A game is designed so that a player wins when the game piece lands on or passes the box W. The game piece starts on box S. A fair six-sided number die is tossed. If the number tossed is 1 or 2, the game piece stays put. If the number tossed is 3 or 4, the game piece moves one box to the right. If the number tossed is 5 or 6, the game piece moves two boxes to the right.

a).Find the probability that a player will win after tossing the dice once. b).Find the probability that a player will win after tossing the dice twice

Answers

Answer 1

a) The probability of winning after tossing the die once is 1/3 or approximately 0.333.

b) The probability of winning after tossing the die twice is 5/18 or approximately 0.278.

a) To calculate the probability of winning after tossing the die once, we need to consider the possible outcomes. There are six equally likely outcomes corresponding to the numbers on the die. Out of these, two outcomes (1 and 2) result in staying put, which means the player does not win. The remaining four outcomes (3, 4, 5, and 6) move the game piece, increasing the chances of winning. As the game piece can only reach or pass the winning box W by moving two boxes to the right, there are two favorable outcomes out of six possibilities. Thus, the probability of winning after one toss is 2/6 or simplifying further, 1/3.

b) To find the probability of winning after tossing the die twice, we need to consider the possible combinations of outcomes. Each toss of the die has six equally likely outcomes, resulting in a total of 36 possible combinations for two tosses. Out of these combinations, there are three scenarios in which the game piece can win: (3, 3), (4, 4), and (5, 6). Therefore, the probability of winning after two tosses is 3/36, which simplifies to 1/12.

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Related Questions

Find the missing dimensions. Use the scale factor 1 inch:12 feet. A plastic toy bird has a wingspan of 5 inches. What is the actual bird wingspan? USE NUMBERS ONLY Your answer

Answers

Answer: 60 feet

Step-by-step explanation:

Fron the question, we have been told to use a scale factor of 1 inch:12 feet. This simply means that 1 inch has been represented to 12 feet of the actual dimension.

We are further told that a plastic toy bird has a wingspan of 5 inches. The actual bird wingspan will therefore be 5 multiplied by 12 feet and this will be:

= 5 × 12 feet

= 60 feet

A plastic toy bird that has a wingspan of 5 inches has an actual bird wingspan of 60 feet

can anyone help with integers?

Fill in the blanks.

6) 83 + 17 = 17 +

7) |46| – |50| =

8) 42 – 2 + (18 – 10) =

9) 18 – (3 – 1) =

10) 8 - 0 =

Answers

Answer:

a) 83,b) -4,c) 48,d) 16,e) 8

Problem 1: Consider the following matrix A E M (3,3) 1 -42 0 0 t-3 Where t E R is a real parameter. Determine the rank of the matrix as function of the parameter t

Answers

Answer:

rank(A) = 2 if t ≠ 3

rank(A) = 3 if t = 3

Step-by-step explanation:

For the matrix A, we can perform the following row operations:

R2 = R2 - 42R1

This gives us the following matrix:

[1 -42 0]

[0 t-3 0]

The second row is a multiple of the first row, so it is linearly dependent on the first row. Therefore, the rank of the matrix is 2.

The rank of the matrix is a function of the parameter t. When t = 3, the second row is not a multiple of the first row, so the rank of the matrix is 3. When t ≠ 3, the second row is a multiple of the first row, so the rank of the matrix is 2.

Therefore, the rank of the matrix is given by the following function:

rank(A) = 2 if t ≠ 3

rank(A) = 3 if t = 3

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for breakfast you eat a bowl of oatmeal and 1/4 cup of added raisins, for lunch, a turkey sandwich and a glass of fresh orange juice. how many servings of fruit and cereal have you had?

Answers

For breakfast, you have had 1/2 a serving of cereal and 1/4 cup of raisins, which count as one serving of fruit.

For breakfast, you have had one serving of cereal and one serving of fruit. In general, one serving of cereal is considered to be one cup, while one serving of fruit is considered to be one half cup. Therefore, in your bowl of oatmeal, you would have had two servings of cereal, and in your quarter cup of raisins, you would have had one serving of fruit. For lunch, you have had one serving of fruit in your glass of orange juice.

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In the data set below, what is the median

Answers

The answer is: 2
arrange numbers in numerical order than what ever is in the middle is the answer is there are two numbers in the middle add then then divide by 2

A penny is commonly a commonly used coin in the U.S monetary system. A penny has a diameter of 19 millimeters and a thickness of 1.27 millimeters. The volume of a penny is 360 cubic millimeters. Suppose you stack 10 pennies on top of each other to form a cylinder.A. what is the height of the stack of penniesB. What is the volume of the stack of pennies

Answers

The volume of the stack of pennies is 3600 cubic millimeters.

To find the height of the stack of pennies, we need to first find the height of one penny. Since the diameter of a penny is 19 millimeters, its radius is half of that, which is 9.5 millimeters. We can use the formula for the volume of a cylinder (V = πr^2h) to find the height of one penny:

360 cubic millimeters = π(9.5 mm)^2h

h ≈ 0.99 millimeters

So the height of one penny is approximately 0.99 millimeters. To find the height of the stack of 10 pennies, we simply multiply the height of one penny by 10:

height of stack = 10 x 0.99 mm

height of stack = 9.9 millimeters

Therefore, the height of the stack of pennies is approximately 9.9 millimeters.

B. The volume of the stack of pennies can be found by multiplying the volume of one penny by the number of pennies in the stack. The volume of one penny is given as 360 cubic millimeters. Since we have 10 pennies in the stack, we can find the volume of the stack as follows:

volume of stack = volume of one penny x number of pennies in stack

volume of stack = 360 mm^3 x 10

volume of stack = 3600 cubic millimeters

Therefore, the volume of the stack of pennies is 3600 cubic millimeters.

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What is the value of the discriminant, b2 − 4ac, for the quadratic equation 0 = −2x2 − 3x + 8, and what does it mean about the number of real solutions the equation has?

The discriminant is −55, so the equation has 2 real solutions.
The discriminant is −55, so the equation has no real solutions.
The discriminant is 73, so the equation has 2 real solutions.
The discriminant is 73, so the equation has no real solutions.

Answers

The value of the discriminant b² - 4ac is 73.

The number of real solutions the equation has is two.

What is an equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

-2x² - 3x + 8 = 0

This is in the form of ax² + bx + c = 0

a = -2, b = -3, and c = 8

Now,

b² - 4ac

= (-3)² - 4 x (-2) x 8

= 9 + 64

= 73

This is a positive value.

This means,

The equation has two real solutions.

Thus,

The equation has two real solutions.

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7 moive tickets for $56

Answers

Answer:

what movie, cuz $8 per ticket for some reason feels super cheap

Step-by-step explanation:

while playing a game, amy defeated 6 enemies with each enemy defeated earning her 2511 points. if she traded all her points for 3 extra lives, how many points is it per life

Answers

Therefore , the solution of the given problem of unitary method comes out to be Points equal 5020 for each life.

What is meant by unitary method?

The unitary strategy is a way of solving problems that involves first figuring out how much of a single model there is, then multiplying that value to achieve the solution. Simply described, the unit technique is used to retrieve a single program value from a supplied many. As an example, 40 pens cost 400 rupees ($1.01), or Rs. It's possible that the procedure utilized to do this will be regulated. a single country. Anything has a distinguishing feature. Its capable of integrating and reciprocal are equal (mathematics, algebra).

Here,

There are 5 enemies.

Each adversary is worth 3012 points.

Total points: 15060 (or 3012 multiplied by 5)

There are 3 lives left.

Points for every life equal?

Points per life are calculated as follows: total points / quantity of life = 15060/3

Points equal 5020 for each life.

Therefore , the solution of the given problem of unitary method comes out to be Points equal 5020 for each life.

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a dairy farmer is interested in knowing the true mean april 2023 retail whole milk price ($/gallon) for all us cities. previous studies have shown the standard deviation of the milk prices is $0.60. determine the number of cities that must be sampled in order to estimate the true mean within $.10 with 95% confidence.

Answers

The dairy farmer needs to sample at least 139 cities to estimate the true mean April 2023 retail whole milk price within $0.10 with 95% confidence.

To estimate the true mean April 2023 retail whole milk price with a margin of error of $0.10 and 95% confidence, a dairy farmer can use the sample size formula for estimating population means. The formula is:
n = (Z² × σ²) / E²
where n is the sample size, Z is the z-score corresponding to the desired confidence level, σ is the standard deviation of the population, and E is the margin of error.
For a 95% confidence level, the z-score (Z) is 1.96. The standard deviation (σ) of milk prices is $0.60, and the margin of error (E) is $0.10. Plugging these values into the formula, we get:
n = (1.96² × 0.60²) / 0.10²
n = (3.8416 × 0.36) / 0.01
n ≈ 138.56
Since the sample size must be a whole number, we round up to the nearest whole number to ensure the desired level of accuracy. Therefore, the dairy farmer needs to sample at least 139 cities to estimate the true mean April 2023 retail whole milk price within $0.10 with 95% confidence.

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Find the 30th term of the geometric sequence 100, 80, 64,...
Give
your answer to 3 significant figures.

Answers

Answer:

0.155

Step-by-step explanation:

nth term of a geometric sequence = ar^n-1

Where,

a = first term

r = common ratio

n = number of terms

Given:

100, 80, 64,...

a = 100

r= 80/100

= 4/5

30th term of a geometric sequence = ar^30-1

= ar^29

= 100 × (4/5)^29

= 100 × (0.8)^29

= 100 × 0.00155

= 0.155

Therefore,

30th term of the geometric progression = 0.155

A sports team came to town. the stadium filled all 10,000 seats at two-level pricing. level 1 tickets are $50 each, and level 2 tickets are $150 each. the stadium made $75,000 in ticket sales. the system of equations that models this scenario is: x + y = 10,000 50x + 150y = 75,000 what do the x and y represent in the system?

Answers

x represents the number of tickets of level 1 and y represents the number of tickets of level 2 in the system given that there are 10,000 seats, level 1 tickets are $50 each, and level 2 tickets are $150 each and equation representing the situation:x + y = 10,000, 50x + 150y = 75,000. This can be obtained by understanding the question and observing the equations.

What do the x and y represent in the system?

Given that total number of seats is 10,000 and there are two levels pricing.

Thus by observing the equation, x + y = 10,000,

10,000 is the sum of 2 variable which obviously will be the number of tickets in level 1 and number of tickets in level 2.

Since there are two level pricing,

50x + 150y = 75,000 represent the addition of total cost of tickets of level 1 and 2.

Hence x represents the number of tickets of level 1 and y represents the number of tickets of level 2 in the system given that there are 10,000 seats, level 1 tickets are $50 each, and level 2 tickets are $150 each and equation representing the situation:x + y = 10,000, 50x + 150y = 75,000.

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PLEASE HELP ASAP 100 POINTS BRAINLIST
uppose you toss a coin and then roll a number cube.

What is the sample space for the compound event?

Question 9 options:

H1 T1 H2 T2 H3 T3 H4 T4 H5 T5 H6 T6

TH1 TH2 TH3 TH4 TH5 TH6

H T 1 2 3 4 5 6

H1 T1 H6 T6

Answers

Two at once

Sample space for coin

{H,T}

Sample space for cube

{1,2,3,4,5,6}

Combine sample space

{H1,H2,H3,H4,H5,H6,T1,T2,TE,T4,T5,T6}

Option A

The side lengths of a 30-60-90 triangle are in the ratio 1 : 3:2. What is
sin 30°?

Answers

Answer:

1/2

Step-by-step explanation:

Answers

Answer:

Step-by-step explanation:

answer B

since for all real positive r, r^x >0

The unique function who give a negative answer is f(x)=-3* 2^x

I need the answer, pls help!!!

Answers

Answer:

x = 19

Step-by-step explanation:

M is the mid-point of XZ. So , XM = ZM ( A mid-point divides a line segment into 2 equal parts. )

It's given that length of XM = 2x + 35 & length of MZ = 5x - 22

So ,

$2x+35=5x-22\\=>5x-2x=35+22\\=>3x=57\\=>x=\frac{57}{3} =19$

Sam, Joe and Nancy are all diving. They each have the following pressure rates in their aluminum cylinders tank:

Sam has 3000.805, Joe has 3000.895 and Nancy has 3000.804. Who has the highest amount of pressure in their tank? Who has the least amount of pressure?

I've asked this question 3 times please answer

Answers

Answer:

Nancy High

Joe Low

mary drew a picture of a building. she used the scale shown 1 in:16 ft. the building in her pictures 9 inches tall. what is the height, in feet, of the actual building.

Answers

Answer:

okay

i am not sure the answer but hi i am ok

Suppose there is a 1.6°F drop in temperature for every thousand feet that an airplane climbs into the sky. If the temperature on the ground is 58.3°F, what will be the temperature when the plane reaches an altitude of 2,000 ft?

Answers

Answer: 55.1°F

Step-by-step explanation:

We are informed that there is a 1.6°F drop in temperature for every thousand feet that an airplane climbs into the sky, if the plane reaches an altitude of 2,000ft, the drop in temperature will be:

= 1.6° × 2

= 3.2°F

If the temperature on the ground is 58.3°F, then the temperature when the plane reaches an altitude of 2,000 ft will be:

= 58.3°F - 3.2°F

= 55.1°F

What is the solution for the equation?

-5/2=3/4+n

A. N=-13/4
B. N=-7/4
C. N=7/4
D. N=13/4

Answers

Answer:

A. n = -13/4

Step-by-step explanation:

well, it can be changes to

-10/4 = 3/4 + n

subtract 3/4

-13/4 = n

A compressive load of 80,000 lb is applied to a bar with
circular section0.75indiameter and a length of 10 in. if the
modulus of elasticity of the bar material is10,000 ksi and the
Poisson’s ratio i

Answers

The decrease in diameter of the bar due to the applied load is -0.005434905d and the final diameter of the bar is 1.005434905d.

A compressive load of 80,000 lb is applied to a bar with a circular section of 0.75 in diameter and a length of 10 in.

if the modulus of elasticity of the bar material is 10,000 ksi and the Poisson's ratio is 0.3.

We have to determine the decrease in diameter of the bar due to the applied load.

Let d be the initial diameter of the bar and ∆d be the decrease in diameter of the bar due to the applied load, then the final diameter of the bar is d - ∆d.

Length of the bar, L = 10 in

Cross-sectional area of the bar, A = πd²/4 = π(0.75)²/4 = 0.4418 in²

Stress produced by the applied load,σ = P/A

= 80,000/0.4418

= 181163.5 psi

Young's modulus of elasticity, E = 10,000 ksi

Poisson's ratio, ν = 0.3

The longitudinal strain produced in the bar, ɛ = σ/E

= 181163.5/10,000,000

= 0.01811635

The lateral strain produced in the bar, υ = νɛ

= 0.3 × 0.01811635

= 0.005434905'

The decrease in diameter of the bar due to the applied load, ∆d/d = -υ

= -0.005434905∆d

= -0.005434905d

The final diameter of the bar,

d - ∆d = d + 0.005434905d

= 1.005434905d

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3. x + y = 15
X - y = 3
solving systems of equations

Answers

Answer: x=10 y=5 = 15xy

Step-by-step explanation:

Graph each of the following. Label the axis of symmetry and the vertex.
y=2x^2-4x+1
y=2x^2+8x+6

Plz help!!!

Answers

Answer:

See below

Step-by-step explanation:

Attached are the two graphs where the blue line represents the axis of symmetry.

Graph each of the following. Label the axis of symmetry and the vertex. y=2x^2-4x+1 y=2x^2+8x+6Plz help!!!

guys pls help me!!!!!!!

Answers

Answer:

Step-by-step explanation:

9y - 6 + 51 = 90

9y + 45 = 90

9y = 45

y = 5.

The answer is y is equal to 5.

The symbol in the corner tells us that the corner is 90 degrees. So much sides added together is 90.
9y - 6 + 51 = 90
9y + 45 = 90
9y = 45
y = 5

What is the equation of the line that passes through the points 1/2/3 and (-1,-1

a.y=-6x+5

b.Y=5/6X-1/6

C.Y=2/3X+1/5

D.y=6/5x+1/5

Answers

Answer:

(1, 2/3) (-1, -1) are the points. use the slope formula to find the slope y2-y1/x2-x1

(-1 - 2/3) / (-1 -1) (answer both sides of the division side)

-5/3 / -2 (divide)

slope = 5/6 (the slope)

plug in values you know into point-slope form (y -y1) = m(x-x1)

y - (-1) = 5/6 (x - (-1) (i chose the easier point to plug in. two neg. make a pos. )

y +1 = 5/6 (x +1) (use the distributive property)

y +1 = 5/6x+5/6 (subtract 1 from both sides)

y = 5/6x - 1/6 or B (this is the equation)

Step-by-step explanation:

I hope this helped :))

what is the probability, to the nearest hundredth, that a point chosen randomly inside the rectangle is in the triangle?

Answers

The probability that a point chosen randomly inside the rectangle is in the triangle is 1/3, or approximately 0.33 to the nearest hundredth.

The probability that a point chosen randomly inside the rectangle is in the triangle is equal to the area of the triangle divided by the area of the rectangle.

To find the area of the triangle, we need to first find its base and height. The base of the triangle is the length of the rectangle, which is 8 units. To find the height, we need to draw a perpendicular line from the top of the rectangle to the base of the triangle. This line has a length of 4 units. Therefore, the area of the triangle is (1/2) x base x height = (1/2) x 8 x 4 = 16 square units.

The area of the rectangle is simply the length times the width, which is 8 x 6 = 48 square units.

Therefore, the probability that a point chosen randomly inside the rectangle is in the triangle is 16/48, which simplifies to 1/3.

In conclusion, the probability that a point chosen randomly inside the rectangle is in the triangle is 1/3, or approximately 0.33 to the nearest hundredth.

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just need a little homework help (slopes)

Answers

The Y- Intercept (b) is (0,-5)
And the Slope (m) is 2/3
Also (x,y) are of the points on the line <3
Hope this helps, I was doing this in class ealier today!

Lola's school is 2.8 kilometers west of her house and 8.4 kilometers south of her friend Deion's house. Every day, Lola bicycles from her house to her school. After school, she bicycles from her school to Deion's house. Before dinner, she bicycles home on a bike path that goes straight from Deion's house to her own house. How far does Lola bicycle each day? If necessary, round to the nearest tenth.

Answers

The distance that Lola bicycles each day totals to the nearest tenth to 20.1 km.

Given that,

Lola's school is 2.8 kilometers west of her house and 8.4 kilometers south of her friend Deion's house.

Using the Pythagoras theorem,

Distance between Lola's house and her friend Deion's house is,

D = √(2.8)² + (8.4)² = √78.4 = 8.854

Total distance she travels in a day = 2.8 + 8.4 + 8.854

= 20.054 km ≈ 20.1 km to the nearest tenth.

Hence the total distance is 20.1 km.

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The following data (stored in ) represent the amount of soft drink in a sample of 50 2-liter bottles: 2.109 2.086 2.066 2.075 2.065 2.057 2.052 2.044 2.036 2.038 2.031 2.029 2.025 2.029 2.023 2.020 2.015 2.014 2.013 2.014 Construct a cumulative percentage distribution and discuss one suitable graph for the given data set.

Answers

The following is the cumulative percentage distribution of the given data set. Class intervals Frequency Cumulative frequency Percentage Percentage cumulative frequency 2.01-2.0456 12 24.00% 24.00% 2.046-2.0815 28 56.00% 80.00% 2.082-2.1177 6 12.00% 92.00% 2.118-2.154 1 2.00%

The best-suited graph for the given data set is a histogram. A histogram shows the spread of the data by forming groups, or classes of the data and displaying the data in a bar-like manner with the height of the bar representing the frequency or count of the observations in the respective class intervals.

A cumulative percentage distribution is used to determine the percentage of the total frequency that is less than the given class interval.The cumulative frequency column is created by adding the frequency of each class to the sum of all frequencies below it. The percentage column is created by dividing the frequency column by the total number of observations (50), then multiplying by 100.The best-suited graph for the given data set is a histogram. A histogram shows the spread of the data by forming groups, or classes of the data and displaying the data in a bar-like manner with the height of the bar representing the frequency or count of the observations in the respective class intervals.

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whats the answer!! please asap

Answers

Answer:1/90

Step-by-step explanation:

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