Choose the function table that matches the given rule. Output = Input – 3 (1 point) Input Output –2 –5 1 –2 6 3 Input Output 2 –1 –2 3 0 –6 Input Output 5 2 2 –5 0 9 Input Output 6 3 –6 –3 5 0

To determine the number of additional days that would make the cost equivalent for both Heather's Moving and Newton Rent-a-Truck, we can set up an equation:

Heather's Moving: 10 + 8x
Newton Rent-a-Truck: 80 + x

To find the point at which the costs are equal, we can set the equations equal to each other:

10 + 8x = 80 + x

Now, we can solve for x (additional days):

7x = 70
x = 10

So, the costs would be equivalent after 10 additional days. To find the total cost, we can plug the value of x back into either equation:

Total cost = 10 + 8(10) = 10 + 80 = $90.

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Answer:Therefore, the total number of players on the team is 21.

Step-by-step explanation:Let's start by using algebra to represent the information given in the problem.

Let p be the total number of players on the team.

The number of players who chose water is given as 14.

This is also equal to 2/3 of the total number of players, so we can write:

14 = (2/3) * p

To solve for p, we can isolate it on one side of the equation by multiplying both sides by the reciprocal of 2/3, which is 3/2:

14 * (3/2) = (2/3) * p * (3/2)

21 = p

The remaining trigonometric functions are:

sin (θ) = 3/√34

cos (θ) = 5/√34

csc(θ) =  (√34)/3

sec (θ) = (√34)/5

cot(θ) = 5/3

Trigonometry is a branch of mathematics that deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.

Since tan θ = 3 /5

Recall: tan = opposite/adjacent. Thus, opposite = 3, adjacent = 5

hypotenuse = √(3²+5²) = √34

Therefore, the remaining trigonometric functions are

sin (θ) = 3/√34

cos (θ) = 5/√34

csc(θ) =  (√34)/3     (csc (θ) = 1/sin (θ))

sec (θ) = (√34)/5     (sec(θ) = 1/cos (θ))

cot(θ) = 5/3       (cot(θ) = 1/tan (θ))

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The original price of the novel is $21.5

The first step is to write out the parameters given in the question

Last year, Gloria buys a novel for $18.70

This price is with a discount of 15% form the original price

The original price of the novel can be calculated as follows

15/100 × 18.70

= 0.15 × 18.70

= 2.805

The next step is to add 2.805 to the price of the novel last year($18.70)

= 18.70 + 2.805

= 21.5

Hence the original price of the novel before the addition of the discount is $21.5

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The resulting graph of g(x) will resemble the graph of f(x), but it will be stretched vertically and pushed leftward by three units.

Each element of a set (referred to as the domain) is mapped by a rule known as a function to a particular element of this other set (called the range). A function is, in other words, a connection between two subsets in which every member of the domain has a unique relationship to every element of the range. One popular approach to write a function is via function notation, which entails writing the function name surrounded by the incoming signal in parentheses, as in the following example: f (x). For instance, the formula f(x) = 2x + 1 takes the input x and produces the result 2x + 1.

given,

The fundamental quadratic function f(x) = x² serves as the parent function for g(x) = (x + 3)².

Since the argument of the function (x + 3) is x shifted left by 3 units, the graph of f(x) is horizontally displaced to the left by 3 units.

Given that the coefficient of the squared term is 1, the graph of the resulting function is shifted up by a factor of 1.

As a result, the transformation can be represented as a 3 unit horizontal shift and a 1 unit vertical stretch.

The resulting graph of g(x) will resemble the graph of f(x), but it will be stretched vertically and pushed leftward by three units.

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Jay has 7 $100 bills in his wallet.

Let's assume the number of $50 bills as x. So, in terms of x, the number of $100 notes can be represented as x - 5.

Now, the total amount contributed by $50 notes is $50x.

And the total amount contributed by $100 bills is $100*(x-5).

Since the total amount of money in his wallet is $1300, we can write an equation:

$50x + $100*(x-5) = $1300

Simplifying this equation, we get:

$50x + $100x - $500 = $1300

$150x = $1800

x = 12

So, Jay has 12 $50 bills in his wallet.

Using the earlier equation, the number of $100 bills can be found:

x - 5 = 12 - 5 = 7

Therefore, Jay has 7 $100 bills in his wallet.

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A.  The number of shortest lattice paths from (2, 2) to (11, 11) that pass through (8, 10) is 28 * 4 = 112.

B. The number of shortest lattice paths from (2, 2) to (11, 11) that avoid (8, 10) is the total number of paths minus the number of paths that pass through (8, 10), which is 48620 - 112 = 48508.

What is combinatorics?

Combinatorics is a branch of mathematics that deals with counting and arranging the possible outcomes of different arrangements and selections of objects.

For part (a), the number of shortest lattice paths from (2, 2) to (11, 11) that pass through (8, 10) is given by the product of the number of shortest lattice paths from (2, 2) to (8, 10) and from (8, 10) to (11, 11).

To find the number of shortest lattice paths from (2, 2) to (8, 10), we can count the number of ways to choose 6 steps up out of 8 total steps (the remaining 2 steps are to the right), which is 8 choose 6 = 28.

Similarly, the number of shortest lattice paths from (8, 10) to (11, 11) is the number of ways to choose 1 step up out of 4 total steps (the remaining 3 steps are to the right), which is 4 choose 1 = 4.

Therefore, the number of shortest lattice paths from (2, 2) to (11, 11) that pass through (8, 10) is 28 * 4 = 112.

b) To find the number of shortest lattice paths from (2, 2) to (11, 11) that avoid (8, 10), we can use the principle of inclusion-exclusion.

Let's first count the number of shortest lattice paths from (2, 2) to (11, 11) without any restrictions. Since we can only move up or to the right, the number of such paths is the number of ways to choose 9 steps up out of 18 total steps (the remaining 9 steps are to the right), which is 18 choose 9 = 48620.

Next, we count the number of shortest lattice paths from (2, 2) to (11, 11) that pass through (8, 10). Using the method described in part (a), we found that the number of such paths is 28 * 4 = 112.

Therefore, the number of shortest lattice paths from (2, 2) to (11, 11) that avoid (8, 10) is the total number of paths minus the number of paths that pass through (8, 10), which is 48620 - 112 = 48508.

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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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The vertex form of the equation of the parabola is:

r = (1/24)(y - 1)^2 + 3

Since the directrix is a horizontal line, the axis of the parabola is vertical. Therefore, the vertex form of the equation of the parabola is:

r = a(y - k)^2 + h

where (h, k) is the vertex of the parabola and "a" is a constant that determines the shape and orientation of the parabola.

Since the focus is (3,-5), the vertex of the parabola is halfway between the focus and the directrix. The directrix is 6 units above the vertex, so the vertex is (3,1).

We can use this information to write the vertex form of the equation:

r = a(y - 1)^2 + 3

To find the value of "a", we need to use the distance formula between the vertex and the focus:

distance = |y-coordinate of focus - y-coordinate of vertex| = 6

| -5 - 1 | = |-6| = 6

Using the definition of the parabola, the distance from the vertex to the focus is also equal to 1/(4a). Therefore:

1/(4a) = 6

a = 1/(4*6) = 1/24

Substituting this value of "a" into the vertex form equation, we get:

r = (1/24)(y - 1)^2 + 3

Therefore, the vertex form of the equation of the parabola is:

r = (1/24)(y - 1)^2 + 3

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Cos(165) in terms of sine and cosine of an acute angle is -1 + 2sin^2(7.5).

We can use the trigonometric identity cos(180 - x) = -cos(x) to find cos(165) in terms of cosine of an acute angle.

Since 165 = 180 - 15, we have:

cos(165) = cos(180 - 15) = -cos(15)

To express cos(15) in terms of sine and cosine of an acute angle, we can use the following trigonometric identities:

sin(2x) = 2sin(x)cos(x) and cos(2x) = cos^2(x) - sin^2(x)

Let's take x = 7.5, which is half of 15 (the acute angle):

sin(15) = 2sin(7.5)cos(7.5)

cos(15) = cos^2(7.5) - sin^2(7.5)

Now, we can solve for cos(15):

cos(15) = cos^2(7.5) - sin^2(7.5)

= (1 - sin^2(7.5)) - sin^2(7.5)

= 1 - 2sin^2(7.5)

Therefore, we have:

cos(165) = -cos(15)

= -[1 - 2sin^2(7.5)]

= -1 + 2sin^2(7.5)

So, cos(165) in terms of sine and cosine of an acute angle is -1 + 2sin^2(7.5).

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Kianah can finish the game in 1, 2, 3, 4, 6, or 12 days, depending on how many levels he plays each day.

To find all the possibilities for the number of days Kianah can play the game without repeating a level, we need to find all the factors of 12. The factors of 12 are 1, 2, 3, 4, 6, and 12. These are all the possible numbers of levels Kianah can play each day without repeating a level.

If Kianah plays 1 level each day, he will finish the game in 12 days. If he plays 2 levels each day, he will finish in 6 days. If he plays 3 levels each day, he will finish in 4 days. If he plays 4 levels each day, he will finish in 3 days. If he plays 6 levels each day, he will finish in 2 days. And if he plays all 12 levels each day, he will finish in 1 day.

Therefore, Kianah can finish the game in 1, 2, 3, 4, 6, or 12 days, depending on how many levels he plays each day. It's important to note that these possibilities assume that Kianah is able to complete all the levels he plays each day without getting stuck or repeating any levels.

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a. The slope and intercept of the least-squares line are -0.752 and 88.761, respectively.

b. The linear model may be useful for predicting ozone levels from relative humidity, but only to a limited extent. The R-squared value of 0.22 indicates that only 22% of the variation in ozone levels can be explained by relative humidity.

Additionally, the 95% prediction interval for a new observation (20.86, 66.37) is relatively wide, which suggests that the model may not be very precise in its predictions.

c. To predict the ozone level for a day when the relative humidity is 50%, we plug in x = 50 into the regression equation: Ozone = 88.8 - 0.752(50) = 53.8 ppb.

d. The correlation between relative humidity and ozone level can be found by taking the square root of the R-squared value, which gives us a correlation coefficient of 0.47.

This indicates a moderate positive correlation between relative humidity and ozone levels.

e. To find a 90% confidence interval for the mean ozone level for days where the relative humidity is 60%, we use the formula:

Mean ozone level ± (t-value)*(SE Fit)/sqrt(n), where the t-value is obtained from a t-distribution with n-2 degrees of freedom and a 90% confidence level.

For n = 120 and a 90% confidence level, the t-value is approximately 1.66. Plugging in the values, we get: 43.62 ± 1.66*(1.2)/sqrt(120), which simplifies to (42.39, 44.85).

f. To determine if a predicted ozone level of 80 ppb is reasonable when the relative humidity is 60%, we can calculate the 95% prediction interval for a new observation with x = 60: 43.62 ± 2.064*(11.43) = (21.18, 66.06).

Since the predicted value of 80 ppb falls outside of this range, it is not a reasonable prediction.

A more reasonable range of predicted values would be the 95% prediction interval, which gives us a range of (21.18, 66.06).

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If after 2.00 minutes, Ethan is 195km away from his house towards west, Ethan's velocity is approximately 6393 km/h.

To find Ethan's velocity, we need to first determine the distance he traveled and the time he spent traveling.

Given:
1. Initial position: Ethan's house
2. Distance to park: 85 km south
3. Final position: 195 km west from house after 2 minutes

To find the total distance, we can use the Pythagorean theorem, as the path forms a right triangle:
Distance = √(85² + 195²) = √(7225 + 38025) = √(45250) ≈ 212.72 km

Now, let's convert the time from minutes to hours:
2 minutes = 2/60 hours ≈ 0.0333 hours

Finally, we can calculate Ethan's velocity:
Velocity = Distance / Time = 212.72 km / 0.0333 hours ≈ 6393 km/h

Ethan's velocity is approximately 6393 km/h.

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The closest measurement to the circumference of the parachute in feet is 78.54 feet. The calculation was done by multiplying the radius by 2π (the constant pi, approximately equal to 3.14), which gives the circumference of a circle is 78.54 feet.

The circumference of the parachute can be calculated using the formula

C = 2πr

where r is the radius of the parachute.

Given that the radius of the parachute is 12.5 feet, we can substitute this value in the formula and calculate the circumference

C = 2πr

C = 2π(12.5)

C ≈ 78.54 feet

Therefore, the circumference of the parachute is closest to 78.54 feet.

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--The given question is incomplete, the complete question is given

" Which measurement is closest to the circumference of circumference of the parachute in feet if radius is 12.5.  "--

Answer:

C is the right answer I think

To find the cost of the house in 1980, divide the cost of the house in 1990 by the rate of increase. The house would have cost approximately $62,200 in 1980 when the CPI was 82.4.

To find the cost of the house in 1980, we need to use the concept of inflation. In this case, we can use the consumer price index (CPI) to compare the prices of the house in 1990 and 1980.

First, we need to determine the rate of increase from 1980 to 1990. The rate of increase is calculated by dividing the CPI in 1990 by the CPI in 1980:

Rate of increase = CPI in 1990 / CPI in 1980 = 130.7 / 82.4 = 1.585

Next, we can use the rate of increase to find the cost of the house in 1980. We divide the cost of the house in 1990 by the rate of increase:

Cost in 1980 = Cost in 1990 / Rate of increase = $98,700 / 1.585 = $62,200.

Therefore, the house would have cost approximately $62,200 in 1980 when the CPI was 82.4.

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Unfortunately, there is no way to answer this question without more information.

We would need to know the amount of the ATM withdrawal, as well as the starting balance before the withdrawal, in order to calculate the ending balance.

For example, if the starting balance was $1500 and the withdrawal was for $50, the ending balance would be $1450.

However, if the starting balance was $1300 and the withdrawal was for $50, the ending balance would be $1250.

Without this information, we cannot determine the correct answer.

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The taxi travels 140 kilometers in 210 minutes at a speed of 40 km/h.

Let's calculate the distance a taxi travels in 210 minutes at a speed of 40 km/h.
Convert minutes to hours
Since the speed is given in km/h, we need to convert 210 minutes into hours.

There are 60 minutes in an hour, so divide 210 by 60:
210 minutes ÷ 60 = 3.5 hours
Calculate the distance
Now that we have the time in hours, we can use the formula for distance:
Distance = Speed × Time
In this case, the speed is 40 km/h, and the time is 3.5 hours.

Plug these values into the formula:
Distance = 40 km/h × 3.5 hours
Compute the result
Multiply the speed by the time to find the distance:
Distance = 140 km.

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By increasing their recycling by 500 pounds per month, the school conserves 4,800 gallons of water in a year.

Determine the ratio of water conserved per pound of paper recycled:

8 gallons of water are saved for every 10 pounds of paper recycled.

Calculate the water saved for each pound of paper:

8 gallons/10 pounds = 0.8 gallons/pound.

Find the increase in paper recycled per month:

500 pounds/month.

Calculate the water saved per month:

[tex]500 $ pounds/month \times  0.8 $ gallons/pound = 400 $ gallons/month.[/tex]

Calculate the water saved in a year:

[tex]400 $ gallons/month \times  12 months = 4,800 $ gallons/year.[/tex]

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When the parallelogram, diagonals bs and et bisect at each other at o, we get the following answers:

1. In a parallelogram, the diagonals bisect each other. So, if ES = 10 cm, then EO = OS = 5 cm. Since EO and OS are half of the diagonal ET, then ET = EO + OS = 5 cm + 5 cm = 10 cm. Similarly, diagonal BT will also be equal to 10 cm, as it has the same length as diagonal ET.

2. In a parallelogram, opposite sides are equal. So, if BE = 13 cm, then TS = 13 cm, as they are opposite sides.

3. If EO = 6 cm and SO = 7 cm, then the length of diagonal ET is EO + OS = 6 cm + 7 cm = 13 cm. Since the diagonals of a parallelogram are equal, the length of diagonal BS will also be 13 cm.

4. If ET + BS = 18 cm and SO = 5 cm, we can use the fact that diagonals bisect each other to find ET and BS. Let EO = x cm. Then, ET = 2x cm and BS = 2(5-x) cm. Now, we can set up the equation: 2x + 2(5-x) = 18. Solving for x, we get x = 4 cm. So, ET = 2x = 8 cm and BS = 2(5-x) = 10 cm.

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The measure of the angles are m∠DWC=138°, ∠AWB = 138°, ∠AWD = 42°, ∠BWC = 42°

The Vertical angle theorem states that if two lines intersect at a point then vertically opposite angles are congruent.

To find the measure of all the angles:

∠AWB and ∠DWC are vertically opposite angles.

Therefore, ∠AWB = ∠DWC

⇒ ∠AWB = 138°

we know that the Sum of all the angles in a straight line = 180°

⇒ ∠AWD + ∠DWC = 180°

⇒ ∠AWD + 138° = 180°

⇒ ∠AWD = 180° – 138°

⇒ ∠AWD = 42°

Since ∠AWD and ∠BWC are vertically opposite angles.

Therefore, ∠AWD = ∠BWC

⇒ ∠BWC = 42°

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#complete question:

Lines AC←→ and DB←→ intersect at point W. Also, m∠DWC=138° .

Enter the angle measure for the angle shown.

see attached image:

The vector field for  7 (x,y) = xî + xyî (1,3), (-1,2), (3,-2) can be plotted with arrows with magnitude 4 at point (1,3), magnitude 3 at point (-1,2), and magnitude 3 at point (3,-2).

The  given vector field 7 (x,y) = xî + xyî (1,3), (-1,2), (3,-2) can be drawn by plotting arrows at each point (x,y) in the plane with the direction and magnitude of each arrow presented  by the vector

7 (x,y) = xî + xyî.

over point (1,3),

the vector is 7(1,3) = 1î + 3î = 4î.

over point (-1,2),

the vector is 7(-1,2) = -1î - 2î = -3î.

Over point (3,-2),

the vector is 7(3,-2) = 3î - 6î = -3î.

The vector field for  7 (x,y) = xî + xyî (1,3), (-1,2), (3,-2) can be plotted with arrows with magnitude 4 at point (1,3), magnitude 3 at point (-1,2), and magnitude 3 at point (3,-2).

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The house is currently 6 years old.

It is mentioned that when the mortgage is completely paid off for Mark and Lynne's house, it will be 3 times as old as it is now. They have 12 years left on the mortgage.

Let's denote the current age of the house as x. When the mortgage is paid off, the house will be x + 12 years old (since they have 12 years left on the mortgage). At that point, the house will be 3 times its current age, so we can write the equation:

x + 12 = 3x

Now we can solve for x:
12 = 2x
x = 6

So, the house is currently 6 years old.

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The approximate length of the base of the triangle is 5 units

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. The area of a triangle is expressed as;

A = 1/2 bh

The hexagon is divided into six equal triangles.

The area of the hexagon is 65 units²

Therefore, the area of the triangle = 65/6

= 10.83

Area of a triangle = 1/2 b h

height = 4.3 units

10.83 = 1/2 × 4.3 × b

4.3b = 10.83 × 2

4.3b = 21.66

divide both side by 4.3

b = 21.66/4.3

b = 5.04

therefore the approximated value of the base is 5 units.

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The coordinates of the images after the translation are K' (-4, 6).

To find the image coordinates of K', we need to translate the coordinates of K 6 units up.

This can be done by adding 6 to the y-coordinate of K.

So, the y-coordinate of K' will be:

y-coordinate of K' = y-coordinate of K + 6

= 0 + 6

= 6

To find the x-coordinate of K', we just need to keep the x-coordinate of K the same, since the translation is only in the vertical direction.

Therefore, the image coordinates of K' are (-4, 6).

So, the correct answer is C. K′(−4, 6).

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Stevie will need to work at least 150 hours to make at least $1200 after accounting for the initial cost of equipment.

to find the business hours of work, Let's start by defining the variables given in the problem:

The initial cost of equipment is $175.

Stevie charges $12 per hour for cleanup.

Stevie wants to make at least $1200.

The number of hours worked is represented by h.

Now, we can set up an equation to solve for h:

Total earnings - Total cost = Desired profit

We can express the total earnings as the product of the hourly rate and the number of hours worked:

Total earnings = $12h

The total cost includes the initial cost of equipment plus any additional costs incurred during cleanup:

Total cost = $175 + additional costs

Since we don't know the value of the additional costs, we'll leave it as a variable.

Substituting these expressions into the equation, we get:

$12h - ($175 + additional costs) = $1200

Simplifying the equation, we get:

$12h - $175 - additional costs = $1200

$12h - $1375 = additional costs + $1200

$12h - $1375 = additional costs

Now we have an equation that relates the number of hours worked to the additional costs incurred during cleanup. We want to find the minimum value of h that satisfies this equation, since Stevie wants to make at least $1200.

To do this, we need to estimate the additional costs incurred during cleanup. Let's assume that Stevie spends an average of $4 per hour on additional costs (e.g., gasoline, trash bags, etc.). Then, the equation becomes:

$12h - $1375 = $4h + $175

Simplifying further, we get:

$8h = $1200

h = 150

Therefore, Stevie will need to work at least 150 hours to make at least $1200 after accounting for the initial cost of equipment and the estimated additional costs incurred during cleanup.

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Trapezoid 1. Has one pair of parallel sides.

Parallelogram 2. Has two pairs of parallel sides and its opposite sides are equal.

Square 3. Is a parallelogram and four right angles and four equal sides.

Rhombus 4. A parallelogram and four equal sides (a slanted square)

Rectangle 5. A parallelogram that has four right angles and it's opposite sides are parallel.

1. Trapezoid: A trapezoid has one pair of parallel sides, while the other two sides are non-parallel. The parallel sides are called bases, and the non-parallel sides are called legs.

2. Parallelogram: A parallelogram has two pairs of parallel sides and its opposite sides are equal. The opposite angles are also equal, and the consecutive angles are supplementary.

3. Square: A square is a parallelogram with four right angles and four equal sides. It is a special case of both a rectangle and a rhombus, as it has all their properties.

4. Rhombus: A rhombus is a parallelogram with four equal sides, which can be thought of as a slanted square. It has opposite equal angles, and its diagonals are perpendicular bisectors, dividing the rhombus into four congruent right-angled triangles.

5. Rectangle: A rectangle is a parallelogram that has four right angles, and its opposite sides are parallel. The opposite sides are also equal, and its diagonals are congruent, bisecting each other at right angles.

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Both the chess and checkers group have the same range.

The box plots range for the ages of club members in the chess and checkers group are given. Based on the box plots, it appears that both groups have similar ranges, and it is difficult to determine which group has a greater range.

The range is a measure of variability that indicates the difference between the smallest and largest values in a dataset. In the chess group, the smallest value is 18, and the largest value is 20, which gives a range of 2. In the checkers group, the smallest value is 10, and the largest value is 20, which also gives a range of 10.

Although the difference between the smallest and largest values in the checkers group is greater than that in the chess group, the box plots suggest that the checkers group has more outliers than the chess group. An outlier is a data point that is significantly different from other observations in a dataset. The presence of outliers can increase the range of a dataset.

Therefore, despite the larger difference between the smallest and largest values in the checkers group, the presence of outliers makes it difficult to determine which group has a greater range. Overall, the box plots show that both groups have similar ranges, but the checkers group has more variability in the form of outliers.

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