Two number cubes are rolled to determine how a token moves on a game board. The sides of
each number cube are numbered 1, 2, 3, 4, 5 and 6.
There are two options describing how the token will be moved.

Option A: If the product is even, move forward 4 spaces. Otherwise, move backward 8.

Option B: If the product is even, move forward 5 spaces. Otherwise, move backward 9.

Use mathematical expectation to determine which option offers the greater likelihood of moving
closer to the finish line on the game board.

Which statement best explains the better option?


The mathematical expectation of Option A is 1. The mathematical expectation of Option B is 1.5. Option A offers a greater likelihood of advancing to the finish line.

The mathematical expectation of Option A is . The mathematical expectation of Option B is 1. Option B offers a greater likelihood of advancing to the finish line.

The mathematical expectation of Option A is 1.5.The mathematical expectation of Option B is 1. Option A offers a greater likelihood of advancing to the finish line.

The mathematical expectation of Option A is 1. The mathematical expectation of Option B is 1.5. Option B offers a greater likelihood of advancing to the finish line.

Answers

Answer 1

Answer:

D. The mathematical expectation of Option A is 1. The mathematical expectation of Option B is 1.5. Option B offers a greater likelihood of advancing to the finish line.

Step-by-step explanation:

The result of a product is odd only when the two numbers are odds.

There are 6*6 = 36 possible outcomes when two dice are rolled. Only 9 of them are a combination of two odd numbers: {1, 1} {1, 3} {1, 5} {3, 1} {3, 3} {3, 5} {5, 1} {5, 3} {5, 5}. Then 36 - 9 = 27 outcomes are even.

P(even) = 27/36 = 0.75

Option A) Mathematical expectation: 0.75*4 + 0.25*(-8) = 1

Option B) Mathematical expectation: 0.75*5 + 0.25*(-9) = 1.5


Related Questions

if the 897 step stairwell has 50 landings, how many steps would be between landings

Answers

Answer:

17.94

I think you would do 897 divided by 50. Tell me if im wrong.

To find the number of steps between each landing in an 897-step stairwell with 50 landings, divide the total steps by the number of segments, resulting in approximately 17 to 18 steps per segment.

Step by Step Solution:

To determine how many steps are between each landing in an 897-step stairwell with 50 landings, follow these steps:

First, note that there are 50 landings, which divide the stairwell into 51 segments (since the top step is considered the last segment).Then, divide the total number of steps by the number of segments: 897 steps / 51 segments = 17.588 steps per segment.Since you can't have a fraction of a step, you may need to adjust for some rounding. Usually, some segments may have 17 steps and others may have 18 steps to total correctly.

Therefore, each segment will have approximately 17 or 18 steps.


The box plot suggests that about 25% of gyms in Shanesville have more than what number of gym members?

Answers

Answer:

Step-by-step explanation:

70

Answer:

it is 70 hahaha thanks

Step-by-step explanation:

A rectangular picture frame has a perimeter of 54 inches. The height of the frame is 14 inches. What is the width of the frame?
The solution is ____( ___+w)= ___. The width of the frame is ____ inches.

Answers

The solution is 2( 14 + w ) = 54. The width of the frame is 13 inches.

What is perimeter of rectangle?

The perimeter of a form is the space surrounding its edge. Find the perimeter of various forms by summing the lengths of their sides.

Perimeter of the rectangle = 2(length+width)

Given the parameters are;

Rectangular picture frame has a perimeter of 54 inches. The height of the frame is 14 inches.

Perimeter of the rectangle = 2(length+width)

Perimeter = 2( 14 + w )

2( 14 + w ) = 54

Solving;

28 + 2w = 54

2w = 54 - 28

2w = 26

w = 13

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The width of the frame is 13 inches.

To find the width of a rectangular picture frame when the perimeter is 54 inches and the height is 14 inches, we start by understanding the formula for perimeter of a rectangle, which is P = 2l + 2w, where P is the perimeter, l is the length (or height), and w is the width. In this case, we are given that the perimeter (P) is 54 inches and one dimension (the height/length, l) is 14 inches.

Substitute the known values into the perimeter formula to get 54 = 2(14) + 2w. Simplify the equation by first multiplying 2 by 14, which gives 54 = 28 + 2w. To isolate w, subtract 28 from both sides of the equation: 26 = 2w. Finally, divide both sides by 2 to find the width: w = 13 inches.

The solution is 54 = 2(14) + 2w = 28 + 2w. The width of the frame is 13 inches.

Over what interval is the graph of
y = |x + 2] increasing?

Answers

The answer is B my guy

Over (-2, ∞) the graph of function y = | x + 2| is increasing.

Given that,
To determine over what interval the graph of y = |x + 2] increases.

What are functions?

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
y = | x + 2|
Since from (∞, -2), the graph is decreasing, but at -2 the graph has zero ordinate and afterward, the graph starts increasing. So, over (-2, ∞) the graph of function y = | x + 2| is increasing.

Thus, over (-2, ∞) the graph of function y = | x + 2| is increasing.

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Emma conducted an experiment in which she rolled a
six-sided, fair number cube 300 times. How many times
would you predict she rolled a 6?

Answers

Answer:

50

Step-by-step explanation:

A six-sided fair number cube has numbers 1, 2, 3, 4, 5, and 6 on each side.

so, 300/6= 50

For each number it is predicted that it will roll 50 times.

Answer:

Sample Response: A number cube has six sides. The probability of landing on any of the numbers is equal. The theoretical probability of rolling a 6 is 1/6. I expect a 6 to be rolled (1/6)(300), or 50 of 300 times.

Step-by-step explanation:

What is the scale factor of this dilation? Line segments X Y and X prime Y prime. From the point of dilation, the distance to point Y is 3 and the distance to point X is 2. The distance from point Y to Y prime is 6, and the distance from X to X prime is 4. One-half One-third 2 3

Answers

Answer:

Option D or 3

Step-by-step explanation:

It says so on edge 2020. I thought it was option c, but it is D. Can anyone tell me whyyyyyy.

The solution is, the scale factor of this dilation is option D. 3.

What is scale factor?

A scale factor is when you enlarge a shape and each side is multiplied by the same number. This number is called the scale factor. Maps use scale factors to represent the distance between two places accurately.

here, we have,

given that,

Line segments X Y and X prime Y prime.

From the point of dilation, the distance to point Y is 3 and the distance to point X is 2.

The distance from point Y to Y prime is 6, and the distance from X to X prime is 4.

Hence, The solution is, the scale factor of this dilation is option D. 3.

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Choose the graph of the function

Answers

Answer:

sorry I don't see the grap or the function

Which equation is equivalent to (one-third) Superscript x Baseline = 27 Superscript x + 2?

Answers

Answer: Hello!

It's Option D.

Hope I helped! ♡

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Edge 2020

hey! I need help asap. thank you in advance!

Answers

Answer:

-2, 6

Hope this helps :)

Please may you answer this I am on a rush and I got to do a piece of work due in 10 minutes please help out :( xx

Answers

6) X=8

7) X=3

8) X=7

9) X=1.5

10) X=0.9

good luck

Answer:

6.) x = 8

7.) x = 3

8.) x = 7

9.) x = 3/2

10.) x = 9/10

Step-by-step explanation:

refer to the pics. Please rate and thumbs up :)

If 2 Apple watches out of every 250 are defective, how many defective ones would there be out of 2000 total watches

Answers

Step-by-step explanation:

Simple if there are 2 watches defective from 250 then 2000 ÷ 250 = 8

So total 10 watches are defective

Answer:

16 are defective

Step-by-step explanation:

2000/250=8

8*2=16

what is the slope of the line that passed through (-2,-1) and (12,6)

Answers

Answer:

1/2

Step-by-step explanation:

The slope is given by

m = (y2-y1)/(x2-x1)

   = (6 - -1)/(12 - -2)

    = (6+1)/(12+2)

    7/14

   1/2

Step-by-step explanation:

Step 1:  Find the slope

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{6-(-1)}{12-(-2)}[/tex]

[tex]m=\frac{6+1}{12+2}[/tex]

[tex]m=\frac{7}{14}[/tex]

[tex]m=\frac{1}{2}[/tex]

Answer: The slope is 1/2

factor 8x^2+ 12x-16​

Answers

Answer:

-4( -2x^2 -3x+4)

Step-by-step explanation:

8x^2+ 12x-16​

Factor out a 4 from each term

4 (2x^2 +3x-4)

We can also factor out a negative 4

-4( -2x^2 -3x+4)

it is the first one -4(-2x^2-3x+4)

Please help! ASAP! (Stay Safe!)

Answers

Answer:

6

Step-by-step explanation:

Divide 144 by 8. Then divide that answer by 3.

Answer:

c)

Step-by-step explanation:

Because first you do 8x3= 24 and you 144 divided by 24 and you get 6

PLease help
The line plots show the number of minutes two different age groups of teenagers spent online the previous week.

Answers

Answer:

Range: 13 and 15        Mean: 247 and 286

Step-by-step explanation:

How did Alexander Grothendieck affect other mathematicians 100 points

Answers

Answer:

Grothendieck used his remarkable capacity for abstract thinking to make advances across the entire spectrum of mathematics. He developed unifying concepts that could be applied to a variety of avenues of mathematical thought, including number theory, category theory, functional analysis and topology

Step-by-step explanation:

6, 18, 54, 162, ...
Is the sequence above arithmetic or geometric?

Arithmetic

Geometric

Answers

The sequence is Geometric

Carol bought some items at a variety store. All the items were the same price, and she bought as many items as the price of each item in cents. (For example, if the items cost 10 cents, she would have bought 10 of them.) Her bill was $2.25. How many items did Carol buy?

Answers

Answer:

15

Step-by-step explanation:

b/c .15 tims 15 =2.25

p.s can  u mark me brainliest if i got it right plz?

The number of items carol can buy is 225.

What is unit conversion?

Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.

Given that Carol bought some items at a variety store. All the items were the same price, and she bought as many items as the price of each item in cents. The items cost 10 cents, she would have bought 10 of them.) Her bill was $2.25.

The number of the items will be calculated as below:-

1 dollar = 100 cents

2.25 dollars = 2.25 x 100 cents

2.25 dollars = 225 cents.

It is given that the number of items bought is equal to the number of cents.

Therefore, the number of items carol can buy is 225.

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Cindy went to the salon to get highlights and a haircut. Her total cost
was $95. Cindy decided to tip her stylist 22% because she loved her
hair so much. How much was the tip?
Select one:
$20.90
$117
O $115.90
$74.10
Check

Answers

Answer:

$20.90

Step-by-step explanation:

To find the tip paid, you simply need to find 22% of the amount paid. This can be done by:

95×0.22=  20.90 dollars.

Answer:

$20.90

Step-by-step explanation:

22% of $95 is $20.90

Marina wants to install security cameras in her store, which has dimensions 48 feet by 48 feet. Each camera can view an area of approximately 128 ft2, with a viewing area shaped like a right triangle. The distance between grid lines is 4 feet. The viewing area of a camera is shown on a grid. The grid is 48 feet by 48 feet, with each square having side lengths of 4 feet. The camera has a triangular viewing area of 128 feet squared. The right triangle has 2 side lengths of 16 feet. How many cameras will be necessary to cover the entire store? 6 9 12 18

Answers

Answer:  18

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

Candice wants to estimate the proportion of the freshmen at her high school that likes sports drinks. She interviews a simple random sample of 75 of the 215 freshmen on campus. She finds that 18 students like sports drinks. Is the Normal condition for finding confidence intervals met? Explain.

Answers

Yes, the Normal condition for finding confidence intervals is met because np = 18 and n(1 − p) = 57, both of which are greater than 10.

The following information should be considered:

Since there is the simple random sample of 75 of the 215 freshmen on campus. She finds that 18 students like sports drinks.So, it is the normal condition as np = 18 and n (1- p) = 57.

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The Normal condition for constructing confidence intervals is met if both np and n(1-p) are greater than 10. In Candice's case, both conditions are met, so she can proceed with constructing a confidence interval for the proportion of freshmen who like sports drinks.

In order to determine if the Normal condition for constructing confidence intervals is met, we need to check if both np and [tex]\( n(1-p)[/tex] are greater than 10. Here n is the sample size and p is the sample proportion.

For Candice's sample:

n = 75 (sample size)p (sample proportion) = [tex]\frac{18}{75} = 0.24[/tex]

Now, calculate np and n(1-p):

[tex]\[ np = 75 \times 0.24 = 18 \][/tex][tex]\[ n(1-p) = 75 \times (1 - 0.24) = 75 \times 0.76 = 57 \][/tex]

Both values (18 and 57) are greater than 10, so the Normal condition is met. Therefore, it is appropriate to proceed with constructing a confidence interval for the proportion of freshmen who like sports drinks.

Joe has a spinner. The probability of landing on green is 3/8. Joe spins the spinner 184 times. How many times should Joe expect the spinner to land on green? Explain using complete sentences and proper grammar.


please help, You'll get 35 points & more if you get it right, ill mark you as brainliest!

Answers

Let x represent the number of times Joe should expect the spinner to land on green.

We have been Joe has a spinner. The probability of landing on green is 3/8. Joe spins the spinner 184 times. We are asked to find the number of times Joe should expect the spinner to land on green.

We will use proportions to solve our given problem.

[tex]\frac{\text{Green}}{\text{Total}}=\frac{3}{8}[/tex]

Upon substituting our given values in above equation, we will get:

[tex]\frac{x}{184}=\frac{3}{8}[/tex]

[tex]\frac{x}{184}\cdot 184=\frac{3}{8}\cdot 184[/tex]

[tex]x=3\cdot 23[/tex]

[tex]x=69[/tex]

Therefore, Joe should expect the spinner to land on green 69 times.

A rectangle has a height of 5 and a width of 4x^2-2x-6 . Express the area of the entire rectangle.

Answers

Answer:

20x² - 10x - 30

Step-by-step explanation:

Height = 5

Width = 4x² - 2x - 6

Area of rectangle = length × breadth

Area of triangle = height × width

Area = 5 × (4x² - 2x - 6)

Area = 20x² - 10x - 30

Area of the rectangle is 20x² - 10x - 30

Which of the following terms correctly describe the object below? Check all that apply

Answers

Where is the object

don't understand please help ;-;

Answers

Answer:

72cm^2

Step-by-step explanation:

12x6

Answer:

283 cm²

Step-by-step explanation:

r = 3 cm

2 × 3.14 × 3 (3 + 12)

= 2 × 3.14 × 3(15)

= 2 × 3.14 × 45

= 282.6 cm²

= 283 cm²

Find the indicated side of the right triangle

Answers

Answer:

x = 14

Step-by-step explanation:

[tex] \sin \: 30 \degree = \frac{7}{x} \\ \frac{1}{2 } = \frac{7}{x} \\ x = 7 \times 2\\ x=14[/tex]

Can someone please help me with this question ASAP?

Answers

Answer:

a = 2

b = -1

7(2y^2 + (-1)y - 3) =

14y^2 - 7y -21

Step-by-step explanation:

Which could be the dimensions of a rectangle with an area of 60 square units?
1 by 60 units
4 by 15 units
8 by 8 units
10 by 6 units
60 by 2 units

PLEASE HURRY!!! WILL GIVE BRAINLIEST!!

Answers

Answer:

The answer is 1 by 60 4 by 15 and 10 by 6

Step-by-step explanation:

Answer:a,b.d

Step-by-step explanation:

Beth and Dave are hiking on a
5-mile trail. When they stopped
for a picnic lunch, they had hiked
2 miles of the trail. How much
farther do they have to hike after
lunch to complete the trail?​

Answers

Answer:

3 miles

Step-by-step explanation:

5-2=3

What is the mathematical shape made by each net

Answers

Answer:

a) cylinder

b) Tetrahedron

Step-by-step explanation:

Thank you

(a) Cylinder is the figure formed by the given net of two circles and rectangle.

(b) Tetrahedron is the figure formed by given net of triangles.

(a) The net made up of two circles and a rectangle represents a shape known as a cylinder.

The two circles form the top and bottom faces of the cylinder, and the rectangle wraps around the circles to form the curved surface.

(b) the triangles are connected with their bases adjacent to each other, forming a closed figure, the resulting shape is a tetrahedron (a specific type of pyramid with four triangular faces).

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