In a restaurant 1/5 of the customers are vegetarian and 3/4 eat meat. The remainder of the customers are dairy intolerant. What fraction of the customers are dairy intolerant? Give your answer as a fraction in its lowest terms

Answer:

134° + (2x)° = 180°

(2x)° = 46°

x = 23

So angles 1, 2, 3, and 4 all measure 23°.

To determine how long it would take Jose to read 20 pages at his average rate, you can use a proportion.

Let x be the time in minutes it would take Jose to read 20 pages.

Then, you can set up the following proportion:

2.5 pages / 4 minutes = 20 pages / x minutes

To solve for x, you can cross-multiply:

2.5 pages * x minutes = 4 minutes * 20 pages

2.5x = 80

Finally, divide both sides by 2.5 to isolate x:

x = 32

Therefore, it would take Jose 32 minutes to read 20 pages at his average rate.

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To cover a rectangular lawn of 160 feet by 160 feet with dichondra lawn food, you would need 210 pounds of fertilizer.

To find the area of the rectangular lawn

Area = Length x Width

Area = 160 ft x 160 ft

Area = 25,600 sq ft

Since one bag of lawn food can cover 4000 square feet, we need to divide the total area of the lawn by the coverage of one bag

Number of bags = Total area ÷ Coverage of one bag

Number of bags = 25,600 sq ft ÷ 4000 sq ft

Number of bags = 6.4

Since we cannot buy a fraction of a bag, we need to round up to the nearest whole number of bags, which is 7.

Therefore, we need 7 bags of lawn food to cover the rectangular lawn. To find the total weight of fertilizer needed, we multiply the number of bags by the weight of one bag

Total weight of fertilizer = Number of bags x Weight of one bag

Total weight of fertilizer = 7 bags x 30 pounds/bag

Total weight of fertilizer = 210 pounds

Thus, we need 210 pounds of fertilizer to cover the rectangular lawn.

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Geometric transformations can be found in everyday life, such as moving furniture (translation), opening a door (rotation), using mirrors (reflection), zooming in and out of maps (scaling), skewing images in Photoshop (shearing), and stretching a rubber band (stretching).

Here are some examples of different types of transformations and their applications:

Translation:

Moving furniture in a room

Moving a vehicle on a map

Shifting a picture on a wall

Rotation:

Swinging a pendulum

Turning a key in a lock

Opening a door

Reflection:

Mirrors reflecting images

Water reflections of a landscape

Reflective surfaces on cars and buildings

Scaling:

Enlarging or reducing a picture on a screen

Adjusting the size of a printout

Shearing:

Skewing an image in Photoshop

Tilting a picture frame on a wall

Slanting the roof of a building for better drainage

Stretching:

Stretching a rubber band

Stretching a balloon before inflating it

Stretching a canvas for painting

These are just a few examples of the many ways geometric transformations are used in our everyday lives. By understanding these concepts, we can appreciate the beauty and functionality of the world around us.

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The t-test statistic value that has a P-value of 0.10 when the alternative hypothesis is

(a) Ha: μ ≠ 0 is ±1.711.

(b) Ha: μ > 0 is 1.319.

(c) Ha: μ < 0 is -1.319.

(d) Ha: μ ≠ 0 is ±1.711.

To find the t-test statistic value for a given P-value and alternative hypothesis, we need to use a t-distribution table or a statistical software program. Here, we will use a t-distribution table to find the t-test statistic value for a sample of 24 observations and a P-value of 0.10 for each alternative hypothesis.

(a) Ha: μ ≠ 0 (two-tailed test)

The critical t-value for a two-tailed test with a P-value of 0.10 and degrees of freedom (df) of 23 (sample size - 1) is:

t = ±1.711

Therefore, the t-test statistic value that has a P-value of 0.10 when the alternative hypothesis is Ha: μ ≠ 0 is ±1.711.

(b) Ha: μ > 0 (one-tailed test)

The critical t-value for a one-tailed test with a P-value of 0.10 and df of 23 is:

t = 1.319

Therefore, the t-test statistic value that has a P-value of 0.10 when the alternative hypothesis is Ha: μ > 0 is 1.319.

(c) Ha: μ < 0 (one-tailed test)

The critical t-value for a one-tailed test with a P-value of 0.10 and df of 23 is:

t = -1.319

Therefore, the t-test statistic value that has a P-value of 0.10 when the alternative hypothesis is Ha: μ < 0 is -1.319.

(d) Ha: μ ≠ 0 (two-tailed test)

To find the t-test statistic value when Ha: μ ≠ 0, we can use the inverse t-distribution function in a statistical software program or a calculator. The t-test statistic value that corresponds to a P-value of 0.10 with 23 degrees of freedom is:

t = ±1.711

Therefore, the t-test statistic value that has a P-value of 0.10 when the alternative hypothesis is Ha: μ ≠ 0 is ±1.711.

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The lowest price she can charge per gift box to earn $2,000 in profit in her first month is approximately $3.2.

Jill is starting her own business called Fuzzy Socks Box, where she'll knit and sell gift boxes of fuzzy socks online.

Jill's profit per gift box is x - 2 dollars. To earn $2,000 in profit in her first month, she needs to sell

2000 / (x - 2) gift boxes.

According to her survey, the number of gift boxes she'll sell is

-10x + 350

Setting these two expressions equal to each other, we can find the lowest price Jill can charge per gift box to earn $2,000 in profit

-10x + 350 = 2000 / (x - 2)

Multiplying both sides by (x - 2), we get

-10[tex]x^{2}[/tex] + 12x - 470 = 0

Solving this quadratic equation, we find that

x = (6 +[tex]\sqrt{196[/tex] )/5 ≈ 3.2

or

x = (6 -[tex]\sqrt{196[/tex] )/5 ≈ 0.7

Since Jill cannot charge a negative price for her gift boxes, the lowest price she can charge per gift box to earn $2,000 in profit in her first month is approximately $3.2.

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The demand equation can be used to estimate the demand for air travel at different price levels, and can help airlines make pricing decisions based on the expected demand.

The demand equation is given as:

q = 55.1 - 0.023p

where q is the quantity demanded and p is the price of the airfare.

This equation shows an inverse relationship between price and quantity demanded. As the price of the airfare increases, the quantity demanded decreases, and vice versa.

For example, if the airfare price is $100, we can calculate the quantity demanded as:

q = 55.1 - 0.023(100) = 52.8

This means that at a price of $100, the quantity demanded is approximately 52.8 units.

Similarly, if the airfare price is $200, we can calculate the quantity demanded as:

q = 55.1 - 0.023(200) = 50.4

This means that at a price of $200, the quantity demanded is approximately 50.4 units.

So, demand equation can be used to estimate the demand for air travel at different price levels, and can help airlines make pricing decisions based on the expected demand.

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To find the number of minutes it will take for both Aquarium A and Aquarium B to contain the same amount of water, we can set up an equation using the given information.

Aquarium A starts with 6 gallons and is filled at 2 gallons per minute. The equation for Aquarium A will be:

A = 6 + 2t

Aquarium B starts with 54 gallons and is filled at 1 gallon per minute. The equation for Aquarium B will be:

B = 54 + 1t

We want to find the time 't' when the amount of water in both aquariums is equal, so we can set the equations equal to each other:

6 + 2t = 54 + 1t

Now, solve for 't':
2t - 1t = 54 - 6
t = 48

After 48 minutes, both Aquarium A and Aquarium B will contain the same amount of water.

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X = 0 and Y = 6 are the answers to the equation system. The system's two equations are satisfied at the location (0, 6). Choice D

To solve the system of equations:

2x + 3y = 18

3x + y = 6

We can employ the substitution or elimination strategy. Let's solve this system via the process of elimination:

To make the coefficients of x in both equations equal, multiply the second equation by two:

2(3x + y) = 2(6)

6x + 2y = 12

Now we have the system of equations:

2x + 3y = 18

6x + 2y = 12

Next, by deducting the first equation from the second equation, we can remove the y term:

(6x + 2y) - (2x + 3y) = 12 - 18

6x + 2y - 2x - 3y = -6

4x - y = -6

4x - y = -6

y = 4x + 6

At this point, we can add this expression for y to one of the initial equations. Let's employ the first equation:

2x + 3(4x + 6) = 18

2x + 12x + 18 = 18

14x + 18 = 18

14x = 0

x = 0

Replacing x = 0 in the equation y = 4x + 6 now:

y = 4(0) + 6

y = 6

Thus, x = 0 and y = 6 are the answers to the system of equations. The system's two equations are satisfied at the location (0, 6). Basketball or baseball in option D is 5/6, or approximately 0.8333.

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Answer:

Option D, (0,6)

Step-by-step explanation:

took the test xx

Answer:

100

Step-by-step explanation:

8000/80=100

8 thousands= 8000

8 tens= 80

Expert Answer, Mark AS BRAINLIEST!!!

If 75 people chose tulips as their favourite flower then Yelina surveyed 500 people.

What is surveying?

Surveying is a branch of mathematics that deals with the measurement, analysis, and representation of physical features on land or in space. It uses geometry, trigonometry, and infinitesimal calculus to accurately measure distances, angles, elevations, and positions. Surveying is used in various fields such as civil engineering, construction, mapping, and geology to obtain valuable information about the earth's surface and to create maps and plans for various purposes.

According to the given information

Since the central angle for tulips is 54°, we can set up a proportion:

54/360 = 75/x

Simplifying this proportion, we get:

0.15 = 75/x

Multiplying both sides by x, we get:

x * 0.15 = 75

Dividing both sides by 0.15, we get:

x = 500

Therefore, Yelina surveyed 500 people.

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In the event of describing the likelihood that the team rebounds the next missed shot is likely, and the number of rebounds that the team should expect to have missed in 15  shots is 10.5 rebounds.

Given

Number of shots missed by the given team is 7

Total number of shots fired is 10

a) Then, moving on to the first part of the question

Here we have to apply probability to evaluate the likelihood of the given team rebounds the next missed shot.

Then,

Probability = no of shots attended / total number of shots fired

Probability = 7 /10

Then the event is likely

b) Now the second part

Then the number of rebounds the given team expect to have in the next 15 missed shots

= 7/10 ×15

= 105/10

= 10.5 rebounds

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There are 1140 different predictions possible for this game of chance.

In this scenario, customers have an opportunity to predict three numbers out of 20, which will be drawn from a bin. The order in which the numbers are selected does not matter, which means the same set of numbers in different orders will be considered as the same prediction.

To solve this problem, we can use the formula for combinations, which is

=> [tex]^nC_x = \frac{n!}{ x! \times (n-x)!}[/tex]

where n is the total number of items, and x is the number of items to be selected.

In this case, we have 20 balls, and we want to select three balls without replacement. So, the formula becomes

=> [tex]^{20}C_3 = \frac{20!} { 3! \times (20-3)!}[/tex]

Using a calculator or simplifying the equation, we get:

[tex]= > ^{20}C_3 = \frac{201918} { 321} = 1140[/tex]

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Answer: 10

Step-by-step explanation:

just trust me

The regular membership fee of the Holiday Health Club is $300.

Let the regular membership fee be x. According to the problem, the club has reduced its annual membership by 10%, so the discounted membership fee is 0.9x. We know that Jorge Sanchez has purchased a year's membership for $270, which is the discounted membership fee. Therefore, we can set up an equation as follows:

0.9x = 270

Solving for x, we get:

x = 270/0.9

x = 300

Hence, the regular membership fee of the Holiday Health Club is $300.

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If regular hexagon, regular octagon are inscribed in circle, perimeter of hexagon is greater than perimeter of octagon, each perimeter is greater than circumference of circle. Therefore, statement B is true.

The perimeter of a polygon is the sum of the lengths of all its sides. In a regular polygon, all sides have equal length, so the perimeter is simply the number of sides multiplied by the length of one side. The circumference of a circle is the distance around its outer edge.

Since both polygons are inscribed in the same circle, they have the same circumcircle, which means that their perimeters are both less than the circumference of the circle.

To compare the perimeters of the two polygons, we need to know the number of sides of each polygon and the length of one side. A regular hexagon has six sides, and a regular octagon has eight sides. Since the circle is inscribed in both polygons, the sides of each polygon are tangents to the circle, forming right angles with the radii of the circle.

Thus, we can draw a right triangle with the radius of the circle as the hypotenuse, and the side of the hexagon (or octagon) as one leg. Using trigonometry, we can find the length of one side of the hexagon (or octagon) in terms of the radius of the circle.

After calculating the lengths of one side of each polygon, we can compare their perimeters. It turns out that the perimeter of the octagon is greater than the perimeter of the hexagon, since the octagon has more sides.

Therefore, statement B is true.

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Complete question is:

A regular hexagon and a regular octagon are both inscribed in the same circle. which of these statements is true?

A) the perimeter of the hexagon is less than the perimeter of the octagon, and each perimeter is less than the circumference of the circle.

B) the perimeter of the hexagon is greater than the perimeter of the octagon, and each perimeter is greater than the circumference of the circle.

Therefore, the solutions of tan x = -1/2 in the interval (0, 2) are:

x ≈ 2.034, 5.176

We can simplify the given equation as follows:

4 tan 2x - 4 cot x = 0

4(tan 2x - cot x) = 0

4[(2tan x)/(1 - tan^2 x) - (1)/(tan x)] = 0

Multiplying both sides by (1 - tan^2 x) * (tan x), we get:

8tan^3 x - 4tan^2 x - 8tan x + 4 = 0

Dividing both sides by 4 and rearranging, we get:

2tan^3 x - tan^2 x - 2tan x + 1 = 0

Factorizing, we get:

(tan x - 1)(2tan^2 x - tan x - 1) = 0

Using the quadratic formula to solve for the roots of 2tan^2 x - tan x - 1 = 0, we get:

tan x = [1 ± sqrt(1 + 8)] / 4 = [1 ± sqrt(9)] / 4 = 1, -1/2

Therefore, the solutions of the given equation in the interval (0, 2) are the values of x such that tan x = 1 or tan x = -1/2.

We know that tan (π/4) = 1 and tan (-π/4) = -1, so the solutions of tan x = 1 in the interval (0, 2) are:

x = π/4, 5π/4

We can find the solutions of tan x = -1/2 in the interval (0, 2) by finding the reference angle and using the signs of sine and cosine in the corresponding quadrants. We have:

tan x = -1/2

Let θ be the reference angle such that tan θ = 1/2. We know that θ is in the second or fourth quadrant.

In the second quadrant, sine is positive and cosine is negative, so we have:

sin θ = sqrt(1/(1 + tan^2 θ)) = sqrt(1/5)

cos θ = -tan θ = -1/2

Therefore, we get:

x = π - θ = π + arctan(1/2) ≈ 2.034

In the fourth quadrant, both sine and cosine are negative, so we have:

sin θ = -sqrt(1/(1 + tan^2 θ)) = -sqrt(1/5)

cos θ = -tan θ = -1/2

Therefore, we get:

x = 2π - θ = 2π + arctan(1/2) ≈ 5.176

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The approximate area of the figure is 40 square meters. So, the correct answer is B).

Recall the formula for the area of a kite, which is

Area = (1/2) x Base x Height

where "Base" is the length of one of the diagonals and "Height" is the length of the other diagonal.

Identify the base and height of the given kite from the problem statement. Here, it is given that the height is 10 meters and the base is 8 meters.

Substitute the values of the base and height into the formula for the area of a kite

Area = (1/2) x 8 meters x 10 meters

Simplify the expression by multiplying the base and height together and dividing by 2

Area = 40 square meters

Round the answer to the nearest whole number or keep the answer as a decimal, depending on the instructions of the problem.

Therefore, the approximate area of the given kite is 40 square meters. So, the correct answer is B).

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A sample size of 40 attorneys is needed to estimate the mean IQ with 98% confidence and a margin of error of 3 IQ points.

To find the sample size, we use the formula:

n = (z*σ/E)²

where n is the sample size, z is the z-score for the desired level of confidence given as 98% , σ is the population standard deviation given as 15, and E is the margin of error given as 3 IQ points.

using the above values, we get:

n = (2.33*15/3)²

n = 39.05

Therefore, we need a sample size of at least 40 attorneys to estimate the mean IQ with 98% confidence and a margin of error of 3 IQ points.

Whether this sample size is practical or not depends on various factors, such as the availability of attorneys with the desired characteristics, the cost and time required to collect the data, and the resources available for analysis. In general, a sample size of 40 is considered moderate to large for many applications, and it may be feasible depending on the specific context.

A sample size of 40 attorneys is needed to estimate the mean IQ with 98% confidence and a margin of error of 3 IQ points.

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A) The distribution is a negative binomial distribution with parameters r and p.

B) The probability that the 8th success occurs on the 17th spin is approximately 0.8%.

C) The probability that the 13th success occurs between the 31st and 34th spin is approximately 0.6%.

A) The distribution is a negative binomial distribution with parameters r = number of successes (in this case, r = 1 since we are only interested in the first success), and p = probability of success (landing in a green slot).

B) To find the probability that the 8th success occurs on the 17th spin, we use the formula for the negative binomial distribution:

P(X = k) = (k-1)C(r-1) * [tex]p^r[/tex] * [tex](1-p)^{(k-r)[/tex]

where X is the number of spins until the Rth success, k is the number of spins, and C(n,r) is the binomial coefficient (n choose r).

In this case, we want to find P(X = 17) when r = 8 and p = 2/38 (since there are 2 green slots out of 38 total slots):

P(X = 17) = (16 C 7) * (2/38)⁸ * (36/38)⁹
          ≈ 0.008 or 0.8%

So the probability that the 8th success occurs on the 17th spin is approximately 0.8%.

C) To find the probability that the 13th success occurs between the 31st and 34th spin, we need to find the probability of getting exactly 12 successes in the first 30 spins, followed by a success on one of the next 4 spins (31st, 32nd, 33rd, or 34th).

P(31 ≤ X ≤ 34) = P(X ≤ 34) - P(X ≤ 30)
               = ∑[k=13 to 34] (k-1 C 12-1) * (2/38)¹² * [tex](36/38)^{(k-12)[/tex] - ∑[k=1 to 30] (k-1 C 12-1) * (2/38)¹² * [tex](36/38)^{(k-12)[/tex]
               ≈ 0.006 or 0.6%

So the probability that the 13th success occurs between the 31st and 34th spin is approximately 0.6%.

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Step-by-step explanation:

B

26 = 13.5 + m/2.5; m = 31.25

26 = 13.5 + 31.25/2.5

26 = 13.5 + 12.5

26 = 26

The dimensions of the package of largest volume are 18 inches by 18 inches by 36 inches. The largest possible volume is 11664 cubic inches.

To find the dimensions of the package of largest volume. Let the dimensions of the square end be x, and the length of the rectangular end be y. The girth of the package is 4x, and the length is y. According to the problem statement, the girth plus length may not exceed 108 inches, so we have:

We want to maximize the volume V(x,y) of the package, which is given by:

We can use the equation 4x + y = 108 to express y in terms of x:

Substituting this into the formula for V(x,y), we get:

The domain of V(x) is determined by the constraints that x and y must be positive and the girth plus length may not exceed 10 inches. Since the girth is 4x, we have:

Solving for x, we get:

Since x must be positive, the domain of V(x) is:

The maximum volume and the optimal dimensions

To find the absolute maximum of V(x) on the domain 0 < x ≤ 32/3, we take the derivative of V(x) with respect to x and set it equal to zero:

[tex]V'(x) = 216x - 12x^2 = 0[/tex]

Solving for x, we get:

To confirm that this is a maximum, we take the second derivative of V(x) with respect to x:

At x = 18, we have V''(18) = 0, which means that the second derivative test is inconclusive. However, we can see that V(x) is increasing on the interval 0 < x < 18 and decreasing on the interval 18 < x ≤ 32/3, which means that x = 18 is indeed the absolute maximum of V(x) on the domain.

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It's actually asking you to find the angles within the circles and match it with the angles it's supposed to be. For example if angle COE is 90° (im taking a fake angle value), you should put arc CE <——> 90

If you are still confused and need me to do it so that you can understand what I mean, reply and I'll help you!

Answer:

See below

Step-by-step explanation:

The objective of the question has been well explained by user vaishub1101.

I am just adding an additional hint and one answer to get you going

Since you just needed one example, I am providing just that
One thing to note in the figure is that segments DEF, ACD and ABF are all tangents to the circle. This fact is important since at the point of tangency (where the tangent touches the circle), the tangent to a circle is always perpendicular to the radius.

Using this knowledge and the given angles we can compute all the other angles but not the arc length [tex]\frown \atop {CE}[/tex] since to find arc length we need the value of the radius

As an example to help you get going,
[tex]\angle{DFA} \longleftrightarrow 58^\circ[/tex]

You would drag the tile with ∠DFA to the top left box and the tile with 58° to the top right box

I am sure you can figure out the rest or else user vaishub1101 can help you out with the rest

Answer:

pls mrk me brainliest (⁠・⁠(⁠ｪ⁠)⁠・⁠）

Answer:

Billy can buy 19 or less than 19 stickers.

Step-by-step explanation:

  Let the unknown variable - number of stickers be 'x'.

   Cost of one sticker = $1.34

   Cost of 'x' stickers = 1.34 * x = 1.34x

   Maximum amount that can be spent for buying stickers = 80 - 54.50

                                                                                                 = $25.50

   Inequality:

          1.34x ≤ 25.50

 Solving:

         Divide both sides by 1.34,

            [tex]\sf x \leq \dfrac{25.50}{1.34}[/tex]

            x ≤ 19.03

            x ≤ 19

Billy can buy 19 or less than 19 stickers.

The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.

We are given that the radius is increasing at a rate of 5 mm per second. This means that the rate of change of the radius with respect to time is dr/dt = 5 mm/s.

To find the rate at which the area is changing, we need to find dA/dt, the derivative of the area with respect to time. We can use the chain rule to find this derivative:

dA/dt = dA/dr * dr/dt

We can find dA/dr by taking the derivative of the area formula with respect to r:

dA/dr = 2πr

Now we can substitute the values we know into the chain rule formula:

dA/dt = dA/dr * dr/dt = 2πr * 5

When the radius is 28 mm, the rate of change of the area is:

dA/dt = 2π(28) * 5 = 280π ≈ 879.64 mm^2/s

Therefore, the area is changing at a rate of approximately 879.64 mm^2/s when the radius is 28 mm.

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After calculating the distance, Ranjan has driven 358.55 miles so far.

To solve this problem, we need to use the formula:

distance = fuel efficiency x fuel consumed

Let's start by calculating the total fuel consumed. At the first stop, Ranjan adds 6.7 gallons of gas, which means he consumed 6.7 gallons of gas since his tank was full at the beginning of the trip. At the second stop, he adds 3.4 gallons of gas, which means he consumed 3.4 gallons of gas between the first and second stops. Therefore, the total fuel consumed is:

6.7 + 3.4 = 10.1 gallons

Now we can calculate the distance driven using the fuel efficiency of 35.5 miles per gallon:

distance = 35.5 miles/gallon x 10.1 gallons = 358.55 miles

Therefore, Ranjan has driven 358.55 miles so far.

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The polynomial represented by the model is [tex]]x^2 - x + 2[/tex]

Based on the provided model, the polynomial represented is:

1 black square block: x^2
2 white thin blocks: -2x
1 black thin block: x
1 white small square block: -1
3 black small blocks: +3

The polynomial that the model represents is:
[tex]x^2 - 2x + x - 1 + 3[/tex]

Combining like terms, we get:
[tex]x^2 - x + 2[/tex]

So, the polynomial represented by the model is [tex]x^2 - x + 2[/tex].

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The volume of the cone with the same radius and height as the cylinder is 36 cm³.

To find the volume of a cone with the same radius and height as the cylinder, we first need to find the radius and height of the cylinder.

The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.

We are given that the volume of the cylinder is 108 cm^3.

So, 108 = πr^2h

To solve for r and h, we need more information. However, we can use the fact that the cone has the same radius and height as the cylinder to our advantage.

The formula for the volume of a cone is V = (1/3)πr^2h.

Since the cone has the same radius and height as the cylinder, we can substitute the values of r and h from the cylinder into the cone formula.

V = (1/3)π( r^2 )(h)

V = (1/3)π( r^2 )(108/π)

V = (1/3)( r^2 )(108)

V = 36( r^2 )

Therefore, the volume of the cone with the same radius and height as the cylinder is 36 cm³

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IF the median height is exactly 68 inches, then exactly 50% of the heights are at least 68 inches.

Without seeing the box-and-whisker plot, it is difficult to determine the exact fraction of heights that are at least 68 inches. However, we can make an estimate based on the general characteristics of a box-and-whisker plot.

In a box-and-whisker plot, the "box" represents the middle 50% of the data, with the median (50th percentile) marked by a line inside the box. The "whiskers" represent the minimum and maximum values within 1.5 times the interquartile range (IQR) of the data. Any points outside the whiskers are considered outliers.

Assuming that there are no outliers in the data, we can estimate that at least 50% of the heights are above the median, which is marked by the line inside the box. If the median height is at least 68 inches, then at least 50% of the heights are at least 68 inches.

If we assume that the median height is exactly 68 inches, then exactly 50% of the heights are at least 68 inches.

If the median height is less than 68 inches, then we can estimate that slightly less than 50% of the heights are at least 68 inches.

In summary, without more information about the box-and-whisker plot or the data it represents, we can estimate that at least 50% of the heights are at least 68 inches.

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