Assume that playing soccer requires 540 Calories per hour. On a particular day, you ate 2,000 Calories in food. You played soccer for 2.5 hours. Your body used 800 Calories in other activities. Did you use more energy than you consumed on this day?

The minimum sample size is  n = 97

The minimum sample size is define as the sample size used in a study is usually determined based on the cost, time, or convenience of collecting the data, and the need for it to offer sufficient statistical power.

We have the information from the question is:

The margin of error is  E = 1.25

The  standard deviation is  s = 7.5

The confidence level is  90% then the level of significance is mathematically represented as:

[tex]\alpha =100-90[/tex]

[tex]\alpha =10%[/tex]%

[tex]\alpha =0.10[/tex]

Now, The critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table  

The value is [tex]Z_\frac{\alpha }{2}=1.645[/tex]

The minimum sample size is mathematically evaluated as:

[tex]n=\frac{Z_\frac{\alpha }{2}(s^2)}{E^2}[/tex]

Plug all the values in above formula:

[tex]n=\frac{1.645^2(7.5)^2}{1.25^2}[/tex]

After calculation, we get :

n = 97

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The given question is incomplete, complete question is:

What is the minimum sample size required to estimate a population mean with 90% confidence when the desired margin of error is 1.25? The standard deviation in a pre-selected sample is  7.5

Step-by-step explanation:

To determine two points that would lie on the graph of function g(x) = f(x) + 4, we need to add 4 to the y-coordinates of the points that lie on the graph of f.

Let's first find the equation of the exponential function f. We know it passes through the points (-3,5) and (-1,-3). Using two-point form for exponential functions, we have:

f(x) = a * (b)^x

where a and b are constants to be determined. Plugging in the two points, we get the following equations:

5 = a * (b)^(-3)

-3 = a * (b)^(-1)

Dividing the second equation by the first, we get:

(b)^2 = -3/5

Taking the square root of both sides, we get:

b = i * sqrt(3/5) or b = -i * sqrt(3/5)

where i is the imaginary unit.

Substituting b into the first equation and solving for a, we get:

a = 5 / (b)^(-3) = -125i / (3 * sqrt(5))

Therefore, the equation for f is:

f(x) = (-125i / (3 * sqrt(5))) * (i * sqrt(3/5))^x

Simplifying this expression, we get:

f(x) = (25/3) * (3/5)^(x+1/2)

Now we can find the two points that lie on the graph of g by adding 4 to the y-coordinates of the points that lie on the graph of f. Using the given points:

(-3,5) and (-1,-3)

Adding 4 to the y-coordinate of the first point, we get:

(-3,9)

Adding 4 to the y-coordinate of the second point, we get:

(-1,1)

Therefore, the two points that would lie on the graph of function g are:

(-3,9) and (-1,1)

Answer: B.

Answer:

Step-by-step explanation:

Given two of three numbers correct, you want to find the correct value for the third number of 8 faces, 7 vertices, and 10 edges.

The relation between faces, vertices, and edges is ...

  F + V = E + 2

The given numbers are off by 3:

  8 + 7 = 15 ≠ 12 = 10 + 2

We can decrease the numbers of Faces or Vertices by 3, or we can increase the number of Edges by 3.

The numbers will be correct if we change to ...

#95141404393

Answer:

AB = √(4^2 + 1^2) = √(16 + 1) = √17

GH = √(4^2 + 4^2) = √(16 + 16) = √32

= 4√2

The correct answer is b. Cost(k) = a k + b.

Affine gap penalties in sequence alignment involve a linear function that considers the number of gaps in a row. The function typically includes two components: a linear term to represent the initial gap and an additional linear term to account for each consecutive gap.

In option a, the cost function includes a quadratic term (k^2), which does not represent a linear affine penalty.

In option c, the cost function includes a logarithmic term (log(k)), which also does not represent a linear affine penalty.

Option b, with the cost function of a k + b, correctly represents an affine gap penalty, as it includes a linear term (a k) to account for the number of gaps in a row.

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The value of expected number of the boxes that will weigh 25 oz or less from the 1200 boxes of rice in shipment is 935.

When we got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z-score.

Since,

X ~ N (μ, σ)

Where, X is following normal distribution with mean  and standard deviation.

When transformed into a typical normal distribution, it may be used as follows:

z = X - μ / σ

Z ~ N (0, 1)

so we can write

P (Z ≤ z) = P (Z < z)

Also, know that for Z = z in z tables, the p-value we get is

P (Z ≤ z) = p value

Let;

X is the weights of the rice boxes made at the hypothetical factory, expressed in ounces.

then, as stated in the issue, we have;

X ~ N (μ  = 24,  σ= 1.3)

The probability is:

P (X ≤ 25)

Converting X to standard normal distribution, we get:

Z = X - μ / σ = X - 24 / 1.3

The probability P (X ≤ 25) can be rewritten as:

P (X ≤ 25) = P (Z ≤ 25 - 24/1.3)

                 = P (Z ≤ 0.77)

Z = 0.77 has a p-value of 0.7794 according to the z-tables.

Thus, we get:

P (X ≤ 25) = P (Z ≤ 0.77) = 0.7794 = 77.94%

Let;

n = 1200 boxes being bernoulli experiments, each of them prone to success with probability p = 0.7794 or failure (weight > 25 oz) with probability

q = 1-p = 0.2206.

And, Y = the number of successes for 1200 trials.

Then we get:

Y ~ B (n = 1200, p = 0.7794)

The predicted value of Y is the anticipated number of successes, or the anticipated number of boxes that weigh 25 oz or less.

We get:

E (Y) = np = 1200 x 0.7794 = 935

Thus, Out of the 1200 boxes of rice being shipped, 935 are anticipated to weigh 25 ounces or less.

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The reasonable estimate for the forecast value for January using exponential smoothing would be 208 cat trees.

Exponential smoothing is a statistical technique used for time series forecasting. It involves a weighted average of past observations, with more recent observations given greater weight than older ones.

The level of smoothing is controlled by a smoothing parameter, which determines the extent to which past observations influence the forecast.

Here we have

Chairman cat products produces cat trees that are sold by several large pet stores. They sold 190, 210, and 208 cat trees in january, february, and march, respectively.

To estimate the forecast value for January using exponential smoothing, we need to use the following formula:

F₁ = A × D₀ + (1 - A) × F₀

Where:

F₁ = forecast for January

D₀ = actual demand for December (last period)

F₀ = forecast for December (last period)

A = smoothing factor (a value between 0 and 1)

Since we do not have a forecast for December, we can assume that F₀ is equal to the actual demand for December.

Therefore, we can use the following formula to estimate F₁:

F₁ = A × D₀ + (1 - A) × F₀

We need to choose a value for A.

This value represents the weight or importance that we give to the most recent demand observation when making the forecast.

A smaller value of A gives more weight to past observations, while a larger value of A gives more weight to the most recent observation.

A reasonable estimate for A would be between 0.1 and 0.3.

Let's assume we choose A = 0.2.

Using the given data, we have:

D₀ = 208 (demand for March)

F₁ = 0.2 × 208 + (1 - 0.2) × 208

= 0.2 × 208 + 0.8 × 208

= 208

Therefore,

The reasonable estimate for the forecast value for January using exponential smoothing would be 208 cat trees.

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when we flip four coins, each coin has two possible outcomes, so the total number of possible outcomes is 2 x 2 x 2 x 2 = 16. The random variable X represents the number of tails observed when these 4 coins are flipped, and can take on values from 0 to 4.

Each of these 16 outcomes has a corresponding number of tails. For example, the outcome HHHH has 0 tails, HTTT has 4 tails, and so on.

Therefore, we can define a random variable X to represent the number of tails observed when four coins are flipped. X can take on values from 0 (when all four coins are heads) to 4 (when all four coins are tails), and the probability of each value can be determined by counting the number of outcomes that correspond to that value and dividing by the total number of possible outcomes (16). This approach does not use the binomial distribution, which is a formula used to calculate the probability of a certain number of successes in a fixed number of independent trials with a constant probability of success.

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The statements about the location of the point that are true include:

The point (5, 5) is in the first octant, has a positive x-coordinate, and a positive y-coordinate. It lies above the xy plane and to the right of the x-plane. Therefore, the following statements are true:

The point is in the first octant.

The x-coordinate is 5.

The y-coordinate is positive.

The point lies above the xy plane.

The point does not lie below the xy plane, so the statement is false:

The point lies below the xy plane.

The point does not lie to the left of the x-plane, so the statement is false.

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The distance from the bottom of the slide to the bottom of the ladder is approximately 160.9 feet.

We can use the Pythagorean theorem to find the distance from the bottom of the slide to the bottom of the ladder. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the distance we want to find, and the other two sides are the length of the slide (150 feet) and the height of the ladder (58 feet). Therefore, we have:

Distance² = 150² + 58²

Distance²= 22,500 + 3,364

Distance² = 25,864

Taking the square root of both sides, we get:

Distance = 160.9 feet (rounded to the nearest tenth)

Therefore, the distance from the bottom of the slide to the bottom of the ladder is approximately 160.9 feet.

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The value of x in the quadratic equation using quadratic formula to the nearest hundredths place is x = 1.29 and x = 2.71.

The correct answer choice is option B.

2x² - 8x + 7 = 0

[tex]x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }[/tex]

[tex]x = \frac{ -(-8) \pm \sqrt{(-8)^2 - 4(2)(7)}}{ 2(2) }[/tex]

[tex]x = \frac{ 8 \pm \sqrt{64 - 56}}{ 4 }[/tex]

[tex]x = \frac{ 8 \pm \sqrt{8}}{ 4 }[/tex]

[tex]x = \frac{ 8 \pm 2\sqrt{2}\, }{ 4 }[/tex]

[tex]x = \frac{ 8 }{ 4 } \pm \frac{2\sqrt{2}\, }{ 4 }[/tex]

[tex]x = 2 \pm \frac{ \sqrt{2}\, }{ 2 }[/tex]

[tex]x = 2.70711[/tex]

or

[tex]x = 1.29289[/tex]

Hence,

Approximately, x = 1.29 or x = 2.71

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Dot plot 1 would be the most appropriate to display the data collected, while dot plots 2 and 3 would not be correct.

Dot plot 1: This shows positive values ranging from 5 to 20 minutes and represents the opinion of 10 different people, making it appropriate.

Dot plot 2: This includes 10 people but the values provided are too high (80 to 300 minutes) and they do not match the intervals in the number line.

Dot plot 3: This includes 10 people but also negative values, which is impossible as we are representing time.

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The expression w / 6 represents the number of new watercolor palettes on each table

Let's assume that Mr. Chen bought a total of "w" new watercolor palettes.

Since he wants to distribute an equal number of palettes on each of the 6 tables, we can divide the total number of palettes by the number of tables.

Expression: (number of new watercolor palettes) ÷ (number of tables)

Expression: w / 6

This expression represents the number of new watercolor palettes on each table, given that there are "w" total palettes and 6 tables in Mr. Chen's class.

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The profit function -400·p² + 12,400·p - 50,000, is a quadratic function and the maximum profit is $46,100

A quadratic function is a function that can be expressed in the form f(x) = a·x² + b·x + c, where a ≠ 0 and, a, b, and c are numbers.

The specified function is; P = -400·p² + 12,400·p - 50,000

The possible function in the question, obtained from a similar online question is the profit function

The possible requirement is to find the maximum profit of the company

The profit function, P = -400·p² + 12,400·p - 50,000 is a quadratic function, therefore;

The input value for the maximum value of the function, f(x) = a·x² + b·x + c, is the point x = -b/(2·a)

The price, p value when the profit function value reaches the maximum point is therefore;

p = -12,400/(2 × (-400)) = 15.5

The maximum profit is therefore;

P = -400 × 15.5² + 12,400 × 15.5 - 50,000 = 46,100

The maximum profit is $46,100

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Each person living in the Sighet ghetto would have had an estimated personal space of 12.8 square feet, which is extremely cramped and overcrowded.

A two-dimensional figure, form, or planar lamina's area is a measurement of how much space it takes up in the plane.

First, we need to calculate the total number of rooms in the ghetto:

Number of people = 13,000

Number of people per room = 20

Total number of rooms = Number of people / Number of people per room = 13,000 / 20 = 650

Next, we can calculate the total area of all the rooms:

Total area of all the rooms = Number of rooms x Average room size = 650 x 256 = 166,400 square feet

Finally, we can calculate the amount of personal space each person had by dividing the total area of all the rooms by the number of people:

Personal space per person = Total area of all the rooms / Number of people = 166,400 / 13,000 = 12.8 square feet

Therefore, each person living in the Sighet ghetto would have had an estimated personal space of 12.8 square feet, which is extremely cramped and overcrowded.

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Using​ Green's Theorem ModifyingAbove ModifyingBelow Contour integral With Upper C f dy minus g dx With font size decreased by 6 ∮Cf dy−g dx​, the total line integral is 0.

To use Green's Theorem to evaluate the line integral, we first need to find the partial derivatives of f and g:
∂f/∂x = 0
∂g/∂y = 0
∂f/∂y = 11x^2
∂g/∂x = -6y^2
Now we can apply Green's Theorem:
∮Cf dy − g dx = ∬D (∂g/∂x − ∂f/∂y) dA
where D is the region enclosed by the contour C.
Since C consists of the upper half of the unit circle and the line segment -1 ≤ x ≤ 1 oriented clockwise, we can split region D into two parts: the upper half of the unit circle and the rectangle -1 ≤ x ≤ 1, 0 ≤ y ≤ 1.
For the upper half of the unit circle, we have x^2 + y^2 = 1 and y ≥ 0. So we can parametrize the curve as x = cos(t), y = sin(t), where t goes from 0 to π. Then we have:
∮Cf dy − g dx = ∫0^π (−6sin^3(t))dt = 0
For the rectangle -1 ≤ x ≤ 1, 0 ≤ y ≤ 1, we have:
∂g/∂x − ∂f/∂y = -12y^2
So the line integral over this part of the contour is:
∮Cf dy − g dx = ∫0^1 ∫−1^1 (−12y^2)dxdy = 0
Therefore, the total line integral is 0.

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The exact value of the trigonometric function at the given real number is: 1. 0      2. -1      3. undefined.

To find the exact value of the trigonometric function at the given real numbers, we can use the unit circle and the properties of trigonometric functions.

(a) sin(34π):

Since the unit circle repeats every 2π radians, we can subtract multiples of 2π to find the equivalent angle within one full revolution.

34π = 17π + π

The angle π is equivalent to 180 degrees, so sin(π) = 0.

Therefore, sin(34π) = sin(17π + π) = sin(π) = 0.

(b) sec(67π):

Similar to the previous case, we can rewrite 67π as:

67π = 33π + π

The angle π is equivalent to 180 degrees, and the secant function is the reciprocal of the cosine function. Since the cosine function has a value of -1 at π, the reciprocal, sec(π), is -1.

Therefore, sec(67π) = sec(33π + π) = sec(π) = -1.

(c) cot(-3π):

To find the cotangent function, we need to determine the tangent function at -3π.

The tangent function has a period of π, so we can rewrite -3π as:

-3π = -2π - π

The angle -π is equivalent to -180 degrees, and the tangent function is the sine divided by the cosine. Since sin(-π) = 0 and cos(-π) = -1, the tangent function is undefined at -π.

Therefore, cot(-3π) is also undefined.

In summary:

(a) sin(34π) = 0

(b) sec(67π) = -1

(c) cot(-3π) is undefined.

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The partial derivative of z with respect to s is $\frac{\partial z}{\partial s} = \frac{\partial f}{\partial x} r^3 + \frac{\partial f}{\partial y} 2re^{2s}$

The partial derivative of z with respect to s can be found using the chain rule of differentiation as follows:

$\frac{\partial z}{\partial s} = \frac{\partial z}{\partial x} \frac{\partial x}{\partial s} + \frac{\partial z}{\partial y} \frac{\partial y}{\partial s}$

Given that $x = r^3s$ and $y = re^{2s}$, we have:

$\frac{\partial x}{\partial s} = r^3$ and $\frac{\partial y}{\partial s} = 2re^{2s}$

Taking partial derivatives of z with respect to x and y:

$\frac{\partial z}{\partial x} = \frac{\partial f}{\partial x}$ and $\frac{\partial z}{\partial y} = \frac{\partial f}{\partial y}$

Hence, the partial derivative of z with respect to s is:

$\frac{\partial z}{\partial s} = \frac{\partial f}{\partial x} r^3 + \frac{\partial f}{\partial y} 2re^{2s}$

where $\frac{\partial f}{\partial x}$ and $\frac{\partial f}{\partial y}$ are the partial derivatives of f with respect to x and y, respectively.

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The areas of the circular sectors are listed below:

Case 7: A = 50π / 3 in²

Case 8: A = 177.884 cm²

Case 9: A = 937.312 m²

Case 10: A = 10π / 3 ft²

In this problem we must determine the areas of four circular sectors, whose area formula is equal to:

A = (θ / 360°) · π · r²

Where:

Now we proceed to determine the areas:

Case 7

A = (60 / 360) · π · (10 in)²

A = 50π / 3 in²

Case 8

A = (104 / 360) · π · (14 cm)²

A = 177.884 cm²

Case 9

A = (137 / 360) · π · (28 m)²

A = 937.312 m²

Case 10

A = (75 / 360) · π · (4 ft)²

A = 10π / 3 ft²

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The correct answers are option C for when n is odd and option E for when n is even.

The number of loops in the polar curves given by r sin(n), where n is a positive integer, is related to the parity of n. If n is odd, then the curve will have n loops, and if n is even, the curve will have 2n loops. Therefore, options C and E are correct.

To understand why this is the case, we can consider how the sine function behaves. The sine function oscillates between -1 and 1 as its argument increases from 0 to 2π. When n is odd, the argument of sin(nθ) increases from 0 to 2π as θ goes from 0 to π, resulting in n oscillations of the sine function in this interval. When n is even, the argument of sin(nθ) increases from 0 to 4π as θ goes from 0 to π, resulting in 2n oscillations of the sine function in this interval. This behavior translates into the number of loops in the polar curve, where each oscillation of the sine function corresponds to one loop.

Therefore, the number of loops in the polar curve r sin(n) depends on the parity of n, with n loops for odd values of n and 2n loops for even values of n.

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4/9 = A

2/3 to the power of 2 is 4/9

Option A: 18.169 and 27.690.

The confidence interval for the true slope of the population regression line is (0.2, 0.4), indicating that we are 95% confident that the true slope falls within this interval.

What is Statistics?

Statistics is the branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data

In regression analysis, a regression line is a straight line that describes how a response variable y changes as an explanatory variable x changes. The slope of the regression line represents the change in the response variable y per unit change in the explanatory variable x.

Sure, here is a numerical example:

Suppose we want to estimate the relationship between height and weight among adults, and we collect a sample of 100 adults and measure their height and weight. We can use linear regression to model the relationship between these variables, and estimate the slope and intercept of the population regression line.

Suppose the slope of the true population regression line is unknown, but we calculate a 95% confidence interval for it based on the sample data, and obtain the interval (0.2, 0.4). This means that we are 95% confident that the true slope of the population regression line falls between 0.2 and 0.4.

If we were to repeat the sampling process many times and construct confidence intervals in the same way, we would expect that about 95% of those intervals would contain the true value of the population slope. However, we cannot be completely certain that the true value falls within this interval, as there is always some degree of uncertainty in statistical inference.

In the given question, the statement "we are 95% confident that the true population regression line (i.e. slope) will fall between" implies that a confidence interval is being constructed for the true slope of the regression line. The four options represent different intervals for the true slope, and only one of them can be correct.

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1. The first term is a_1 = 1.
2. The difference between any two consecutive terms, 1 - a_n, is 17 for n ≥ 1.

Using the information above, we can define the arithmetic sequence as follows:

a_n = a_1 + (n - 1)d, where a_n is the nth term, a_1 is the first term, n is the position of the term, and d is the common difference between terms.

Now let's use the information given to find the common difference (d).

1 - a_n = 17

We know that a_1 = 1, so when n = 1:

1 - a_1 = 17
1 - 1 = 17
d = -16

Now that we know d = -16, we can plug it into the formula for the nth term of an arithmetic sequence:

a_n = a_1 + (n - 1)d
a_n = 1 + (n - 1)(-16)

So, the formula for the nth term of the arithmetic sequence is:

a_n = 1 - 16(n - 1)

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To solve this equation, the particular solution is: y = √[2ln|x| + 4]

To solve the differential equation x dy/dx = 1/y³, we can begin by separating the variables. To do this, we can write the equation as:
y³ dy = dx/x
Next, we can integrate both sides. For the left-hand side, we can use the power rule of integration:
∫ y³ dy = y⁴/4 + C₁
For the right-hand side, we can use the natural logarithm rule of integration:
∫ dx/x = ln|x| + C₂
Putting these together, we have:
y⁴/4 + C₁ = ln|x| + C₂
Solving for y, we get:
y = ± √[2ln|x| + K]
where K = 4(C₁ - C₂).
Now we have the general solution to the differential equation. To find a particular solution, we need an initial condition. For example, if we know that y(1) = 2, we can use this to solve for the constant K:
2 = ± √[2ln|1| + K]
2 = ± √K
K = 4
Therefore, the particular solution is:
y = √[2ln|x| + 4]
Note that there is another solution given by y = -√[2ln|x| + 4], but it is not valid since y must be positive according to the original equation.

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A player would need to hit approximately 56 home runs in the 2001 season to claim they were as dominant as Duke Snyder was during his 1956 season.

What is the mean and standard deviation?

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

To compare the dominance of Duke Snyder's 1956 MLB season to a player's 2001 MLB season, we need to calculate the number of standard deviations above the mean that Duke Snyder's 43 home runs represents and then find the number of home runs that a player in 2001 would need to hit to achieve the same number of standard deviations above the mean.

To do this, we can use the formula:

z = (x - μ) / σ

where:

z is the number of standard deviations above the mean

x is the number of home runs

μ is the mean number of home runs

σ is the standard deviation

For Duke Snyder's 1956 season, we have:

z = (43 - 13.34) / 9.39 = 2.99

This means that Duke Snyder's 43 home runs were 2.99 standard deviations above the mean for that season.

To find the number of home runs that a player in 2001 would need to hit to achieve the same number of standard deviations above the mean, we can rearrange the formula:

x = μ + z * σ

For the 2001 season, we have:

x = 18.03 + 2.99 * 13.37 = 55.84

Therefore, a player would need to hit approximately 56 home runs in the 2001 season to claim they were as dominant as Duke Snyder was during his 1956 season.

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By the Angle Bisector Theorem, we know that QT/RP = PW/QV, then W1 = TRQ.

Given: APQR is an equilateral triangle inscribed in a circle.

V is a point on the circle.

QP produced meets RV produced at T.

PR and QV intersect at W.

To prove:.W1 = TRQ

Since APQR is an equilateral triangle, then PQ = QR = RP.

QP produced meets RV produced at T. Therefore, QT = RP.

PR and QV intersect at W. Therefore, PW = QV.

By the Angle Bisector Theorem, we know that QT/RP = PW/QV.

Substituting in the values from step 1, we get QT/RP = PW/QV = 1/1.

Therefore, QT = RP = PW = QV.

Since QT = RP = PW = QV, then W1 = TRQ.

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If each value in a data set is decreased by 7 , when each value in a data set is decreased by 7, the mean, median, and mode are all affected by a decrease of 7.However, if the mode was not one of the values that was decreased by 7, then it will remain the same .

The median, on the other hand, may or may not change. The median is the middle value in a data set, so if the data set has an odd number of values, the median will remain the same because the middle value will still be the same. However, if the data set has an even number of values, the median may change because there will no longer be a single middle value. In this case, the new median will be the average of the two middle values, which may or may not be different from the original median.

The mode, or the most common value in the data set, may or may not change as well. If the mode is one of the values that was decreased by 7, then it will no longer be the most common value and a new value will take its place as the mode. However, if the mode was not one of the values that was decreased by 7, then it will remain the same.

Mean: The mean, or average, is calculated by adding all the data values and dividing by the total number of values. When each value is decreased by 7, the overall sum of the values is reduced by 7 times the total number of values. As a result, the mean will also decrease by 7.

Median: The median is the middle value in a data set when the values are arranged in ascending or descending order. Since each value is decreased by the same amount (7), the order of the values does not change, and the median value will also be decreased by 7.

Mode: The mode is the value that occurs most frequently in a data set. Decreasing each value by 7 does not affect the frequency of the values, only their magnitude. Thus, the mode will also be decreased by 7.

When each value in a data set is decreased by 7, the mean, median, and mode are all affected by a decrease of 7.

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Surface area of larger triangular pyramid is 49cm².

Given,

Altitude of smaller pyramid = 3 cm.

Altitude of larger pyramid = 7 cm.

Surface area of smaller pyramid = 9cm².

Now,

Relation between altitudes of similar pyramids and surface area :

Surface area of smaller pyramid / Surface area of larger pyramid = (altitude of smaller pyramid / altitude of larger pyramid)²

Let us assume the surface area of larger pyramid be x cm²

Substituting the given values in the relation,

9 cm²/x cm² = (3/7)²

x = 49 cm² .

Thus the surface area of larger pyramid is 49 cm².

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Answer:

I don't understand what the question is can you be more specific please?