4. Use the data below for the calculations.
Average hours sleeping per weeknight: 4, 5, 8, 12, 10, 6, 7, 9, 8, 8, 6, 6, 4, 3, 9
Mean:

Median:

Mean Absolute Deviation:


Absolute Deviation from Median:

Answers

Answer 1

The mean is 7

The median is the middle value, which is 7.

Mean Absolute Deviation: 2

How to solve for the mean absolute deviation

Step 3: Find the absolute deviation of each value from the mean:

|4-7.067|, |5-7.067|, |8-7.067|, |12-7.067|, |10-7.067|, |6-7.067|, |7-7.067|, |9-7.067|, |8-7.067|, |8-7.067|, |6-7.067|, |6-7.067|, |4-7.067|, |3-7.067|, |9-7.067|

These absolute deviations are: 3.067, 2.067, 0.933, 4.933, 2.933, 1.067, 0.067, 1.933, 0.933, 0.933, 1.067, 1.067, 3.067, 4.067, 1.933.

Step 4: Find the mean of these absolute deviations to find the mean absolute deviation:

Mean Absolute Deviation = (3.067+2.067+0.933+4.933+2.933+1.067+0.067+1.933+0.933+0.933+1.067+1.067+3.067+4.067+1.933) / 15 = 2

Step 5: Find the absolute deviation of each value from the median:

|4-8|, |5-8|, |6-8|, |6-8|, |6-8|, |7-8|, |8-8|, |8-8|, |8-8|, |9-8|, |9-8|, |10-8|, |12-8|, |8-8|, |3-8|

These absolute deviations are: 4, 3, 2, 2, 2, 1, 0, 0, 0, 1, 1, 2, 4, 0, 5.

Therefore, the absolute deviation from the median is 5.

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Related Questions

Russ placed $8000 into his credit union account paying 6% compounded semiannually (twice a year). How much will be in Russ’s account in 4 years

Answers

Answer:

Step-by-step explanation:

A rectangular garden has an area of 100 square meters. The length of the garden is 10 meters more than the width. What is the perimeter of the garden?

Answers

Answer:

40 meters

Step-by-step explanation:

Let's assume the width of the garden is x meters, then the length of the garden would be (x+10) meters since we know that the length is 10 meters more than the width.

We also know that the area of the garden is 100 square meters, therefore:

Area = Length x Width

100 = (x+10) x x

Expanding the equation we get:

100 = x^2 + 10x

Rearranging the terms we have:

x^2 + 10x - 100 = 0

Solving for x using the quadratic formula, we get:

x = 5 or x = -20

Since the width cannot be negative, we discard the negative solution and conclude that the width of the garden is 5 meters. Therefore, the length of the garden is (5+10) = 15 meters.

The perimeter of the garden is the sum of the four sides, which is:

Perimeter = 2 x (Length + Width)

Perimeter = 2 x (15 + 5)

Perimeter = 2 x 20

Perimeter = 40 meters

Therefore, the perimeter of the garden is 40 meters.

Answer:

Let's start by using algebra to solve for the width of the garden:

- Let w be the width of the garden.

- Then the length of the garden is w + 10.

- The area of the garden is length x width, so we can write the equation: (w + 10)w = 100.

- Expanding the left side of the equation, we get: w^2 + 10w = 100.

- Rearranging the equation, we get: w^2 + 10w - 100 = 0.

- Factoring the left side of the equation, we get: (w + 20)(w - 10) = 0.

- Solving for w, we get: w = -20 or w = 10. Since the width cannot be negative, we have w = 10.

Now that we know the width of the garden is 10 meters, we can find the length by adding 10 meters:

- Length = width + 10 = 10 + 10 = 20 meters.

Finally, we can find the perimeter of the garden by adding up the lengths of all four sides:

- Perimeter = 2(length + width) = 2(20 + 10) = 2(30) = 60 meters.

Therefore, the perimeter of the garden is 60 meters.

What can be the universal sets from which the following substes can be formed? a) set of cricket players of class 9.
b)set of cricket players of the school.
c)The set of odd numbers less than 10.​

Answers

The only option that represents the universal set from the subsets is:

B: A set of cricket players of the school.

How to identify the universal set?

The universal set is defined as a set that is said to consist of all the elements or objects, which includes its own elements. This universal set is represented by just a symbol 'U'

Now, a subset is also defined as a part of the universal set which is basically a group under the universal set.

Now, from the given options, the only one that could possible represent a universal set of all the options given is "a set of cricket players of the school."

Therefore we conclude that Option B provides the correct answer to the universal set definition.

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what’s is the distance between (-2,7) and (-5,9)

Answers

We can use the distance formula to find the distance between two points in a coordinate plane:

d = √[(x2 - x1)² + (y2 - y1)²]

where (x1, y1) and (x2, y2) are the coordinates of the two points, and d is the distance between them.

Using the given coordinates of the two points, we have:

x1 = -2, y1 = 7

x2 = -5, y2 = 9

Substituting these values into the distance formula, we get:

d = √[(-5 - (-2))² + (9 - 7)²]

d = √[(-3)² + 2²]

d = √(9 + 4)

d = √13

Therefore, the distance between the points (-2, 7) and (-5, 9) is approximately √13 units. We can also approximate this value as 3.61 units (rounded to two decimal places).

(2x−3)(2x−3)=left parenthesis, 2, x, minus, 3, right parenthesis, left parenthesis, 2, x, minus, 3, right parenthesis, equals

Answers

The expression (2x-3)(2x-3) is equal to (2x-3)^2.

To expand the expression (2x-3)(2x-3), we can use the FOIL method (which stands for First, Outer, Inner, Last).

Multiplying the first terms of each binomial, we get 2x times 2x, which is 4x^2.

Multiplying the outer terms, we get -3 times 2x, which is -6x.

Multiplying the inner terms, we get -3 times 2x again, which is also -6x.

Multiplying the last terms of each binomial, we get -3 times -3, which is 9.

Combining like terms, we get 4x^2 - 12x + 9.

Therefore, (2x-3)(2x-3) is equal to (2x-3)^2, which is equivalent to 4x^2 - 12x + 9.

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Find AB if AC = 21 and BC =9.

Answers

Answer:

12

Step-by-step explanation:

Length AC is the total length between ABC

If we already know BC=9, and we're solving for AB, then we just subtract the total amount (AC) from BC

21-9

We get 12

xyz medical facility provides medical services to patients in russellville. the design capacity is 40 patients per hour, and the effective capacity is 35 patients per hour. yesterday the medical facility worked for 7 hours and served 200 patients. what is the effective utilization? a. 60% b. 81.63% c. 3600% d. 19% e. 76.78%

Answers

The effective utilization for the XYZ medical facility provides medical services to patients in Russellville is 81.63%, option B.

The percentage of your available resources that are now being used is known as resource utilization. To make sure your business is as productive as possible, it might assist to plan how to use your resources more wisely.

Employers and workers may both benefit from efficient resource management. On one side of the spectrum, it may also avoid overworking and burnout, resulting in a more balanced work life overall. On the other, it makes sure that workers have enough work to keep their position sustainable and lucrative.

Design capacity = 40 patients per hour,

Effective capacity is 35 patients per hour

Actual capacity is given by,

200/7 patients per hour

Effective utilization is given by = 200 x 100 /7 x 35

= 20000/245

= 81.63%.

Therefore, the effective utilization is 81.63%.

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Please help with this math problem!

Answers

The equation of the ellipse is x^2/9 + y^2/6.75 = 1

Finding the equation of the ellipse

To find the equation of an ellipse, we need to know the center, the major and minor axis, and the foci.

Since we are given the eccentricity and foci, we can use the following formula:

c = (1/2)a

Since the foci are (0, +/-3), the center is at (0, 0). We know that c = 3/2, so we can find a:

c = (1/2)a

3/2 = (1/2)a

a = 3

The distance from the center to the end of the minor axis is b, which can be found using the formula:

b = √(a^2 - c^2)

b = √(3^2 - (3/2)^2)

b = √6.75

So the equation of the ellipse is:

x^2/a^2 + y^2/b^2 = 1

Plugging in the values we found, we get:

x^2/3^2 + y^2/6.75 = 1

Simplifying:

x^2/9 + y^2/6.75 = 1

Therefore, the equation of the ellipse is x^2/9 + y^2/6.75 = 1

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Suppose that someone is offering to sell you raffle tickets. there are blue, green, yellow, and red tickets available.


each ticket costs the same to purchase regardless of color. the person selling the tickets tells you that 369 blue tickets,


488 green tickets, 523 yellow tickets, and 331 red tickets have been sold. at the drawing, one ticket of each color will


be drawn, and four identical prizes will be awarded. which color ticket would you buy? explain your answer.

Answers

Buy yellow or green ticket for best chance of winning.

Which color ticket to buy?

To determine which color ticket to buy, we need to calculate the probability of winning with each color.

First, we need to determine the total number of possible combinations of one ticket of each color. This can be calculated by multiplying the number of tickets of each color together:

Total number of possible combinations = 369 x 488 x 523 x 331 = 39,123,833,144

Next, we need to determine the probability of winning with each color. Since there are four identical prizes, the probability of winning with any one color is the same. We can calculate the probability of winning with a specific color by dividing the number of tickets of that color by the total number of possible combinations:

Probability of winning with blue ticket = 369 / 39,123,833,144 ≈ 0.00000943

Probability of winning with green ticket = 488 / 39,123,833,144 ≈ 0.00001248

Probability of winning with yellow ticket = 523 / 39,123,833,144 ≈ 0.00001337

Probability of winning with red ticket = 331 / 39,123,833,144 ≈ 0.00000846

From the calculations above, we can see that the highest probability of winning is with the yellow ticket, followed closely by the green ticket. Therefore, if we want to maximize our chances of winning one of the prizes, we should buy the yellow or green ticket.

It's important to note that the difference in probabilities between the yellow and green tickets is very small, so the decision of which color to choose ultimately depends on personal preference.

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How you can solve real-life problems involving mean or expected value

Answers

Solving real-life problems involving mean or expected value can be quite useful in various situations, such as finance, statistics, and decision-making.

To begin, identify the problem that requires the calculation of mean or expected value.

The mean is the average of a set of numbers, while expected value is the anticipated result based on probability distribution.

Next, collect the necessary data for the problem.

In calculating the mean, gather all values in the data set.

For expected value, you'll need the probability of each outcome and its corresponding value.

To calculate the mean, add all the values together and divide by the total number of values. For expected value, multiply each outcome's value by its probability and then sum up the results.

Once you have the mean or expected value, apply it to the real-life problem to make informed decisions or predictions. This can help in areas such as budgeting, risk assessment, and determining the likelihood of future events.

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Use the variable x to write the phrase in symbols. the sum of 148 and the product of a number raised to the third power and 19

Answers

The expression 148 + 19x³ represents the sum of 148 and the product of a number raised to the third power and 19.

To write the phrase "the sum of 148 and the product of a number raised to the third power and 19" in symbols using the variable x, we can write it as:

148 + 19x³

Here, we are adding 148 to the product of 19 and x raised to the third power. This expression represents the sum of 148 and the product of a number raised to the third power and 19. We can substitute any value for x to get the result of the expression. For example, if x is 2, then the expression becomes:

148 + 19(2³) = 148 + 19(8) = 300

Therefore, the sum of 148 and the product of a number raised to the third power and 19 is represented by the expression 148 + 19x³.

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A freezer chest is in the shape of a rectangular prism. Measured on the inside, the chest is 4 feet wide, 2. 5 feet tall, and 2 feet long. How much space is inside to hold frozen foods?

Answers

The freezer chest has 20 cubic feet of space inside to hold frozen foods.

To find the amount of space inside the freezer chest, we need to calculate its volume. The formula for the volume of a rectangular prism is V = lwh, where l is the length, w is the width, and h is the height.

Using the measurements given, we can plug them into the formula and calculate:

V = 4 ft x 2.5 ft x 2 ft
V = 20 cubic feet

Therefore, there is 20 cubic feet of space inside the freezer chest to hold frozen foods.

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PLEASE HELP ME ASSAP!!!!!!!!!

Answers

The slope of UF is 1/6

What is a slope of a line?

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

The slope is given = change in point on y axis/ change in point on x axis

slope = y2-y1/x2-x1

The cordinate of F = (-2,-3) and U ( 4, -2)

y1 = -3 and y2 = -2

x1 = -2 and x2 = 4

slope = -2-(-3)/4-(-2)

= -2+3/(4+2)

= 1/6

therefore the slope of UF is 1/6

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A paper pulp company has discovered their cost and revenue functions for each day: C(x) = 2x2 - 250x + 525 and R(x) = -3x2 + 750x + 125, where x is the amount of pulp in tons. If they want to make a profit, what is the range of pulp in tons per day that they should produce? Round to the nearest tenth of a ton which would generate profit

Answers

Based on the cost and revenue function, if they want to make a profit, the range of pulp in tons per day that they should produce is between 152.6 and 152.8 tons per day.

To find the range of pulp in tons per day that will generate profit, we need to set the profit function equal to zero and solve for x. The profit function P(x) is given by:

P(x) = R(x) - C(x)

Substituting the given revenue and cost functions, we get:

P(x) = -3x^2 + 1000x - 400

Setting P(x) = 0, we can solve for x using the quadratic formula:

x = [-b ± sqrt(b^2 - 4ac)] / 2a

Plugging in the values from our profit function, we get:

x = [-(1000) ± sqrt((1000)^2 - 4(-3)(-400))] / 2(-3)

Simplifying, we get:

x = [1000 ± sqrt(1000000 + 4800)] / 6

x = [1000 ± sqrt(1004800)] / 6

x ≈ 152.7 or x ≈ 55.6

Since we're looking for the range of pulp in tons per day that will generate profit, we only want the positive solution, which is approximately 152.7 tons per day. Therefore, the company should produce between 152.6 and 152.8 tons per day to generate profit, rounded to the nearest tenth of a ton.

Note: The question is incomplete. The complete question probably is: A paper pulp company has discovered their cost and revenue functions for each day: C(x) = 2x^2 - 250x + 525 and R(x) = -3x^2 + 750x + 125, where x is the amount of pulp in tons. If they want to make a profit, what is the range of pulp in tons per day that they should produce? Round to the nearest tenth of a ton which would generate profit.

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Eddie's dog weighs 31. 8 kilograms. How many grams are equivalent to 31. 8 kilograms?



A). 0318 grams


B) 318 grams


() 3,180 grams


D) 31,800 grams

Answers

31.8 kilograms is equivalent to 31,800 grams.

What is the weight in grams of Eddie's 31.8 kg dog?

The correct answer is (D) 31,800 grams.

To convert kilograms to grams, we multiply the number of kilograms by 1000. So, to convert 31.8 kilograms to grams, we can use the following formula:

31.8 kilograms x 1000 grams/kilogram = 31,800 grams

Therefore, 31.8 kilograms is equivalent to 31,800 grams.

To convert kilograms to grams, we need to multiply the number of kilograms by 1000 because there are 1000 grams in one kilogram. In this case, Eddie's dog weighs 31.8 kilograms. To find out how many grams this is, we simply multiply 31.8 by 1000, which gives us 31,800 grams. Therefore, 31.8 kilograms is equivalent to 31,800 grams. It's important to understand the basic metric system conversions, like kilograms to grams, as they are commonly used in everyday life, particularly when it comes to measuring weight. Knowing how to make these conversions can be helpful in many different situations, from cooking and baking to medical and scientific contexts.  

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Find the surface area of the square pyramid (above) using its net (below).

Answers

The surface area of the square pyramid is approximately 41.83 cm².

To start with, let's define a square pyramid.

The slant height of the pyramid can be found using the formula:

l = √(h² + (s/2)²)

where h is the height of the pyramid and s is the length of one side of the base.

Plugging in the given values, we get:

l = √(7² + (4/2)²) = √(57)

Now that we know the slant height, we can find the area of each triangular face using the formula:

A = (1/2)bh

where b is the base of the triangle, and h is the height of the triangle.

Plugging in the given values, we get:

A = (1/2)(4)(√(57)) = 2√(57)

Since there are four triangular faces, the total area of all the triangular faces is:

4A = 8√(57)

Finally, we can find the total surface area of the pyramid by adding the area of the square base to the area of all the triangular faces:

surface area = 16 + 8√(57) = approximately 41.83 cm²

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Complete Question:

Find the surface area of the square pyramid where the base is 4cm and the  height is 7cm.

Javier and ellema both get there cars wash and filled there gas tanks at the same gas station javier pays 26. 96 for a car wash and 5. 6 gallon of gas. Ellema pays 48. 62 for a car wash and 13. 2 gallons of gas

Answers

We can start by finding the cost per gallon of gas for each person:

Javier: 5.6 gallons of gas for $26.96, so cost per gallon = 26.96/5.6 = $4.79/gallon

Ellema: 13.2 gallons of gas for $48.62, so cost per gallon = 48.62/13.2 = $3.68/gallon

Now we can find the cost of just the car wash for each person:

Javier: $26.96 - (5.6 gallons * $4.79/gallon) = $-1.344, which doesn't make sense. It's possible there was a mistake in the numbers given.

Ellema: $48.62 - (13.2 gallons * $3.68/gallon) = $1.958, which also doesn't make sense. There may be an error in the given information.

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What’s the answer? I need help asap help me

Answers

The matrix that represents a dilation by a factor of 3 followed by a reflection over the horizontal axis is given as follows:

[tex]\left[\begin{array}{cc}3&0\\0&-3\end{array}\right][/tex]

What is a dilation?

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

The scale factor for this problem is given as follows:

k = 3.

Hence the matrix is:

[tex]\left[\begin{array}{cc}3&0\\0&3\end{array}\right][/tex]

For the reflection over the horizontal axis, we have that the y-coordinate is multiplied by -1, hence the matrix rule is:

[tex]\left[\begin{array}{cc}3&0\\0&-3\end{array}\right][/tex]

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A​ salesperson's commission rate is 6​%. What is the commission from the sale of $37,000 worth of​ furnaces? Use pencil and paper. Suppose sales would double. What would be true about the​ commission? Explain without using any calculations.

Answers

The sale's person commission from the sale of $37,000 worth of furnaces is $2,220. If this is doubled, he would have $4,440.

What would the commission be?

If the salesperson's commission from the sale of $37,000 is at the rate of 6%, then we will do the following:

6/100 × $37,000 = $2,220

If sales, double, we will now record the amount, 74,000. Now 6% of 74,000 will be $4,440. So, the resultant amount, if the salesperson was to increase his sales to double the original, will be $4,440.

This follows a simple logic. When you have a number and are told to double it, you simply multiply by 2. In the same manner, we multiply the salesperson's commission by 2.

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Determine whether each situation can have only one value for the variable or more than one value for the variable.
select only one or more than one for each situation.
the total cost to buy t movie tickets for $8.50 each
o only one
more than one
the number of ounces of tomato juice, j, in 2 quarts
o only one
o more than one
the number of pizzas to order, p, if each person eats 2 slices
only one
more than one
the greatest number of $6 notebooks, n, ed can buy with $36
only one
0. more than one
the area, a, of a wall with a length of 5 meters and a height of 3 meters
o only one
o more than one

Answers

The total cost to buy t movie tickets for $8.50 each is o only one, the number of ounces of tomato juice, j, in 2 quarts o only one, the number of pizzas to order, p, if each person eats 2 slices more than one, the greatest number of $6 notebooks, n, ed can buy with $36 only one, and the area, a, of a wall with a length of 5 meters and a height of 3 meters o only one.

1. The total cost to buy t movie tickets for $8.50 each:
- Only one value for the variable

The cost to buy a specific number of movie tickets at a fixed price will have only one total cost value.

2. The number of ounces of tomato juice, j, in 2 quarts:
- Only one value for the variable

There are 32 ounces in a quart, so 2 quarts will always have 64 ounces.

3. The number of pizzas to order, p, if each person eats 2 slices:
- More than one value for the variable

The number of pizzas needed depends on the number of people attending, which can vary, leading to different values for p.

4. The greatest number of $6 notebooks, n, Ed can buy with $36:
- Only one value for the variable

Since each notebook costs $6, Ed can buy exactly 6 notebooks with $36 (36/6 = 6).

5. The area, a, of a wall with a length of 5 meters and a height of 3 meters:
- Only one value for the variable

The area of a rectangle is calculated by multiplying its length and height. In this case, the area will always be 15 square meters (5m x 3m = 15m²).

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What is the approximate area of the triangle?





A. 12. 5 square units


B. 18 square units


C. 21. 5 square units


D. 31 square units

Answers

The approximate area of the triangle is 21. 5 square units (option c).

Triangles are three-sided polygons that can have different shapes and sizes. Now, let's focus on your question about finding the area of a triangle.

To begin with, the area of a triangle is given by the formula:

Area = (base × height) ÷ 2

where the base is the length of the side that is perpendicular to the height. The height, on the other hand, is the distance between the base and the opposite vertex.

In your problem, the base of the triangle is given as 7 units, and the height is given as 6.1 units. So, we can substitute these values into the formula to get:

Area = (7 × 6.1) ÷ 2

Area = 21.35 square units

Therefore, the approximate area of the triangle is 21.35 square units. In the answer choices provided, the closest option is C, which is 21.5 square units.

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Complete Question:

What is the approximate area of the triangle when base = 7 and height = 6.1?

A. 12. 5 square units

B. 18 square units

C. 21. 5 square units

D. 31 square units

Jamie McAllister is a wonderful rebounder for her high school basketball team. Of


her final 10 games, here are her rebound totals for each game:


8 12 8 11 15 6 9 8 10 13


1.


2.


From the collected data, what


is the mean number of


rebounds Jamie had per


game?


From the collected data, what


is the median number of


rebounds Jamie had for her


final 10 games?

Answers

Step-by-step explanation:

1. To find the mean number of rebounds Jamie had per game, we need to add up all the rebounds she had and then divide by the total number of games played:

Mean = (8 + 12 + 8 + 11 + 15 + 6 + 9 + 8 + 10 + 13) / 10

Mean = 100 / 10

Mean = 10

Therefore, the mean number of rebounds Jamie had per game was 10.

2. To find the median number of rebounds Jamie had for her final 10 games, we need to first arrange the data in order from least to greatest:

6, 8, 8, 8, 9, 10, 11, 12, 13, 15

Since there are an even number of data points, the median will be the average of the two middle values, which are 9 and 10:

Median = (9 + 10) / 2

Median = 9.5

Therefore, the median number of rebounds Jamie had for her final 10 games was 9.5.

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Desmond kept track of his results for all 72 rolls. The table at right shows some of his results. Based on his partial results, how many times did he roll a 5 or a 6?

Answers

The number of times of rolling a 5 or a 6 in the fair die is 24

What is a reasonable prediction for the number of times of rolling a 5 or a 6?

From the question, we have the following parameters that can be used in our computation:

Fair 6-sided die = 72 times

In a 6-sided die, we have

P(5 or 6) = 2/6

When evaluated, we have

P(5 or 6) = 1/3

So, when the die is rolled 72 times, we have

Expected value = 1/3 * 72

Evaluate

Expected value = 24

Hence, the number of times is 24

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Can someone help me asap? It’s due today!!

Answers

Based on the information provided, James would have 20 different waffle options.

How many options will James have?

Since each waffle cone can hold two scoops of ice cream and James must choose a different flavor for each scoop, we can approach this problem by using the multiplication principle of counting.

There are 5 different ice cream flavors to choose from for the first scoop, and 4 different flavors remaining for the second scoop. This is because James must choose a different flavor for each scoop.

Therefore, the number of different waffle cone options that James has is:

5 x 4 = 20

So, James has 20 different waffle cone options if he chooses a different flavor of ice cream for each scoop.

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Determine the product of 23.5 and 2.3

Answers

Answer:

Therefore, the product of 23.5 and 2.3 is 54.05.

Step-by-step explanation:

To determine the product of 23.5 and 2.3, we can use the following steps:

Align the numbers vertically with the ones digit of the second factor (2.3) under the tenths digit of the first factor (3 in 23.5).

   23.5

 x 2.3

 -----

Multiply the ones digit of the second factor by the first factor and write the result below, shifted one place to the right.

   23.5

 x 2.3

 -----

    71

Multiply the tenths digit of the second factor by the first factor and write the result below, shifted two places to the right.

   23.5

 x 2.3

 -----

    71

   470

Add the two partial products together.

   23.5

 x 2.3

 -----

    71

   470

 -----

   54.05

Therefore, the product of 23.5 and 2.3 is 54.05.

There are (2a+b) books in a pile. The thickness of each book is 2cm. Find the height of the pile of books in terms of a and b, expressing the answer in the expanded form

Answers

The height of the pile of books in terms of a and b is 4a cm + 2b cm.

To find the height of the pile of books in terms of a and b, we need to multiply the number of books by the thickness of each book. Since there are (2a+b) books in the pile and the thickness of each book is 2cm, the height of the pile can be expressed as:

(2a+b) x 2cm

Expanding this expression, we get:

4a cm + 2b cm

Therefore, the height of the pile of books in terms of a and b is 4a cm + 2b cm. This means that for every additional 'a' book, the height of the pile will increase by 4cm and for every additional 'b' book, the height of the pile will increase by 2cm.

It's important to note that this formula assumes that all the books are the same size and have the same thickness. If there are any variations in size or thickness, the formula may not accurately represent the height of the pile. Additionally, it's important to ensure that all units of measurement are consistent (in this case, cm for both the thickness of the book and the height of the pile).

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QUESTION IN PHOTO I MARK BRAINLIEST

Answers

The value of x for the circle is,

⇒ x = 13.2

We have to given that;

In circle Y,

m arc WX = 142°

m ∠WZX = (8x - 35)°

Since, angle WZX is half the measure of arc WX,

Hence, We get;

⇒ (8x - 35)° = 142 / 2

⇒ 8x - 35 = 71

⇒ 8x = 35 + 71

⇒ 8x = 106

⇒ x = 13.2

Thus, The value of x for the circle is,

⇒ x = 13.2

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Explain the role of the brackets, and how they effects the sum. Provide the answer for both sums. Sum 1 Sum 2 10 + 7 – 5 + 3 = 10 + 7 – (5 + 3) =

Answers

The role of the brackets, and how they effects the sum is given as the inside signs get changed after the opening of the bracket.

The associative property of addition is a mathematical statement that asserts that the arrangement of three or more integers does not affect their total. This indicates that no matter how the numbers are organised, the total of three or more integers remains the same.

The associative property of addition is a mathematical principle that asserts that when adding three or more integers, the amount obtained is constant regardless of how the numbers are grouped. Grouping here refers to where the brackets are positioned.

The sum for the 1st term is 10 + 7 – 5 + 3 = 15

The sum of the 2nd term is 10 + 7 – (5 + 3) = 17 - 8 = 9

Here, the bracket used made all the difference so after opening of the bracket the sign inside changed which impacted the summation of the terms above.

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How would the variation that exists between the distance that a man walks in one hour and the rate at which the man is walking be described? f inversely g directly h both inversely and directly j irregular​

Answers

The relationship between these two variables can be described as inversely proportional.

The variation between the distance that a man walks in one hour and the rate at which the man is walking can be described as inversely proportional.

This means that as the rate at which the man is walking increases, the distance that he walks in one hour decreases. Similarly, as the rate at which he is walking decreases, the distance that he walks in one hour increases.

Therefore, the relationship between these two variables can be described as inversely proportional.

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Triangles UVW and WXY are similar right triangles. Which proportion can be used to show that the slope of uw is equal to the slope of wy ?

a: 1-2 -3 - ( -1 )

9-8 1-2

b: 2-8 -1-2

1-9 -3-1

c: 1-9 -3-1

2-8 -1-2

d: 2 - ( -1 ) -1 - ( -3 )

9 -8 2 -1

Answers

The proportion that can be used to show that the slope of uw is equal to the slope of wy is B) 2-8 -1-2.

Let the angles opposite to sides UV, VW, and WU be denoted by theta1, theta2, and theta3, respectively, in triangle UVW. Similarly, let the angles opposite to sides WY, YX, and XW be denoted by theta4, theta5, and theta6, respectively, in triangle WXY. Since triangles UVW and WXY are similar right triangles, we have:

theta1 = theta4 = 90 degrees (both triangles are right triangles)

theta2 = theta5 (corresponding angles in similar triangles are equal)

theta3 = theta6 (corresponding angles in similar triangles are equal)

UW/VW = WY/YX (sides in similar triangles are proportional)

The slope of uw is given by the rise over run or (VU - UW)/(WV), and the slope of wy is given by the rise over run or (XY - WY)/(YW). Using the similar triangles proportion, we can substitute UW/VW = WY/YX and simplify to get (VU - UW)/(WV) = (XY - WY)/(YW). This equation shows that the slope of uw is equal to the slope of wy.

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