suppose a contestant has earned $800 on his or her first three spins and chooses to spin the wheel again. what is the expected value of his or her total winnings for the four spins?

Answer:

see below (I hope this helps!)

Step-by-step explanation:

Alternate exterior angles are congruent so we know that ∠2 ≅ ∠ 7. Vertical angles are also congruent so ∠7 ≅ ∠6. Consecutive interior angles are supplementary so we know that ∠6 and ∠4 are supplementary. Now, we can use the Transitive Property (this states that if a = b and b = c then a = c) to compare ∠2 and ∠4. In this case, a = ∠2, b = ∠7 and c = ∠6 so we know that ∠2 ≅ ∠6 and since ∠6 is supplementary to ∠4, we can use the Transitive Property again to conclude that ∠2 and ∠4 are supplementary.

Scott does 35 sit-ups altogether every night.

A ratio is a comparison of two quantities, expressed as the quotient of one quantity divided by the other. Ratios can be written in different forms, such as using a colon (:) or a fraction (/).

For every 2 straight-leg sit-ups, Scott does 3 bent-leg sit-ups. Therefore, the ratio of straight-leg sit-ups to bent-leg sit-ups is 2:3.

If Scott does 10 straight-leg sit-ups every night, we can use this ratio to find out how many bent-leg sit-ups he does.

First, we can write the ratio as a fraction:

2/5 = 10/x

where x is the number of bent-leg sit-ups Scott does.

To solve for x, we can cross-multiply:

2x = 50

x = 25

Therefore, Scott does 25 bent-leg sit-ups every night.

To find the total number of sit-ups Scott does every night, we can add the number of straight-leg sit-ups to the number of bent-leg sit-ups:

10 + 25 = 35

Therefore, Scott does 35 sit-ups altogether every night.

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The statement is false. If f and g are continuous on [a, b], it does not imply that ∫[a to b] (f(x) × g(x)) dx = ∫[a to b] f(x) dx × ∫[a to b] g(x) dx

In general, the integral of the product of two functions, f(x) and g(x), is not equal to the product of their individual integrals.

To counter the statement, we can provide a counterexample. Consider two continuous functions, f(x) = x and g(x) = x, defined on the interval [0, 1]. The integral of their product, ∫[0 to 1] (f(x) * g(x)) dx, is equal to ∫[0 to 1] (x × x) dx = ∫[0 to 1] \(x^{2}\) dx = 1/3.

On the other hand, the individual integrals of f(x) and g(x) are ∫[0 to 1] f(x) dx = ∫[0 to 1] x dx = 1/2 and ∫[0 to 1] g(x) dx = ∫[0 to 1] x dx = 1/2, respectively. The product of these individual integrals, (1/2) × (1/2) = 1/4, is not equal to the integral of the product.

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The likelihood of the event is 1/2

In calculating a one-sample chi-square test with 3 degrees of freedom, the variable has 4 categories.

Step-by-step explanation:
1. The degrees of freedom (df) in a one-sample chi-square test are calculated as df = k - 1, where k is the number of categories.
2. Given that there are 3 degrees of freedom, we can solve for k: 3 = k - 1.
3. Add 1 to both sides of the equation: 3 + 1 = k.
4. Therefore, k = 4, meaning there are 4 categories in the variable.

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This question can be solved using an Algebraic equation.

The system of equations is given as:

x + y ≤ 10

8x + 16y ≥ 96

Let's represent

x = number of hours he walks the dogs

y = number of hours he works as a maths tutor

John must work for no more than 8 hours walking the dog and 2 hours as a Maths tutor to earn at least $96.

Our system of equations is given as:

He wants to work no more than 10 hours.

No more is represented by the inequality "≤ " = Less than or equal to

x + y ≤ 10 ...........Equation 1

He also wants to earn at least 96.

At least is represented by the inequality" ≥" = Greater than or equal to

$8 × x + $16 × y  ≥ 96

8x + 16y ≥ 96........Equation 2

Solving for the number of hours

x + y = 10

x = 10 - y

Substitute 10 - y for x in Equation 2

8(10 - y) + 16y = 96

80 - 8y + 16y = 96

Collect like terms

8y = 96 - 80

8y = 16

Divide both sides by 8

8y/8 = 16/8

y = 2 hours

Solving for x

x = 10 - y

x = 10 - 2

x = 8 hours

Therefore, John must work for no more than 8 hours walking the dog and 2 hours as a Maths tutor to earn at least $96.

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Answer:

85

Step-by-step explanation:

So you know that there are 26 letters in the alphabet and 3 letters in the license plate, so that would be 26 multiplied by 3 to cover all of those letters.  The first letter can't be I or O, so you subtract 2 from the product.  26 times 3 is 78, minus 2 is 76. There are 10 single digits, but only one in the plate and it can't be 0.  This leaves 9 digits so you add that to the total number.  

76 + 9 = 85

I hope this helps!  :)

Sorry for my previous answer, I misread the question, but this is the correct answer now, hope this helped!

Answer:

129600 license plates

Step-by-step explanation:

This time, we will use an option of solving where we take the number of possibilities for one letter, then multiply it by the next, then multiply it by the next, then multiply it by the number of possibilities for the number. We would have 24 letters to start (not including I or O), then after we pick one, we need to remove it since we can't repeat letters. So just for our letters, we would get:

24 * 25(only the first digit can't have I or O) * 24

Then, we need to multiply that by 9 (since we are not including 0), giving us:

24 * 25 * 25 * 9 = 129600

Meaning, we can have 129600 different license plates.

Hope this helped!

Answer:

A reflection then a different reflection.

Step-by-step explanation:

Figure Q is the result of applying two distinct and consecutive operations on Figure P: (i) x-Axis Reflection, (ii) y-Reflection. Now we explained what each operation consists in.

x-Axis Reflection:

\((x, y) \longrightarrow (x, -y)\), \(\forall\,(x,y) \in \mathbb{R}^{2}\)

y-Axis Reflection:

\((x, y) \longrightarrow (-x, y)\), \(\forall \,(x,y)\in \mathbb{R}^{2}\)

Hence, the correct answer is "a reflection then a different reflection".

Answer:

As we do not have any information about the ages of the existing teachers in the data set, we cannot determine the exact impact of adding a teacher with an age of 45 on the mean.

However, we can make some general observations. If the age of the new teacher (45 years) is less than the mean age of the original data set, then the addition of the new teacher would decrease the mean age. Conversely, if the age of the new teacher is greater than the mean age of the original data set, then the addition of the new teacher would increase the mean age.

Answer: D trust me it is 100

Step-by-step explanation:

The maximum area the goat can graze is 100Tt ft2​, the correct option is D.

Given

A goat is tethered to a rope that is 10 ft. long.

The area of the circle is equal to the pie times of the square of the radius of the circle.

The maximum area that the goat can graze in the area of the circle that can be formed due to its circular movement.

The length of the rope represents the radius of the circle, so that;

\(\rm Area \ the \ goat \ can \ graze =r^2 \times Tt\\\\ Area \ the \ goat \ can \ graze =(10)2 \times Tt\\\\Area \ the \ goat \ can \ graze =100 \ Tt\\\)

Hence, the maximum area the goat can graze is 100Tt ft2​.

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Answer:

y - 1 = 6(x+7)

Step-by-step explanation:

point slope form is  y-y₁=m(x-x₁)

given m = 6 and the point is (-7,1)

plug in your values

remember that an ordered pair is (x,y)

y-y₁=m(x-x₁) ----> y-1 = 6(x+7)...............just plug in values

Answer:

Calculate the skid speed by multiplying the drag factor times the braking efficiency times the skid distance times 30 and taking the square root of the result. For example, if the car skidded 120.5 feet on a road with a drag factor of 0.5 and left four skid marks, the car was going about 42.51 mph.

Step-by-step explanation:

Answer:

Solution given:

65mph

divide the speed value by 2.237

65/2.237=29.05m/s

So

speed =29.05 m/s

now we have

.speed =~30 d (0.5)

29.05/30=0.5d

d=0.96855/0.5

d=1.93

So

the length of the skid marks to be is 2 m.

Answer:

The distance between them is 230.65 miles

Step-by-step explanation:

Here we use the Cosine formula

\(a^2 = b^2 + c^2 - 2bc\ cos\ A\\\\a^2 = 200^2 + 300^2 - 2\times 200\times 300cos50^{\circ}\\\\= 40,000 + 90,000 - 120,000cos50^{\circ}\\\\= 130,000 - 120,000 \times 0.64\\\\= 130,000 - 76,800\\\\a^2= 53,200\\\\a = \sqrt{53,200} \\\\= 230.65\ miles\ per\ hour\)

Now the distance for one hour is

= 230.65 ÷ 1

= 230.65 miles

Answer:

30 x ^2 y ^2

Step-by-step explanation:

Answer:

No.

In a right triangle one of the angles is right angle i.e 90° and, therefore, sum of other two angles will always be equal to 90°, which means the other two angles will be acute angles

Answer:

Left box:  1/2n

Right box = 2n - 22

Step-by-step explanation:

Since we want one-half the number and n represents the unknown number, we have 1/2n on the left-hand side of the equation.

Thus, you want to put 1/2n in box on the left.

Twice the number and 22 less than this is given by:  y: 2n - 22 less than this means we subtract.  Thus, we have 2n - 22 as the numerator on the right hand side of the equation.

Thus, you want to put 2n - 22 in the box on the right.

answers

6. y = -1/2x + 8

7. y = 15

8. y = -3/4x + 1

9. y = 6x + 3

10. y = 1/3x - 4

steps

equation of the line that is perpendicular means the number next to the x should be a negative reciprocal

number next to the x is the slope

6. y=2x+5

y = mx + b

m = 2

b = -5

negative reciprocal would be

-1/2x

m = -1/2

(2, 7) means x = 2 y = 7

substitute

7 = -1/2(2) + b

7 = -1 + b

b = 8

answer is y = -1/2x + 8

7.

y = 5; (11, 15)

b = 5

m would be 0 because there is no slope

15 = 0*11 + b

b = 15

y = 15

8.

line goes through

(0,-2) and (3,2)

get slope

y2-y1/x2-x1

2-(-2) / 3 - 0

4/3

y = 4/3x

point slope form

y - y1 = m (x-x1)

y - -2 =  4/3 (x - 0)

y+2 =  4/3x

y = 4/3x - 2

negative reciprocal slope would be for perpendicular

-3/4x

(12, 10)

y = mx + b

10 = 3/4(12) + b

10 = 9 + b

1 =  b

b = 1

y = -3/4x + 1

9.

y = -1/6x + 1; (− 2, — 9)

negative reciprocal slope would be for perpendicular

+6x

(− 2, — 9)

y = mx + b

get b

-9 = 6(-2) + b

-9 = -12 + b

b = 3

y = 6x + 3

10.

6x+2y=14; (12, 0)

2y= -6x+14

y= -3x+7

negative reciprocal slope would be for perpendicular

1/3x

y = mx + b

get b

0 = 1/3(12) + b

0 = 4 + b

b = -4

y = 1/3x - 4

In charts, the axis that shows the descriptive labels for the data points is the category axis, also known as the x-axis. The value axis, also known as the Y axis, is used to display the values ​​or measurements of data points. Data axes and series axes are generally not used in charts.

In charts, the category axis is the horizontal axis used to display categories or groups of data.

For example, if you are creating a chart that compares sales of various products over time, the category axis might display months. The data points in the chart are plotted along the category axis, with each data point representing sales for a particular product in a particular month.

A value axis, on the other hand, is a vertical axis used to display the values ​​or measurements of data points. For example, in the sales chart above, the value axis might display sales amounts in dollars. The data points in the chart are plotted along the value axis, with the height of each data point representing sales for a particular product in a particular month.

Data and series axes are not commonly used in charts. A data axis is sometimes used to show additional categories or groups of data, while a series axis is used to show different data series within the same chart. However, these axes are used less frequently than the category and value axes.

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The code calculates the total cost for electricity consumption based on the given conditions and adds the basic service fee of $5. It then rounds the total cost to two decimal places and displays the output.

# defining function to calculate total cost

def total_cost(units):

   if units <= 500:

       return units * 0.02

   elif units <= 1000:

       return (500 * 0.02) + ((units - 500) * 0.05)

   else:

       return (500 * 0.02) + (500 * 0.05) + ((units - 1000) * 0.10)

# Driver Code

consumptions = [200, 500, 700, 1000, 1500]

for i in consumptions:

   total = total_cost(i)

   print("Total cost of Electricity for", i, "units is", round(total + 5, 2))

Output:

Total cost of Electricity for 200 units is 9.0

Total cost of Electricity for 500 units is 15.0

Total cost of Electricity for 700 units is 25.0

Total cost of Electricity for 1000 units is 40.0

Total cost of Electricity for 1500 units is 90.0

The code calculates the total cost for electricity consumption based on the given conditions and adds the basic service fee of $5. It then rounds the total cost to two decimal places and displays the output.

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Answer:

A: 3 hours and 55 minutes

B: 3 hours and 40 minutes more time hiking than resting.

Step-by-step explanation:

The area of the canvas which was covered by the red rose is 333 square inches.

Width of the canvas = 30 inches

Length of the canvas = 37 inches

Area of the canvas = length × width

= 30 × 37

= 1110 square inches

If the painted red rose covered 30% of the painting

Area of the canvas which was covered by the red rose = 30% × 1110

= 0.3 × 1110

= 333 square inches

In conclusion, 333 square inches of the canvas is covered by the red rose.

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The size of the population at the beginning of month 7 is 112.

A. The recurrence relation for the size of the population at the beginning of month n can be expressed as follows:

P(n) = \(2 * P(n-1) - 2^{n-2}\)

This relation represents the doubling of the population from the previous month (2 * P(n-1)) minus the number of specimens that have died due to the infection\((2^{n-2}).\) Note that for the first month (n = 1), no specimens have died, so the term \(2^{n-2}\)  is equal to zero.

B. To solve this recurrence relation, we can use a recursive approach or use the closed-form formula. Let's use the closed-form formula:

P(n) = \(2^n - 2^{n-2}\)

This formula directly gives us the size of the population at the beginning of month n.

C. To find the size of the population at the beginning of month 7, we substitute n = 7 into the formula:

P(7) =\(2^7 - 2^{7-2}\)

    = 128 - 16

    = 112

Therefore, the size of the population at the beginning of month 7 is 112.

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The cost to move in for Victoria and Michael is $7,645.

The cost to move into the apartment for Victoria and Michael can be found by calculating the sum of the application deposit, credit report cost, security deposit, first and last month's rent, and the broker fee.

Using the given information:

$150 is the application deposit

$35 is the cost of the credit report

Security deposit is 1 month's rent which is $2,200

First and last month's rent are also $2,200 each.

Thus, the total amount for these two months will be $4,400

The broker charged 2.5% of the yearly rent.

The yearly rent is $2,200 × 12 months = $26,400.

Therefore, the broker fee will be 2.5% of $26,400 which is $660.

Total cost to move in = $150 + $35 + $2,200 + $2,200 + $660 + $2,200 = $7,645

Therefore, the cost to move in for Victoria and Michael is $7,645.

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Answer:

r=6.4

Step-by-step explanation:

Get r by itself you need to add 8.5 to get 6.4

Hope this helps (:

Answer:

r-8.5=-2.1

r=-2.1+8.5

r=6.4

Step-by-step explanation:

To fill in each blank so that the values are in order from smallest to largest, we have;

4° , 1⁴ = 4, 2² , 3³ , 4³ , 2⁹

We need to know that index forms are defined as mathematical forms used to represent numbers or variables that are too large or too small in more convenient forms.

These index forms are also known as scientific notation or standard forms.

Some examples of index forms are;

3²

4³

2³

From the information given, we have that;

To arrange the numbers;

4° = 1

1⁴ = 4

2² = 4

3³ = 27

4³ = 64

2⁹ = 512

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Answer:

308

Step-by-step explanation:

Hello the answer is

14 times 44 = 616

then do 616 divided by 2 because half = 308

Answer:

nvm :(

Explanation:

Answer:

"Games played in a workplace environment to achieve status, advancement and money"

Answer:

Step-by-step explanation:

10x + 8x = 180 (angles on straight line)

x = 10

AFH = 10x = 100

AFE = 8x = 80

The hotel should overbook enough rooms to maximize revenue without incurring expensive costs due to last-minute cancellations. To determine the optimal number of rooms to overbook, consider the following:

1. The average number of cancellations is 5 with a standard deviation of 3.
2. The average room rate is $80.
3. The cost of accommodating overbooked customers in a nearby hotel is $200.

Using these figures, the hotel can calculate the expected revenue for each room overbooked, while considering the risk of cancellations. The best approach is to use a probabilistic model, such as the normal distribution, to estimate the optimal number of rooms to overbook based on these statistics.

A detailed analysis would require further calculations and simulations, which are beyond the scope of this answer. However, a basic guideline for the hotel would be to overbook only a few rooms (e.g., 1-3) to minimize the risk of incurring the high cost of accommodating customers in nearby hotels while still maximizing the revenue from potential cancellations.

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