I NEED HELP ASAP IT'S DUE IN 20MIN
Question 2
The box plot represents the number of tickets sold for a school dance.

A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the number line. A line in the box is at 19. The lines outside the box end at 10 and 27.

Which of the following is the appropriate measure of center for the data, and what is its value?
The mean is the best measure of center, and it equals 19.
The median is the best measure of center, and it equals 4.
The median is the best measure of center, and it equals 19.
The mean is the best measure of center, and it equals 4.


Question 5

A recent conference had 900 people in attendance. In one exhibit room of 80 people, there were 65 teachers and 15 principals. What prediction can you make about the number of principals in attendance at the conference?
There were about 820 principals in attendance.
There were about 731 principals in attendance.
There were about 208 principals in attendance.
There were about 169 principals in attendance.
Question 6
A teacher was interested in the subject that students preferred in a particular school. He gathered data from a random sample of 100 students in the school and wanted to create an appropriate graphical representation for the data.
Which graphical representation would be best for his data?

Stem-and-leaf plot
Histogram
Circle graph
Box plot
Question 7

A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.
Sports Basketball Baseball Soccer Tennis
Number of Students 17 12 27 44

Which of the following graphs correctly displays the data?
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
Question 8

A New York City hotel surveyed its visitors to determine which type of transportation they used to get around the city. The hotel created a table of the data it gathered.
Type of Transportation Number of Visitors
Walk 120
Bicycle 24
Car Service 45
Bus 30
Subway 81
Which of the following circle graphs correctly represents the data in the table?
circle graph titled New York City visitor's transportation, with five sections labeled walk 80 percent, bus 16 percent, car service 30 percent, bicycle 20 percent, and subway 54 percent
circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 40 percent, bus 8 percent, car service 15 percent, bicycle 10 percent, and walk 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 80 percent, bicycle 20 percent, car service 30 percent, bus 16 percent, and walk 54 percent
Question 9
A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students.
Ice Cream Candy Cake Pie Cookies
81 9 72 36 27

Which statement is the best prediction about the scoops of ice cream the college will need?
The college will have about 480 students who prefer ice cream.
The college will have about 640 students who prefer ice cream.
The college will have about 1,280 students who prefer ice cream.
The college will have about 1,440 students who prefer ice cream.

Amy needs 78 inches of fabric for her pants if she follows the given rule.

Define inches ?

An inch is a unit of length that is equal to exactly 2.54 centimeters. It is commonly used in the United States and other countries that use the Imperial system of measurement.

To determine how much fabric Amy needs for her pants, we can use the rule provided to us. The first step is to measure from the waist to the finished length of the pants, which in this case is 35 inches.

Next, we need to double this measurement, which gives us 2 * 35 = 70 inches. This is because we need to account for the fabric that will make up both the front and back of the pants.

Finally, we need to add 8 inches to the doubled measurement, which gives us 70 + 8 = 78 inches. This additional 8 inches is to account for any seams, hems, or other finishing touches that may be required to complete the pants.

Therefore, Amy needs 78 inches of fabric for her pants.

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The density of a sample of an unknown substance with a mass of 6 grams and a volume of 12 cm³ is 0.5 grams.

Density is a fundamental physical property that measures the amount of matter (mass) packed into a particular space (volume). The mathematical definition of density is simply the mass of an object divided by its volume. Density is typically measured in units of mass per unit volume, such as grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³). One crucial aspect of density is that it is an intrinsic property of a substance, meaning it is a characteristic that depends solely on the material and is not affected by the amount of the substance. By using density, we can identify the material a particular object is made of. For example, a piece of gold will have a higher density than a piece of silver because gold is a more dense metal. Additionally, the density of an object can be used to determine its buoyancy in a fluid. Objects with a higher density will sink in a fluid with a lower density, while objects with a lower density will float.

Density is defined as the amount of mass per unit of volume. Mathematically, it can be represented as:

Density = Mass/Volume

Substituting the given values, we get:

Density = 6 grams/12 cm³

Density = 0.5 grams/cm³

Therefore, the density of the sample is 0.5 grams/cm³.

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The correct expression showing the total area of the five rooms is A. (3 x 14²) + (2 x 17²), which simplifies to 1918 square feet.

An expression is a combination of numbers, symbols, and operators (such as addition, subtraction, multiplication, and division) that represent a mathematical calculation. An expression can be a single number, a variable, or a combination of both, and can be used to represent mathematical formulas, equations, or relationships.

In the given question,

C. (3 × 17²) + (2 × 14²)

To find the total area of the five rooms, we need to add the area of each room. The area of a square is found by squaring the length of one side.

For the three rooms with sides of 14 feet each, the area of each room is:

14^2 = 196 square feet

So the total area of these three rooms is:

3 × 196 = 588 square feet

For the two rooms with sides of 17 feet each, the area of each room is:

17^2 = 289 square feet

So the total area of these two rooms is:

2 × 289 = 578 square feet

Therefore, the total area of all five rooms is:

588 + 578 = 1166 square feet

Option C, (3 × 17²) + (2 × 14²), gives the correct expression for this calculation.

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The amount of fencing, dirt and sod for the baseball field are;

Length of fencing ≈ 1410.5 feet

Area of the sod ≈ 118017.13 ft²

Area of of the field covered with dirt ≈ 7,049.6 ft²

The fencing of a baseball field is the outer enclosure of the field, which typically, is located along the outfield boundary.

The amount of fencing, dirt, and sod can be found using the formula for finding the circumference of a circle and the area of a circle as follows;

Area of a circle = π × r²

Circumference of a circle = 2 × π × r

Where r is the radius of the circle

The area of a quarter of a circle is therefore; Area of a circle ÷ 4

The perimeter of a quarter of a circle is; The perimeter of a circle ÷ 4

Fencing = (1/4) × 2 × π × 380 + 2 × 15 + 2 × 380 + (1/4) × 2 × π × 15

Fencing = 190·π + 790 + 7.5·π = 197.5·π + 790 ≈ 1410.5

Grass = π/4 × (380 - 6)² + 87² - π/4 × (87 + 30)² + 2 × 380 × 15 + π/4 × 15² - (3/4) × π × 10² - 25·π = 31528·π + 18969 ≈ 118017.13

Dirt; π/4 × 380² - π/4 × (380 - 6)² + π/4 × (87 + 30)²- 87² + π·100 = (18613·π - 30276)/4 ≈ 7049.6

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The rejection of the null hypothesis in a hypothesis test that claims the mean gestation period for a fox is more than 48.9 weeks implies there is sufficient evidence to support the claim, indicating a statistically significant difference between the observed sample mean and the hypothesized mean.

If a hypothesis test is performed that rejects the null hypothesis that the mean gestation period for a fox is 48.9 weeks or less, it means that there is sufficient evidence to support the claim that the mean gestation period for a fox is more than 48.9 weeks.

The rejection of the null hypothesis implies that the observed sample mean is significantly different from the hypothesized mean, and this difference is unlikely to have occurred by chance alone. The statistical test used to evaluate the hypothesis would have produced a p-value less than the significance level, indicating that the evidence against the null hypothesis is strong.

Therefore, the scientist can conclude that there is evidence to support their claim that the mean gestation period for a fox is more than 48.9 weeks, and this finding could have important implications for understanding fox reproductive biology and management.

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3. The area of the shaded region is 5x² + 2x - 3

4. The area of the shaded region is 18x² + 21x + 6

From the question, we are to determine the area of the shaded region in the given diagrams.

3.

Area of the shaded region = {[(x - 1) + (2x - 1)] × [(x + 1) + (x + 1)]} - (x + 1)(x - 1)

Area of the shaded region = [(x - 1 + 2x - 1) × (x + 1 + x + 1)] - (x + 1)(x - 1)

Area of the shaded region = [(3x - 2) × (2x + 2)] - [(x + 1)(x - 1)]

Area of the shaded region = [(3x - 2)(2x + 2)] - [(x + 1)(x - 1)]

Area of the shaded region = (6x² + 6x - 4x - 4) - (x² - x + x -1)

Area of the shaded region = 6x² + 6x - 4x - 4 - x² + x - x + 1

Area of the shaded region = 6x² + 2x - 4 - x² + 1

Area of the shaded region = 6x² - x² + 2x - 4  + 1

Area of the shaded region = 5x² + 2x - 3

4.

Area of the shaded region = [(6x + 4)(4x + 2)] - [1/2(1/2(6x +4) × (4x + 2))]

Area of the shaded region = [(6x + 4)(4x + 2)] - [1/2((3x + 2)(4x + 2))]

Area of the shaded region = [24x² + 12x + 16x + 8] - [1/2(12x² + 6x + 8x + 4)]

Area of the shaded region = (24x² + 12x + 16x + 8) - (6x² + 3x + 4x + 2)

Area of the shaded region = (24x² + 28x + 8) - (6x² + 7x + 2)

Area of the shaded region = 24x² + 28x + 8 - 6x² - 7x - 2

Area of the shaded region = 24x² - 6x² + 28x - 7x + 8 - 2

Area of the shaded region = 18x² + 21x + 6

Hence, the area is 18x² + 21x + 6

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The balloon payment at the end of 7 years would be $173,819.97, which is option A.

A 7/23 balloon mortgage means that April will make payments on the loan as if it were a 23-year mortgage, but the remaining balance of the loan will be due in full after 7 years.

To find the balloon payment at the end of 7 years, we can first calculate the monthly payment using the loan amount, interest rate, and loan term:

n = 23 * 12 = 276 (total number of payments)

r = 4.15% / 12 = 0.003458 (monthly interest rate)

P = (r * PV) / (1 - (1 + r)^(-n))

where

PV = $197,000

P = (0.003458 * $197,000) / (1 - (1 + 0.003458)^(-276)) = $1,007.14 (monthly payment)

Now we can calculate the remaining balance on the loan after 7 years. Since April is making payments as if it were a 23-year mortgage, she will have made 7 * 12 = 84 payments by the end of the 7th year.

Using the formula for the remaining balance of a loan after t payments:

B = PV * (1 + r)^t - (P / r) * ((1 + r)^t - 1)

Where

t = 84 (number of payments made)

B = $197,000 * (1 + 0.003458)^84 - ($1,007.14 / 0.003458) * ((1 + 0.003458)^84 - 1)

B = $173,819.97

Therefore, the balloon payment at the end of 7 years would be $173,819.97, which is option A.

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Answer:

r = 2

center: ( -7,0 )

Step-by-step explanation:

Step-by-step explanation:

2x+20  and 2x-4  are supplementary angles...they form a straight line and thus = 180 degrees when added together

2x+20      +    2x-4     = 180          simplify

4x + 16 = 180                               subtract 16 from both sides

4x  = 164                                     divide both sides by 4

x = 41 degrees

The x-axis and y-axis are two parallel number lines that meet at (0, 0) to form the shape of the letter t.

Geometric objects and mathematical equations are represented on the coordinate plane, a two-dimensional graph. It is made up of the x-axis and y-axis, two parallel number lines that meet at the starting point (0, 0). The horizontal coordinate is represented by the x-axis, while the vertical coordinate is represented by the y-axis. They combine to create the Cartesian coordinate system.

Positive numbers are labelled to the right of the origin and negative values are labelled to the left of the origin on the x-axis. Positive numbers are written above the origin of the y-axis, and negative numbers are written below it. An ordered pair (x, y), where x denotes the horizontal coordinate and y denotes the vertical coordinate, is used to represent each point on the coordinate plane.

For graphing linear equations, quadratic equations, and other functions, the coordinate plane is a helpful tool. Additionally, it is employed to depict geometric forms like polygons, circles, and lines. The distance between two points, the slope of a line, and other significant features of mathematical objects can be calculated by graphing points on the coordinate plane. With applications in physics, engineering, economics, and computer science, the coordinate plane is a fundamental idea in mathematics.

The graph is shown below when y=1.

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Graph attached below,

The coordinates of the plane is

x       y

1       -3.5

2      -3

4      -2

6      -1.

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here the given equation is y = [tex]\frac{1}{2}x-4[/tex].

Now put x= 1 then y = [tex]\frac{1}{2}\times1-4 =\frac{1-8}{2}=\frac{-7}{2}=-3.5[/tex]

Now put x=2 then [tex]y=\frac{1}{2}\times2-4=1-4=-3[/tex]

Now put x=4 then [tex]y=\frac{1}{2}\times4-4=2-4=-2[/tex]

Now put x=6 then [tex]y=\frac{1}{2}\times6-4=3-4=-1[/tex]

Then coordinates of the plane is

x       y

1       -3.5

2      -3

4      -2

6      -1.

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The answer is: The answers will vary from person to person.

The statement that is true about statistical questions is that the answers will vary from person to person. Statistical questions are questions that can be answered using data and statistics. These questions involve gathering information from a population or a sample of that population, analyzing the data, and making conclusions based on the results. Since different people may have different data and different ways of analyzing that data, the answers to statistical questions can vary. This is why it is important to consider the sample size, the sample method, and the statistical methods used to analyze the data when interpreting the results of statistical questions. A well-designed study can help minimize variability and improve the accuracy of the results, but some degree of variability is still expected due to natural differences in the data collected by different individuals or groups

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The answer is 24. To calculate this, 8 1/2% needs to be converted to a decimal by dividing it by 100.

Numbers are often used to measure and compare objects, and they can be used to solve problems and make predictions.

8 1/2% is equal to 0.04.

To calculate the number of poetry books for children, multiply 0.04 by 600.

0.04 x 600 = 24

To find the number of poetry books for children, the decimal equivalent of 8 1/2% needs to be multiplied by the total number of poetry books.

In conclusion, 8 1/2% of 600 poetry books is equal to 24 books.

To calculate this, 8 1/2% needs to be converted to a decimal by dividing it by 100.

Then, the decimal needs to be multiplied by the total number of poetry books. This will give the answer, which can be rounded down if necessary.

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For the given diagram, the square ABCD is transformed into square A'B'C'D' by the dilation using the scale factor of 5.

On a map, scales are frequently present. The scale factor in geography usually applies to how accurately the scale depicted on the map reflects actual distance. Find the corresponding sides upon that two figures before obtaining the scale factor.

Then, divide the new figure's measurement by the old figure's measurement. Your scale factor, i.e., how many times bigger or less than your new image is in comparison to the old, is the consequence.

From the diagram:

coordinate of A = (1,1)

coordinate of A' = (5,5)

Thus, the coordinates of A is multiplied by 5 to get the coordinates of A'

Same applies with the coordinates of B, C and D.

Thus, for the given diagram, the square ABCD is transformed into square A'B'C'D' by the dilation using the scale factor of 5.

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Answer:

5 1/4

Step-by-step explanation:

The domain of the function is (-∞, ∞) and the range of the function is [2, ∞).

In mathematics, the range of a function refers to the set of all possible output values (dependent variable) that the function can produce for its corresponding input values (independent variable).

The given function is y = 3x² + 2.

The domain of a function is the set of all possible values of the independent variable (x) for which the function is defined. Since the given function is a polynomial function, it is defined for all real numbers.

Therefore, the domain of the function y = 3x² + 2 is (-∞, ∞), which means that the function is defined for all real values of x.

The range of a function is the set of all possible values of the dependent variable (y) that the function can take. In this case, the function is a quadratic function with a leading coefficient of 3, which means that the parabola opens upwards and its vertex is at the point (0,2).

Since the minimum value of the function is 2, the range of the function is [2, ∞).

Therefore, the domain of the function is (-∞, ∞) and the range of the function is [2, ∞).

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1) The equation (x + 6)² + (y + 4)² = 36 represents a circle centered at the point (-6, -4) with a radius of 6. Therefore, the signal is located at the point (-6, -4).

2) The range of the signal refers to the maximum distance that the signal can travel before it becomes too weak to be detected. In this case, the range of the signal is equal to the radius of the circle, which is 6. This means that any point on the circle (x + 6)² + (y + 4)² = 36 is 6 units away from the signal located at (-6, -4).

To visualize this, imagine the signal as a point source located at (-6, -4), and the range of the signal as a circle centered at the signal with a radius of 6. Any point on this circle represents the farthest distance that the signal can reach and still be detected.

In summary, the signal is located at (-6, -4) and its range is 6 units, as represented by the circle (x + 6)² + (y + 4)² = 36.

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Answer: Problems Involving FractionsIn solving word problems, first, identify what is asked. Then, look for the given facts. Establish the number sentence and the operation/s to be used. Make sure that the operation/s used will bring out the correct answer. Check the answer using the number sentence and see if it will satisfy the given condition.

Step-by-step explanation: Learning Task 2:Answers:16 1/4 square meters₱322,362.50Step-by-step explanation:Solutions:1. Given: 6 1/2 square meters - area which Ruben can paint in an hour

Answer:

D. y ≥ x² - 4x - 5

Step-by-step explanation:

We can observe two characteristics of this graphed inequality:

1. its shading is above it, therefore the inequality sign must be greater than

2. its boundary line is continuous, not dotted, so the inequality sign must include or equal to

From these two observations, we can assert that D. x² - 4x - 5 is the correct answer because it is the only one which has a greater than or equal to sign.

____________

Note:

We can also check that the equation for the inequality is correct by converting it to vertex form by completing the square, then graphing it ourselves:

[tex]y \ge (x-2)^2 - 9[/tex]

Answer:

The answer is y≥ x²-4x-5

Step-by-step explanation:

x=a,x=b

where a,b are roots of the equation

a= -1 b=5

x= -1,x=5

x+1=0,x-5=0

(x+1)(x-5)=0

x²-5x+x-5=0

x²-4x-5=0

The radius of convergence is 4.

To find the radius of convergence, R, of the collection, we can use the ratio test:

[tex]lim_n→∞ |(a_(n+1)/[/tex][tex]a_n)|[/tex]

[tex]lim_n→∞ |(a_{(n+1})/[/tex]

[tex]= lim_n→∞ |(x+8) / 4| * |ln(n+1) / ln(n)|[/tex]

For the series to converge, this limit need to be less than 1. therefore, we've:

[tex]|(x+8) / 4| * lim_n→∞ |ln(n+1) / ln(n)| < 1[/tex]

For the reason that[tex]lim_n→∞ |ln(n+1) / ln(n)| = 1[/tex], we will simplify this to:

|(x+8) / 4| < 1

Taking the absolute cost under consideration, we have cases:

Case 1: (x+8)/4 < 1

In this case, we have x < -4.

Case 2: (x+8)/4 > -1

In this case, we have x > -12.

Consequently, the radius of convergence is the distance from the center of the collection (x = -8) to the closest endpoint of the c language (-12 on the left and -4 at the right):

R = min{8, 4} = 4

So, 4 is the radius of convergence.

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Answer:

negative

y=-x

y=-2x+6

y=(-1/2)x+1

y=-5x+20

undefined

x=4

x=-3

zero slope

y=2

y=-100

When comparing the data from the two locations, the measure of center that should be used to determine which location typically has the cooler temperature is the median.

In Sunny Town, the histogram shows that the shaded bars are skewed to the right, indicating that the distribution is positively skewed. This means that there are a few high temperatures that pull the mean towards the higher end.

However, the median, which represents the middle value when the data is arranged in ascending order, is less affected by extreme values and is a better measure of the center for skewed distributions.In Desert Landing, the histogram shows a symmetric distribution, with the shaded bars evenly distributed around the center.

In this case, both the mean and median can be considered reliable measures of the center.Therefore, to determine which location typically has the cooler temperature, we should use the median.

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Answer:

The answer is 59 ½

Step-by-step explanation:

4×4×4-2×1 ½×1 ½

= 64 - 2× 3/2 × 3/2

= 64 - 9/2

= 128/2 - 9/2

= 119/2

= 59 ½ in3

Hope this helped :)

The required equation in the given situation is C = 35 + 2.50m where C is the total cost and m is the number of miles driven.

Equation: A declaration that two expressions with variables or integers are equal.

In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

A formula would be 3x - 5 = 16, for instance.

The equation would be:

C is the total cost and m is the miles driven.

We know that:
Charge of the truck: $35

Charge per mile: $2.50

Then, form the equation as follows:

C = 35 + 2.50m

Therefore, the required equation in the given situation is C = 35 + 2.50m where C is the total cost and m is the number of miles driven.

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Answer:

6 inches

Step-by-step explanation:

Angle relationship and algebra are closely related in geometry, as we often use algebraic expressions to represent angle measures and their ratios.

For example, if we are given that angle A and angle B are complementary (meaning that their sum is 90 degrees), we can write an algebraic equation:

Similarly, if we know that angle A is three times larger than angle B, we can write:

We can use algebraic equations to solve for unknown angle measures or to find relationships between angles.

For example, let's say we are given that angle A is complementary to angle B, and that angle B is twice as large as angle C. We can write:

We can substitute the second equation into the first equation to get:

This equation relates the three angles A, B, and C. We can use algebra to solve for any of the unknown angles, given the measures of the others.

Therefore, algebraic equations and expressions are an important tool in understanding and analyzing angle relationships in geometry.

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The two coterminal angles for 3/4 radians are (3π + 4)/4 and (-5π + 4)/4 radians.

Coterminal angles are two or more angles that have the same initial and terminal sides, but differ by a multiple of 360 degrees or 2π radians. In other words, coterminal angles are angles that overlap each other when drawn in standard position (with their initial side on the positive x-axis).

To find two coterminal angles with 3/4 radians, we can add or subtract multiples of 2π radians (which is equivalent to a full circle).

One positive coterminal angle is obtained by adding 2π radians to 3/4 radians:

3/4 + 2π = 3/4 + 8π/4 = 3/4 + 2π

Simplifying, we get:

3/4 + 2π = (3π + 4)/4

Therefore, one positive coterminal angle is (3π + 4)/4 radians.

One negative coterminal angle is obtained by subtracting 2π radians from 3/4 radians:

3/4 - 2π = 3/4 - 8π/4 = 3/4 - 2π

Simplifying, we get:

3/4 - 2π = (-5π + 4)/4

Therefore, one negative coterminal angle is (-5π + 4)/4 radians.

Hence, the two coterminal angles for 3/4 radians are (3π + 4)/4 and (-5π + 4)/4 radians.

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The probability of Laura missing 3 free throws before making 12 is approximately 0.0037 or 0.37%.
The basketball free throw.

A success would be considered when Laura makes a free throw.

A failure would be when Laura misses a free throw.
The negative binomial distribution is a probability distribution that calculates the probability of obtaining a certain number of failures before a specified number of successes occur.

The specified number of successes is 12, and the number of failures is represented by the variable x.
To calculate the probability of x failures, we need to know the probability of a single failure.

Since Laura is an 82% free throw shooter, the probability of her missing a free throw is 18%.
We can use the formula for negative binomial distribution to determine how many failures are required before 12 successes are achieved.

The formula is:
[tex]P(X = x) = (r+x-1)C(x) \times p^r \times (1-p)^x[/tex]
Where:
P(X = x) is the probability of having x failures before achieving 12 successes
r is the number of successes required (in this case, 12)
p is the probability of a single success (in this case, 0.82)

[tex](r+x-1)C(x)[/tex]is the combination of r+x-1 choose x

For example, if we want to find the probability of Laura missing 3 free throws before making 12, we will plug in x = 3, r = 12, p = 0.82 into the formula:

[tex]P(X = 3) = (12+3-1)C(3) \times 0.82^1^2\times (1-0.82)^3[/tex]
[tex]P(X = 3) = 14C3 \times 0.082^1^2 \times 0.18^3[/tex]
[tex]P(X = 3) = 364 \times 0.000018 \times 0.005832[/tex]
P(X = 3) = 0.000037
Overall, the trial in this scenario is each individual attempt at a free throw, the success is making a free throw, and 12 successes are required before the shooting session is considered complete.

The negative binomial distribution is used to calculate the probability of obtaining a certain number of failures before achieving the specified number of successes.

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'x' follows a negative binomial distribution with 'r' being 12 successes.

In this scenario, a trial refers to each individual attempt at shooting a free throw. A success is when Laura successfully makes a free throw. To achieve her goal of making 12 free throws, she needs to have 11 successes (since she will miss on the final attempt). Therefore, r = 11.

In this context, a "trial" refers to each individual attempt Laura makes to shoot a basketball free throw. A "success" is when Laura makes a free throw (hits the basket), while a "failure" (not mentioned in the question) would be when Laura misses a free throw. Since Laura keeps shooting free throws until she makes 12, the number of successes required, denoted as 'r', is 12.

Therefore, 'x' follows a negative binomial distribution with 'r' being 12 successes.

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By using the unitary method, we found that 60 items were sold at $25 each, while 90 items were sold at $5 each at the charity's craft fair.

In this problem, we know the total number of items sold and the total revenue earned. Let's assume that the number of items sold at $5 each is x, and the number of items sold at $25 each is y. Therefore, we can write two equations based on this information:

x + y = 150 (Equation 1)

5x + 25y = 1950 (Equation 2)

Equation 1 represents the total number of items sold, while Equation 2 represents the total revenue earned from the sale. Now, we can use the unitary method to find the value of y, which represents the number of items sold at $25 each.

Let's rearrange Equation 2 to solve for y:

5x + 25y = 1950

25y = 1950 - 5x

y = (1950 - 5x)/25

Now, we can substitute this expression for y into Equation 1:

x + (1950 - 5x)/25 = 150

Simplifying this equation, we get:

25x + 1950 - 5x = 3750

20x = 1800

x = 90

Therefore, we know that 90 items were sold at $5 each. Now, we can use Equation 1 to find the number of items sold at $25 each:

y = 150 - x

y = 150 - 90

y = 60

Hence, 60 items were sold at $25 each.

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The probability of exponential random variables that your job will be ready before 10:01 is approximately 0.0693, or about 6.93%.

We can use the cumulative distribution function (CDF) of the exponential distribution to solve this problem. Let X be the random variable representing the time it takes to print a job. Then, X follows an exponential distribution with parameter λ = 1/12, since the expectation of X is 12 seconds.

The probability that your job will be ready before 10:01 is equal to the probability that the printer finishes the first two jobs in less than 1 minute since your job is third in line.

Let Y be the random variable representing the time it takes to print the first job. Then, Y also follows an exponential distribution with parameter λ = 1/12.

The probability that the first job is finished before 10:01 is given by:

P(Y < 60) = 1 - [tex]$e^{(-\lambda t)}$[/tex] = 1 - [tex]e^{(-(1/12)(60))}[/tex] = 0.3935

Similarly, the probability that the second job is finished before 10:01 is also 0.3935, since it is also an exponential random variable with the same parameter. Therefore, the probability that your job will be ready before 10:01 is:

P(X < 60) = P(Y < 60) × P(Y < 60) × P(X < 60) = 0.3935² × (1 - [tex]$e^{(-\lambda t)}$[/tex]) = 0.0693

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Answer:

Step-by-step explanation:

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