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Question 12

A recent conference had 750 people in attendance. In one exhibit room of 70 people, there were 18 teachers and 52 principals. What prediction can you make about the number of principals in attendance at the conference?

There were about 193 principals in attendance.
There were about 260 principals in attendance.
There were about 557 principals in attendance.
There were about 680 principals in attendance.

Question 13

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 number of cookies the college will need?
The college will have about 480 students who prefer cookies.
The college will have about 640 students who prefer cookies.
The college will have about 1,280 students who prefer cookies.
The college will have about 1,440 students who prefer cookies.

Question 14

A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.


Sport 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 15

The line plots represent data collected on the travel times to school from two groups of 15 students.

A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4, 6, 14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.

A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9, 18, 20, and 22. There are two dots above 6, 10, 12, 14, and 16. The graph is titled Bus 18 Travel Times.

Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.

Bus 18, with a median of 13
Bus 47, with a median of 16
Bus 18, with a mean of 13
Bus 47, with a mean of 16

According to the function, the rate of change with respect to the number of minutes purchased is $1.05 per minute.

The function given in the problem is y = 5.45 + 1.05(x + 7), where y represents the cost in dollars for a prepaid cell phone plan of x minutes. This means that if you want to know how much it will cost to purchase a certain number of minutes, you can simply plug in that number for x and the equation will give you the corresponding cost in dollars.

Now, the rate of change with respect to the number of minutes purchased is also known as the slope of the function. This tells us how much the cost will change for each additional minute purchased. To find the slope, we need to take the derivative of the function with respect to x.

The derivative of y with respect to x is given by:

dy/dx = 1.05

This means that for each additional minute purchased, the cost will increase by $1.05.

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The measure of angle FCD is 130 degrees.

What is an angle?

In planar geometry, an angle is a shape made up of two rays or lines that share an endpoint. The Latin word "angulus" (which means "corner") is where the word "angle" first arose.

The pair of alternative internal angles that are congruent must first be found. The angles formed on the opposing sides of the transversal EF are known as alternate internal angles since AB and CD are parallel lines. We possess

Angle AGE and angle FCD are alternate interior angles.

Angle AGE measures 130 degrees.

Therefore, we can conclude that angle FCD also measures 130 degrees. So, the measure of angle FCD is 130 degrees.

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Using probability, we can find the following:

a. In the figure.

b. The probability that the first set is green is = 0.8

c. Probability that the second set is green is = 0.06

d. The probability that both the sets are green is = 0.48

e. The probability that at least one set is green is = 0.86

The likelihood that an event will occur is described by probability. There are many circumstances in real life where we may need to foresee how something will turn out. We might be able to predict the outcome of an event or we might not. At this point, we say, "There is a chance that the event will happen or not."

Here in the question,

b.

The probability that the first set is green is:

P = 1 - 0.2

= 0.8

c.

Now the first set is given as not green.

Probability that the second set is green is:

p = 0.2 × 0.3

= 0.06

d.

Now probability that both the sets are green is:

P = 0.8 × 0.6

= 0.48

e.

When both the sets are not green, probability is:

0.2 × 0.7

= 0.14

So, probability that at least one set is green is:

P = 1- 0.14

= 0.86

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For given data, Carrie threw the ball highest = 35ft and ball stayed in the air longest = 3s for Carrie as well.

Any object that is fired into the air and travels in that direction is referred to as a projectile. Gravitation, however, is another force that an object experiences after the first force that pushes it.

Three distinct individuals, Alberto, Ben, and Carrie, each toss a ball straight up into the air.

Following equation may be used to explain Alberto's throw.

[tex]H = -16t^2 + 32t + 4[/tex]

Now , to find the maximum height, we solve for first derivative w.r.t.t,

[tex]-32t + 32 = 0[/tex]

[tex]32t=32\\t = 1s[/tex]

Using t=1, we can find maximum height as

[tex]H =-16(1)^2 + 32(1) + 4\\\\H=(-16)+32+4[/tex]

[tex]H= 20[/tex] ft

Thus, when Alberto threw ball, maximum height attained= 20 ft and total time duration ball was in air = 1s.

From the given table( refer to attached image),

Fom given table,

we can drive the function for maximum height as,

[tex]H=at^2+bt+c[/tex]

now, putting values of t, to get values of H,

from table, for t=0,H=6

6=[tex]a(0)+b(0)+c[/tex]

[tex]c=6[/tex]

[tex]H=at^2+bt+6[/tex]

for t=1,H=14

[tex]14=a(1)^2+b.1+6\\\\8=a+b............(1)[/tex]

similarly,for t=2,H=14

[tex]14=a(2)^2+b.2+6\\\\8=4a+2b........(2)[/tex]

solving equation 1 and 2,

a=(-4) and b=12

∴[tex]H=-4t^2+12t+6[/tex]

we know, [tex]t=\frac{-b}{2a}\\\\t=\frac{-12}{-8}=3/2=1.5s[/tex]

When Ben threw ball, the maximum height ball attained was 14 ft and total time duration for which ball was in air was 1.5 seconds.

From the given graph(refer to attached image),When Carrie threw the ball Maximum Height attained = 35ft and Time duration ball was afloat is 3s

Thus,When Carrie threw the ball attained Maximum Height 35ft  and ball stayed in the air longest.

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Complete Question: A ball is thrown straight up into the air by three different people, Alberto, Ben and Carrie. Below are different representations of their throws. Alberto’s throw can be described by the equation height=−16(time)^2+32(time)+4 Ben's throw can be described by the following table(refer to attached image).Who threw the ball highest and for whom the ball was in air for the longest?

The approximate shortest distance, to the art hundredth of a foot, between first and third base is 127.28 feet.

Distance refers to the amount of space between two objects or points. It can be measured in units such as meters, kilometers, miles, or feet, and is commonly used to describe the length or extent of a journey, path, or separation.

According to the given information:

The distance between first and third base in a baseball diamond is the diagonal of the square with side lengths of 90 feet. Using the Pythagorean theorem, we can calculate this distance as follows:

d² = 90² + 90²

d²= 8,100 + 8,100

d²  = 16,200

d = √(16,200)

d ≈ 127.28 feet

Therefore, the approximate shortest distance, to the nearest hundredth of a foot, between first and third base is 127.28 feet. The correct answer is option (b).

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The side length of the square that has the given area would be = 1/4

To calculate the side length of a given square the formula for the area of a square should be used. That is;

Area of a square = a²

where;

a = length = ?

area = 1/16

That is = 1/16 = a²

a = √1/16

= 1/4

Therefore the side of the square whose area is given should have the length of 1/4

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The weight of the tallest dog which is of height 20 inches on this scatter-plot showing dog heights and their weights is 30 pounds.

The graphs, scatter plots, or scatter charts show the relationship between two variables in a data set that has been analysed.  Both a two-dimensional plane and the Cartesian-system are used to represent the data points. Observing and illuminating correlations between two numerical variables is the main purpose of scatter plots. When the data are viewed as a whole, the dots in a scatter plot show patterns in addition to the values of the individual data points. The Y-axis is used to plot the dependent variable, while the X-axis is used to represent the independent variable or attribute. Using a scatter plot, you may see what happens to one variable when another variable is altered. To determine whether the two variables are connected, a scatter plot is utilised.

The scatter plot shows the dog weights & their heights surveyed.

Data represented on X-axis(independent variable) : heights of dogs

Data represented on Y-axis(dependent variable) : weights of dogs

Lowest weight of dog=5 pounds(approx)

Greatest weight of the dog surveyed=41 pounds(approx)

Lowest height of surveyed dog=5 inches.

Greatest height of surveyed dog=20 inches.

∴The weight of tallest dog with 20 inches if height=30 pounds

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The first month in which HBM Corporation's cumulative donation total exceeds the Gades Foundation's cumulative total is the sixth month. This is calculated by finding an equation for each organization's cumulative donation total and solving an inequality.

Let's start by finding an equation for the cumulative donation total for each organization after n months. Let GF(n) and HBM(n) represent the cumulative donation totals for the Gades Foundation and HBM Corporation, respectively.

The Gades Foundation's cumulative donation total can be represented by the arithmetic sequence

GF(n) = 250 + 100(n-1)

The HBM Corporation's cumulative donation total can be represented by the geometric sequence

HBM(n) = 64(1.75)ⁿ⁻¹

To find the month in which HBM Corporation's cumulative donation total exceeds the Gades Foundation's cumulative total, we need to solve the inequality

HBM(n) > GF(n)

Substituting the expressions for GF(n) and HBM(n), we get

64(1.75)ⁿ⁻¹ > 250 + 100(n-1)

Simplifying and solving for n, we get

1.75ⁿ⁻¹ > (250/64) + (100/64)(n-1)

Taking the logarithm of both sides, we get

(n-1)log(1.75) > log(250/64) + log(1+(100/250)(n-1))

Using a calculator to evaluate the logarithms, we can solve for n

n > 5.74

Since n must be an integer, the smallest integer greater than 5.74 is 6. Therefore, the first month in the Gades Foundation's cumulative total is the sixth month.

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The unit rate of water dropped per day is [tex]$\frac{12}{5}$[/tex] gallons per day.

We can start by finding the unit rate of water dropped per hour.

If the sink drips [tex]$\frac{2}{5}$[/tex] gallon of water in 4 hours, then it drips [tex]\frac{1}{5}$[/tex] gallon of water in 2 hours (since [tex](\frac{2}{4} = \frac{1}{2}$).[/tex]

The unit rate of water dropped per hour is:

[tex]$\frac{1/5}{2} = \frac{1}{10}$[/tex] gallon per hour.

To find the unit rate of water dropped per day, we can multiply the unit rate per hour by the number of hours in a day:

[tex]$\frac{1}{10} \text{ gallon per hour} \cdot 24 \text{ hours per day} = \frac{12}{5} \text{ gallons per day}$[/tex]

Therefore, the unit rate of water dropped per day is [tex]$\frac{12}{5}$[/tex] gallons per day.

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The unit rate of water dropped per day is 12/5 gallons.

To find the unit rate of water dropped per day for a sink that drips 2/5 gallons of water in 4 hours, we'll follow these

steps:

Determine how many gallons of water are dripped in one hour.

Calculate the gallons of water dripped in 24 hours (one day).

Calculate gallons per hour.

Since the sink drips 2/5 gallons in 4 hours, we'll divide the gallons by the number of hours:

(2/5) / 4 = (2/5) × (1/4) = 2/20 = 1/10

So, the sink drips 1/10 gallons per hour.

Calculate gallons per day.

Now, we'll multiply the gallons per hour by 24 hours to find the gallons per day:

(1/10) × 24 = 24/10 = 12/5

The unit rate of water dropped per day is 12/5 gallons.

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"A transformation T is linear if and only if [tex]T(c1v1 + c2v2) = c1T(v1) + c2T(v2)[/tex] for all v1 and v2 in the domain of T and for all scalars c1 and c2" is true.

To understand why this statement is true, we need to first define what it means for a transformation to be linear.

A linear transformation is a function that satisfies two properties:

Additivity and homogeneity.

Additivity means that [tex]T(u + v) = T(u) + T(v)[/tex]for all vectors u and v in the domain of T, while homogeneity means that [tex]T(cv) = cT(v)[/tex] for all vectors v in the domain of T and all scalars c.
Let's look at the given statement. It states that [tex]T(c1v1 + c2v2) = c1T(v1) + c2T(v2)[/tex] for all v1 and v2 in the domain of T and for all scalars c1 and c2.

This is equivalent to saying that T is both additive and homogeneous, since we can rewrite the statement as [tex]T(c1v1 + c2v2) = T(c1v1) + T(c2v2) = c1T(v1) + c2T(v2).[/tex]
A transformation satisfies the given statement, it is both additive and homogeneous, and hence it is linear.

On the other hand, if a transformation is linear, it must satisfy the given statement by definition.

The statement "A transformation T is linear if and only if [tex]T(c1v1 + c2v2) = c1T(v1) + c2T(v2[/tex]) for all v1 and v2 in the domain of T and for all scalars c1 and c2" is true.

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Answer:48

Step-by-step explanation:

Given the survey, the completed table is as follows:

                   Print             Electronic             Total

Youth             23               40                          63

Adults               23             36                           59

Total                46               76                           122

To fill in the missing values, we can use the fact that the total number of youths is 63 and the total number of adults is 59. Thus, we can subtract the number of known values from the total to find the missing values.

For the number of youths who prefer printed books, we have:

Print + Electronic = Total

Print + ? = 63

23 + ? = 63

? = 63 - 23

? = 40

For the number of adults who prefer electronic books, we have:

Print + Electronic = Total

? + Electronic = 59

23 + Electronic = 59

Electronic = 59 - 23

Electronic = 36

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Answer:

The electrons in the battery will flow from the negative electrode (anode) to the positive electrode (cathode) through an external circuit, driven by the potential difference created by the ionic paste.

Step-by-step explanation:

In a battery, the ionic paste, which is usually an electrolyte solution, allows the flow of ions between the electrodes of the battery. This flow of ions creates a potential difference between the two electrodes, which in turn creates an electric field.

The electrons in the battery will flow from the negative electrode (anode) to the positive electrode (cathode) through an external circuit, driven by the potential difference created by the ionic paste. As the electrons move through the external circuit, they can be used to power a device or do useful work.

It is important to note that the flow of electrons occurs only in the external circuit, while the flow of ions occurs only within the battery itself, through the ionic paste. The flow of electrons and ions is connected but separate processes that work together to generate electrical energy in a battery.

In "Pointed Roofs," Dorothy Richardson makes use of conversation and stream of consciousness to improve her writing. Using stream of consciousness, in the given expert.

An excerpt is indeed a quotation from that other resource that the author introduces with fresh language in a sentence. This phrase is taken from Thomas Jefferson's 1801 inaugural speech: As he warned his audience, "I may often go wrong by defect of judgement," Jefferson admitted the fallibility of human nature. "I shall frequently err through lack of judgement" is the excerpt.

In "Pointed Roofs," Dorothy Richardson makes use of conversation and stream of consciousness to improve her writing. Using stream of consciousness, the author lets readers peek inside the protagonist, Miriam, to understand her feelings and thoughts as they happen. For instance, readers can feel Miriam's mild dizziness 

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Answer:

Answers below

Step-by-step explanation:

Answer for 10

6x3=18 --> 18×4=72

6x6=36 --> 36x2=72

72+72=144

144

Answer for 11

18x6=108 --> 108x2=216

20x6=120 --> 120x2=240

20x18=360 --> 360x2=720

216+240+720=1176

1176

Answer for 12

10x7=70 --> 70x2=140

20x7=140 --> 140x2=280

20x10=200 --> 200x2=400

140+280+400=820

820

Answer for 13

16x16=256 --> 256x4=1024

16x20=320 --> 320x2=640

1024+640=1664

1664

Sorry I forgot how to calculate triangles.

The loose sweets are better value, as they cost only £0.0089 per gram, compared to £0.01242 per gram for the pre-packed sweets.

We need to calculate their price per gram.

Price per gram of pre-packed sweets:

120 g of pre-packed sweets cost £1.49

1 g of pre-packed sweets costs £1.49 / 120 = £0.01242 (rounded to 5 decimal places)

Price per gram of loose sweets:

100 g of loose sweets cost £0.89

1 g of loose sweets costs £0.89 / 100 = £0.0089

So, the loose sweets are better value, as they cost only £0.0089 per gram, compared to £0.01242 per gram for the pre-packed sweets.

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Answer:

9/4.

Step-by-step explanation:

Hope this helps! =D

The graph K must represent an investment that was compounded continuously because investments that are compounded continuously increase at a faster rate than investments that use either simple interest or are compounded monthly.

In Mathematics and Financial accounting, continuous compounding interest can be determined or calculated by using this mathematical equation (formula):

[tex]A(t) = P_{0}e^{rt}[/tex]

Where:

By critically observing the given graph, we can reasonably infer and logically deduce that the graph with line K represent an investment that was compounded continuously because the principal (initial amount of money) increases at a faster rate

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

(4, 0)

Explanation:

The difference between -5 and -1 is 4 and the difference between-3 and -3 is 0.

The area of the floor of the igloo is 842.9 m²

We know that the formula for the volume of hemisphere is given by,

V = (2/3) × π × r³

where r is the radius of the hemisphere

Here, a hemisphere igloo has a volume of about 9,202.8 m³

Using above formula of the volume of hemisphere,

V = (2/3) × π × r³

9202.8 = (2/3) × π × r³

r³ = 9202.8 × (3/2π)

r³ = 4394.01

r = 16.38 m

We know that the area of the floor of the igloo is equivalent to the area of circle, as the base of hemisphere is a circle.

So, the area of the floor of the igloo would be,

A = π × r²

A = π × 16.38²

A = 842.9 m²

Therefore, the required area is 842.9 m²

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The requried equation of the circle with center (-3,0) passing through (-3,3/2) is 4(x + 3)² + 4y² = 9

We are given that the center of the circle is (-3,0) and it passes through (-3, 3/2). Since the x-coordinate of both points is the same, we know that the center lies on a vertical line passing through (-3, 3/2). Therefore, the distance between the center and the point (-3, 3/2) is the radius of the circle.

The radius is found using the distance formula:

r = √[(x₂ - x₁)² + (y₂ - ₁)²]

r = √[(-3 - (-3))² + (0 - 3/2)²] = √[9/4] = 3/2

So, the equation of the circle in standard form is:

(x - (-3))² + (y - 0)² = (3/2)²

(x + 3)² + y² = 9/4

4(x + 3)² + 4y² = 9

Therefore, the standard form of the equation for the circle is: 4(x + 3)² + 4y² = 9

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Kalani deposited $200 into her checking account every week and $400 into her savings account every month.

A group of equations that must be solved simultaneously is referred to as a system of equations. Typically, a system of equations involves multiple variables, and the goal is to find the values of those variables that satisfy all of the equations in the system.

Let's start by using the given information to write equations for the total amount deposited in each account over the course of the year.

For the checking account, Kalani deposited x dollars every week for 52 weeks, so the total amount deposited for the year is:

52x

For the savings account, Kalani deposited y dollars every month for 12 months, so the total amount deposited for the year is:

12y

We are also told that each checking account deposit was half the amount of each savings account deposit, so we can write:

x = (1/2)y

Finally, we are given that the total of all deposits for the year was $15,200, so we can write:

52x + 12y = 15200

A system of two equations with two variables is now available:

x = (1/2)y

52x + 12y = 15200

We can solve this system to determine the values of x and y. The result of putting the first equation into the second equation is:

52(1/2)y + 12y = 15200

Simplifying:

26y + 12y = 15200

38y = 15200

y = 400

Substituting y = 400 into the first equation, we get:

x = (1/2)y = (1/2)(400) = 200

Therefore, Kalani deposited $200 into her checking account every week and $400 into her savings account every month.

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The circumference of the circle actually is  25.12 inches

So the diameter is 8 inches, and the circumference is pi times the diameter, so you must have:

c = 3.14*8in = 25.12 inches

That is the circumference of the circle, im not sure of what did you did to ger 43.96 inches.

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Answer:

y=1.6x+3

Step-by-step explanation:

Answer: y=1/2x+3 i don’t know if I’m right, be warned!

Step-by-step explanation:

first find the slope (the m) by doing rise over run or you can find 2 points and find slope by using subtraction. Then get the +b by finding out where the line crosses the y intercept and put that all together leaving the y and x variables the same.

At x=0 only, the function f with first derivative f'(x) = x(x-5)²(x+1) has a relative minimum.

Hence the correct option is (A) 0 only.

The first derivative of the function is,

f'(x) = x(x-5)²(x+1)

Differentiating the function with respect to x we get, The second derivative of the function is,

f''(x) = x(x-5)².(1) + x(x+1).2(x-5) + (x-5)²(x+1).1 = (x-5)² (x+x+1) + 2x(x+1)(x-5) = (x-5)²(2x+1) + 2x(x+1)(x-5)

Now, f'(x) = 0 gives,

x(x-5)²(x+1) = 0

We know that if product of more than one terms is zero then either of them is zero.

Either, x=0

Or, (x-5)² = 0

x-5 = 0

x = 5

Or, x+1 = 0

x = -1

So the extremum points of the function are, x = -1, 0, 5.

At x=-1, f''(-1) = (-6)²(-2+1) + 2(-1)(-1+1)(-6) = -36

At x=0, f''(0) = (-5)²*1 + 0 = 25

At x=5, f''(5) = 0 + 0 = 0

Since the value of second derivative is positive at only x = 0.

Thus, at x = 0 only the function has a relative minimum.

Hence the correct option is (A).

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The measure of angle ABD (which is the same as angle CBD) is 45 degrees.

The quadrilateral's opposing sides are equal. Triangles ABC and ABCD have equal angles on either side of their equal sides. In the quadrilateral ACBD, the opposing angles are also equal. A parallelogram is formed by ACBD.

We can use the fact that the total of the angles of a triangle is always 180 degrees to determine the measure of angle CBD. As a result, we have:

Angle ABD + Angle CBD + Angle BCD = 180 degrees

Substituting the given angle measures, we get:

Angle ABD + Angle CBD + 90 degrees = 180 degrees

Simplifying, we get:

Angle ABD + Angle CBD = 90 degrees

But we know that Angle ABD = Angle CBD, so we can substitute:

2 x Angle ABD = 90 degrees

Dividing both sides by 2, we get:

Angle ABD = 45 degrees

So, the measure of angle ABD (which is the same as angle CBD) is 45 degrees.

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The measure of variability that the charity should use to accurately represent the data is B. The IQR of 13 is the most accurate to use, since the data is skewed.

The charity should use the Interquartile Range (IQR) as the measure of variability since the data is skewed. The IQR measures the range of the middle 50% of the data, which is less affected by outliers or skewed data.

Q1 is the median of the first half of the data: 5, 5, 6, 8, 10, 15 (Q1 = 7)

Q3 is the median of the second half of the data: 15, 18, 20, 20, 20, 20, 20 (Q3 = 20)

Now, we can calculate the IQR:

IQR = Q3 - Q1

IQR = 20 - 7

IQR = 13

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The graph of the function q(x) = -9/2x^2 is a downward-facing parabola with vertex at the origin (0, 0).

The graph of the quadratic function q(x) = -9/2x^2 is a downward facing parabola because the coefficient of x^2 is negative. The vertex of the parabola can be found by using the formula x = -b/2a, where a is the coefficient of x^2 and b is the coefficient of x. In this case, a = -9/2 and b = 0, so the vertex is at x = 0.

To find the y-coordinate of the vertex, we substitute x = 0 into the equation q(x) = -9/2x^2. This gives us q(0) = 0, so the vertex is at the point (0, 0).

Since the coefficient of x^2 is negative, the graph of the function opens downwards. The value of the function decreases as we move away from the vertex in either direction.

Therefore, the graph of the function q(x) = -9/2x^2 is a downward-facing parabola with vertex at the origin (0, 0).

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The period for the following graph is 90 degrees. So correct option is C.

In mathematics, a period is a specific type of repetition in a function or a sequence. A period is the smallest positive value of a constant T for which a function or a sequence f(x + T) = f(x) for all x.

Periods are used to describe the behavior of functions and sequences that exhibit a repeating pattern. The length of the period determines the frequency of the pattern, and it is often used to describe the periodicity of functions in various applications, such as signal processing, harmonic analysis, and Fourier series.

For example, the sine function sin(x) is periodic with a period of 2π. This means that sin(x + 2π) = sin(x) for all x. Similarly, the cosine function cos(x) is also periodic with a period of 2π. Other common examples of periodic functions include the tangent function, cotangent function, and exponential function.

In addition to their applications in mathematics, periods also have practical applications in fields such as physics, engineering, and computer science, where they are used to model periodic phenomena such as waves and oscillations.

Overall, periods are an important concept in mathematics and are used to describe the repeating patterns that are found in many mathematical functions and sequences.

The period for the following graph is 90 degrees.

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Step-by-step explanation:

Refer the attachment!!~

Answer:

Step-by-step explanation: