Consider the experiment of rolling fair six-sided die until a 5 is observed. Let A be the event that a 5 is observed on the first roll. Let B be the event that it takes at least two rolls for the first 5 to be observed. Find the following probabilities. (Round to nearest 4 decimal places)
P(A∩B)
P (A)
P(B)

Answers

Answer 1

Answer:

P(A∩B) = 0

P(A) = 0.1667

P(B) = 0.8333

=================================================

Explanation:

The events

A = a 5 is observed on the first rollB = it takes at least two rolls for the first 5 to be observed

are mutually exclusive. There isn't any overlap. This is because event B involves "at least 2 rolls", meaning we cannot get 5 on the first roll. Either event A happens, or B does, but not both at the same time.

This allows us to say P(A∩B) = 0

In a venn diagram, the overlapped region between circles A and B would have probability 0 marked inside.

-----------------------

P(A) = 1/6 since there is exactly one side labeled "5" out of 6 sides total. This converts to the approximate decimal form 1/6 = 0.1667 when rounding to four decimal places. The 6's go on forever, but of course we have to round at some point.

------------------------

We found that P(A) = 1/6. The complement to this is 1-(1/6) = 5/6, which is the probability of rolling anything but a "5". This fraction represents the scenario "at least 2 rolls are needed for the 1st '5' to show up" since we forced the first roll to be anything but 5.

Put another way, we have two options:

Option 1: The first roll is "5". The probability is 1/6Option 2: The first roll is NOT "5" (so you'll need to do at least another roll to get "5"). The probability is 5/6.

The two probabilities 1/6 and 5/6 add to 6/6, aka 1, to represent 100% of all possible cases. This means P(A)+P(B) = 1 for this scenario.

The fraction 5/6 converts to the approximate decimal form of 5/6 = 0.8333; use a calculator or long division to determine this value.


Related Questions

Please help me I’m stuck-

Answers

I think it’s yes I might be wrong tho

Answer:

No

Step-by-step explanation:

to be right angled triangle,

h^2=p^2+b^2

,15^2=12^2+8^2

,225=144+64

,225=208

Since 225 is not equal to 208

It is not a right angled triangle

Please Help ASAP willgive brainliest

Answers

Answer:

B, C, D

Step-by-step explanation

bascially flip the figure upside down. whatever was parallel before stays parallel

Determine the simple interest. The rate is an annual rate. Assume 360 days in a year.

Answers

According to the previous sentence, simple interest is equivalent to $157.92.

Just curious: What is it?

With only the starting principal and a fixed interest rate, simple yearly interest of government debt interest is calculated. Compounding, which results in borrowers paying tax on both the principal and interest across a number of payment intervals, is not included. To calculate simple interest, multiply the original by the timeframe, rates of return, and duration.

Due to it,

P = $582.09

R = 8.3%

T = 89 days

Now, Simple Interest = P*R*T/100

Simple Interest = 582.09 * 8.3 * 89/100

Simple Interest = 4299.89

Simple Interest would be $4299.89 as a result.

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F(x)=[[x]]. What is f(10)

Answers

Fx(10)=10
Y=10
You plug in the 10 for the x

What percentage of the budgeted food is the actual food?

Budgeted: 200
Actual: 230

Answers

The actual food is 115% of the budgeted food.

What is the percentage?

The percentage is defined as a ratio expressed as a fraction of 100.

The data is given in the question, as follows:

Budgeted: 200

Actual: 230

To determine the percentage of the budgeted food that is the actual food, we can divide the actual amount by the budgeted amount and multiply by 100.

Percentage = (Actual / Budgeted) * 100

Percentage = (230 / 200) x 100

Percentage = 1.15 x 100

Apply the multiplication operation, and we get

Percentage = 115%

So, the actual food is 115% of the budgeted food.

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What is the slope of the line passing through the points (2, 5) and (-1,-4)?

Answers

Answer:

m=3

Step-by-step explanation:

slope of the line is 3

mark me the brainliest

Mr. Tabor believes that less than 75% of the students at his school completed their math homework last night. The math teachers inspect the homework assignments from a random sample of 50 students at the school. The math teachers inspect the homework assignments from a random sample of 50 students at the school. Only 68% of the students completed their math homework. A significance test yields a P-value of 0.1265. 1a. Explain what it would mean for the null hypothesis to be true in this setting. 1b . Interpret the p-value. 1c. What conclusion would you make at the alpha = 0.05 signifigance level?

Answers

Answer:

1a. The null hypothesis in this setting would mean that the proportion of students who completed their math homework is equal to or greater than 75%.

1b. The p-value represents the probability of observing a sample proportion as extreme as or more extreme than the sample proportion observed (68%), given that the null hypothesis is true. In this case, the p-value of 0.1265 indicates that there is a 12.65% chance of observing a sample proportion as extreme or more extreme than 68%, assuming the true proportion is equal to or greater than 75%.

1c. At the alpha = 0.05 significance level, we reject the null hypothesis if the p-value is less than 0.05. In this case, the p-value of 0.1265 is greater than 0.05, meaning we fail to reject the null hypothesis. Therefore, at the alpha = 0.05 significance level, we cannot conclude that less than 75% of students completed their math homework.

Sheridan Industries had sales in 2021 of $7,752,000 and gross profit of $1,254,000. Management is considering two alternative budget plans to increase its gross profit in 2022.

Answers

The cost of sales for Sheridan Industries, given the gross profit and the sales, is $ 6, 498, 000

How to find the cost of sales ?

The cost of sales refers to the amount that the company invested to be able to make the sales they did. This includes the cost of purchases of goods which were then sold ( or their cost of manufacturing ).

The cost of sales to Sheridan Industries can be found by the formula :

= Sales - Gross profit

The cost of sales is therefore :

= 7, 752, 000 - 1, 254, 000

= $ 6, 498, 000

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The full question is:

Sheridan Industries had sales in 2021 of $7,752,000 and gross profit of $1,254,000. Management is considering two alternative budget plans to increase its gross profit in 2022. To do this this, management first needs to determine its cost of sales. Find the cost of sales for 2021.

Stefany's salary at her company, Horizon Logistics starts at a base salary of $60,000. The table below shows her salary g(x) after x years. Write an explicit rule for the g(x).
help lssssa​

Answers

The explicit rule for the g(x) is g(x) = 54000 + 6000x

How to determine the explicit rule

The definition of the function is given as

Initial = 60000

And the table of values

The definitions from the table imply that we simply add 6000 to the previous term to get the current term

This means that

Common difference, d = 6000

The sequence is then represented as

f(x) = a + (x - 1)d

So, we have

f(x) = 60000 + (x - 1) * 6000

Evaluate

f(x) = 54000 + 6000x

Hence, the equation is f(x) = 54000 + 6000x

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What is the Cartesian form of (5i-3)?

Answers

Answer: The Cartesian form of a complex number is the expression of the number in the form of x + yi, where x and y are real numbers and i is the imaginary unit.

The Cartesian form of (5i - 3) is 0 + (5i - 3).

Step-by-step explanation:

A bean plant measures 1.5 cm and grows 0.1 cm per day. A tomato plant of 0.85 cm grows steadily too. How much can it grow each day knowing that it will have the same height as the bean plant in no more than 10 days?

Answers

Answer:

Let's call the growth rate of the tomato plant "g". We know that the height difference between the tomato plant and the bean plant decreases by 0.1 cm per day, so we can write the following equation:

1.5 - 0.85 - (10 * g) = 0

Solving for g:

g = (1.5 - 0.85) / 10 = 0.065 cm/day

So the tomato plant grows at a rate of 0.065 cm per day, and will reach the height of the bean plant in no more than 10 days.

The tomato plant will grow 0.165 cm per day.

Solution:

Given,

Height of bean plant = 1.5 cm

Height of tomato plant = 0.85 cm

The growth rate of bean plant = 0.1 cm/ day

The bean plant will grow 1.5 + (0.1* 10) in 10 days = 2.5 cm

So, the tomato plant will have to grow (2.5 - 0.85) cm in 10 days = 1.65 cm

Since, the tomato plant will grow steadily,

Hence, 1.65/ 10 = 0.165

Therefore, the tomato plant will grow at a rate of 0.165 cm per day

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How many solutions does this system have
X+3y=0
Y=-8+2

Answers

Answer: x=18 and y=-6

Step-by-step explanation:

y=-6; x+3y=0    

Composition of Functions
f(x)=-4x+9,g(x)=x^(2)-x-10, find the value of fog(5)

Answers

Answer: Given f(x) = -4x + 9 and g(x) = x^2 - x - 10, the composition of functions fog(x) is defined as fog(x) = f(g(x)).

To find the value of fog(5), we need to evaluate g(5) first:

g(5) = 5^2 - 5 - 10 = 20

Now that we have g(5) = 20, we can substitute it into f(x) to find fog(5):

fog(5) = f(g(5)) = f(20) = -4 * 20 + 9 = -79

So, the value of fog(5) is -79.

Step-by-step explanation:

Translate this sentence into an equation. 171 is the product of 9 and Rhonda’s height. Use the variable R to represent Rhonda’s height

Answers

Answer:

171=9R

Hope this helped! :)

Answer:Rx9=171

Step-by-step explanation:

An item is regularly priced at $47. Joe bought it at a discount of 65% off the regular price. Use the ALEKS calculator to find how much Joe paid. ​

Answers

Joe paid $17 for the item

Using Pythagorean Theorem, Find the area of the right triangle.
Be sure to include the correct unit in your answer.
20 m
25 m

Answers

Answer:

Step-by-step explanation:

Winston installs a fence post every eight yards after the first post he installs 25 more how long is the fence that he builds​

Answers

The length of the fence that Winston installs is 200 yards

What is an equation?

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

Winston installs a fence post every eight yards after the first post he installs 25 more, therefore:

The length of the fence = 8 yards * 25 post = 200 yards

The length of the fence is 200 yards

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Cual es el producto de x(x+1)?

Answers

Answer:

x² + x

Step-by-step explanation:

x(x+1) →

[a(b + c) = ab + ac]

x (x) + x (1) →

[x • x = x²] + [x • 1 = x] →

x² + x

How many quarts of pure antifreeze must be added to 2 quarts of a 30 % antifreeze solution to obtain a 40 % antifreeze solution ?

( blank )quart ( s ) of pure antifreeze must be added

( Round to the nearest tenth as needed )

Answers

Answer:

x = 2

Step-by-step explanation:

To obtain a 40% antifreeze solution, we need to add more antifreeze to the 30% solution. Let's call the amount of pure antifreeze that needs to be added x. Then, the amount of antifreeze in the solution will be 2 + x quarts.

The concentration of antifreeze in the solution will be:

(0.30 * 2) + (0.100 * x) = 0.40 * (2 + x)

Solving for x:

0.60 + 0.100x = 0.40 * (2 + x)

Expanding the right-hand side:

0.60 + 0.100x = 0.80 + 0.40x

Solving for x:

0.100x = 0.20

x = 2

So, 2 quarts of pure antifreeze must be added to obtain a 40% antifreeze solution.

Find the volume of each solid. Round to the nearest tenth if necessary. There’s to questions so there is two answers. 1=? 2=?

Answers

The volume of the sphere with radius 5 yd rounded to the nearest tenth is 523.3 yd³.

What is the volume of the sphere?

The volume of a sphere is expressed as;

V = 4/3 × π × r³

Where r is radius and constant pi π = 3.14.

Given the data in the question;

Radius r = 5 ydVolume V = ?

To find the volume of the sphere, plug the given value into the above formula and simplify.

V = 4/3 × π × r³

V = 4/3 × 3.14 × ( 5 yd )³

V = 4/3 × 3.14 × 125 yd³

V = 523.3 yd³

Therefore, the volume of the sphere is 523.3 yd³.

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URGENT URGENT URGENT !!!
If I make $12 per hour, how many hours must I work to make $30

Answers

Answer:

2 hours and a half

Step-by-step explanation:

The following frequency distribution presents the batting averages Major League Baseball players who had 300 or more plate appearances during recent season; Batting Average Frequency 0.180-0.199 0.200-0.219 0.220-0.239 0.240-0.259 0.260-0.279 0.280-0.299 0.00-0.319 0.320-0,339 0.340-0.359

Answers

The construction of the graph is shown here.

Also cumulative frequency in the table form mentioned here. This can be solved using the concept of frequency distribution.

What is frequency distribution?

Tables or charts of frequency distributions are used to represent them. Frequency distributions can display the proportion of observations or the actual number of observations that fall inside each range. The distribution is known as a relative frequency distribution in the latter case.

Relative frequency distributions and cumulative frequency distributions are the two primary forms of frequency distributions utilised in data analysis. Both depend on frequency, which is the amount of times something happens inside a specific data set in descriptive statistics.

Class                       Frequency                        Cumulative frequency              

0.180-0.199                  2                                      2

0.200-0.219                10                                     12

0.220-0.239               39                                    51

0.240-0.259               56                                    107

0.260-0.279               60                                     167

0.280-0.299               49                                     216

0.300-0.319               27                                      243

0.320-0.339               12                                      255

0.340-0.359                1                                        256

The construction of the graph is shown below:

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The complete question is as follows:

The blocks in a city are all perfect Squares.
A friend gives you.
the following directons
to
a good resturant; "go north 3 blocks
turn East and go sblocks,
and go 76locks,
Turn South
turn West and go
3 blocks" How far away (Straight line
distance) is the resturant ?

Answers

The straight line distance is 13 blocks.

How do you get the straight line distance?

We know that we can be able to obtain the straight line distance by looking at the information that has been provided by the question. We are told in the question that; you go north 3 blocks turn East and go blocks, and go 7 blocks turn South turn West and go 3 blocks.

We know that the distance is not a vector quantity as such, we do not look at the direction of the movement. We would only be concerned about the magnitude of the distance.

Thus we have the straight line distance as; 3 + 7 + 3 = 13 blocks

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for a list of positive numbers, it is possible for the standard deviation to be greater than the mean? if so, give the example. if not, explain why not.

Answers

It is possible that the standard deviation is greater than the mean for a list of positive numbers.

What is standard deviation?

The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability.

Take into consideration, the list of numbers -

1,2,3,4,5,20

The mean formula is - Number of observations / Total observations.

Substitute the values in the equation -

Mean = 1 + 2 + 3 + 4 + 5 + 20 / 6

Mean = 35 / 6

Mean (x') = 5.833

The number of observations is n = 6

The variance is the sum of squared deviations from the mean divided by

n−1.

The standard deviation is the square root of the variance -

s = {√(1 - 35/6)² + .... + (20 - 35/6)²} / (6-1)

s = 7.0828

Therefore, the standard deviation is higher than the mean.

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You have decided to build your shelter close enough to the coastline to be able to fish but far enough away to not bear the brunt of the bitter cold winds. After watching previous seasons of the show, you decide that 50 meters is a good distance away from the coastline. To estimate, you will convert meters to feet (you do not have a tape measure). How many feet is this?

Answers

50 meters in feet is 164.042 feet

How to convert from meters to feet

In order to convert meters to feet we would have to cross multiply

That is. one meter is given as 3.28084 feet

We are to convert 50 meters to feet, hence we would have:

If 1 meter = 3.28084

50 meters = ?

When we cross multiply, we would have

? = 3.28084 * 50 meters

? = 164.042

Hence the amount of 50 meters in feet is given as 164.042 feet

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Find the volume of the figure. Express answers in terms of pi
​, then round to the nearest whole number.

Answers

Answer:

36π in.³

113 in.³

Step-by-step explanation:

V = (4/3)πr³

V = (4/3)π(3 in.)³

V = 36π in.³

V ≈ 113 in.³

The perimeter of a rectangle is 60 cm. Its width measures
16 cm. What is its length?
Let x= the length of the rectangle. Choose the equation that represents this
problem.
O A. 2x-32=60
O B. 2x+16=60
O C. 2x+32=60
O D. x+16=60

Answers

O D. x+16=60

The answer

The subtotal for Abdiel's takeout order is $21.50. What will Abdiel's total be if he uses a coupon for 10% off the subtotal and leaves a 20% tip before the discount? (2 points)
$22.15
$27.95
$23.22
$23.65

Answers

Answer:

Abdiel's total would be $23.22, which is the answer choice C.

Step-by-step explanation:

The total cost of Abdiel's order would be calculated as follows:

Calculate the tip before the discount: $21.50 x 20% = $4.30

Add the tip to the subtotal: $21.50 + $4.30 = $25.80

Calculate the discount: $25.80 x 10% = $2.58

Subtract the discount from the total cost: $25.80 - $2.58 = $23.22

So, Abdiel's total would be $23.22, which is the answer choice C.

Solve for 4|u-2| +6 < 42

Answers

Pls let me know if this is right -10ltxlt14

How can I find the perimeter of rectangle

Answers

Answer:

19

Step-by-step explanation:

top = bottom so 4x-4y = 3x+5y so x = 9y

left = right so 2-2y = x-3y so x= y+2

so 9y = y+2

8y = 2

y= 0.25

x=2.25

so just add them all up

2*(4x-4y) + 2*(2-2y )

= 8*(x-y)+4*(1-y)

=16+4*0.75

=19

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