A cone is shown below.

Which 2-dimensional shape results from slicing a cross section horizontally and parallel to the base.


A. rectangle


B. trapezoid


C. square


D. rhombus


E. ellipse


F. circle

The standard deviation of the sample mean weight will decrease by a factor of √2, so the answer is C) It will decrease by a factor of 2. The mean of the sample mean weight will remain unchanged, so the answer is E) It will remain unchanged. It is a correct statement, and it is a result of the Central Limit Theorem, so the answer is C) It is a correct statement, and it is a result of the Central Limit Theorem.

When the sample size is doubled, the standard deviation of the sample mean weight decreases by a factor of √2 according to the formula σ/√n, where σ is the standard deviation of the population and n is the sample size. So, The correct answer is C).

The mean of the sample mean weight is an unbiased estimator of the population mean and is not affected by the sample size. Therefore, doubling the sample size will not change the mean of the sample mean weight.  So, The correct answer is E).

The Central Limit Theorem states that the distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the underlying distribution of the population. Therefore, the statement is correct and a result of the Central Limit Theorem.  So, The correct answer is C).

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The steps for each expression here is

a.

Step 1: (x)-2

Step 2: 9-2

Step 3: 7

b.

Step 1: 3(y)+2

Step 2: 3*7+2

Step 3: 23

c.

Step 1: 8+((r)/6)

Step 2: 8+(24/6)

Step 3: 12

What is meant by expression?

An expression is a representation of a mathematical equation, logical statement, or string of characters using symbols, numbers, and operators. It can be evaluated to produce a value or result. In programming, expressions can be used to assign values to variables, perform mathematical operations, or compare values. They are an essential part of most programming languages and play a crucial role in the execution of computer programs.

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Answer: If there are 60 questions and the student has to answer 75% of questions then the number of questions the student must answer is 45

Step-by-step explanation:

No of questions= 60,

Answers to be given= 75%

then no of questions to pass the exam= No of questions*Answers to be given in percentage

=60*75/100\

=45

Answer:

Step-by-step explanation:

slope (m) =0

point =(x, y)

         =(3, -4)

equation:

(y-y1) =m(x-x1)

{y-(-4)} =0

y+4 =0

y =-4

Explanation:

as we know, the equation to find the slope of a line is (y-y1) =m(x-x1). here, it is given that the slope of the line (m) is 0 and it passes through points 3 and -4. therefore, we can conclude that equation (y) would be 0 by calculating.

The remainder when p(x) = x^4 - 4x³ - 11x² + 66x - 72 is divided by x - 4 is given as follows:

16.

The Remainder Theorem is a theorem in algebra that provides a quick way to find the remainder of a polynomial division problem. The theorem states that when a polynomial f(x) is divided by (x - a), the remainder is equal to f(a).

Hence for this problem, the remainder is given by the numeric value at x = 4, which is calculated as follows:

p(4) = 4^4 - 4(4)³ - 11(4)² + 66(4) - 72

p(4) = 16.

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Answer:

50/100 or 1/2 or 50%

Step-by-step explanation:

total =  30 + 20 + 50 = 100

the probability of choosing a marble that is not blue is equal to the total minus all marbles that are blue therefore 100-30-20=50 therefore the probability is 50/100 or 1/2 or 50%

The annual interest rate of the account is 3.5%

The formula for simple interest is:

I = Prt

where I is the interest earned, P is the principal (initial amount deposited), r is the annual interest rate (as a decimal), and t is the time in years.

We know that P = £13,000, t = 15 years, and I = £19,825 - £13,000 = £6,825.

Plugging in these values, we get:

£6,825 = £13,000 * r * 15

Simplifying this equation, we get:

r = £6,825 / (£13,000 * 15) = 0.035 = 3.5%

Therefore, the annual interest rate of the account is 3.5% to 1 decimal place.

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The statement that is true is:

The probability that a randomly selected player on Team C is 10 years old is 5/16.

Option A is the correct answer.

We have,

The probability that a randomly selected player on Team C is 10 years old.

= Number of 10 years old players in Team C / Total players in Team C

= 5./16

The probability that a randomly selected player on Team A is 8 years old.

= Number of 8 years old players in Team A / Total players in Team A

= 4/15

The probability that a randomly selected 8-year-old player is on Team C.

= Number of 8 years old players in Team C / Total  8 years old players

= 8/21

The probability that a randomly selected 10-year-old player is on Team B.

= Number of 10 years old players in Team C / Total 10 years old players

= 5/14

Thus,

The probability that a randomly selected player on Team C is 10 years old is 5/16.

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Answer:

2

Step-by-step explanation:

45°-45°-90° triangles are Special Right Triangles. There are some super helpful shortcuts you can learn for a 45°-45°-90° triangle.

The two legs of the triangle are always the same. The longest side, the hypotenuse, is:

hypot = leg•sqrt2

The leg in your problem is sqrt2.

You are asked to find the hypotenuse, k.

hypot = leg•sqrt2

k = leg•sqrt2

k = sqrt2•sqrt2

k = 2

k is 2. Don't be sidetracked by the direction that says "Write your answer in simplest radical form". If there was a radical in your answer, we would simplify it, but there isn't...it's just plain 2.

Answer:

2(5)(5) + 4(5)(10) = 50 + 200 =

250 square centimeters

The equation of the circle passing through (6,1) and having a centre at (2,-3) is (x - 2)² + (y + 3)² = 32.

Explain the term centre

A centre is a point or location that is at the middle or heart of something. It can refer to the physical centre of an object or the conceptual centre of an idea or system. Centres can be used as reference points for measurements, calculations, or decision-making processes.

According to the given information

Here we can use the distance formula:

√((x - 2)² + (y + 3)²) = r

We also know that the circle passes through the point (6, 1). Substituting these coordinates into the equation above, we get:

√((6 - 2)² + (1 + 3)²) = r

√(16 + 16) = r

r = 4√(2)

Now we can use the centre and radius to write the equation of the circle in standard form:

(x - 2)² + (y + 3)² = (4√(2))²

(x - 2)² + (y + 3)² = 32

Therefore, the equation of the circle passing through (6,1) and having a centre at (2,-3) is (x - 2)² + (y + 3)² = 32.

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The first step is to determine the value for c. We know that the joint probability mass function must sum to 1 over all possible values of X and Y. So, we can write:

∑∑ [tex]f_{xy}[/tex](x,y) = 1

Substituting the given function [tex]f_{xy}[/tex](x,y) = c(x + y) for each combination of x and y, we have:

c(1+1) + c(1+2) + c(1+3) + c(2+1) + c(2+2) + c(2+3) + c(3+1) + c(3+2) + c(3+3) = 1

Simplifying this equation, we get:

12c = 1

Therefore, the value of c is 1/12

Now, we can use this value to calculate the covariance between X and Y. The covariance measures the degree to which two random variables vary together. It is defined as

cov(X,Y) = E[XY] - E[X]E[Y]

where E[XY] is the expected value of the product of X and Y, and E[X] and E[Y] are the expected values of X and Y, respectively.

To calculate E[XY], we use the joint probability mass function:

E[XY] = ∑∑ xy [tex]f_{xy}[/tex](x,y)

Substituting the given function [tex]f_{xy}[/tex](x,y) = c(x + y) for each combination of x and y, we have,

E[XY] = c(1+1) + 2c(1+2+2+3) + 3c(1+3+3+2)

Simplifying this equation, we get,

E[XY] = 28/12

To calculate E[X] and E[Y], we use the marginal probability mass functions:

fx(x) = ∑y [tex]f_{xy}[/tex](x,y)

fy(y) = ∑x [tex]f_{xy}[/tex](x,y)

Substituting the given function [tex]f_{xy}[/tex](x,y) = c(x + y) for each combination of x and y, we have:

fx₁ = 2c

fx₂ = 4c

fx₃ = 6c

fy₁ = 2c

fy₂ = 4c

fy₃= 6c

Using these marginal probability mass functions, we can calculate E[X] and E[Y]:

E[X] = ∑x x fx(x) = 2c + 8c + 18c = 28/12

E[Y] = ∑y y fy(y) = 2c + 8c + 18c = 28/12

Therefore, the covariance between X and Y is:

cov(X,Y) = E[XY] - E[X]E[Y] = 28/12 - (28/12)(28/12) = -4/144

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Answer:

1 crown and 1 coin

Step-by-step explanation:

1 crown =10 cents

1 coin = 25 cents

10 +25 = 35

The solution to the given problem of the triangle comes out to be AC are 20 units long.

If a polygon contains at least one more segment, it is a hexagon. It is a simple rectangle in shape. Anything identical to a standard triangle form can only be distinguished from it by edges across A and B. Euclidean geometry does not completely describe the cube, despite the fact that its edges are all collinear. A triangle is formed by a circle with five sides and three angles.

Here,

If DE is the midpoint of triangle ABC, DE is parallel to AC and has a length of 50% of AC.

Let's use "x" units to represent the length of AC.

Given the information, DE equals 10 units, or 50 percent of AC's length. So that we may create the equation:

=>  DE = AC/2

When we enter DE's value as 10 units, we get:

=> 10 = x/2

To separate x, we multiply both sides of the equation by 2 and obtain:

=> 2 * 10 = x

=> x = 20

Therefore, AC is 20 units long.

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Based on the given information, the correct statement is: The area of the rectangle is twice the area of the shaded triangle.

The shaded triangle is a part of the rectangle, as indicated by the given dimensions of 10 in. and 4 in. The shaded triangle is formed by one of the shorter sides of the rectangle and a diagonal line connecting the opposite corner of the rectangle to the midpoint of that shorter side.

Since the area of the rectangle is given by the formula length × width, the area of the rectangle is 10 in. × 4 in. = 40 square inches.

On the other hand, the area of the shaded triangle is given by the formula 1/2 × base × height, where the base is the length of the shorter side of the rectangle (4 in.) and the height is the length of the longer side of the rectangle (10 in.) divided by 2, since the triangle only occupies half of the height of the rectangle.

So, the area of the shaded triangle is 1/2 × 4 in. × (10 in./2) = 1/2 × 4 in. × 5 in. = 10 square inches.

Comparing the area of the rectangle (40 square inches) to the area of the shaded triangle (10 square inches), we can see that the area of the rectangle is indeed twice the area of the shaded triangle. Therefore, the correct statement is "The area of the rectangle is twice the area of the shaded triangle."

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The correct answer is (a) a = 0, b = two-thirds, c = 3.

This can be seen by comparing the given equation, y = two-thirds x squared + 3, to the general form of a quadratic equation, y = ax^2 + bx + c.

In the given equation, the coefficient of x^2 is two-thirds, so a = two-thirds. The coefficient of x is 0, so b = 0. And the constant term is 3, so c = 3.

Therefore, the correct answer is (a) a = 0, b = two-thirds, c = 3.

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if the player in question scored 13.7 points per game with 4.1 free throw attempts per game, his performance is slightly below what the model predicts.

How to solve the question?

To compare the player's performance to what the model predicts, we need to know the factors that the model considers when making predictions. Depending on the complexity of the model, it may take into account a variety of factors, such as the player's position, age, height, weight, shooting percentage, and team performance.

Assuming that we have a relatively simple model that takes into account the player's shooting percentage and free throw attempts, we can make a rough estimate of how the player's performance compares to what the model predicts.

Let's say that the model predicts that a player with a shooting percentage of 50% and 4 free throw attempts per game would score an average of 15 points per game. If the player in question has a shooting percentage of 45%, we can adjust the prediction accordingly. Using a simple linear regression, we can estimate that the player's expected points per game would be:

Expected points per game = 15 - (50 - 45) * 0.2 = 14

So if the player in question scored 13.7 points per game with 4.1 free throw attempts per game, his performance is slightly below what the model predicts. However, it's important to note that this is just a rough estimate based on a simple model, and there may be many other factors that could affect the player's performance, such as injuries, fatigue, or changes in the team's strategy. Therefore, we should not rely solely on statistical models to evaluate a player's performance, but also consider other factors such as the player's overall contribution to the team and their ability to make key plays in crucial moments.

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Approximately 304,657,600 Americans were there in July 2009 based on the estimated 2008 growth rate of 0.88%.

To find the approximate US population in July 2009, we need to apply the growth rate of 0.88% to the initial population in July 2008.

Convert the growth rate from percentage to decimal:

0.88% = 0.0088
Calculate the number of people added to the population in 2008: 302,000,000 * 0.0088 = 2,657,600
Add this number to the initial population to find the population in July 2009:

302,000,000 + 2,657,600 = 304,657,600.

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the condition for a function's graph to pass through the origin in polar coordinates is that the function's value at θ=0 is equal to zero, while the condition for a function's graph to pass through the origin in rectangular coordinates is that the function's value at (0,0) is equal to zero.

How to solve the question?

In polar coordinates, a graph of a function passes through the origin if and only if the function's value at θ=0 is equal to zero. This is because the origin in polar coordinates represents the point (r=0, θ), where r is the distance from the origin and θ is the angle of the point with respect to the positive x-axis. When a function's value at θ=0 is equal to zero, it means that the point on the graph at θ=0 lies on the positive x-axis and has a distance of r=0 from the origin, which is the origin itself.

In contrast, a graph of a function in rectangular coordinates passes through the origin if and only if the function's value at (0,0) is equal to zero. This is because the origin in rectangular coordinates represents the point where the x and y axes intersect, and a point on the graph with coordinates (x,y) passes through the origin if and only if x=0 and y=0, which means the function's value at (0,0) is equal to zero.

In summary, the condition for a function's graph to pass through the origin in polar coordinates is that the function's value at θ=0 is equal to zero, while the condition for a function's graph to pass through the origin in rectangular coordinates is that the function's value at (0,0) is equal to zero.

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The statement "Luby's MIS algorithm is likely to finish in O(log n) parallel steps, where n is the number of vertices." is true because a vertex selecting each group is equal.

An independent set in a graph is a set of vertices that do not share any edges.

The algorithm starts by having each vertex randomly assign itself to one of two groups. The processors then communicate with each other to identify vertices that belong to a group with no neighbors in the same group. These vertices are then marked as part of the MIS.

In each round of communication, the number of vertices in the MIS doubles. This means that the algorithm will converge in O(log n) parallel steps, where n is the number of vertices in the graph.

The complexity of the algorithm is therefore very efficient, and it can handle large graphs with many vertices.

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As a result, the value of x in the equation is zero. option b is correct no solution.

To find x, we will first simplify both sides of the equation by spreading the coefficients as follows:

5/7 * (x + 2) - 3/7x = 2/7(x + 5)

5/7x + 10/7 - 3/7x = 2/7x + 10/7

Then, on each side of the equation, we'll combine like terms:

(5/7x - 3/7x - 2/7x) + 10/7 = 10/7

To simplify the coefficients even further, we have:

(10/7x) + 10/7 = 10/7

Subtraction of 10/7 from either side:

10/7x = 0

Finally, by multiplying both sides by the reciprocal of 10/7, we may find x:

x = 0 * 7/10

x = 0

As a result, the value of x in the equation is zero. option b is correct no solution.

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Katie's claim can be represented by the equation: a² ¢= 4(1/2ab) + b²

Katie's claim can be represented by the equation:

Outer square area = Sum of areas of four triangles + Inner square area or mathematically, a² = 4(1/2ab) + b²

where "a" and "b" are the lengths of the legs of the right triangle and "a²" represents the area of the outer square, while "b²" represents the area of the inner square.

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Answer:

24 points

Step-by-step explanation:

Maria scored a total of 6 points, and Suzanne scored 4 times as many.

something times as many, means to multiply, so 6 x 4=24 points total

Answer:

0.2 oz

Step-by-step explanation:

We Know

1g ≈ 0.035oz

5 gram = ? oz

We Take

0.035 x 5 ≈ 0.175 oz

So, 5 grams ≈ 0.2 oz

The expected length of a staff meeting is approximately 12.5 minutes.

what is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

To calculate the expected length of a staff meeting, we need to find the mean of the probability density function given.

The formula for finding the expected value or mean of a continuous random variable with probability density function f(x) is:

E(X) = ∫ x f(x) dx over the range of the variable

Using this formula, we can find the expected length of a staff meeting as follows:

E(X) = ∫ x f(x) dx over the range of the variable

  = ∫ 0 to 1 x [tex]5(x-0.5)^{5}[/tex] dx  (since the length of a meeting can't be negative)

  = 5 ∫ 0 to 1 x[tex](x-0.5)^{5}[/tex] dx

Now we can use integration by parts or substitution to solve the integral. For simplicity, we can use substitution, with u = x - 0.5 and du = dx:

E(X) = 5 ∫ -0.5 to 0.5[tex]5(x-0.5)(u)^{5}[/tex] du

= 5 ∫ -0.5 to 0.5 [tex](u^6 + 0.5u^5)[/tex] du

= 5 [(1/7)[tex]u^7\\[/tex] + (1/10)[tex]u^6[/tex]] evaluated at -0.5 and 0.5

= 5 [(1/7)[tex](0.5)^7[/tex] + (1/10)[tex](0.5)^6[/tex] - (1/7)[tex](-0.5)^7[/tex] - (1/10)[tex](-0.5)^7[/tex]]

≈ 0.2083 hours or 12.5 minutes

Therefore, the expected length of a staff meeting is approximately 12.5 minutes.

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Answer: y = 3.75x + 2.50

Step-by-step explanation:

The equation that can be used to find y, the total cost of renting a bike, if x represents the number of hours Violet rents the bike is:

y = 3.75x + 2.50

Explanation:

Violet pays an initial fee of $2.50, which is a fixed cost that does not depend on the number of hours she rents the bike. Additionally, she pays $3.75 per hour she rents the bike, which is a variable cost that depends on the number of hours. Therefore, the total cost of renting a bike (y) can be expressed as the sum of the fixed cost ($2.50) and the variable cost ($3.75x), which gives the equation:

The exact amount of copper foil covering the steeple is 720√3 square meters.

The lateral area of the prism is given as 2400 m². We know that the lateral area of a prism is given by the formula:

Lateral area = perimeter of base x height of the prism

Let's denote the side length of the hexagonal base by s. The perimeter of the base is then 6s, and the height of the prism is 100 m. Using the given lateral area, we can solve for s:

2400 = 6s x 100

s = 4 x √15

The base area of the steeple is the same as the base area of the prism, which is given by:

Base area = (3 x √3 x s²) / 2

The steeple is composed of equilateral triangles, so each face of the steeple is an equilateral triangle with side lengths. The area of an equilateral triangle is given by the formula:

Area = (√3 * s²) / 4

The total surface area of the steeple is the sum of the areas of its faces. There are six faces, so the total surface area is:

Total surface area = 6 x Area

Total surface area = 6 x (√3 x s²) / 4

Total surface area = (3 x √3 x s²) / 2

Substituting the value of s we found earlier, we get:

Total surface area = (3 x √3 x (4 x √15)²) / 2

Total surface area = 720 x √3

Therefore, the exact amount of copper foil covering the steeple is 720√3 square meters.

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