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A stem-and-leaf plot can be constructed to display the distribution of test scores. This graphical representation organizes the data by separating the digits into stems and leaves, providing a visual representation of the score distribution.

A stem-and-leaf plot is a data visualization tool that shows the distribution of a dataset by dividing each data point into a stem and a leaf. The stem represents the leading digits of the data, while the leaves represent the trailing digits. By arranging the stems in ascending order and aligning the corresponding leaves, the plot provides a visual representation of the data's distribution.

For example, let's consider a set of test scores: 67, 72, 84, 79, 91, 88, 75, 82. The stem-and-leaf plot for these scores would look like:

6 | 7 9

7 | 2 5 9

8 | 2 4 8

9 | 1

In this plot, the stems represent the tens digit, and the leaves represent the ones digit. The stem-and-leaf plot shows that the majority of the scores fall in the 70s and 80s range, while there is one score in the 60s and one in the 90s. It provides a clear visual representation of the distribution and allows for quick observations about the spread of the scores.

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Answer + Step-by-step explanation:

a) GE = r = GM

Then GEO is an isosceles triangle

b) since GEO is an isosceles triangle  then :

m∠SEG = m∠GOM = measure of the arc GM (mGM)  (result 1)

On the other hand :

m∠SEG = m∠SEG = (1/2)×(mAS - mGM)  (it’s a formula)   (result 2)

Now ,we equate  (result 1) and  (result 2) :

m∠SEG = mGM  

m∠SEG = (1/2)×(mAS - mGM)

Then

mGM = (1/2)×(mAS - mGM)

c) mGM = (1/2)×(mAS - mGM)

⇔ 2mGM = mAS - mGM

⇔ 3mGM = mAS

⇔ 3m∠SEA = m∠SOA

Remember:

mGM = m∠GOM = m∠SEA

The predicted cost for a student attending a arts college with 1,500 students and a rank of 4.5 can be calculated using the given regression model: Tuition = 7 + 4*Rank - 0.20*Size + 8*Private - 0.4*LibArts.

In this case, Rank = 4.5, Size = 1.5 (since it's measured in 1,000s), Private = 1 (since it's a private college), and LibArts = 1 (since it's a liberal arts college). Plugging these values into the model, the predicted tuition cost would be: Tuition = 7 + 4*(4.5) - 0.20*(1.5) + 8*1 - 0.4*1 = $26.1 thousand.

If the student switches from her current private liberal arts college to a public, non-liberal arts college with a rank 0.5 lower and 15,000 more students, we need to adjust the Size and Rank variables accordingly. Assuming the student's current college is still private, the new values would be Rank = 4.5 - 0.5 = 4 and Size = 1.5 + 15 = 16.5 (since it's measured in 1,000s). With the new values, we can calculate the predicted tuition cost for the public college: Tuition = 7 + 4*(4) - 0.20*(16.5) + 8*0 - 0.4*0 = $22.4 thousand.

To determine how much money the student saves in tuition, we calculate the difference between the predicted costs of the two colleges: $26.1 thousand - $22.4 thousand = $3.7 thousand. Therefore, by switching from her current private liberal arts college to a public, non-liberal arts college with a lower rank and larger size, the student saves $3.7 thousand in tuition.

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the optimal solution to maximize Z is x1 = 25 and x2 = 0, with Z = 3000.

To solve the given linear programming model graphically, we need to plot the feasible region and identify the corner points to find the optimal solution. Here's the step-by-step process:

1. Plot the constraints:

  - Plot the line x1 = 40 (vertical line at x1 = 40).

  - Plot the line x2 = 10 (horizontal line at x2 = 10).

  - Plot the line 20x1 + 10x2 = 500 (which can be rewritten as 2x1 + x2 = 50).

  - Shade the feasible region that satisfies all the constraints.

2. Identify the corner points:

  - Determine the coordinates of the corner points where the boundary lines intersect.

3. Evaluate the objective function:

  - Calculate the value of the objective function Z = 120x1 + 80x2 for each corner point.

4. Determine the optimal solution:

  - Select the corner point that maximizes the objective function Z.

Here's the graphical representation of the feasible region:

      |

 40   |           C

      |          /

      |         /

      |        /

      |       /

      |      /

      |     /    Feasible Region

 10   |_____/_________________

      0   10  20  30  40  50

            0`

The corner points of the feasible region are:

A: (0, 0)

B: (0, 10)

C: (25, 0)

D: (20, 5)

Now, we evaluate the objective function Z = 120x1 + 80x2 for each corner point:

Z(A) = 120(0) + 80(0) = 0

Z(B) = 120(0) + 80(10) = 800

Z(C) = 120(25) + 80(0) = 3000

Z(D) = 120(20) + 80(5) = 2400

From the above calculations, we can see that the maximum value of Z occurs at point C: (25, 0).

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The distance Martin climbs in 60 minutes is 18 meters

From the question, we are to determine how many meters Martin can climb in 60 minutes

Let the distance he climbs in 60 minutes be x

From the given information,

Martin climbs 3 meters in the first 10 minutes

If Martin climbs 3 meters in 10 minutes

Then,

Martin will climb x meters in 60 minutes

Thus,

x × 10 = 3 × 60

Solve for x

10x = 180

x = 180/10

x = 18

Hence, the distance is 18 meters

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Answer:

49.0197m

Step-by-step explanation:

The formula is d = c / π, allow d to be diameter and c to be circumference

The area of the kitchen in square feet is 132\(ft^{2}\)

To find the area of the rectangular kitchen, we need to multiply the length by the width.

The length of the kitchen can be found by subtracting the x-coordinates of the two points on the same vertical side. So, the length is 8 - (-3) = 11 feet.

The width of the kitchen can be found by subtracting the y-coordinates of the two points on the same horizontal side. So, the width is 4 - (-8) = 12 feet.

Therefore, the area of the kitchen is:

Area = Length x Width = 11 ft x 12 ft = 132 square feet

So the answer is 132\(ft^{2}\).

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Answer:

n= -1.2

Step-by-step explanation:

I think because if you use slope equation to find the slope which is 3/5 and then you use point slop equation to find out what the equation would be. y=3/5x and then you substitue y for 18 and solve/simplify the equation to get -1.2.

Answer:

g = 59⁰

h = 9

(by using opposite sides and angles of a parallelogram are equal.)

The length of the radius AB is 6 units.

The angle ∠BAC is 90 degrees. The length of arc BC is 3π. The length of  

radius AB can be found as follows:

Hence,

length of arc = ∅ / 360 × 2πr

where

Therefore,

length of arc = 90 / 360 × 2πr

3π = 1 / 4 × 2πr

cross multiply

12π = 2πr

divide both sides by 2π

r = 6 units

Therefore,

radius AB = 6 units

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If the same drug (at different levels) is given to 2 groups of randomaly selected individuals the samples are considered to be dependent is true statement.

If the same drug is given to two groups of randomly selected individuals, the samples are considered to be dependent. This is because the individuals within each group are directly related to each other, as they are part of the same treatment or experimental condition.

The outcome or response of one individual in a group can be influenced by the outcome or response of other individuals in the same group. Therefore, the samples are not independent and are considered dependent.

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The probability of selecting a black checker from a bag of 6 black and 4 red checkers, replacing it, and selecting another black is 9/25.

To find the probability follow these-

Determine the probability of selecting a black checker on the first draw.

There are 6 black checkers and a total of 10 checkers (6 black + 4 red).

So, the probability of selecting a black checker on the first draw is 6/10,

which can be simplified to 3/5.

Since the black checker is replaced, there are still 6 black checkers and

a total of 10 checkers in the bag. Therefore, the probability of selecting a

black checker on the second draw is also 3/5.

To find the probability of both events occurring, multiply the probabilities together: (3/5) × (3/5) = 9/25.

So, the probability of selecting a black checker from a bag of 6 black and

4 red checkers, replacing it, and selecting another black is 9/25.

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The sum in summation notation of the expression (a) 1 + 2 + 3 + 4 + X5, where X takes the values 1-4, is ΣX from 1 to 4. In other words, it represents the summation of X over the range 1 to 4.

In summation notation, the expression (a) 1 + 2 + 3 + 4 + X5 can be written as ΣX, where X takes the values from 1 to 4. The capital sigma (Σ) represents the summation operator, and the variable X is summed over the range 1 to 4. This means that we need to substitute X with each value from 1 to 4 and add them together.

When we evaluate the expression, we have:

ΣX = 1 + 2 + 3 + 4 = 10

However, the expression also includes X5, indicating that X takes the value 5 as well. Therefore, we add 5 to the sum:

ΣX = 10 + 5 = 15

So, the sum of 1 + 2 + 3 + 4 + X5, where X takes the values 1-4, is equal to 15.

Moving on to expression (b) y2 + y3 + Y, where Y takes the values y₁ = -1, y₂ = -0.5, y₃ = 0, y₄ = 1.35, we can express it in summation notation as ΣY from 1 to 3. This represents the summation of Y over the range 1 to 3.

Since Y has a different value for each term, we simply substitute Y with each value from 1 to 3 and add them together:

ΣY = y₁ + y₂ + y₃ = -1 + (-0.5) + 0 = -1.5

Hence, the sum of y₂ + y₃ + Y, where Y takes the values y₁ = -1, y₂ = -0.5, y₃ = 0, y₄ = 1.35, is equal to -1.5.

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The cost of the calculator before the total is $24.95

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

Total cost = $28.19

Tax = 13%

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

Total cost = Initial cost * (1 + Tax)

substitute the known values in the above equation, so, we have the following representation

Initial cost  * (1 + 13%) = 28.19

So, we have

Initial cost   = 28.19/(1.13)

Evaluate

Initial cost = 24.95

Hence, the cost of the calculator before the total is $24.95

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Answer:

x = 5

Step-by-step explanation:

Since the triangles have to be congruent (through SSS), we know that:

2x + 3 = 4x - 7

We simplify this to: 2x = 10

And then: x = 5

Answer:

thw

the difference of 4 from 12

= 8

Once the Water Rush ride is built, Ms. Luca begins safety tests to ensure the ride's safety. For every 10 tests, she finds and fixes 15 safety errors.

Once the Water Rush ride is built, Ms. Luca begins safety tests to ensure that the ride is safe for riders. For every 10 tests she runs, Ms. Luca finds and fixes 15 safety errors. This means that for every 10 safety tests, she discovers 15 errors and addresses them promptly.

To fill in the missing numbers in the table, we can use the information given. If we assume that Ms. Luca runs 10 safety tests each time, we can calculate the number of safety errors she finds and fixes.

| Number of Safety Tests | Number of Safety Errors |
|-----------------------|------------------------|
|           10          |           15           |
|           20          |           30           |
|           30          |           45           |
|           40          |           60           |

As we can see from the table, the number of safety errors found and fixed by Ms. Luca increases in proportion to the number of safety tests she runs. For instance, when she runs 20 safety tests, she finds and fixes 30 safety errors.

In conclusion, once the Water Rush ride is built, Ms. Luca begins safety tests to ensure the ride's safety. For every 10 tests, she finds and fixes 15 safety errors. The table shows the number of safety errors found and fixed as the number of safety tests increases.

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Answer:

X=5

Step-by-step explanation:

3+12x=63

Subtract 3 from both sides

12x=60

Divide both sides by 12

X=5

Answer:

Ummm... Ok... Answer: X = 187 / 39 OR X = 4.794872

Step-by-step explanation:

Multiply all terms by the same value to eliminate fraction denominators

/3  + 1 2  = 63

3(​x/3 + 12x) = 3.63

Simplify

37x = 189

Divide both sides of the equation by the same term

37x = 189

37x / 37 = 189 / 37

Simplify

x = 187 / 39

OR

x = 4.794872

Answer:

18.75

Step-by-step explanation:

80 = 100%

1% = 100%/100 = 80/100 = 0.8

the grades changed by 95 - 80 = 15.

how many % is that ?

we find the answer by checking how often 1% fits into 15. and we do this kind of check by division :

15 / 0.8 = 18.75

so, the grades changed by 18.75%.

The approximate area of the baking sheet left uncovered if π is 3.14 with a rectangular length of 12 cm and width of 18 cm is 46 cm²

Area of rectangle = Length × Width

Area of the rectangle = 12 × 18

= 216cm²

The diameter of one of the circle = Length/3

The diameter of one of the circle = 18/3 or 6/2

= 6cm

Area of a circle = πd²/4

= π(6)²/4

= π36/40

= 36π/4

Area of a circle = 9π cm ²

Area of the six circular biscuit = 6(9π)

= 54πcm²

Area of the six circular biscuit = 54π cm²

= 54(3.14)

= 169.56cm²

The area of the baking sheet left uncovered = Area of rectangle - Area of the 6 circular biscuits

= 216 - 169.56

= 46.44cm²

Therefore, area of the baking sheet left uncovered is approximately 46cm²

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Answer:

10,060

Step-by-step explanation:

Answer:

v = 87

Step-by-step explanation:

the angle v+39 lies on a straight line. so substract v+39 from 180 to get the interior angle for that side.

afterwards, knowing that the sum of interior angles of a triangle = 180, form an equation with all the angles and solve for v

a) The campaign manager has a random sample of potential voters in a large city and records the number of individuals within each of the categories.

b) A Chi-Square goodness of fit test.

a) A campaign manager would like to show that the distribution of individuals within several social economic categories is different than what a newspaper reported and that's why we know that the campaign manager has a random sample of potential voters in a large city and records the number of individuals within each of the categories.

Chi-Square goodness of fit is used to find out how the observed value of a given phenomenon is significantly different from the expected value. In Chi-Square goodness of fit test, the sample data is divided into intervals.

In this case, we have one categorical variable which is the distribution of individuals within several social groups. We want to see if the actual distribution of the variable is significantly different from the distribution within several social groups as claimed(expected) by the newspaper.

Hence, we will use chi-square goodness of fit test for this case.

b) A Chi-Square goodness of fit test.

Here the variable is the distribution of individuals purchasing season pass at an amusement park. The variable has 4 categories based on the age group of the individuals.

A tourist company wants to test the actual distribution of individuals within each age group and wants to check if it is significantly different from the expected distribution i.e the one claimed by the amusement park.

The tourist company randomly sampled 200 individuals entering the park.

The proportion of individuals within each group as claimed by the amusement park is given.

Hence, we will use chi-square goodness of fit test to test if the actual distribution within each group is significantly different or not from the claimed distribution.

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The cartesian equation of the curve \(r=2 \hspace{0.1cm} csc \hspace{0.1cm} \theta\) is \(y=2\).

A Cartesian equation is essential in mathematics. It corresponds to a mathematical formula that expresses the connection between elements as a function of their positions on a plane known as Cartesian.

A two-dimensional coordinate scheme called the Cartesian plane employs a horizontal x-axis and an upward y-axis to identify locations in space.

Given that, \(r=2 \hspace{0.1cm} csc \hspace{0.1cm} \theta\).

So, \(csc\hspace{0.1cm}\theta=cosec \hspace{0.1cm}\theta\).

The equation becomes as follows:

\(r=2cosec\hspace{0.1cm} \theta\)

By using the trigonometric equation \(cosec\hspace{0.1cm} \theta=\frac{1}{sin\hspace{0.1cm}\theta}\), we get

\(r= \frac{2}{sin \hspace{0.1cm} \theta}\)

Multiplying both sides by \(sin\hspace{0.1cm}\theta\), we get

\(r \hspace{0.1cm}sin\hspace{0.1cm}\theta =2\hspace{0.1cm}\frac{sin\hspace{0.1cm}\theta}{sin\hspace{0.1cm}\theta}\)

\(rsin\hspace{0.1cm}\theta=2\)

By the parametric equations \(x=rcos\hspace{0.1cm}\theta\) and \(y=rsin\hspace{0.1cm}\theta\), we get

\(y=2\)

It is a horizantal line.

Hence, the cartesian equation of the curve \(r=2 \hspace{0.1cm} csc \hspace{0.1cm} \theta\) is \(y=2\).

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The cartesian equation for the curve is: y = 2 This is a horizontal line passing through the point (0,2).

To find a Cartesian equation for the curve given by the polar equation r = 2 csc(θ), we will convert the polar coordinates (r, θ) into Cartesian coordinates (x, y) using the following relationships:

x = r * cos(θ)
y = r * sin(θ)

Step 1: Express r in terms of θ
r = 2 csc(θ)

Step 2: Since csc(θ) = 1 / sin(θ), rewrite the equation as
r = 2 / sin(θ)

Step 3: Express x and y in terms of r and θ
x = r * cos(θ)
y = r * sin(θ)

Step 4: Substitute r from Step 2 into the y equation
y = (2 / sin(θ)) * sin(θ)

Step 5: Simplify the equation
y = 2

The Cartesian equation for the given polar equation is y = 2, which represents a horizontal line passing through the point (0, 2).

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The surface area of the soccer ball to the nearest square centimeter is 744.68 square centimeters .

Given :

The volume of a soccer ball is 1,930. 75 cubic centimeters .

we know that ,

shape of soccer ball is same as the sphere

Volume of sphere = 4 / 3 * pi * r^3

1930.75 = 4 / 3 * 3.14 * r^3

1930.75 = 4.18 * r^3

r^3 = 1930.75 / 4.18

= 462

r = 7.7 cm

Surface area  of soccer ball = 4 * pi * r^2

= 4 * 3.14 * 7.7^2

= 12.56 * 59.29

= 744.68 square centimeters

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Answer: attached a picture

The fourth clock shows the time 25 minutes after 4:00.

The correct option is IV.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

There are four clocks.

To watch the time on the clock:

The small arrow line shows the time in hours.

And the large arrow shows the time in minutes.

At the first clock;

The time is 11:20.

At the second clock;

The time is 11:40.

At the third clock;

The time is 12:20.

At the fourth clock;

The time is 4:25.

25 minutes after 4:00 means the large arrow will be pointing towards 5.

Because 25 = 5 x 5.

Therefore, all the times on the clocks are given above.

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The complete question;

From the given choices,

which clock shows 25 minutes after 4:00?

The options are given in the attached image.

Answer:

x=12

Step-by-step explanation:

If the triangles are similar:

x/8=18/12

x/8=1.5

x=12

Answer:

X=14

Step-by-step explanation:

If you measure them, they'll be very close to the same length.

Also, the triangles are very similar. Given this information, a simple way to solve it is:

12-4=8 so to find X subtract 4 from 18.

18-4=14 so X=14

I hope my brain did the correct math for you.

It probably didn't, but I tried.

The proof for <2 is congruent to <3 is given below.

Linear pair of angles are the pair of angles formed when two lines are intersected at a point forming on a line.

Sum of the measures of angles of linear pair is supplementary.

Given are,

<1 and <2 form linear pair

m<1 + <3 = 180°

We have, <1 and <2 form linear pair.

We know that, sum of the measures of angles of linear pair is supplementary.

So, <1 + <2 = 180°

⇒ <2 = 180° -  <1

Also we have,

<1 + <3 = 180°

⇒ <3 = 180° - <1

So measures of both angles <2 and <3 are equal.

So they are congruent.

Hence the angles <2 is congruent to <3.

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