Find the area of the shaded Sector
A. 8pi
B. 6pi
C. 16pi
D. 4pi

The kinetic energy of the roller coaster at the bottom of the hill is approximately 594,576 J.

The potential energy of the roller coaster at the top of the hill can be calculated as:

PE = mgh

where m is the mass of the car and its passengers, g is the acceleration due to gravity \((9.8 m/s^2\)), and h is the height of the hill (62 m). Thus, we have:

PE =\((1088 kg)(9.8 m/s^2)(62 m) = 670,720 J\)

At the bottom of the hill, all of the potential energy has been converted to kinetic energy. The kinetic energy of the roller coaster can be calculated as:

\(KE = (1/2)mv^2\)

where v is the speed of the roller coaster at the bottom of the hill. Thus, we have:

\(KE = (1/2)(1088 kg)(33 m/s)^2 = 594,576 J\)

Therefore, the kinetic energy of the roller coaster at the bottom of the hill is approximately 594,576 J.

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Answer:

2x-42=64

Step-by-step explanation:

An equation that matches the table include the following: y = x + 5.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (6 - 5)/(1 - 0)

Slope (m) = 1/1

Slope (m) = 1.

At data point (0, 5) and a slope of 1/, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = 1(x - 0)

y - 5 = x

y = x + 5

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the answer should be 21

I hope that's the right answer I really wouldn't rely on me but hope that helps

Answer:

30

Step-by-step explanation:

The annual growth rate in population of 1.2% means that the population is increasing by 1.2% of the current population each year. To find the time it will take for the population to reach 10 billion, we need to use the following formula:P(t) = P0 × (1 + r)^twhere P0 is the initial population, r is the annual growth rate, t is the time (in years), and P(t) is the population after t years.

We can use this formula to solve the problem as follows: Let \(P0 = 7.6 billion, r = 0.012 (since 1.2% = 0.012)\), and P(t) = 10 billion. Plugging these values into the formula, we get: 10 billion = 7.6 billion × (1 + 0.012)^t Simplifying the right side of the equation, we get:10 billion = 7.6 billion × 1.012^tDividing both sides by 7.6 billion, we get:1.3158 = 1.012^tTaking the natural logarithm of both sides,

we get:ln\((1.3158) = ln(1.012^t)\) Using the property of logarithms that ln \((a^b) = b ln(a)\), we can simplify the right side of the equation as follows:ln(1.3158) = t ln(1.012)Dividing both sides by ln(1.012), we get:t = ln(1.3158) / ln(1.012)Using a calculator to evaluate the right side of the equation, we get:t ≈ 36.8Therefore, it will take about 36.8 years for the world's population to reach 10 billion at an annual growth rate of 1.2%.

In conclusion, It will take approximately 36.8 years for the world's population to reach 10 billion at an annual growth rate of 1.2%. The calculation was done using the formula P(t) = P0 × (1 + r)^t, where P0 is the initial population, r is the annual growth rate, t is the time (in years), and P(t) is the population after t years.

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Answer: It is not a right triangle as it has no right angles in it but it is a parallelogram.

Answer:

10.

A = 12² - 2(6×5)

A = 144 - 2×30

A = 144 - 60

A = 84 in²

11.

A = π(12/2)² - (π3² + 3×6)

A = π36 - (π9 + 18)

A = π36 - (π3² + 18)

A = 113.04 - (28.26 + 18)

A = 66.8 yd²

12.

A = 9² - (10×2 + π3²)

A = 81 - (20 + 28.26)

A = 81 - 48.26

A = 32.7 m²

y = -1/3x + 1

y = -2x - 3

We can compare the equations to the graphs and see which graph represents the intersection point of the two equations.

The first equation, y = -1/3x + 1, has a negative slope (-1/3) and a y-intercept of 1.

The second equation, y = -2x - 3, also has a negative slope (-2) and a y-intercept of -3.

Based on the slopes and y-intercepts, we can identify the correct graph by finding the point where the two lines intersect.

Unfortunately, since the graphs are not provided, I am unable to determine which specific graph shows the solution to the system of linear equations. I recommend referring to the graph representation of the equations and identifying the intersection point to determine the correct graph.

Answer:

y=2x+16

Step-by-step explanation:

Answer:

y=2x+16 is the correct answer

Answer:

The volume of the hemisphere  

       V = 121.33086 cubic centimeter

Step-by-step explanation:

Step(i):-

Given that the total surface area of a hemisphere = 45π cm²

The total surface area of a hemisphere = 3π r²

Equating

              3π r² = 45π

                   \(r^{2} = \frac{45}{3} =15\)

                    r = \(\sqrt{15} = 3.87\)

The radius of the sphere 'r' = 3.87

Step(ii):-

The volume of the hemisphere

                 \(V = \frac{2}{3} \pi r^{3}\)

                \(V = \frac{2}{3} \pi (3.87)^{3}\)

we know that   π = 3.14

                \(V = \frac{2}{3} (3.14) (3.87)^{3}\)

               V = 121.33086 cubic centimeter

Answer:

\(\frac{29}{72}\)

Step-by-step explanation:

There are 360° in one complete rotation , thus angle turns

fraction = \(\frac{145}{360}\) ( divide numerator and denominator by 5 )

             = \(\frac{29}{72}\) ← in simpest form

Answer:

The correct answer would be $126.00

Step-by-step explanation:

If you see how many times 40% goes into 100%, it would be 2.5 times. Then you multiply the 40% of the overall price ($50.40) times 2.5 and that gives you $126.

Hope this helps!!

Answer:

Annalise is correct because the outputs are closest when x = 1.35

Step-by-step explanation:

The solution to the equation 1/(x-1) = x² + 1 means the one x value that will make both sides equal. If we look at the table, notice how when x = 1.35, f(x) values are closest to each other for both equations, signifying that x = 1.35 is approximately the solution. Thus, Annalise is correct.

D, divide and figure out how much the picture is increasing lengthwise and use that to find the wideness

The dimension of the enlarge picture will be 150 inches (3.81 meters) wide and 180 inches (4.57 meters) long. Then the correct option is D.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

There is no effect of dilation on the angle.

A photograph measures 5 inches (0.13 meters) wide and 6 inches (0.15 meters) long.

The picture is enlarged to fit on a wall.

If the new larger picture is 150 inches (3.81 meters) wide.

Then the scale factor of the enlargement will be

Scale factor = 150 / 5

Scale factor = 30

Then the length of the picture will be

The length of the picture is given by the product of the scale factor and original length.

Length = 30 x 6

Length = 180 inches (4.57 meters)

Then the dimension of the enlarge picture will be 150 inches (3.81 meters) wide and 180 inches (4.57 meters) long.

Then the correct option is D.

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There are two correct statements regarding a 5 by 5 matrix with three eigenvalues, one of which has a three-dimensional eigenspace.

First, there must be at least two linearly independent eigenvectors associated with the eigenvalue that has a three-dimensional eigenspace. Second, the sum of the dimensions of the eigenspaces must be equal to the size of the matrix, which is 5 in this case.

To understand the first statement, recall that the dimension of an eigenspace is equal to the multiplicity of the associated eigenvalue, which is the number of times it appears as a root of the characteristic equation. Since one of the eigenvalues has a three-dimensional eigenspace, its multiplicity must be at least 3. This means there are at least 3 linearly independent eigenvectors associated with this eigenvalue, which is necessary to span a three-dimensional space. However, the sum of the multiplicities of all eigenvalues cannot exceed the size of the matrix, which is 5. Therefore, the remaining two eigenvalues must have a combined multiplicity of 2 at most, which implies that there are at most 2 linearly independent eigenvectors associated with each of them.

To understand the second statement, note that the sum of the dimensions of the eigenspaces is equal to the sum of the multiplicities of all eigenvalues. This follows from the fact that the eigenspaces associated with distinct eigenvalues are linearly independent. Since there are three distinct eigenvalues in this case, the sum of their multiplicities is at most 5, which means the sum of the dimensions of their eigenspaces is also at most 5. Since one of the eigenspaces has dimension 3, the sum of the dimensions of the other two eigenspaces must be at least 2, which means each of them has at least one linearly independent eigenvector.

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For a sample of adults from country A, related to their unconfident that the food they eat in country A is safe, the point estimate of population proportions p and q are equals 0.202 and 0.798 respectively.

One sample proportion test is conducted to check whether the population proportion (P) shows a significant difference from the hypothesized value (p)or not. Sample proportion

\((\hat p)\) can be defined as the ratio of number of successes in the sample and the size of the sample. We have a sample survey of 1562 adults from country A, in which, 316 were not confident that the food they eat in country A is safe.

So, Sample size (n)= 1562

The number of successes (x) = 316

Let's consider X be the number of adults that were not confident with the food that they eat in country A is safe. The point estimate of the population proportion (p) is written as below,

\(\hat p=\frac{x}{n}\) \( = \frac{316}{1562}\)

= 0.2023047

≈ 0.202

Therefore, the point estimate of the population proportion is 0.202. The point estimate for q is \(\hat q = 1 - \hat p\) = 1 -0.202

= 0.797695 ≈ 0.798

Therefore, the point estimate for q is 0.798.

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For a sample of adults from country A, related to their unconfident that the food they eat in country A is safe, the point estimate of population proportions p and q are equals 0.202 and 0.798 respectively.

One sample proportion test is conducted to check whether the population proportion (P) shows a significant difference from the hypothesized value (p)or not. Sample proportion

can be defined as the ratio of number of successes in the sample and the size of the sample. We have a sample survey of 1562 adults from country A, in which, 316 were not confident that the food they eat in country A is safe.

So, Sample size (n)= 1562

The number of successes (x) = 316

Let's consider X be the number of adults that were not confident with the food that they eat in country A is safe. The point estimate of the population proportion (p) is written as below,

= 0.2023047

≈ 0.202

Therefore, the point estimate of the population proportion is 0.202. The point estimate for q is  = 1 -0.202

= 0.797695 ≈ 0.798

Therefore, the point estimate for q is 0.798.

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The difference between one cycle and the period of a sine curve is that the period represents the length of one complete cycle, while one cycle refers to the interval between two consecutive points where the curve starts and ends at the same position and direction.

The period of a sine curve refers to the length of one complete cycle of the curve. In other words, it is the distance between two consecutive points where the curve repeats itself. The period is usually denoted by the symbol T.

On the other hand, one cycle of a sine curve refers to the interval between two consecutive points where the curve starts and ends at the same position and direction. It represents the complete oscillation of the curve from its minimum value to its maximum value and back to its minimum value. One cycle is equivalent to one full revolution or rotation of the sine curve.

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Answer: I do not have enough information to solve this equation

Step-by-step explanation:

I do not have enough information to solve this equation

Answer:

180 - 90 - 41 = 49

Step-by-step explanation:

Have a great day :)

Answer: 49

Step-by-step explanation:

90 + 41 + G = 180

131 + G = 180

G = 49

1.When all the three cut outs of the angles A, B, C placed adjacent to each other at a point, then it forms a line forming a straight angle, i.e. 180°.

Flence, it is proved that the sum of the three angles of a triangle is 180°.

Therefore, ∠A + ∠B + ∠C =180

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To construct the matrix P that represents the orthogonal projection onto the subspace W spanned by the orthonormal basis β = {x1, ..., xk} in R^n, we can use the formula:

P = X (X^T X)^(-1) X^T

Here, X is the matrix with columns x1, ..., xk. The matrix P will have dimensions n x n.

To justify that Lp is the orthogonal projection with R(Lp) = W, we need to show two properties:

Lp is an orthogonal projection:

Lp is idempotent: (Lp)^2 = Lp

Lp is self-adjoint: (Lp)^T = Lp

R(Lp) = W:

Every vector in the range of Lp is in W

Every vector in W is in the range of Lp

Let's break down the steps to construct P and verify these properties:

Step 1: Compute the matrix X^T X

X^T is the transpose of X

Multiply X^T with X to obtain X^T X

Step 2: Invert the matrix (X^T X)^(-1)

If X^T X is invertible, calculate its inverse (if it is not invertible, the orthogonal projection does not exist)

Step 3: Compute the matrix P = X (X^T X)^(-1) X^T

Multiply X by (X^T X)^(-1)

Multiply the result by X^T

Step 4: Verify the properties of Lp

Check if (Lp)^2 = Lp

Check if (Lp)^T = Lp

Step 5: Verify R(Lp) = W

Check if every vector in W is in the range of Lp

Check if every vector in the range of Lp is in W

By following these steps and verifying the properties, we can rigorously show that Lp is indeed an orthogonal projection with R(Lp) = W.

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Answer:

for the first 14 hours it doubles to 20,000, then once it reaches 28 hours it'll be 40,000. its an exponential growth

The population growth of bacteria after 28 hours will be equal to 40,000.

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the set of information in the question,

Total population of Bacteria = 10,000

Rate of growth of bacteria = Twice in 14 hours

Rate of growth in 28 hours = 4 times the total population.

Then the total bacteria (B) in the colony after 28 hours,

B = 4 × 10,000

B = 40,000

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After driving for four days, Margaret will have 9.6 gallons of gas left in her car.

Margaret starts with a full tank of 19 gallons of gas. Each day, she uses an average of 2.4 gallons.

To find out how many gallons she will have left after four days, we multiply the daily usage (2.4 gallons) by the number of days (4). This gives us a total usage of 9.6 gallons (2.4 gallons/day * 4 days).

Subtracting the total usage from the initial tank capacity (19 gallons - 9.6 gallons) gives us the amount of gas left after four days, which is 9.6 gallons.

Therefore, Margaret will have 9.6 gallons of gas remaining in her car after four days of driving.

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So the maximum number of edges in an undirected graph with 100 vertices is 4950.

In an undirected graph, each edge connects two vertices, and as such, it is counted twice, once for each vertex it connects. Therefore, the total number of edges in the graph is the sum of the degrees of all vertices, divided by 2.

In a complete graph with n vertices, every vertex is connected to every other vertex, except itself, and so the degree of each vertex is n-1 (it is connected to n-1 other vertices). Therefore, the total number of edges in the graph is:

n * (n-1) / 2

Substituting n = 100, we get:

100 * 99 / 2 = 4950

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64 + 16 would be the answer.

Based on the expanded the expression (2 - 3x)², the student who got the answer 4 – 12 x + 9x² is the first student.

In Mathematics, a quadratic function can be defined as a mathematical expression which defines and represent the relationship that exists between two (2) or more variable on a graph, with a maximum exponent of two (2).

In Mathematics, the standard form of a quadratic function is given by ax² + bx + c = 0.

By applying the following binomial expression to the given quadratic function, we have:

(a - b)² = a² - 2ab + b²

(2 - 3x)² = 4 - 2(2)(3x) + 3x²

4 - 2(2)(3x) + 3x² = 4 - 12x + 9x².

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Answer:

Hey there!

The domain of the graph would be \(-2\leq x<9\).

Let me know if this helps :)

Answer:

-2 to 9

Step-by-step explanation:

The domain of a graph consists of all the input values shown on the x-axis

Answer:Here are some statements to describe the given function:

The function f is an exponential function.

The base of the exponential function is 3.

The function f has a horizontal intercept at the point (-1, 0).

The function f has a vertical intercept at the point (0, 8).

The function f is increasing because the base is greater than 1.

The function f approaches but does not touch the x-axis as x approaches negative infinity.

The function f approaches positive infinity as x approaches positive infinity.

Step-by-step explanation:

The correct statements for the given function are: The y-intercept of the function is (0, 8). The graph of the function would initially increase slowly and then increases rapidly.

The function is a type of relation, or rule, that maps one input to specific single output.

Consider the function below.

\(f(\text{x})=5(3)^{\text{x}}+3\)

The intersection of the graph of the function with the y-axis gives the y-intercept of that function.

The y-intercept is the value of y on the y-axis at which the considered function intersects it.

The correct statements are:

The y-intercept of the function is (0, 8).

The graph of the function would initially increase slowly and then increases rapidly.

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The complete question is-

Consider the function below.

f(x) = 5(3)^x + 3

Complete the statement below to describe the given function. They y-intercept of the function is (___). The graph of the function initially (___) and then (___).

First blank answers:

(8, 0)

(0, 8)

(-8, 0)

(0, -8)

Second blank answers:

Increases rapidly

Increases slowly

Decreases rapidly

Decreases slowly

Third blank answers:

Increases slowly

Decreases rapidly

Decreases slowly

Increases rapidly

Answer:

Division property

Step-by-step explanation:

you would need to set up your equation. Then divide -3x by -3 to get x alone. then you do 348 divided by -3 to get your answer

-3x=348

-3= -3

x=-116