The data set shows the admission prices at several glass-blowing workshops.

$20, $20, $16, $12, $15, $25, $11​


Find and interpret the range, interquartile range, and mean absolute deviation of the data.

The range is . The interquartile range is . The mean absolute deviation is .


Question 2

The prices vary by no more than $. The middle half of the prices vary by no more than $. The admission prices differ from the mean price by an average of $

Finally, we need to subtract one-half the original number, which is $\frac{x}{2}$. So the final expression is:$$\frac{x+100}{2} - \frac{x}{2} = 50$$

1. Let's call the original number x.
2. Double the number: 2x
3. Add 200: 2x + 200
4. Divide the answer by 4: (2x + 200) / 4
5. Subtract one-half the original number: ((2x + 200) / 4) - (x / 2)

Now let's simplify the expression:

((2x + 200) / 4) - (x / 2)

= (2x/4 + 200/4) - (x / 2)

= (x/2 + 50) - (x / 2)

= x/2 - x/2 + 50

= 0 + 50

So, the value of the result is 50.

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The area of the face of the cube given is 4225 in².

Given that a cube has a total surface area of 25312 in², we need to find the area of one face of the cube,

So,

TSA of a cube = 6 × side²

So,

6 × side² = 25312

side² = 4225

side ≈ 65

Hence the cube has a side length of 65 inches,

Now we know that the face of a cube is in shape of square so the area of the face = side²

= 4225 in²

Hence the area of the face of the cube given is 4225 in².

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The translated question is

A cube has a total area of 25312

square inches. What is the area of a cube face in square inches?

The probability that the first grape candy chosen from the bag will be, at least, the third candy chosen overall is 0.5608.

To solve this problem, we need to use the probability formula:
P(at least third grape candy) = P(first candy is not grape) x P(second candy is not grape) x P(third candy is grape) + P(first candy is not grape) x P(second candy is grape) x P(third candy is grape) + P(first candy is grape) x P(second candy is not grape) x P(third candy is grape) + P(first candy is grape) x P(second candy is grape) x P(third candy is grape)

From the given information, we know that the probability of choosing a grape candy from the bag is 26%. Therefore, the probability of choosing a non-grape candy is 74%.

Using this information, we can substitute the values into the formula:

P(at least third grape candy) = 0.74 x 0.74 x 0.26 + 0.74 x 0.26 x 0.26 + 0.26 x 0.74 x 0.26 + 0.26 x 0.26 x 0.26

Simplifying this expression, we get:

P(at least third grape candy) = 0.4524 + 0.0508 + 0.0508 + 0.0068

P(at least third grape candy) = 0.5608

Therefore, the probability that the first grape candy chosen from the bag will be, at least, the third candy chosen overall is 0.5608.

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8 cups = 64cm

From the catalog, we know that a stack of 2 cups is 16 cm tall, and a stack of 4 cups is 20 cm tall.

To find the height of a stack of 8 cups, we can use proportionality.

Let x be the height, in cm, of a stack of 8 cups. Then, we can set up the following proportion:

2 cups / 16 cm = 8 cups / x cm

Cross-multiplying, we get:

2 cups * x cm = 16 cm * 8 cups

Simplifying, we get:

2x = 128

x = 64 cm

Therefore, the height of a stack of 8 cups is 64 cm.

The sample size should be selected as 100 in order to be 99% confident that the sample mean differs from the population mean by ±0.5 km (or within a range of 0.5 km).

To determine the sample size needed to estimate the distance students travel to school with a 99% confidence level and a margin of error of ±0.5 km, we can use the formula for sample size calculation:

n = (Z * σ / E)^2

where:

n = required sample size

Z = Z-score corresponding to the desired confidence level (in this case, 99% confidence level, which corresponds to Z = 2.576)

σ = population standard deviation

E = margin of error

Plugging in the given values:

n = (2.576 * 2.25 / 0.5)^2

Calculating this equation gives us the required sample size:

n ≈ 99.98

Since we cannot have a fractional sample size, we round up to the nearest whole number.

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Answer:

a cycle is a sequence of non-repeated vertices and the degree of a graph is the number of neighbors the vertex has.

Mindy's pay depends on the number of boots she produced. According to the given pay scale, we can break down her pay as follows:

For the first 50 boots, Mindy earns $1.65 per boot. So, for the first 50 boots, her pay is 50 * $1.65 = $82.50.

For the next 100 boots (51-150), Mindy earns $3.30 per boot. So, for these 100 boots, her pay is 100 * $3.30 = $330.

For the next 50 boots (151-200), Mindy earns $4.95 per boot. So, for these 50 boots, her pay is 50 * $4.95 = $247.50.

In total, Mindy has produced 200 boots so far, and her pay for these boots is $82.50 + $330 + $247.50 = $660.

Now, for the remaining 192 - 200 = -8 boots (less than 200), Mindy earns $6.00 per boot. Since she hasn't produced any additional boots beyond 200, we don't need to consider this part.

Therefore, Mindy's pay for producing 192 boots is $660 (according to the breakdown above).

So, the correct answer is E. None of these.

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The calculated elements in the set B is {4, 5, 6}

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

The above means that

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

The numbers greater than 3 in the above set are

Elements = 4, 5 and 6

This means that the elements in the set B is {4, 5, 6}

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Answer: The form of payment that Courtney can lose and not get back would be cash.

Step-by-step explanation:

The reason why cash couldn't be returned back because it doesn't have a piece of U.S money wouldn't have a specific certified owner that they can be returned to.

Other forms of payment like credit cards, debit cards, and checks have specific bank information with the card holder's name on it so if Courtney actually lost one of those, she would be most likely to receive it back without any complicated  verification process.

Therefore, Courtney would not be able to receive her cash back if she accidentally loses it. Hope this helps you with your Imagine Math homework or assignment!

-From Certified 5th Grade Honors Student

the probability of drawing 3 or more white marbles when 5 marbles are drawn from the bag without replacement.

To calculate this probability, we can use the formula for the hypergeometric distribution, which is:

P(X ≥ 3) = [C(10,3) * C(10,2)] / C(30,5) + [C(10,4) * C(10,1)] / C(30,5) + [C(10,5)] / C(30,5)

Where C(n,r) is the number of ways to choose r items from a set of n items.

formula is that we need to consider three different cases: drawing exactly 3 white marbles, drawing exactly 4 white marbles, and drawing all 5 white marbles. For each case, we calculate the probability of drawing the required number of white marbles and the probability of drawing the remaining marbles (non-white marbles), and then multiply them together. Finally, we add up the probabilities for all three cases to get the total probability of drawing 3 or more white marbles.

Using the formula, we get:

P(X ≥ 3) = [(C(10,3) * C(20,2)) + (C(10,4) * C(20,1)) + C(10,5)] / C(30,5)

= [(120 * 190) + (210 * 20) + 252] / 142506

= 0.209

Therefore, the probability of drawing 3 or more white marbles when 5 marbles are drawn from the bag without replacement is 0.209.

using the hypergeometric distribution formula, we can calculate the probability of drawing 3 or more white marbles from a bag containing 5 red marbles, 6 blue marbles, 10 white marbles, and 9 yellow marbles when 5 marbles are drawn without replacement. The probability is 0.209.

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To find the equation of the tangent line, we need to find the derivative of both x and y with respect to t and evaluate them at t = 1 to get the slope of the tangent line. The equation of the line tangent to the curve at the point determined by t = 1 is y = (5/4)(x - 3) + 2.

dx/dt = 2t + 2

dy/dt = 3t^2 + 2t

At t = 1, dx/dt = 4 and dy/dt = 5

So the slope of the tangent line is m = dy/dx = (dy/dt)/(dx/dt) = 5/4

Now we need to find the point on the curve where t = 1.

x = t^2 + 2t = 1^2 + 2(1) = 3

y = t^3 + t^2 = 1^3 + 1^2 = 2

Therefore, the point on the curve where t = 1 is (3, 2)

Using the point-slope form of a line, we can write the equation of the tangent line as:

y - 2 = (5/4)(x - 3)

Simplifying:

y = (5/4)x - (7/2)

So the equation of the line tangent to the curve at the point determined by t = 1 is y = (5/4)x - (7/2).

A curve is described by the parametric equations x = t^2 + 2t and y = t^3 + t^2. An equation of the line tangent to the curve at the point determined by t = 1 is given by the formula y = m(x - x1) + y1, where m is the slope, and (x1, y1) is the point of tangency.

First, find the point of tangency (x1, y1) by plugging t = 1 into the parametric equations:
x1 = (1)^2 + 2(1) = 3
y1 = (1)^3 + (1)^2 = 2

Next, find the derivatives of x and y with respect to t:
dx/dt = 2t + 2
dy/dt = 3t^2 + 2t

Now, find the slope m by dividing dy/dt by dx/dt at t = 1:
m = (dy/dt) / (dx/dt) = (3(1)^2 + 2(1)) / (2(1) + 2) = (5/4)

Finally, plug the slope m and point (x1, y1) into the equation of the tangent line:
y = (5/4)(x - 3) + 2

So, the equation of the line tangent to the curve at the point determined by t = 1 is y = (5/4)(x - 3) + 2.

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A direct variation includes the points (-20,-40) and (7,n) ,The value of n is 14..

in a direct variation, two variables are related in a way that can be expressed as y = kx, where k is a constant of proportionality. in this case, we are given two points that are related by a direct variation:

(-20,-40) and (7,n)

to find the value of n, we need to first determine the value of k. we can do this by using the formula for a direct variation:

y = kx

using the first point (-20,-40), we can substitute x = -20 and y = -40 to get:

-40 = k(-20)

solving for k, we get:

k = -40/-20 = 2

now that we know k, we can use it to find n using the second point (7,n):

n = kx

n = 2(7)

n = 14

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The radius of the circle is 13.

To find the radius of the circle with the center at the origin and passing through the point (-12, 5), we can use the distance formula.

The distance formula between two points (x1, y1) and (x2, y2) is given by:

Distance = √[(x2 - x1)² + (y2 - y1)²]

In this case, the center of the circle is at the origin (0, 0), and the given point is (-12, 5). Plugging these values into the distance formula, we get:

Distance = √[(-12 - 0)² + (5 - 0)²]

= √[(-12)² + 5²]

= √[144 + 25]

= √169

= 13

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Answer:

Step-by-step explanation:

You want the values of the variables x and y, and the measure of angle Q in the given figure when ∆QPR ≅ ∆SPR.

The triangles are congruent by the ASA postulate when the angles at P are congruent and the angles at R are congruent.

  (2x +1)° = (x +18)°

  x = 17 . . . . . . . . . . . divide by °, subtract x+1

  (x +18)° = (17 +18)° = 35° . . . . the measures of the angles at P

  (8y -4)° = (4y +28)°

  4y = 32 . . . . . . . . . . . divide by °, add 4-4y

  y = 8 . . . . . . . . . divide by 4

  (4y +28)° = (32 +28)° = 60° . . . . . . the measures of the angles at R

The sum of angles in ∆QPR is 180°, so ...

  Q +35° +60° = 180°

  Q = 85° . . . . . . . . . . . subtract 95°

For x = 17 and y = 8, the triangles are congruent. m∠Q = 85°.

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It takes 7 hours to travel 385 miles at a constant speed.

To solve this problem, we need to use the direct variation formula, which states that distance traveled is directly proportional to time spent driving. This means that if we double the time spent driving, the distance traveled will also double.

Using this formula, we can set up a proportion to find the answer. We know that the car travels 330 miles in 6 hours, so we can write:

330/6 = 385/x

Where x is the time it takes to travel 385 miles.

To solve for x, we can cross-multiply and simplify:

330x = 2310

x = 7


It's important to note that this problem assumes that the car maintains a constant speed throughout the entire trip. If the car speeds up or slows down at any point, the distance traveled and time spent driving will not follow a direct variation relationship.

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Let's visualize the parallelogram-shaped land with sides of 240m and 160m. We know that the distance between the 240m sides is 40m. Let's denote this distance as "d".

To find the distance between the 160m sides, we can use the concept of similar triangles. The triangles formed by the sides of the parallelogram are similar. In the smaller triangle, the base is 160m, and the corresponding side in the larger triangle is 240m. Similarly, the height of the smaller triangle is "d", and the corresponding side in the larger triangle is 40m. Using the property of similar triangles, we can set up the following proportion:

160m / 240m = d / 40m

Simplifying the proportion, we get:

2/3 = d / 40m

Cross-multiplying, we have:

d = (2/3) * 40m

Calculating the value, we find:

d = 26.67m

Therefore, the distance between the 160m sides of the parallelogram-shaped land is approximately 26.67m.

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The value of the length of the hypotenuse is,

⇒ c = √85

Since, Three vertices and three angles totaling 180 degrees make up a triangle, a three-sided polygon with three sides.

And, Two rays (half-lines) that share a terminal make up an angle. The rays serve as the angle's sides, occasionally serving as the angle's legs and occasionally serving as its arms, while the latter is referred to as the vertex of the angle.

We have to given that;

In triangle ,

Perpendicular side = 9 mm

Base = 2 mm

Since, We know that;

The Pythagorean theorem states that the square of the hypotenuse of a right triangle equals the sum of the squares of its two opposite sides.

Hence, By Pythagoras theorem we get;

⇒ Hypotenuse² = Perpendicular² + Base²

⇒ c² = 9² + 2²

⇒ c² = 81 + 4

⇒ c = √85

Thus, The length of the hypotenuse is,

⇒ c = √85

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Answer: 271 square units

Answer:

x = -2 and y = 2.5

Step-by-step explanation:

using elimination method:

y = 0.25x + 3                 call this equation '1'

x = -4y + 8

bring 4y on its own

4y = -x + 8                       call this equation '2'

multiply '1' by 4:

4y = x + 12                      call this equation '3'

add '2' and '3'

8y = (-x + x) + 20

8y = 20

y = 20/8 = 2.5.

go back to '1'

we have y = 0.25x + 3

              2.5 = 0.25x + 3

 subtract 3 from both sides

2.5 - 3 = 0.25x

-0.5 = 0.25x

multiply both sides by 4

-2 = x

x = -2

now put both y =2.5 and x = -2 into '2' to see if all is fine

4y = -x + 8

4(2.5) = -(-2) + 8

10 = +2 + 8

10 = 10

so x = -2 and y = 2.5

Answer:

[tex] {2}^{ \frac{2}{7} } \times {2}^{ \frac{2}{7} } = {2}^{ \frac{2}{7} + \frac{2}{7} } [/tex]

[tex] {2}^{ \frac{2}{7} } \times {2}^{ \frac{2}{7} } = {2}^{ \frac{4}{7} } [/tex]

The best approximate for the total number of registered users in year 12 would be B. 31. 2 million.

First, we can find the differences over the years in the total number of registered users.

Year 4 = 26. 9 - 26. 5 = 0. 4

Year 6 = 28.0 - 27. 4 = 0. 6

Year 8 = 29. 1 - 28. 6 = 0. 5

Year 10 = 30. 2 - 29. 6  = 0. 6

This shows that the largest increase has been by 0. 6 in a year. Assuming that there are 0. 6 increases over two years till Year 12, the total number becomes :

= 30. 2 + 0. 6 + 0. 6

= 31. 4

The closest option that is lower is 31. 2 million users so this is the best approximate.

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According to the U.S. Census Bureau, in 2010, by the age of 40, approximately 85% of individuals had ever been married.

This statistic is based on data from the American Community Survey, which is conducted by the U.S. Census Bureau. The survey includes questions about marital status and provides information on the percentage of individuals who have ever been married by various ages. The statistic that 85% of individuals had ever been married by the age of 40 suggests that marriage is still a common life experience in the United States. However, it's important to note that this statistic may be influenced by a variety of factors, including changes in societal attitudes towards marriage, cultural and religious practices, and economic factors. Additionally, it's important to consider that this statistic may not be representative of all populations or demographic groups, as marriage rates can vary significantly based on factors such as race, ethnicity, and income.

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The slope of the line above include the following: 1/5.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the slope of a line, we have the following;

Slope (m) = (3 - 0)/(7 + 8)

Slope (m) = (3)/(15)

Slope (m) = 1/5.

Based on the graph, the slope is the change in y-axis with respect to the x-axis and it is equal to 1/5.

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The function y = 14(1.49)ˣ is categorized as growth with 49% percentage increase

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

y = 14(1.49)ˣ

An exponential function is represented as

y = abˣ

If b > 1, then it is a growth function

Otherwise, it a decay function

Using the above as a guide, we have the following:

y = 14(1.49)ˣ is a growth function because 1.49 is greater than 1

The percentage increase is then calculated as

percentage increase = 1.49 - 1

percentage increase = 0.49

Express as percentage

percentage increase = 49%

Hence, the percentage increase is 49%

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The distance between the Woozy Wheel and the Roller Rail is 13 units.

To determine the distance between the Woozy Wheel and the Roller Rail, we can use the distance formula in the coordinate plane.

The coordinates of the Woozy Wheel are (-14, 1), and the coordinates of the Roller Rail are (-2, -4).

Using the distance formula, the distance (d) between two points (x₁, y₁) and (x₂, y₂) is given by:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Substituting the coordinates of the Woozy Wheel and the Roller Rail into the formula:

d = √((-2 - (-14))² + (-4 - 1)²)

= √(12² + (-5)²)

= √(144 + 25)

= √169

= 13

Therefore, the distance between the Woozy Wheel and the Roller Rail is 13 units.

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The solution is: 3.7%, is the probability that the next customer will be a woman who requests a convertible.

Here, we have,

given that,

At a car rental office, 63% of the customers are men and 37% are women.

If 25% of people request a compact car, 37% request a full-sized, 10% request a convertible,16% request an SUV, and 12% request a luxury car

As per given

P(woman)= 37%

P(convertible) = 10%

So combined probability is:

P = 37%*10%

  = 37%*0.1

  = 3.7%

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complete question:

At a car rental office, 63% of the customers are men and 37% are women. If 25% of people request a compact car, 37% request a full-sized, 10% request a convertible,16% request an SUV, and 12% request a luxury car, what is the probability that the next customer will be a woman who requests a convertible?

The probability of choosing 3 men and 1 woman at random for a 4 person committee can be calculated using the combination formula.

We want to choose 3 men from a pool of 10 men, which can be done in 10 choose 3 ways. We also want to choose 1 woman from a pool of 6 women, which can be done in 6 choose 1 ways. The total number of ways to choose a 4 person committee from a pool of 16 people is 16 choose 4. Therefore, the probability of choosing 3 men and 1 woman at random for a 4 person committee is:

(10 choose 3) * (6 choose 1) / (16 choose 4) = 120 * 6 / 1820 = 0.3956

So, the probability of choosing 3 men and 1 woman at random for a 4 person committee is approximately 0.3956 or 39.56%. This means that if we randomly choose a 4 person committee from a pool of 10 men and 6 women, there is a 39.56% chance that the committee will consist of 3 men and 1 woman.

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The area of the middle square should be = 36.

To calculate the area of the middle square, the formula for the area of a square should be used an sit is given below:

Area of a square = a²

where;

a = Length of sides

But,the length of sides of a square are equal therefore;

Area of square = 6×6 = 36

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The value of x is 35 degree.

We know,

The angle sum property of a quadrilateral states that the sum of the interior angles of any quadrilateral is always equal to 360 degrees.

In other words, if you add up the measures of all the interior angles of a quadrilateral, the total will always be 360 degrees.

So, applying angle sum property in Trapezium

145 + 110 + 70 + x = 360

325 + x = 360

x = 360 - 325

x = 35 degree

Thus, the value of x is 35 degree.

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