2. Container P contains 800 ml of solution. 0.4 of the solution in container Q is poured into container P. Then,3/8 of the solution in the container P is poured into an empty container R. If the container R contains 540 ml of solution now, find the initial volume, in litres, of the solution in container Q. ​

The 1,000 feet and 200 feet distances of the top and the base of the skyscraper from the point on the ground, indicates, using Pythagorean Theorem that the height of the skyscraper is 400·√6 feet

Pythagorean Theorem states that the square of the length of the hypotenuse side of a right triangle is equivalent to the sum of the squares of the other two sides.

The distance of the top of the skyscraper from a point on the ground = 1000 feet

The distance of the base of the skyscraper from the same point = 200 feet

Therefore, according to the Pythagorean Theorem, in the right triangle formed by the ray from the top of the skyscraper to the point on the ground, the height, h, of the skyscraper, and the distance of the point on the ground from the skyscraper, we get;

1000² = h² + 200²

h² + 200² = 1000²

h² = 1000² - 200² = 960,000

h = √(960,000) = 400·√6

The height of the skyscraper is 400·√6 feet

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The total foam needed to make n cones is (n/3)πr^2h cubic inches.

The volume of a cone can be calculated using the formula:

V = (1/3)πr^2h

where r is the radius of the base, h is the height, and π is the mathematical constant pi.

In this case, the height of each cone is given as h inches, and the radius of the base is given as r inches. So, the volume of each cone can be calculated as:

V = (1/3)πr^2h

Now, let's assume that the company wants to make n cones. Then, the total amount of foam needed to make these cones would be:

Total foam needed = n × V

Substituting the expression for V, we get:

Total foam needed = n × (1/3)πr^2h

Therefore, the total foam needed to make n cones is (n/3)πr^2h cubic inches.

Note that the given values of h and r are necessary to compute the total foam required.

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Answer:

36/49.

Step-by-step explanation:

Probability if rains on one day = (6/7)

Probabiilty it rains the next day  also

= 6/7 * 6/7

= 36/49.

Answer:

It is C

Step-by-step explanation:

It cannot be d bc - 7-4=-11 so rejected

Not b bc the first number is - 7

The same w a

The approximate height of the tall oak tree is 60.0 feet.

To find the height of the tree, follow these steps:

1. Convert the distance between you and the mirror from inches to feet: 36 inches = 3 feet.
2. Create a proportion using similar triangles, where the height of the tree (h) divided by the distance from the tree to the mirror (24 feet) equals your eye height (5 feet) divided by the distance from your eyes to the mirror (3 feet).
3. Set up the proportion: h / 24 = 5 / 3.
4. Solve for h: h = (5 / 3) * 24.
5. Calculate h: h = 40 feet (height of tree above your eye level).
6. Add your eye height (5 feet) to the height of the tree above your eye level: 40 + 5 = 60 feet.
7. Round the answer to the nearest tenth: 60.0 feet.

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A circular flower garden surrounds a sculpture on a square base as show being 6x and 4x. The expression for the area of the flower garden is π(26x - 12√2x).

Find the expression for the area of the flower garden, we need to first find the area of the square base.

The area of a square is calculated by multiplying the length of one side by itself. In this case, the length of one side is 4x, so the area of the square base is (4x)^2 = 16x^2.
Next, we need to find the area of the circular flower garden that surrounds the square base.

Since the flower garden is circular, we use the formula for the area of a circle, which is A = πr^2, where A is the area and r is the radius.
The radius of the flower garden is the distance from the center of the circle to any point on the circumference.

Since the flower garden surrounds the square base, we can find the radius by subtracting the side length of the square base from the diameter of the circle.

The diameter of the circle is equal to the diagonal of the square base, which is √(6x)^2 + (6x)^2 = √72x^2 = 6√2x. Therefore, the radius of the flower garden is (6√2x - 4x)/2 = (3√2x - 2x).
Now we can substitute this expression for the radius into the formula for the area of a circle to find the area of the flower garden: A = π(3√2x - 2x)^2 = π(18x - 12√2x + 8x) = π(26x - 12√2x).
Therefore, the expression for the area of the flower garden is π(26x - 12√2x).

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Mrs. Ross should expect to have about 26,417 books with no damage in the entire collection. Rounded to the nearest whole number, the answer is 26,417.

Mrs. Ross found that 902 out of the sample of (902 + 80 + 43) = 1025 books had no damage. This means that the proportion of books with no damage in the sample is 902/1025. We can use this proportion to estimate the number of books with no damage in the entire collection.

Let X be the number of books with no damage in the collection of 30,000 books. Then we can write:

902/1025 = X/30000

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

902 × 30000 = 1025 × X

X = 902 × 30000 / 1025

X ≈ 26,417.07

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The result should be interpreted with caution and cannot be directly extrapolated to the real-world Fender's blue butterfly populations, and the simulation does not take these factors into account.

The result of the simulation suggests that in a hypothetical scenario where the Fender's blue butterfly population is restricted to stepping stones, and the leave prairie probability is set to 0.9, the population is likely to increase over time. However, it is important to note that the simulation represents an idealized scenario and may not reflect the complexity of real-world butterfly populations.

Furthermore, the absence of fires in the simulation may not reflect the natural habitat of Fender's blue butterfly, as fire is a crucial factor in maintaining prairie habitats. In the real world, fire suppression and habitat fragmentation are major threats to the survival of Fender's blue butterfly populations, and the simulation does not take these factors into account.

In summary, while the simulation result may provide insights into the potential effectiveness of using stepping stones to conserve butterfly populations, it should be interpreted with caution and cannot be directly extrapolated to the real-world Fender's blue butterfly population. Further research and monitoring of butterfly populations in their natural habitats are necessary to fully understand their dynamics and inform conservation efforts.

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The inequalities in the given options are: B) t > 0, C) 3 < a, E) k < -5/7, The correct option is B,C,E.

B) t > 0: This represents an inequality because the symbol ">" indicates "greater than." It states that the variable "t" is greater than zero. In other words, it means that "t" has to be a positive number and cannot be zero or negative.

C) 3 < a: This represents an inequality because the symbol "<" indicates "less than." It states that the number 3 is less than the variable "a." In other words, it means that "a" has to be greater than 3 for the inequality to hold true.

E) k < -5/7: This represents an inequality because the symbol "<" indicates "less than." It states that the variable "k" is less than -5/7. In other words, it means that "k" has to be a value smaller than -5/7 for the inequality to be true.

The other options, such as -3 = y, g = 5 and one-half, and x = 1, do not represent inequalities because they either show an equation (equality) or simply assign values to variables without any comparison.

Therefore the correct option is B,C,E.

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The surface area be 243 square feet.

Hence option (d) is correct.

In the given regular pyramid

Slant height = l = 6 ft

Edge of base = s = 9ft

Then,

Area of base = a = 9x9 = 81 square ft

Perimeter of base = p = 4x9 = 36 ft

Since surface area of regular pyramid = A  = a + (1/2)ps

                                                                       = 81 + (36x9)/2

                                                                       = 81 + 162

                                                                       =  243

Hence, A = 243 square ft.

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Answer:

The surface area be 243 square feet.

Step-by-step explanation:

The dimensions that will minimize the cost of the metal to make the can are approximately r = 2.82 inches and h = 7.10 inches.

We can use the following steps:

Step 1: Write the volume formula for the cylinder.
The volume (V) of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height. Since the volume is given as 181 in³, we have:

181 = πr²h

Step 2: Solve for h in terms of r.
Divide both sides by πr²:

h = 181 / (πr²)

Step 3: Write the surface area formula for the cylinder without a top.
The surface area (S) of a cylinder without a top is given by the formula S = 2πrh + πr², where r is the radius and h is the height.

Step 4: Substitute h from step 2 into the surface area formula.
Replace h with 181 / (πr²) in the surface area formula:

S = 2πr(181 / (πr²)) + πr²

Step 5: Simplify the surface area formula.
After simplifying the surface area formula, we get:

S = (362 / r) + πr²

Step 6: Minimize the surface area.
To minimize the surface area, differentiate S with respect to r and set the derivative equal to 0:

dS/dr = -362/r² + 2πr = 0

Step 7: Solve for r.
To find the value of r that minimizes the surface area, solve the equation for r:

r³ = 181/π

r = (181/π)¹/³

Step 8: Find the height h.
Substitute the value of r back into the equation for h from step 2:

h = 181 / (π((181/π)¹/³)²)

Step 9: Calculate the dimensions.
Calculate the dimensions r and h using the values obtained in step 7 and step 8:

r ≈ 2.82 inches
h ≈ 7.10 inches

So, the dimensions that will minimize the cost of the metal to make the can are approximately r = 2.82 inches and h = 7.10 inches.

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The values are,

x =  15[tex]\sqrt{2}[/tex]([tex]\sqrt{2}[/tex] -1)/2

y = 15([tex]\sqrt{2}[/tex] -1)/2

z = 15

Labelling the given figure;

In ΔABC

Cos 60 = (y + z)/15[tex]\sqrt{2}[/tex]

⇒y + z = 15[tex]\sqrt{2}[/tex]/2   ....(i)               (since cos 60 = 1/2)

In ΔADC

sin 45 = z/15[tex]\sqrt{2}[/tex]

⇒ z = 15  ....(ii)                            (since sin45  = 1/[tex]\sqrt{2}[/tex])  

Now from (i) and (ii)

y = 15([tex]\sqrt{2}[/tex] -1)/2

In ΔABD

Sin 45 = y/x

⇒  1/[tex]\sqrt{2}[/tex] = (15([tex]\sqrt{2}[/tex] -1)/2)/x

⇒ x =  15[tex]\sqrt{2}[/tex]([tex]\sqrt{2}[/tex] -1)/2

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To make a profit of $281, the number of tickets that need to be sold is 150.

The profit from selling local ballet tickets can be determined by using the given function: [tex]p = -0.25x^2 + 0.30x + 6[/tex].

To find the number of tickets required to achieve a profit of $281, we can set p equal to 281 and solve for x. This results in a quadratic equation that can be solved using the quadratic formula.

Once we obtain the two possible values of x, we can select the positive value which represents the ticket price. Using this ticket price, we can then calculate the number of tickets required to achieve a profit of $281, which is 150.

In order to increase the profit, we can try adjusting the ticket price or increasing the number of tickets sold. However, it is important to keep in mind that there may be practical limits to both of these options.

For example, increasing the ticket price too much may deter customers from purchasing tickets, while increasing the number of tickets sold may require additional marketing efforts or larger venues.

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The number of people who did not like pop songs is 175.

Given data :

In a survey, the ratio of people who liked pop songs and rap songs is 7: 9.

The number of people who liked both songs = 60.

The number of people who liked only rap songs =  30.

The number of people who liked none of the songs = 40

First of all, we will find the number of people who only like pop songs. We are given a ratio of 7:9 for the people who liked pop songs and rap songs. Let us assume that the number of people who liked pop songs is x and those who liked rap songs is y. According to the ratio given,

[tex]\frac{x}{y} = \frac{7}{9}[/tex]   .....(1)

As we know the number of people who only liked rap songs are 30. Therefore, y - x = 30

x = y - 30

We will substitute the value of x in equation 1.

[tex]\frac{y - 30}{y} = \frac{7}{9}[/tex]

9y - 270 = 7y

2y = 270

y = 135

Now, x = 135 -30

x = 105

Total number of people in survey = x + y + 40

105 + 135 + 40 = 280

Out of 280, the number of people who liked pop songs is 105. So, the number of those who did not like pop songs is ( 280 - 105) = 175.

Therefore, the number of people who did not like pop songs are 175.

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Sylvia can fit 9 large cubic boxes and 240 small rectangular boxes into her car trunk.

We first need to convert all measurements to the same unit. Since the large cubic boxes are given in inches, we need to convert the dimensions of the trunk to inches as well.

The trunk measures 51 inches wide (4.25 ft x 12 in/ft), 48 inches deep (4 ft x 12 in/ft), and 53.33 inches high (4*1/3 ft x 12 in/ft).

Next, we need to determine how many large boxes can fit in the trunk. Since each large box is 16 inches wide,

we can fit 3 boxes across the width of the trunk:

(51 inches ÷ 16 inches = 3.19)

Similarly, we can fit 3 boxes deep and 3 boxes high.

Therefore, the maximum number of large boxes Sylvia can fit in her trunk is:

27 (3 x 3 x 3 = 27)

After fitting as many large boxes as possible, we can calculate the remaining volume of the trunk and use this to determine how many small boxes can fit.

The remaining volume is approximately 59,712 cubic inches (51 in x 48 in x 20 in).

Dividing this by the volume of each small box:

(3 in x 6 in x 4 in = 72 cubic inches)

We can fit 829 small boxes in the remaining space.

Therefore, Sylvia can fit a total of 27 large boxes and 829 small boxes in her trunk.

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Answer:

168

Step-by-step explanation:

Volume is the ''area'' of a 3d shape

to find the volume, multiply the length, width, and height of the shape.

6x7x4

=42x4

=168 cubic yards

hope it helps

pls mark brainliest!!!

Answer:

168 cubic yards

Step-by-step explanation:

The formula for a rectangular prism volume is:

[tex]V=lwh[/tex]

Since we have all 3, the length, the width, and the height, we can plug in the numbers to substitute:

V=6·7·4

=168

So, the volume of this rectangular prism is 168 cubic yards.

Hope this helps :)

The expected value of a ticket in this raffle is $12.50.

We have to given that;

1000 raffle ticket are sold for $1 each and there are ten $20, five $50, and one $100 prize.

Now, For the expected value of a ticket, we need to multiply the probability of winning each prize by the amount of each prize, and then add up those values.

Hence, In this case, there are a total of 16 prizes as,

⇒ (10 $20 prizes, 5 $50 prizes, and 1 $100 prize),

Thus, the probability of winning any one prize is,

⇒ 1/16

So, the expected value of a ticket would be:

= (10/16) $20 + (5/16) $50 + (1/16) x $100

= $12.50

Therefore, the expected value of a ticket in this raffle is $12.50.

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The required answer is a possible scenario where BC (c) is less than AC * sin(angle A)

To justify if it is possible to have BC < AC sin(angle A) for an acute triangle ABC, let's consider the sine formula for a triangle.

The sine formula for a triangle states that:

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the angles opposite to those sides, respectively.

Now let's isolate side BC (b) in the equation:

b = c * sin(B) / sin(C)

Since triangle ABC is acute, all angles A, B, and C are less than 90°. Therefore, sin(B) and sin(C) will be positive values between 0 and 1.

Let's now compare BC (b) to ACsin(angle A):

b < AC * sin(A)

c * sin(B) / sin(C) < AC * sin(A)

We can rewrite the inequality in terms of angle C:

sin(B) / sin(C) < (AC * sin(A)) / c

Now let's recall that angle C is the angle opposite to side AC (c), and angle B is the angle opposite to side BC (b). Since sine is a positive increasing function for acute angles (0° to 90°), it follows that the sine of a larger angle will result in a larger value.

As angle C is opposite to the longer side (AC), angle C > angle B. Therefore, sin(C) > sin(B), and their reciprocals will have the opposite relationship:

1 / sin(C) < 1 / sin(B)

Now, let's multiply both sides of the inequality by c * sin(B):

c < AC * sin(A)

This inequality represents a possible scenario where BC (c) is less than AC * sin(angle A), justifying the initial claim. So, yes, it is possible to have BC < AC sin(angle A) for an acute triangle ABC.

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(a) The expression for the total area of the tablet = (8 + 2z)(5 + 2z)

(b) Equation is: (8 + 2z)(5 + 2z) = 50.3125 and the solution to this equation refers to the thickness of frame for which the area of the tablet is 50.3125.

(c) Solution or the thickness of the frame must be 0.375 inches.

The dimensions of the screen of a tablets are 8 inches by 5 inches.

border around the screen has thickness z.

So the length with frame = 8 + 2z

and the width of the screen with frame = 5 + 2z

So the expression for the total area of the tablet = Length* Width = (8 + 2z)(5 + 2z)

Equation for which the expression is equal to 50.3125 is given by,

(8 + 2z)(5 + 2z) = 50.3125

So the solution to this equation refers to the thickness of frame for which the area of the tablet is 50.3125.

Solving the equation we get,

(8 + 2z)(5 + 2z) = 50.3125

40 + 10z + 16z + 4z² = 50.3125

4z² + 26z - 10.3125 = 0

Solving this quadratic equation we get the solutions,

z = -6.875, 0.375

Since the thickness cannot be negative so -6.875 must be neglected.

Hence the thickness of the frame is 0.375 inches.

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The surface area  of the given volume of the rectangular prism is equal to 13.86 square centimeters.

Volume of the rectangular prism is 6 cubic centimeters.

Let the dimensions of the rectangular prism be length (l), width (w), and height (h).

Volume of the rectangular prism = l x w x h

⇒ l x w x h = 6

Use the given volume to find one of the dimensions .

Then use that information to find the surface area.

To calculate the surface area at least two of the dimensions known.

Let us assume that the height (h) is 1 centimeter.

⇒l x w x 1 = 6

⇒ l x w = 6

Use this equation to solve for one of the dimensions.

⇒ l = 6/w

Substituting this value of l into the surface area formula, we get,

Surface area = 2lw + 2wh + 2lh

⇒Surface area = 2(6/w)w + 2w(1) + 2(6/w)(1)

⇒Surface area = 12/w + 2w + 12/w

⇒Surface area = 2w + 24/w

Value of w that gives the minimum surface area,

Take the derivative of the surface area formula with respect to w and set it equal to 0,

d/dw (2w + 24/w) = 0

⇒ 2 - 24/w^2 = 0

Solving for w, we get,

⇒w = √(12)

Substituting this value of w back into the surface area formula, we get,

⇒ Surface area = 2(√(12)) + 24/√(12)

⇒Surface area = 4√3 + 4√3

⇒Surface area = 8√3

⇒ Surface area = 13.86 square centimeters

Therefore, the surface area of the rectangular prism is approximately 13.86 square centimeters.

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The measures of the angles A = 81.2, B = 65.2, and C = 33.6 to the nearest tenth using the cosine and sine rule.

In trigonometry, the cosines rule relates the lengths of the sides of a triangle to the cosine of one of its angles. While sine rule is a relationship between the size of an angle in a triangle and the opposing side.

Considering the given triangle, angle C is calculated with cosine rule as follows;

c² = a² + b² - 2(b)(c)cosC

14² = 25² + 23² - 2(25)(23)cosC

196 = 1154 - 1150cosC

C = cos⁻¹(958/1150)

C = 33.6

by sine rule;

14/sin33.6 = 25/sinA

sinA = (25 × sin33.6)/14 {cross multiplication}

A = sin⁻¹(0.9882)

A = 81.2

B = 180 - (33.6 + 81.2) {sum of interior angles of a triangle}

B = 65.2

With proper application of the cosine and sine rule, we have the measures of the angles A = 81.2, B = 65.2, and C = 33.6 to the nearest tenth.

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the free cash flow for Joyner Company in Year 2, we need to follow these steps:

Step 1: Calculate operating cash flow (OCF).
Operating cash flow is calculated by taking the company's net income, adding back non-cash expenses (depreciation and amortization), and adjusting for changes in working capital.

Step 2: Calculate capital expenditures (CapEx).
Capital expenditures are the funds used by the company to acquire, upgrade, and maintain physical assets, such as equipment or buildings. In this case, we need to find the net change in equipment and accumulated depreciation.

Step 3: Subtract the cash dividend.
The cash dividend paid by the company during Year 2 should be subtracted from the operating cash flow.

Step 4: Calculate the free cash flow.
Free cash flow is the remaining cash after deducting capital expenditures and cash dividends. It represents the cash available for the company to repay debt, reinvest in the business, or distribute to shareholders.

Unfortunately, the provided information is not sufficient to compute the free cash flow for Year 2. Specifically, the net income, changes in working capital, and complete equipment transactions are needed to perform these calculations. Please provide the missing information so that a detailed step-by-step explanation can be given to compute the free cash flow for Joyner Company in Year 2.

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The total surface area of the solid is approximately 1818 [tex]cm^{2}[/tex]. Let's call the radius of the hemisphere and cylinder "r".

The volume of the solid is the sum of the volumes of the hemisphere and cylinder: V = (2/3)π[tex]r^{3}[/tex] + π[tex]r^{2}[/tex]h. Substituting in the given values, we get: 2707 = (2/3)π [tex]r^{3}[/tex] + π[tex]r^{2}[/tex](80)

To solve for r, we can rearrange the equation and use a numerical method or calculator. We get: r ≈ 11.6 cm

Now, we can use the radius to find the surface area of the solid. The surface area is the sum of the curved surface areas of the hemisphere and cylinder, plus the area of the circular base of the cylinder: A = 2π[tex]r^{2}[/tex] + 2πrh + π[tex]r^{2}[/tex].

Substituting in the given values and solving for A, we get: A ≈ 1818 [tex]cm^{2}[/tex]. Therefore, the total surface area of the solid is approximately 1818 [tex]cm^{2}[/tex].

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Answer:

It’s an hour

Answer:

11:15 to 12:15 is 1 hour.

11:15 is 1 hour and 15 minutes after 10:00. 12:15 is 1 hour and 15 minutes after 11:00. Therefore, the time span between 11:15 and 12:15 is 1 hour.

Step-by-step explanation:

The length of the hose to reach any part of the pool surface from there will be 22.36 feet.

Length of hose = √(L² + W²)

The pool is 20 feet long and 10 feet wide, the length of the hose needed would be approximately:

Length of hose = √(20² + 10²) = √500 = 22.36 feet

Therefore, Peter would need a vacuum hose that is approximately 22.36 feet long to reach any part of the pool surface from the outlet.

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The area covered by a sprinkler that sprays water in a circle of an 8-foot radius is 200.96 square feet.

Circle is a 2-Dimensional shape. It has no vertex and edges. It has a center point which equidistant from any point of boundary or circumference of a circle.

Radius refers to the distance between the center and any point on the boundary or circumference of the circle.

The area of a circle is given as the product of a constant pi and the square of the radius.

A =  π[tex]r^2[/tex]

A is the area

r is the radius

r = 8 feet

A = π * 8 * 8

= 3.14 * 8 * 8

= 200.96 square feet

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The volume of a cube with edge length 8 ft are V = 512 ft³

The volume of a cube is calculated by multiplying the length of one of its sides by itself three times (V = s³). Therefore, for a cube with an edge length of 8 ft, its volume would be V = 8³ = 512 ft³.

Therefore, the correct answer is: V = 512 ft³

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Answer:

I'm assuming that A and B are two different items, and you want me to work with the same data set for both items. Here are the calculations:

1. Mean price of milkshake:

To find the mean price of a milkshake, you need to add up all the prices and divide by the total number of prices:

(4 + 2 + 9 + 14 + 6) / 5 = 7

Therefore, the mean price of a milkshake is $7.

2. Median price of milkshake:

To find the median price of a milkshake, you need to put the prices in order from lowest to highest:

2, 4, 6, 9, 14

The median is the middle value. Since there are five values, the middle value is the third value, which is 6.

Therefore, the median price of a milkshake is $6.

3. Mode of price of milkshake:

To find the mode of the price of a milkshake, you need to find the price that appears most frequently in the data set. In this case, there is no price that appears more than once, so there is no mode.

Therefore, there is no mode for the price of a milkshake.

I hope that helps! Let me know if you have any further questions.

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Statement 2 is false because while the median score of Group A is higher than Group B, it is not 10 points greater as claimed.

Statement 1 is false because the box plots provide limited information, making it impossible to determine whether at least 50% of students in each group scored more than 165 push-ups.

Statement 3 is false because Group A has more variability in push-up scores than Group B, as indicated by the larger interquartile range (IQR) of Group A.

Looking at the box plots, we can see that the median score of Group A is higher than Group B, but it is not 10 points greater. Therefore, statement 2 is False.

We cannot determine whether at least 50% of students in each group scored more than 165 push-ups. The box plots only show us the quartiles and the minimum and maximum values, so we do not know the exact number of students who scored above 165 push-ups. Therefore, statement 1 is False.

The interquartile range (IQR) of Group A is greater than the IQR of Group B, indicating that Group A has more variability in push-up scores than Group B. Therefore, statement 3 is False.

Hence, All the statement are False.

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