a circle of radius r has area a = πr2. if a random circle has radius that is uniformly dis- tributed on [0, θ]: what are the mean and variance of the area of the circle?

Answers

Answer 1

The variance of the area of the circle is [tex]\pi^2\theta^{4/45}[/tex].

The mean area of the circle is [tex]\pi\theta^{2/3}.[/tex]

Let X be the radius of the circle, uniformly distributed on [0, θ].

The probability density function of X is given by:

[tex]f(x) = 1/\theta, for 0 \leq x \leq θ[/tex]

= 0, otherwise

Let Y be the area of the circle. Then[tex]Y = \pi X^2.[/tex] We want to find the mean and variance of Y.

Mean of Y:

By the law of the unconscious statistician, the mean of Y is given by:

[tex]E(Y) = E(\pi X^2) = \pi E(X^2)[/tex]

[tex]E(X^2)[/tex] using the formula for the variance of X:

[tex]Var(X) = E(X^2) - [E(X)]^2[/tex]

Since X is uniformly distributed on [0, θ], we have:

[tex]E(X) = (0 + \theta)/2 = \theta/2[/tex]

[tex]Var(X) = [(\theta - 0)^2]/12 = \theta^{2/12}[/tex]

Solving for [tex]E(X^2)[/tex], we get:

[tex]E(X^2) = Var(X) + [E(X)]^2 = \theta^2/12 + (\theta/2)^2 = \theta^{2/3}[/tex]

Substituting this into the expression for E(Y), we get:

[tex]E(Y) = \pi E(X^2) = \pi (\theta ^{2/3}) = \pi \theta^{2/3}[/tex]

Variance of Y:

To find the variance of Y, we can use the formula for the variance of a function of a random variable:

[tex]Var(Y) = E(Y^2) - [E(Y)]^2[/tex]

We can find[tex]E(Y^2)[/tex] using the law of the unconscious statistician:

[tex]E(Y^2) = E[(\pi X^2)^2] = \pi^2E(X^4)[/tex]

To find [tex]E(X^4)[/tex], we can use the formula for the fourth moment of a uniform distribution:

[tex]E(X^4) = (\theta^4 + 2\theta^2)/5[/tex]

Substituting this into the expression for[tex]E(Y^2)[/tex], we get:

[tex]E(Y^2) = \pi^2E(X^4) = \pi^2[(\theta^4 + 2\theta^2)/5] = \pi^2\theta^{4/5} + 2\pi^2\theta^{2/5}[/tex]

Substituting this and the expression for E(Y) into the formula for the variance of Y, we get:

[tex]Var(Y) = E(Y^2) - [E(Y)]^2[/tex]

[tex]= \pi^2\theta^{4/5} + 2\pi^2\theta^{2/5} - (\pi\theta^2/3)^2[/tex]

[tex]= \pi^2\theta^4/45[/tex]

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Related Questions

what is f square plus g square i need the answer for my test!!​

Answers

The value of f square plus g square is 61.

How to find square of any number?

To find the square of a number, you can multiply that number by itself.

Write the number you want to square. Let's use the number "x" as an example.

Raise the number to the power of 2 by using the exponentiation operator (^) or by multiplying the number by itself. Either way, the result is the same. The expression to calculate the square of a number can be written as x² = x × x = x²

For example, to find the square of 5, you can multiply 5 by 5, which gives you 25.

So,the square of 5 is 25.

In mathematical notation, the square of a number "x" can be represented as "x²". So, the square of 5 can also be written as 5², which equals 25.

If f = 5 and g = 6, then f square (f²) is 5² = 25 and g square (g²) is 6² = 36. Therefore, f² + g² = 25 + 36 = 61. So, f square plus g square when f is 5 and g is 6 is 61.

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Correct question is "What is f square plus g square? Where f is equal to 5 and g is equal to 6."

What is the answer to this problem?

Answers

The area of the shaded area is 3.27 ft²

How to the area of the shaded area?

We can find the area of the shaded area by subtracting the area of the triangle from the area of the sector. That is;

Area of shaded area = Area of sector - area of triangle

Area of shaded area = (60/360 * π * 6²) - (1/2 * 6 * 6 * sin 60)

Area of shaded area = (60/360 * 22/7 * 36) - (1/2 * 36 * 0.866)

Area of shaded area = 3.27 ft²

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The pattern continues. Fill in the blanks.

2 x 4 + 1 = 3 x 3

3 x 5 + 1 = 4 x 4

4 x 6 + 1 = __ + __

__ x 7 + 1 = __ x __

__ x __ + __ = __ + __

Describe patterns that you see.

What will the equation look like when the first term is 25?

Answers

Based on the given pattern:

2 x 4 + 1 = 3 x 3

3 x 5 + 1 = 4 x 4

4 x 6 + 1 = __ + __

__ x 7 + 1 = __ x __

__ x __ + __ = __ + __

The general pattern is that the first term is multiplied by one more than itself, and then 1 is added to the result, which is equal to the second term squared.

When the first term is 25, the equation would look like:

25 x 26 + 1 = __ + __

The first blank would be filled with 26, and the second blank would be filled with 676 (which is 26 squared). So the complete equation would be:

25 x 26 + 1 = 26 + 676

8 students are enrolled in a competition. they all solve the same 8 qs. after correction, it can be seen that each problem has been correctly solved by exactly 5 students. show that there are 2 students who, together, have solved all the problems?

Answers

Let's label the 8 questions as Q1, Q2, Q3, Q4, Q5, Q6, Q7, and Q8.

Let's label the 8 students as A, B, C, D, E, F, G, and H.

Since each problem has been correctly solved by exactly 5 students, we can say that the following is true:

Q1: A, B, C, D, E

Q2

help would be absolutely appreciated

Answers

Thus, the given quadratic equation has two real roots x = 3 and x = -2.

Explain about the solution of quadratic function:

A function or mathematical statement of degree two is a quadratic function. This indicates that two is the function's highest power. The roots of all quadratic functions are two.

The quadratic formula is employed to solve a quadratic to discover its roots, which can either be distinct or the same. A quadratic function must first be converted into a quadratic equation by being made equal to zero in order to be solved.

Given equation:

x² - x - 6 = 0

Using the quadratic formula:

x = [-b ± √(b² - 4ac) ] / 2a

a = 1 , b = -1 and c = -6

x = [1 ± √((-1)² - 4*1*(-6) ] / 2*1

x = [1 ± √(1 + 24) ] / 2

x = [1 ± 5 ] / 2

Now,

x = (1 + 5)/2 = 3

x = (1 - 5)/ 2 = -2

Thus, the given quadratic equation has two real roots x = 3 and x = -2.

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complete question:

Check whether the given equation has, one solution, two solution ,many solution or no real solution.

x² - x - 6 = 0

state the name for this figure​

Answers

Answer:

square, quadrilateral, rhombus, parallelogram, rectangle



Answer:

Quadrilateral, rectangle, parallelogram, rhombus, square

Step-by-step explanation:

It is a quadrilateral bc it has four sides.

It is a rectangle bc it has four right angles.

It is a parallelogram bc it has two pairs of parallel sides.

It is a rhombus bc all four sides are congruent.

It is a square bc it is both a rectangle and a rhombus.

Select the GCF of these numbers. 48 and 60 22 ·3 2· 112 32 23 · 5 13· 193 ·232

Answers

The GCF of 48 and 60 is 12

To find the greatest common factor (GCF) of 48 and 60, we can start by finding the prime factorization of each number

48 = 2^4 × 3

60 = 2^2 × 3 × 5

Next, we can identify the common factors of both numbers by looking at their prime factorization

The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

The common factors of 48 and 60 are: 1, 2, 3, 4, 6, and 12.

The greatest common factor is the largest number that both 48 and 60 can be divided evenly by. In this case, that number is 12. Therefore, the GCF is 12.

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The given question is incomplete, the complete question is:

Find the GCF of 48 and 60.

The radius of a circle is 10 cm. Find its area in terms of π.

Answers

The area of a circle is given by the formula:

A = πr^2

where r is the radius of the circle.

Substituting the value of the radius as r = 10 cm, we get:

A = π(10)^2

A = 100π

Therefore, the area of the circle with radius 10 cm is 100π square centimeters.

~~~Harsha~~~

20. MP Use Math Tools Use the table at the right.
a. What is the approximate volume of the small truck?
b. The Davis family is moving, and they estimate that
they will need a truck with about 1,250 cubic feet.
Which truck would be best for them to rent?
c. About how many cubic feet greater is the volume
of the Mega Moving Truck than the 2-bedroom
moving truck?
2016-3-1002360
Inside Dimensions of Moving Trucks
Width
Length
(ft)
(ft)
Truck
Van
Small Truck
a.
2-Bedroom
Moving Truck
3-Bedroom
Moving Truck
10
Mega
Moving Truck
11-7/3
14/2
20
6-1/2
22/
Height
(ft)
7/7/2
7/7/2
Mlet
7/1/16
8
12
8

Answers

The approximate volume of the small truck is 577.5 cubic feet.

A truck that would be best for them to rent is the 3-Bedroom Moving Truck.

The volume of the Mega Moving Truck is about 641.25 cubic feet greater than the 2-bedroom moving truck.

How to calculate the volume of a rectangular prism?

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.

For the approximate volume of the small truck, we have;

Volume of small truck = 11 1/3 × 7 5/12 × 7

Volume of small truck = 577.5 cubic feet.

The approximate volume of each moving truck can be calculated as follows;

2-Bedroom Moving Truck = 14.5 × 7.5 × 7 = 761.25 cubic feet.

3-Bedroom Moving Truck = 21 × 7.5 × 8 = 1,260 cubic feet.

Mega Moving Truck = 22 × 7.5 × 8.5 = 1,402.5 cubic feet.

Difference = 1,402.5 cubic feet - 761.25 cubic feet

Difference = 641.25 cubic feet.

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an actuary determines the following regarding an individual auto policyholder: the probability that the auto policyholder will file a medical claim is 0.30. the probability that the auto policyholder will file a property claim is 0.42. the probability that the auto policyholder will file a medical claim or a property claim is 0.60. calculate the probability that the auto policyholder will file exactly one type of claim, given that the policyholder will not file both types of claims

Answers

The probability that the auto policyholder will file exactly one type of claim is 0.40.

How to calculate the probability?

To calculate the probability, let M be the event that the policyholder files a medical claim and P be the event that the policyholder files a property claim. We are given:

P(M) = 0.30

P(P) = 0.42

P(M or P) = 0.60

We want to calculate the probability that the policyholder files exactly one type of claim, given that the policyholder will not file both types of claims. This can be expressed as:

P(exactly one type of claim | not both types of claims) = P((M and not P) or (not M and P)) / P(not both types of claims)

We can use the fact that:

P(not both types of claims) = P(M or P) - P(M and P)

To calculate the numerator, we have:

P((M and not P) or (not M and P)) = P(M and not P) + P(not M and P)

We can use the fact that:

P(not P) = 1 - P(P)

To calculate:

P(M and not P) = P(M) - P(M and P)

Putting everything together, we get:

P(M and not P) = 0.30 - P(M and P) = 0.30 - (0.60 - 0.30) = 0.00

P(not M and P) = P(P) - P(M and P) = 0.42 - (0.60 - 0.30) = 0.12

P((M and not P) or (not M and P)) = 0.00 + 0.12 = 0.12

P(not both types of claims) = 0.60 - 0.30 = 0.30

Therefore:

P(exactly one type of claim | not both types of claims) = 0.12 / 0.30 = 0.40

So the probability that the auto policyholder will file exactly one type of claim, given that the policyholder will not file both types of claims, is 0.40.

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I need help with the reasons for this two column proof please

Answers

Hence, OC bisects AB, as congruent parts of congruent triangles are equal.

What is congruency in figures?

When two or more geometric figures are similar in size, form, and orientation, this is referred to as congruency in geometry. Two figures can be overlaid on one another by translation, rotation, and/or reflection when they are congruent because they are almost similar to one another and do not alter in size, form, or orientation.

For the given problem, the complete steps of proof with reasoning are:

(a) OC is perpendicular to AB in circle O (given). i.e ∠OCA and ∠OCB are right angles.

Reason: This is given in the problem statement. It establishes that OC forms a right angle with AB at point C in circle O. i

(b) Draw OA and OB (construction).

Reason: This is a construction step that introduces radii OA and OB from the center O of the circle to points A and B on the circle. This sets up the framework for the subsequent steps and establishes the positions of A and B in relation to the circle and the perpendicular OC.

(c) OA = OB (radii of the same circle are equal).

Reason: Radii of the same circle are always equal in length. This is a basic property of circles, where all radii have the same length, which can be stated as OA = OB based on the definition of a circle.

(d) OC = OC (Reflexive Property of Equality)

Reason: It is a property of line segments that they are equal to themselves. This is known as the Reflexive Property of Equality, which states that any quantity is equal to itself.

(f) AC = BC (common side of congruent triangles).

Reason: AC and BC are line segments that are both radii of the same circle, and OA = OB (Step c). Therefore, by the definition of congruent segments, AC = BC.

(e) Triangle ACO is congruent to triangle BCO (HL congruence criterion for right triangles).

Reason: Angle ACO and angle BCO are both right angles based on the given information that OC is perpendicular to AB (Step a). Also, AC = BC (Step d) and OA = OB (Step c). Therefore, by the Hypotenuse-Leg congruence criterion for right triangles, triangle ACO is congruent to triangle BCO.

(g) OC bisects AB (congruent parts of congruent triangles are equal).

Reason: Since triangle ACO is congruent to triangle BCO (Step e), the corresponding parts of congruent triangles are equal. In this case, OC is a common side (hypotenuse) of both triangles, and AB is a side of both triangles. Therefore, by the definition of a segment bisector, OC bisects AB.

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two shaded identical rectangular decorative tiles are first placed (one each) at the top and at the base of a door frame for a hobbit's house, as shown in figure 1. the distance from w to h is 45 inches. then the same two tiles are rearranged at the top and at the base of the door frame, as shown in figure 2. the distance from y to z is 37 inches. what is the height of the door frame, in inches?

Answers

The height of the door frame is approximately [tex]68.2 + 2t = 68.2 + 2\sqrt(131.2) \approx95.1[/tex]inches.

Basic geometry concepts.

Firstly, we need to recognize that the two identical rectangular tiles form a vertical rectangle in both figure 1 and figure 2.

Let's call the height of this rectangle "h" and the width "w".
In figure 1, we can see that the distance from the top of the rectangle to the top of the door frame is "h".

Similarly, the distance from the bottom of the rectangle to the bottom of the door frame is also "h".

Therefore, the height of the door frame is simply the sum of the height of the rectangle and the height of the two tiles.
Height of door frame = h + 2t
"t" is the height of one tile.
Next, we can use the same logic for figure 2.

The distance from the top of the rectangle to the top of the door frame is now "y".

Similarly, the distance from the bottom of the rectangle to the bottom of the door frame is "z".

Therefore, we can write:
[tex]Height of door frame = (h - t) + 2t[/tex]
Where (h - t) is the height of the rectangle above the tiles.
Now, we can equate the two expressions for the height of the door frame:
[tex]h + 2t = (h - t) + 2t[/tex]
Simplifying, we get:
h = 3t
We are given that the distance from w to h is 45 inches, so we can use Pythagoras' theorem to find the length of the rectangle:
[tex]w^2 + h^2 = 45^2[/tex]
Substituting h = 3t, we get:
[tex]w^2 + 9t^2 = 2025[/tex]
Similarly, we can use the information in figure 2 to get another equation:
[tex]w^2 + 4t^2 = 1369[/tex]
Now we have two equations with two variables (w and t), which we can solve simultaneously.

Subtracting the second equation from the first, we get:
[tex]5t^2 = 656[/tex]
Therefore,
[tex]t^2 = 131.2[/tex]
And
[tex]h = 3t = 3sqrt(131.2)[/tex][tex]\approx68.2 inches[/tex]
Finally, we can use the Pythagorean theorem again to find the length of the door frame:
[tex]w^2 + h^2 = 45^2[/tex]
Substituting h = 68.2, we get:
[tex]w^2 + 68.2^2 = 2025[/tex]
Solving for w, we get:
[tex]w \approx 41.2 inches[/tex]

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the scatterplot below shows the relationship between the grams of fat and total calories in different food items. the equation for the least-squares regression line to this data set is y with hat on top equals 13.198 x plus 153.6. what is the predicted number of total calories for a food item that contains 25 grams of fat?

Answers

The predicted total number of calories for a food containing 25 grams of fat is approximately 483.55. 

The equation for the least-squares regression line is:

z = 13.198x + 153.6

where ŷ= predicted value of y (total calories), x = value of the predictor variable (grams of fat), 13.198= slope of the line, and 153.6= y-intercept of the line.

To find the predicted total calories for a food with 25 grams of fat, simplify by substituting x = 25 into the equation.

z = 13.198x + 153.6

ŷ = 13.198(25) + 153.6

ŷ = 329.95 + 153.6

z = 483.55

Therefore, the predicted total number of calories for a food containing 25 grams of fat is approximately 483.55. 

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6 yd
11 cm
5 cm
11 m
12 yd
7m
6 yd
5 cm
4 cm
7m

Answers

The total surface area of the composite shapes are 69 square cm, 63 square cm and 108 square yd

Calculating the surface areas

The surface area of composite shapes can be found by breaking the composite shape down into simpler shapes and then finding the surface area of each individual shape.

Once the surface areas of all the individual shapes are found, they can be added together to find the total surface area of the composite shape.

Figure 1

Here, we have

Area = Area of rectangle + square

So, we have

Area = 5 * 5 + 4 * 11

Area = 69 square cm

Figure 2

Here, we have

Area = Area of  square + triangle

So, we have

Area = 7 * 7 + 1/2 * 7 * 4

Area = 63 square cm

Figure 3

Here, we have

Area = Area of rectangle + square

So, we have

Area = 12 * 6 + 6 * 6

Area = 108 square yd

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explain whether the mean or the median is amore appropriate measure of center for this data set?

Answers

The mean and median are both measures of center, but which one is more appropriate depends on the data set.

What is appropriate?

Appropriate behavior is behavior that is socially acceptable and respectful of others. This includes treating others with kindness, politeness, and respect, refraining from using offensive language, and not engaging in hurtful or violent behavior. Appropriate behavior also means following established rules, laws, and cultural norms. Examples of appropriate behavior include being honest and trustworthy, showing respect for others and their property, and being courteous and polite.

The mean is the average of the data set and is affected by extreme values. The median is the middle value in the data set and is not affected by extreme values. If the data set has extreme values, the median is usually the more appropriate measure of center. If the data set does not have extreme values, the mean is usually the more appropriate measure of center.

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Shannon and Leslie want to carpet is 16 1/2‘ x 16 1/2‘ square room. They cannot put carpet under the entertainment system that jets out. In square feet, what is the area of the space with no carpet?

Answers

The area of space with no carpet is 268.25 sq ft.

In order to calculate the area of square room we have to subtract the section that is not carpeted from the total area of the room.

The given dimensions of the room is 16 1/2‘ x 16 1/2‘ square room

therefore,

16.5 x 16.5 = 272.25 sq ft

now if we consider that the entertainment system is 2 feet in measurement then,

2 x 2 = 4 sq ft

hence, the space with no carpet is

271.25 - 4

= 268.25 sq feet

The area of space with no carpet is 268.25 sq ft.

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the average height of students at uh from an srs of 19 students gave a standard deviation of 3.2 feet. construct a 95% confidence interval for the standard deviation of the height of students at uh. assume normality for the data. a) (1.418, 10.732) b) (1.918, 5.732) c) (2.418, 4.732) d) (6.418, 11.732) e) (5.418, 9.732) f) none of the above

Answers

The 95% confidence interval for the standard deviation of the height of students at UH is (1.918, 5.732), which corresponds to option b.

To construct a 95% confidence interval for the standard deviation of the height of students at UH, we will use the Chi-square distribution. Given the sample standard deviation (s) of 3.2 feet, a sample size (n) of 19 students, and assuming normality for the data, we can find the confidence interval as follows:
1. Determine the degrees of freedom: df = n - 1 = 19 - 1 = 18
2. Identify the Chi-square values for the confidence level (95%): χ²_lower = 7.632, χ²_upper = 32.852 (using a Chi-square table or calculator)
3. Calculate the lower and upper bounds of the confidence interval:
Lower bound = sqrt((n - 1) * s² / χ²_upper) = sqrt(18 * (3.2)² / 32.852) ≈ 1.918
Upper bound = sqrt((n - 1) * s² / χ²_lower) = sqrt(18 * (3.2)² / 7.632) ≈ 5.732

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The 95% confidence interval for the standard deviation of the height of students at UH is approximately (1.918, 5.732), Option B.

Construct a 95% confidence interval for the standard deviation of the height of students at UH, we'll use the given data and the Chi-Square distribution.

Here's a step-by-step explanation:
SRS (simple random sample) of 19 students, which means the degrees of freedom (df) = n - 1 = 19 - 1 = 18.
The sample standard deviation (s) is given as 3.2 feet.
Assume normality for the data.
A 95% confidence interval, we'll use the Chi-Square distribution table to find the critical values.

The two tail probabilities are 0.025 and 0.975, so we'll look up the Chi-Square values for 18 degrees of freedom and these probabilities:
[tex]- X^2_{0.025} = 30.191 (upper limit)[/tex]
[tex]- X^2_{0.975} = 8.231 (lower limit)[/tex]
Calculate the confidence interval for the population standard deviation (σ):
[tex][tex](\sqrt((n - 1) \times s^2 / X^2_{upper}), \sqrt((n - 1) \times s^2 / X^2_{lower}))[/tex][/tex]
Plug in the values:
[tex]- n = 19[/tex]
[tex]- s = 3.2[/tex]
[tex]- df = 18[/tex]
[tex][tex]- X^{2} _{upper} = 30.191[/tex][/tex]
[tex][tex]- X^2_{lower} = 8.231[/tex][/tex]
Calculate the confidence interval:
[tex](√((18 \times 3.2^2) / 30.191), \sqrt((18 \times 3.2^2) / 8.231)) \approx (1.918, 5.732)[/tex]

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Question 9(Multiple Choice Worth 2 points)
(Creating Graphical Representations LC)

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 10(Multiple Choice Worth 2 points)
(Circle Graphs MC)

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 11(Multiple Choice Worth 2 points)
(Circle Graphs LC)

Chipwich Summer Camp surveyed 100 campers to determine which lake activity was their favorite. The results are given in the table.


Lake Activity Number of Campers
Kayaking 15
Wakeboarding 11
Windsurfing 7
Waterskiing 13
Paddleboarding 54


If a circle graph was constructed from the results, which lake activity has a central angle of 54°?
Kayaking
Wakeboarding
Waterskiing
Paddleboarding
Question 12(Multiple Choice Worth 2 points)
(Making Predictions MC)

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(Multiple Choice Worth 2 points)
(Making Predictions MC)

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 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

Answers

1) A histogram would be the best graphical representation for the teacher's data on the subject preferences of students. 2) The correct circle graph is option 2. 3) Option 4: Paddleboarding.

What is a histogram?

The frequency or relative frequency of the data points falling within each interval is depicted by the height of the bars in a histogram, which is a graphical representation of the distribution of continuous data. Histograms are frequently used in data analysis to show how a single variable is distributed and to spot any patterns or trends. Additionally, they can be used to compare the distributions of two or more variables or to spot anomalies or outliers in the data.

1) A histogram would be the best graphical representation for the teacher's data on the subject preferences of students.

2) Given the type of transportation we have he total number of visitors as:

(120+24+45+30+81=300)

Now, for walk we have:

120/300 = 40/100 = 40%

For Bicycle we have:

24/300 = 8%

Thus, the correct circle graph is option 2: 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

3) For the central angle to be 54 the number of campers needs to correspond to this number. The activity that corresponds to 54 degrees is Paddleboarding.

4) For the number of principals in conference we set up a proportionality with total people as follows:

We know that, 52 principals out of 70 people thus:

52/70 = x/750

Now,

x = (52/70) * 750

x = 557.14

Hence, we can predict that there were about 557 principals in attendance at the conference.

5) Given that, out of 225 students 27 prefer cookies thus,

27/225 = 0.12

That is 12% students like cookies.

Now, for the total number of students we have:

0.12 * 4000 = 480

Thus, option A: The college will have about 480 students who prefer cookies.

6) For the given description of the line plot the median is:

For Bus 47 = 16

For Bus 18 = 13

The faster bus is Bus 47, with a median of 16.

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Quadrilateral JKLM has vertices J(3,5), K(7,8), L(13,5), and M(13,0). Which statements are true? Select all that apply.

~a.) Line Segment KL ║ Line Segment JM
~b.) Line Segment KL ≅ Line Segment JM
~c.) Line Segment JK ≅ Line Segment LM
~d.) Line Segment JK ║ Line Segment LM
~e.) Quadrilateral JKLM is a trapezoid.
~f.) Quadrilateral JKLM is an isosceles trapezoid.

Answers

The statements that are true are:

→ Line Segment KL ≅ Line Segment JM

Quadrilateral JKLM is a trapezoid.

What is a trapezoid?

A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the non-parallel sides are called the legs.

According to the given information

In the quadrilateral JKLM

Using the distance formula, we can find the lengths of the line segments:

JK = √[(7-3)² + (8-5)²] = √58

KL = √[(13-7)² + (5-8)²] = √58

LM = √[(13-13)² + (0-5)²] = 5

JM = √[(13-3)² + (0-5)²] = √109

From this, we can analyze each statement:

a.) Line Segment KL ║ Line Segment JM

We can see from the sketch that the two line segments are not parallel. Therefore, statement a is false.

b.) Line Segment KL ≅ Line Segment JM

We found that the length of KL is equal to the length of JM. Therefore, statement b is true.

c.) Line Segment JK ≅ Line Segment LM

We can see from the sketch that the two line segments are not congruent. Therefore, statement c is false.

d.) Line Segment JK ║ Line Segment LM

We can see from the sketch that the two line segments are perpendicular. Therefore, statement d is false.

e.) Quadrilateral JKLM is a trapezoid.

A trapezoid is defined as a quadrilateral with at least one pair of parallel sides. We can see from the sketch that line segments KL and JM are not parallel, but line segments JK and LM are parallel. Therefore, statement e is true.

f.) Quadrilateral JKLM is an isosceles trapezoid.

An isosceles trapezoid is defined as a trapezoid with congruent base angles and congruent non-parallel sides. We can see from the sketch that neither the base angles nor the non-parallel sides are congruent. Therefore, statement f is false.

Therefore, the statements that are true are b and e.

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Answer:

A) KL⎯⎯⎯⎯⎯∥JM⎯⎯⎯⎯⎯

C) JK⎯⎯⎯⎯⎯≅LM⎯⎯⎯⎯⎯⎯

E) Quadrilateral JKLM is a trapezoid.

F) Quadrilateral JKLM is an isosceles trapezoid.

Step-by-step explanation:

These where the correct answer I got when taking the assignment with that question

Scientists measure a bacteria population and find that it is 10,000. Five days later, they
find that the population has doubled. Which function f could describe the bacteria
population d days after the scientists first measured it, assuming it grows exponentially?
A. f(d) 10,000. 2ª
B. f(d) = 10,000. (√2)ª
C. ƒ(d) = 10,000 • (-)ª
D. f(d) = 10,000.25d
=
S

Answers

Answer:

Hm

Step-by-step explanation:

The bacteria population is observed to double after five days, which means that its growth rate is 100% over a period of five days. This corresponds to a daily growth rate of r = 100%/5 = 20%.

If the initial population is 10,000, then the bacteria population after d days can be modeled by the exponential function:

f(d) = 10,000 * (1 + r/100)^d

Substituting r = 20% and simplifying, we get:

f(d) = 10,000 * (1.2)^d

Therefore, the correct option is:

D. f(d) = 10,000 * (1.2)^d

PLSSSS HELP IF YOU TURLY KNOW THISSS

Answers

1. Multiply both sides by 2. 4 + 3x = 5 * 2
2. Simplify. 4 + 3x = 10
3. Subtract 4 from both sides to single out x. 3x = 10 - 4
4. Simplify. 3x = 6
5. Divide by 3. x = 6/3
6. Simplify. x = 2

Input 2 into the original equation to check this answer and you will get 5 = 5 which means that x = 2 is your final answer.

Answer: x = 2

Step-by-step explanation:

    To solve for x, we will isolate the variable (x).

Given:

    [tex]\displaystyle \frac{4+3x}{2}=5[/tex]

Multiply both sides of the equation by 2:

    4 + 3x = 10

Subtract 4 from both sides of the equation:

    3x = 6

Divide both sides of the equation by 3:

    x = 2

Which of these expressions are equivalent to p/3

Answers

Answer:

B) 3p/9

D)1/3p

Step-by-step explanation:

we call a number a mountain number if its middle digit is larger than any other digit. for example, 284 is a mountain number. how many 3-digit mountain numbers are there?

Answers

If we consider a mountain number with its middle digit is larger than any other digit, then there are possible three-digit mountain numbers are equals the 240.

A number is called a 'mountain' if its decimal digits insitiate with 1, i.e. 'base camp', increase continuously to one largest digit, then decrease continuously back to one i.e. back to base camp. We have a number is called a mountain number. Now, there are 100 to 999 total 3-digit numbers. Now, with 2 in the middle, we have = 2 numbers[1 x 2] - 120 = 121

With 3 in the we have = 6 numbers[2 x 3] - 130, 131, 132, 230, 231, 232.......and so on.With 4 in the middle,we have = 12 numbers[3 x4]With 5 in the middle, we have = 20 numbers[4 x 5]With 6 in the middle, we have = 30 numbers[5 x 6]With 7 in the middle, we have = 42 numbers[6 x 7]With 8 in the middle, we have = 56 numbers[7 x 8]With 9 in the middle, we have = 72 numbers[8 x 9]

So, we have a total of Total Number = 2 + 6 + 12 + 20 + 30 + 42 + 56 + 72 = 240 "mountain numbers". Hence, the required number , value is 240.

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Need help with this!

Answers

Answer

Number 14: 7 faces, 15 edges, and 10 vertices.

Number 15: 10 faces, 24 edges, and 16 vertices.

Number 16: 7 faces, 12 edges, and 7 vertices.

:D

Step-by-step explanation:

A random sample of size is selected from a population with. A. What is the expected value of (to 2 decimals)? B. What is the standard error of (to 2 decimals)? C. Show the sampling distribution of (to 2 decimals). D. What does the sampling distribution of show? Blank

Answers

A) The expected value of the sampling distribution is 0.40.

B) The standard error is 0.05.

C) The sampling distribution will be centered around the population proportion of 0.40, with a spread given by the standard error of 0.05.

D) By examining the sampling distribution, we can see how likely it is to obtain a certain sample proportion by chance alone, and therefore make conclusions about the population based on the sample.

A) The expected value (also called the mean) of a sampling distribution is equal to the population parameter being estimated. In this case, the population parameter is the proportion, p, which is 0.40.

B) The standard error is the standard deviation of the sampling distribution. For a proportion, the formula for the standard error is √((p(1-p))/n), where p is the population proportion and n is the sample size. Plugging in the values given, we get √((0.40(1-0.40))/100) = 0.049.

C) The sampling distribution of a proportion is approximately normal if both np and n(1-p) are greater than or equal to 10. In this case, np = 1000.40 = 40 and n(1-p) = 100*0.60 = 60, so the conditions for normality are met.

D) The sampling distribution of a proportion shows the distribution of all possible sample proportions of a given size that could be drawn from a population with a known proportion.

The sampling distribution allows us to make inferences about the population proportion, such as constructing confidence intervals or conducting hypothesis tests.

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Complete Question:

A random sample of size 100 is selected from a population with p =0 .40.

A. What is the expected value (to 2 decimals)?

B. What is the standard error (to 2 decimals)?

C. Show the sampling distribution (to 2 decimals).

D. What does the sampling distribution of show?

PLEASE HELP!! 20 POINTS

Select the correct answer from each drop-down menu. Consider this equation. 1/x + 2/x+10 =1/3 Complete the statements to make them true. The least common denominator is . The equation will have valid solutions.

Answers

Answer: The least common denominator is 3x(x+10)

The equation will have 2 valid solutions

Step-by-step explanation: sorry if wrong

Shopping While shopping for clothes, Tracy spent $34 less than 3 times what Jaclyn spent. Tracy spent $26. Write and solve an equation to find how much Jaclyn spent. Let x represent how much Jaclyn spent. The equation that can be used to determine how much Jaclyn has spent is

Answers

Let x be the amount that Jaclyn spent on clothes.

According to the problem, Tracy spent $34 less than 3 times what Jaclyn spent, which can be expressed as:

3x - 34

And we also know that Tracy spent $26. So we can set up an equation:

3x - 34 = 26

To solve for x, we can add 34 to both sides of the equation:

3x = 60

And then divide both sides by 3:

x = 20

Therefore, Jaclyn spent $20 on clothes.

Approximately how much of the area under a standard curve is within one standard deviation of the mean?


99%


95%


68%


80%

Answers

Answer:

Approximately 68% of the area under a standard normal distribution curve is within one standard deviation of the mean, also known as the 68-95-99.7 rule.

Specifically, the rule states that:

Approximately 68% of the area under the curve falls within one standard deviation of the mean.Approximately 95% of the area under the curve falls within two standard deviations of the mean.Approximately 99.7% of the area under the curve falls within three standard deviations of the mean.

This means that if we have a normally distributed dataset with a mean of 0 and a standard deviation of 1, approximately 68% of the data points will fall within the range of -1 to +1 standard deviations from the mean.

The expression 0.9x represents the amount of pure copper sulfate in x liters of 90% copper sulfate solution.

a. Write an expression for the amount of pure copper sulfate in 3x liters of 25% copper sulfate solution.


b. A chemist added x liters of 90% copper sulfate solution to 3x liters of 25% copper sulfate solution. Use division to find the percentage of pure copper sulfate in the resulting solution.

The percentage of pure copper is
.

Answers

a) The expression for the amount of pure copper sulfate in 3x liters of 25% solution is  0.675x.

b) The percentage of pure copper sulfate in the resulting solution is 39.375%.

Percent compositionTo find the amount of pure copper sulfate in 3x liters of 25% copper sulfate solution, we can first calculate the amount of copper sulfate in the solution and then multiply by the percentage of pure copper sulfate.

Since the solution is 25% copper sulfate, we know that there are 0.25(3x) = 0.75x liters of copper sulfate in the solution.

The amount of pure copper sulfate in the solution is given by 0.9 times the amount of copper sulfate. Therefore, the expression for the amount of pure copper sulfate in 3x liters of 25% copper sulfate solution is:

0.9(0.75x) = 0.675x

To find the percentage of pure copper sulfate in the resulting solution, we need to calculate the total amount of pure copper sulfate in the solution and divide by the total volume of the solution.

The amount of pure copper sulfate added from the 90% copper sulfate solution is 0.9x liters.

The amount of pure copper sulfate in the 25% copper sulfate solution is 0.675x liters.

The total amount of pure copper sulfate in the resulting solution is:

0.9x + 0.675x = 1.575x

The total volume of the resulting solution is:

x + 3x = 4x

To find the percentage of pure copper sulfate in the resulting solution, we divide the amount of pure copper sulfate by the total volume of the solution and multiply by 100:

(1.575x / 4x) * 100 = 39.375%

Therefore, the percentage of pure copper sulfate in the resulting solution is 39.375%.

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Given that £1 = $1.62
a) How much is £650 in $?
b) How much is $405 in £?

Answers

Answer:

a 1053

b 250

multiply 650 by 1.62 for part a.

for part b divide by 1.62 since pound is less than dollar

hope this helps :)

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