

The maximum value is 8, and the minimum value is 1.

[tex]\text{Range} = 8 - 1 = 7[/tex]

For Player B:

The data for Player B is: 1, 4, 5, 1, 2, 4, 5, 5, 10.

To calculate the range:

[tex]\text{Range} = \text{maximum value} - \text{minimum value}[/tex]

The maximum value is 10, and the minimum value is 1.

[tex]\text{Range} = 10 - 1 = 9[/tex]

To calculate the IQR, we need to find the first quartile (Q1) and the third quartile (Q3) for each player:

For Player A:

Arranging the data in ascending order: 1, 1, 2, 2, 3, 3, 4, 4, 8.

To calculate Q1, we find the median of the lower half of the data: 1, 1, 2, 2, 3.

Q1 = 2

To calculate Q3, we find the median of the upper half of the data: 3, 4, 4, 8.

Q3 = 4

The IQR is calculated as:

[tex]\text{IQR} = Q3 - Q1[/tex]

[tex]\text{IQR} = 4 - 2 = 2[/tex]

For Player B:

Arranging the data in ascending order: 1, 1, 2, 4, 5, 5, 5, 10.

To calculate Q1, we find the median of the lower half of the data: 1, 1, 2, 4.

Q1 = 1.5

To calculate Q3, we find the median of the upper half of the data: 5, 5, 5, 10.

Q3 = 5

The IQR is calculated as:

[tex]\text{IQR} = Q3 - Q1[/tex]

[tex]\text{IQR} = 5 - 1.5 = 3.5[/tex]

Based on the calculations, we can conclude:

Player A is the most consistent, with a range of 7.

Player B is the most consistent, with a range of 9.

Player A is the most consistent, with an IQR of 2.

Player B is the most consistent, with an IQR of 3.5.

Therefore, the correct answer is:

Player A is the most consistent, with an IQR of 2.

[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

♥️ [tex]\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

Answer:To find the best measure of variability for the data and determine which player was more consistent, we can calculate the range and the interquartile range (IQR) for both players.

The range is calculated by subtracting the minimum value from the maximum value in a dataset. The IQR is a measure of dispersion that represents the range between the first quartile (Q1) and the third quartile (Q3) in a dataset.

Let's calculate the range and IQR for both players:

For Player A:

The data for Player A is: 2, 1, 3, 8, 2, 3, 4, 4, 1.

To calculate the range:

The maximum value is 8, and the minimum value is 1.

For Player B:

The data for Player B is: 1, 4, 5, 1, 2, 4, 5, 5, 10.

To calculate the range:

The maximum value is 10, and the minimum value is 1.

To calculate the IQR, we need to find the first quartile (Q1) and the third quartile (Q3) for each player:

For Player A:

Arranging the data in ascending order: 1, 1, 2, 2, 3, 3, 4, 4, 8.

To calculate Q1, we find the median of the lower half of the data: 1, 1, 2, 2, 3.

Q1 = 2

To calculate Q3, we find the median of the upper half of the data: 3, 4, 4, 8.

Q3 = 4

The IQR is calculated as:

For Player B:

Arranging the data in ascending order: 1, 1, 2, 4, 5, 5, 5, 10.

To calculate Q1, we find the median of the lower half of the data: 1, 1, 2, 4.

Q1 = 1.5

To calculate Q3, we find the median of the upper half of the data: 5, 5, 5, 10.

Q3 = 5

The IQR is calculated as:

Based on the calculations, we can conclude:

Player A is the most consistent, with a range of 7.

Player B is the most consistent, with a range of 9.

Player A is the most consistent, with an IQR of 2.

Player B is the most consistent, with an IQR of 3.5.

Therefore, the correct answer is:

Player A is the most consistent, with an IQR of 2.

♥️ To find the best measure of variability for the data and determine which player was more consistent, we can calculate the range and the interquartile range (IQR) for both players.

The range is calculated by subtracting the minimum value from the maximum value in a dataset. The IQR is a measure of dispersion that represents the range between the first quartile (Q1) and the third quartile (Q3) in a dataset.

Let's calculate the range and IQR for both players:

For Player A:

The data for Player A is: 2, 1, 3, 8, 2, 3, 4, 4, 1.

To calculate the range:

The maximum value is 8, and the minimum value is 1.

For Player B:

The data for Player B is: 1, 4, 5, 1, 2, 4, 5, 5, 10.

To calculate the range:

The maximum value is 10, and the minimum value is 1.

To calculate the IQR, we need to find the first quartile (Q1) and the third quartile (Q3) for each player:

For Player A:

Arranging the data in ascending order: 1, 1, 2, 2, 3, 3, 4, 4, 8.

To calculate Q1, we find the median of the lower half of the data: 1, 1, 2, 2, 3.

Q1 = 2

To calculate Q3, we find the median of the upper half of the data: 3, 4, 4, 8.

Q3 = 4

The IQR is calculated as:

For Player B:

Arranging the data in ascending order: 1, 1, 2, 4, 5, 5, 5, 10.

To calculate Q1, we find the median of the lower half of the data: 1, 1, 2, 4.

Q1 = 1.5

To calculate Q3, we find the median of the upper half of the data: 5, 5, 5, 10.

Q3 = 5

The IQR is calculated as:

Based on the calculations, we can conclude:

Player A is the most consistent, with a range of 7.

Player B is the most consistent, with a range of 9.

Player A is the most consistent, with an IQR of 2.

Player B is the most consistent, with an IQR of 3.5.

Therefore, the correct answer is:

Player A is the most consistent, with an IQR of 2.

♥️

Step-by-step explanation:

HELP ANSWER HOWLE PAGE PLS

Answers

Step-by-step explanation:

an acute angle is less then 90 degrees, a right angle is 90 degrees, an obtuse angle is more than 90 degrees, a straight angle is 180 degrees, and a reflex angle is more than 180 degrees but less then 360 degrees

Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−1, −1), B′(1, 1), C′(0, 1). Determine the scale factor used.

1
one half
3
one third

Answers

1/3 filler words  im smart filler words i failed geometry filler words  i think its right filler words  

Answer:

1/3

Step-by-step explanation:

How many times does 15 go int 135? who ever gets it right gets 500 points

Answers

Answer:

9 times

Step-by-step explanation:

The number 15 multiplied to the number 9 which gives the value 135.

To find the that how many 15 is to get 135, division should be performed.

So, dividing 135 by 15 gives:

= 135 ÷ 15

                         15 | 135 | 9

                                135

                            _______

                                   0

Thus, the quotient is 9.

Therefore, 15 goes into 135 exactly 9 times.

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*100 POINTS** 7th grade geometry pls help

Answers

Answer:

Height = 10 cm

Step-by-step explanation:

The volume of a pyramid can be found using the following formula:

[tex]\boxed{\large \textsf{$V=\frac{1}{3}Ah$}} \large \textsf{ where:}\\\\ \normalsize \textsf{$\bullet{\,V = $ volume of pyramid$}$}\\ \normalsize \textsf{$\bullet{\,A = $ base area$}$}\\ \normalsize \textsf{$\bullet{\,h = $ perpendicular height$}$}[/tex]

Note: in the question, it states that base area = 12 cm³, however, this is an error (typo), and the area is 12 cm², since area is only in 2 dimensions. length and width, whilst volume is in 3 dimensions. length, width, and height.

Now, we can plug in our data into the formula:

[tex]\large \textsf{$40=\frac{1}{3}12h$}\\\\ \large \textsf{$40=4h$}\\\\\boxed{\boxed{\large \textsf{$\therefore h = 10$ cm}}}\\[/tex]

Help Please, I don't understand this

Answers

Firstly, you have to understand that if you talk about slope is a similar word gradient of the graph. So if you are calculating slope you have to use gradient formula:

m= Y2-Y1

X2-X1

therefore, in order for you getting first box & second box you have to use this formula above.

First box answer is:

Points fromthegraph (-2:-2) & (-3:-3)

m= Y2-Y1

X2-X1

m = -3-(-2)

-3-(-2)

m = 1

Second box answer is:

Points fromthegraph (3:3) & (4:4)

m= Y2-Y1

X2-X1

m= 4-3

4-3

m= 1

Third box answer is:

= 4

Forth box answer is:

= -3

PLSSS HELP, WIL MARK BRAINLIEST!!!

Answers

Answer:

x=10

<DPT=149°

<APW=149°

<WPD=31°

Step-by-step explanation:

4x-9=91-6x

4x+6x=91+9

10x=100

x=10

<DPT=180-(4(10)-9)

<DPT=180-31

<DPT=149

<APW=149 (Same as <DPT)

<WPD=4x-9

<WPD=40-9

<WPD=31

Answer X=10 bc we look at what the numbers say and see if there are crossing or parallel after that we need to figure out the question and solve the question with a calculator and you get your answer. That’s why it’s X=10

What is the surface area of this right triangular prism? PLEASEEE HELPPPP It's 3D geometry

Answers

Answer:

1200 square inches

Step-by-step explanation:

Surface area of right triangular prism:

       [tex]\boxed{\text{\bf Surface area of right triangular prism = bh + $\bf (s_1 + s_2+s_3)* l$}}[/tex]

                 b = base of the triangle = 30 in

                 h = altitude of the triangle = 8 in

                 [tex]\sf s_1, ~ s_2, ~ s_3 \ are \ the \ sides \ of \ the \ triangle.\\\\s_1 = 17 \ in, \ ~~ s_2 = 17 \ in, ~~ s_3 = 30 \ in[/tex]

                 l = length of the rectangle = 15 in

Surface area of right triangular prism = 30*8 + (17 +17 + 30) * 15

                                                               = 30*8 + 64 *15

                                                               = 240 + 960

                                                              = 1200 square inches

Answer: it is going to be 24

Step-by-step explanation:

Part 1 - Application
Indiana plans to purchase a new gaming system during the 15% off sale. Let c represent the cost of the gaming system. How can you write a function to represent this?


Indiana also knows that he will have to pay the state tax of 10% on his purchase (after the discount is taken). Let p represent the price. How can he write a function to represent this?


Write one single function to help Indiana know how to calculate the final cost.

Answers

Answer:

The single function to calculate the final cost of the gaming system, including a 15% off discount and a 10% state tax, is: final_cost(c) = 0.935c.

Step-by-step explanation:

To represent the cost of the gaming system before any discounts or taxes, we can use the variable c:

c represents the cost of the gaming system.

To represent the price after the 15% off discount, we need to calculate the discounted price by subtracting 15% of the cost from the original cost:

p = c - 0.15c

Simplifying, we get:

p = 0.85c

Here, p represents the price after the 15% discount has been applied.

To represent the price after the 10% state tax has been added to the discounted price, we need to calculate the price with the added tax:

final_price = p + 0.1p

Simplifying, we get:

final_price = 1.1p

Here, final_price represents the price after the 10% state tax has been added.

Therefore, the correct single function to help Indiana calculate the final cost is:

final_cost(c) = 1.1(0.85c)

Simplifying further:

final_cost(c) = 0.935c

For which data set is mean the best measure of central tendency?

A: 94, 98, 96, 100, 97

B: 54, 60, 58, 3, 64

C :26, 29, 71, 28, 71

D: 5, 5, 5, 301, 5

Answers

Answer:

The correct answer would be choice A: 94, 98 , 96, 100, 97

The mean is the best measure of central tendency when the values are close together and there are no outliers. Choice A is the only set with no outliers. The rest of the sets have an outlier which will skew the mean.

Step-by-step explanation:

it might be wrong but i am pretty sure

hope it helped;)

A 94 98 96 100 97 is the correct answer according to me

(explanation please so i can understand)
Triangle JKL has vertices at J(−1, −5), K(−2, −2), and L(2, −4). Determine the translation direction and the number of units of the image of triangle JKL if vertex J′ is at (−1, −8).

3 units down
3 units up
7 units to the right
7 units to the left

Answers

Answer:

3 units down

Step-by-step explanation:

J(-1, -5) → J'(-1, -8)

The x coordinate of the vertex J is -1 and does not change in J' (it is still -1)

The y coordinate of J is -5, and for J' is -8.  This means the translation direction of 3 units down.  (-8- -5 = -3)

Please help i will give points

Answers

Hello !

odd = 5, 7, 9

There are 3 numbers out of a total of 5:

3/5 = 0,6 = 60%

Answer is 60%.

I’m pretty sure the The answer is 60%

The figure is the net for a rectangular prism.

What is the surface area of the rectangular prism represented by the net?

Answers

768 is your Awnser
Reason I did the work

I don’t get it, what am I supposed to be multiplying!?!

Answers

Answer: 5400

Step-by-step explanation: image attached

Answer:

5400

Step-by-step explanation:

we need to calculate the area of big box (prism).

volume = 4 1/2 X 5 X 3 3/4

= 84.375 in³.

volume of small cube = 1/4 X 1/4 X 1/4

= 0.015625 in³.

now we need to find how many of the small ones go into the big one.

84.375/0.015625

= 5400.

The table shows the dollar amounts of donations given by 20 people to a local community center. Which histogram matches this data?

Answers

Answer: A

Step-by-step explanation:

Given by the table shown, we can see that the numbers are already put in least to greatest.

We count how many ranges there are:
(0 to 20)

(20 to 40)

(40 to 60)
(60 to 80)

(80 to 100)

There are 2 numbers that are between he range (0-20)

This doesn’t help us figure out wether it’s A or B. So we move on to the second range, 20 to 40.

Here we see that there are 6 numbers between 20 to 40. That’s only one answer, A


Geraldine Winston

PLEASE HELP!!!!!!!!!!!!

The organized list shows all the possible outcomes of an experiment in which three fair coins are flipped. The possible outcomes of each flip are heads​ (H) and tails​ (T).

Sample Space: HHH HHT HTH HTT THH THT TTH TTT

What is the probability that exactly 3 fair coins land heads up when 3 are flipped?

The probability is?

Type an integer or a fraction.

Answers

To find the probability of getting exactly 3 heads when 3 fair coins are flipped, we need to determine the number of favorable outcomes (outcomes with 3 heads) and divide it by the total number of possible outcomes.

From the sample space given, we can see that there is only one outcome with 3 heads: HHH.

The total number of possible outcomes is 2^3 = 8, as each coin can land in either heads or tails, and there are 3 coins.

Therefore, the probability of getting exactly 3 heads when 3 fair coins are flipped is 1/8.

How far did I travel to reach my destination on each day of my three-day Trip?
a. On Day 1, after traveling 5/8 of the way to the first day's destination, I still had 15 miles left to go before reaching my first destination.
b. On Day 2, after traveling 18 miles, I still had 2/5 of that day's distance left to go before reaching my second destination.
c. On Day 3, after traveling 5/11 of that day's distance, I still had 6 more miles to travel than what I had already traveled that day, before reaching my third destination.

Answers

The total distances you traveled to reach your destination on each day of your three-day trip are as follows:

a) Day 1 = 40 miles

b) Day 2 = 30 miles

c) Day 3 = 11 miles.

How the total distances are determined:

The total distances are determined using proportions.

Proportion refers to the fractional value of the whole number or quantity.

a) Day 1:

The fractional distance traveled = ⁵/₈

The remaining distance to travel = 15 miles

15 miles = ³/₈ (1 - ⁵/₈)

Proportionately, the total distance = 40 miles (15 ÷ ³/₈)

b) Day 2:

The distance traveled = 18 miles

The remaining distance to travel = ²/₅

The distance traveled = ³/₅ (1 - ²/₅)

³/₅ = 18 miles

Proportionately, the total distance = 30 miles (18 ÷ ³/₅)

c) Day 3:

The distance traveled = ⁵/₁₁

The distance to travel = 6 miles

The distance to travel in fractions = ⁶/₁₁ (1 - ⁵/₁₁)

Proportionately, if 6 miles = ⁶/₁₁, the total distance = 11 miles (6 ÷ ⁶/₁₁)

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help me, please thanks

Answers

Answer: 120 feet sqaured

Step-by-step explanation:

Surface area for square pyramid formula: 2bh + b^2

Base = 6  Height = 9

2*6*9+6^2 =

108+12 =

120

Answer:

120 feet squared

Step-by-step explanation:

15 POINTS
Ann had twice as many candies as Susan. Then Ann ate 3 of her candies.
This can be modeled using the following equation:
A = 2s - 3
Solve the equation for the number of candies Susan has, S
S = A + [?]/[?]

Answers

Answer: S = [tex]\frac{A}{2}[/tex] + [tex]\frac{3}{2}[/tex]

Step-by-step explanation: Isolate S by timesing it by 2, which means you have to times A and 3 by two and take S to the other side of the equation which makes the minus into a plus.

Answer:

[tex]S=\frac{A+3}{2}[/tex]

Step-by-step explanation:

The original equation is:

A=2S-3

But, we are now solving for S, so we have to isolate S.

To do this, we first must add 3 to both sides:

A+3=2S

Next, divide both sides by 2:

[tex]\frac{A+3}{2}=S[/tex]

Hope this helps! :)

i really need help please

Answers

Answer:

If I am thinking correctly its 72.

Step-by-step explanation:

I multiplied 9 x 8 and I got 72, and if I remember correctly your supposed to multiply to get the area.

Hope this helps :>

Answer : 124ft to the nearest whole number.

Explanation: the formula to find the lateral surface area of a cone is pi times the radius times the slant height. The slant height can be found by rooting the radius squared plus the height squared.

So, 4^2 plus 9^2 rooted multiplied by pi and by the radius, which gives you an answer of 123.7644 which is 124 to the nearest whole number.

Hope this helps.

A group of 500 middle school students were randomly selected and asked about their preferred frozen yogurt flavor. A circle graph was created from the data collected.

a circle graph titled preferred frozen yogurt flavor with five sections labeled Dutch chocolate 21.5 percent, country vanilla 28.5 percent, sweet coconut 13 percent, espresso, and cake batter 27 percent

How many middle school students preferred espresso-flavored frozen yogurt?

10
15
50
100

Answers

Answer:

50

Step-by-step explanation:

21.5%+28.5%+13%+27%=90%

100%-90%=10%

however there are 500 students in the school so you have to work out 10% of 500.

10% of 500 = 50

Answer:

50

Step-by-step explanation:

21.5%+28.5%+13%+27%=90%

100%-90%=10%

however there are 500 students in the school so you have to work out 10% of 500.

10% of 500 = 50

NAH FR HELP ME PLS IM JUST LEARNING THIS TODAY

Answers

the answer is 2. Taking the cube root of a number is seeing what number is multiplied by itself 3 times to go into the number. 2x2x2= 8, so the answer is 2. The root of a number can’t be bigger then the actual number
yeah I agree with that first comment it’s two because

2•2•2
^ ^
4•2=8

how can you represent the relationship between paired data and describe patterns of association?

Answers

With scatter plots.          

Starting at the same point, Tom and Juanita go biking in opposite directions. If Tom rides at a speed of 16 mph, and Juanita rides at a speed of 18 mph, how far apart will they be in 2 hours? Please help I need the answer like right now! But also take your time to think it through!

Answers

Answer:

Tom and Juanita will be 68 miles apart.

Step-by-step explanation:

16 x 2 = 32 miles

18 x 2 = 36 miles

36 + 32 = 68 miles

Answer:

Sure.

Tom and Juanita are moving in opposite directions, so their speeds are added together. Their combined speed is 16+18=34 mph.

If they travel for 2 hours at a speed of 34 mph, they will travel a distance of 34×2=68 miles.

Therefore, they will be 68 miles apart in 2 hours.

Is there anything else I can help you with?

Step-by-step explanation:

10 x 10 to the power of 9 is how many times greater than 5 times 10 to the power of 3
find the answer using scientific notation

Answers

Answer: 2,000,000 or 2*10^6

Step-by-step explanation:

10*10^9 = 10000000000

5*10^3 = 5000

10000000000/5000=2000000

[tex]10x10^9[/tex] = 10 x 1000000000 = 10,000,000,000

5 x 10^3 = 5 x 10 x 10 x 10 = 5,000

Divide 10 x 10^9 / 5 x 10^3 and the answer is

2 x 10^6

I hope this helps you, and if I did anything wrong to this problem, please do let me know :)

someone please help me ASAP!!

Answers

Answer:

P(factor of 20) = P(5) = 1/3

Step-by-step explanation:

The factors of 20 are

1 and 20

2 and 10

4 and 5

or 1, 2, 4,  5, 10, 20

In the spinner wheel, only 5 appears as a factor of 20

Since there are 3 numbers and each of them is equally likely, P(any number landing is) = 1/3

P(5) = 1/3

Other Questions
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