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In a pulley system, the movement of the weight depends on the size of the pulley and the amount of rope or cable wrapped around it.

The angle through which the pulley is rotated and the distance the weight rises are directly related. To determine the answer to part (a), you would need to know the size of the pulley, the length of the rope or cable wrapped around it, and any additional information about the system. Without these details or the ability to view the figure you mentioned, it is not possible to provide a specific measurement.

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Answer: linear combo of terms involving x & y, with respective numbers determining their contribution to the expression

This is the matrix equation that represents the given system of equations. It allows us to solve for the variable matrix X.

The given system of equations can be represented by a matrix equation. Let's break down the system of equations:

2s = 200
150 + s = 52

To write this as a matrix equation, we need to arrange the coefficients and variables into matrices.

First, let's consider the coefficients of the variables:

The coefficient matrix, A, is:
[2]
[1]

Next, let's consider the variables:

The variable matrix, X, is:
[s]

Finally, let's consider the constants on the right side of the equations:

The constant matrix, B, is:
[200]
[52-150]

Now, we can write the matrix equation as:

AX = B

Substituting the values of A, X, and B, we have:

[2] [s] = [200]
[1]      [52-150]

This is the matrix equation that represents the given system of equations. It allows us to solve for the variable matrix X.

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P(X = 7), λ = 6: The Poisson probability of X = 7, with a parameter (λ) value of 6, is 0.1446. P(X = 11), λ = 12: The Poisson probability of X = 11, with a parameter (λ) value of 12, is 0.0946. P(X = 6), λ = 8: The Poisson probability of X = 6, with a parameter (λ) value of 8, is 0.1206.

The Poisson probability is used to calculate the probability of a certain number of events occurring in a fixed interval of time or space, given the average rate of occurrence (parameter λ). The formula for Poisson probability is P(X = k) = (e^-λ * λ^k) / k!, where X is the random variable representing the number of events and k is the desired number of events.

To calculate the Poisson probabilities in this case, we substitute the given values of λ and k into the formula. For example, for the first case (a), we have λ = 6 and k = 7: P(X = 7) = (e^-6 * 6^7) / 7!

Using a calculator, we can evaluate this expression to find that the probability is approximately 0.1446. Similarly, for case (b) with λ = 12 and k = 11, and for case (c) with λ = 8 and k = 6, we can apply the same formula to find the respective Poisson probabilities.

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Answer:

The raduis is half of the diameter. Your question is unclear You do not need pi to find the raduis of the diameter. But the circumference of the circle is 109.9. Rounded to nearest tenth, and used 3.14 for pi.

And the Area of the circle is 961.625, or rounded is 961.6. Again used 3.14 for pi.

Step-by-step explanation:

To complete the table based on the given ratio of squares to circles (4:3), you can assign any numerical values that follow this ratio. Here's an example:

Squares Circles

4           3

8           6

12           9

16             12

20         15

24         18

You can continue this pattern by adding 4 to the square count and 3 to the circle count for each subsequent row.

The given ratio of squares to circles is 4:3, which means that for every 4 squares, there are 3 circles in the pattern. To complete the table, we need to find values that maintain this ratio.

In the first row, we start with 4 squares and 3 circles, which satisfies the ratio.

To find the values for the second row, we can add 4 to the square count and 3 to the circle count. So, we have 4 + 4 = 8 squares and 3 + 3 = 6 circles in the second row.

Similarly, for the third row, we add 4 to the square count and 3 to the circle count again. Therefore, we have 8 + 4 = 12 squares and 6 + 3 = 9 circles.

We continue this pattern for the remaining rows, adding 4 to the square count and 3 to the circle count each time. This ensures that the ratio of squares to circles remains constant at 4:3.

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Assuming that the data is normally distributed, approximately 95.44 percent of customers are willing to pay between $1.30 and $1.70 for a pint of frozen yogurt

Find the area under the normal curve between $1.30 and $1.70. To do this, we can use the z-score formula to standardize these values and then use a table of the standard normal distribution to find the area.

The z-score for a value x is given by the formula:

z = (x - mean) / standard deviation

Plugging in the values given in the question, we get:

z(1.30) = (1.30 - 1.50) / 0.10 = -2

z(1.70) = (1.70 - 1.50) / 0.10 = 2

This means that the area under the curve between $1.30 and $1.70 is the area under the curve between -2 and 2. If we look up these values in a table of the standard normal distribution, we find that they correspond to approximately 2.28% and 97.72%, respectively. Therefore, the area under the curve between these two values is approximately 97.72% - 2.28% = 95.44%.

Hence, approximately 95.44% of customers are willing to pay between $1.30 and $1.70 for a pint of frozen yogurt.

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F = 1.8C + 32

Replace C by 15 and solve:

F = 1.8 (15)+32

F= 27+32

F= 59

tan(41π/36) can be written in terms of the tangent of a positive acute angle as (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

To express tan(41π/36) in terms of the tangent of a positive acute angle, we need to find an angle within the range of 0 to π/2 that has the same tangent value.

First, let's simplify 41π/36 to its equivalent angle within one full revolution (2π):

41π/36 = 40π/36 + π/36 = (10/9)π + (1/36)π

Now, we can rewrite the angle as:

tan(41π/36) = tan((10/9)π + (1/36)π)

Next, we'll use the tangent addition formula, which states that:

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))

In this case, A = (10/9)π and B = (1/36)π.

tan(41π/36) = tan((10/9)π + (1/36)π) = (tan((10/9)π) + tan((1/36)π)) / (1 - tan((10/9)π)tan((1/36)π))

Now, we need to find the tangent values of (10/9)π and (1/36)π. Since tangent has a periodicity of π, we can subtract or add multiples of π to get equivalent angles within the range of 0 to π/2.

For (10/9)π, we can subtract π to get an equivalent angle within the range:

(10/9)π - π = (1/9)π

Similarly, for (1/36)π, we can add π to get an equivalent angle:

(1/36)π + π = (37/36)π

Now, we can rewrite the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Since we are looking for an angle within the range of 0 to π/2, we can further simplify the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Therefore, tan(41π/36) can be written in terms of the tangent of a positive acute angle as the expression given above.

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In the absence of price discrimination, the profit-maximizing conditions would be different, and the resulting prices, quantities, total revenue, total cost, and profit would also be different.

To find the profit-maximizing conditions with third-degree price discrimination, we need to equate the marginal revenue (MR) to the marginal cost (MC) for each market segment.

Given the demand equations and the total cost function:

Market 1: Q1 = 160 - 10P1 or P1 = 16 - 0.1Q1

Market 2: Q2 = 200 - 20P2 or P2 = 10 - 0.05Q2

Total Cost: TC = 120 + 4Q

To find the profit-maximizing prices and quantities, we equate MR to MC for each market segment:

MR1 = MC:

16 - 0.2Q1 = 4

0.2Q1 = 12

Q1 = 60

MR2 = MC:

10 - 0.1Q2 = 4

0.1Q2 = 6

Q2 = 60

Substituting the quantities back into the demand equations, we find:

P1 = 16 - 0.1(60) = 10

P2 = 10 - 0.05(60) = 7

The total revenue (TR) can be calculated by multiplying the price by the quantity for each market segment:

TR = P1 * Q1 + P2 * Q2

TR = (10 * 60) + (7 * 60)

TR = 600 + 420

TR = 1020

The total cost (TC) is given by the total cost function:

TC = 120 + 4Q

TC = 120 + 4(60 + 60)

TC = 120 + 480

TC = 600

Finally, the profit (π) can be calculated by subtracting total cost from total revenue:

π = TR - TC

π = 1020 - 600

π = 420

In the absence of price discrimination, the profit-maximizing conditions would be different, and the resulting prices, quantities, total revenue, total cost, and profit would also be different.

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The cοοrdinates οf the mid pοint M οf the line segment AB are ( 3,1 ) .

A midpοint οf a line segment is the pοint οn a segment that bisects the segment intο twο cοngruent segments. In οther wοrds, The midpοint is halfway between the twο end pοints.

Fοr the given line segment AB with cοοrdinates as (2, -3) and (4, 5) οf A and B respectively.

x₁ = 2           y₁ = -3                  (Cοοrdinates οf A)

x₂ = 4          y₂ = 5                   (Cοοrdinates οf B)

Midpοint οf a line segment = [ (x₁ + x₂ ) / 2   ;    (y₁ +  y₂) /2  ]

= [  (2 +4) /2  ;    (-3 + 5) / 2  ]

= [ 6/2  ;   2/2 ]

= (3,1)

=> Thus, the cοοrdinates οf M are (3,1).

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in my opinion i think there is twooo

The amount of money in Iris's checking account can be modeled by a linear function of the form:

y = mt + b

where y is the amount of money in the account, t is the time (measured in years), m is the rate of interest, and b is the initial amount in the account.

In this case, we have m = 0.04 (since the interest rate is 4% per year) and b = 180 (since that's the initial amount in the account). Therefore, the linear function that models the amount of money in Iris's checking account at any time t is:

y = 0.04t + 180

For example, if t = 5 (years), then the amount of money in Iris's checking account is 0.04 * 5 + 180 = 198 dollars.

The missing values in table should be completed as follows;

X(input)         Y(output)

10                     19

12                     23

Rule: y = 2x - 1.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

At point (3, 5), a linear equation of this line in slope-intercept form can be calculated by using the point-slope form as follows:

y - 5 = (11 - 5)/(6 - 3)(x - 3)

y - 5 = 6/3(x - 3)

y = 2(x - 3) + 5

y = 2x - 1

When x(input) = 10, the y(output) is given by:

y = 2x - 1

y = 2(10) - 1

y = 20 - 1

y = 19.

When y(output) = 23, the x(input) is given by:

y = 2x - 1

23 = 2x - 1

2x = 24

x = 12.

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The two most commonly used measures of variability are variance and standard deviation.

1. Variance: Variance measures how spread out a set of data points is from the mean. It calculates the average of the squared differences between each data point and the mean. The formula for variance is sum of squared differences divided by the number of data points.

Example: Let's say we have a set of data points: 2, 4, 6, 8, and 10. The mean of these data points is 6. The differences between each data point and the mean are: -4, -2, 0, 2, and 4. Squaring these differences gives us: 16, 4, 0, 4, and 16. The sum of these squared differences is 40. Dividing this sum by the number of data points (5) gives us a variance of 8.

2. Standard Deviation: Standard deviation is the square root of variance. It measures the average distance between each data point and the mean. Standard deviation is often preferred over variance because it is in the same unit as the data points, making it easier to interpret.

Example: Using the same set of data points as above, the variance is 8. Taking the square root of 8 gives us a standard deviation of approximately 2.83.

In summary, variance measures how spread out the data points are from the mean, while standard deviation gives us a more intuitive understanding of the variability by providing a measure in the same unit as the data points. These measures help us understand how the data is distributed and how much it deviates from the average.

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Answer:

hosta = $5 each

geranium = $2 each

Step-by-step explanation:

Hi, to answer this question we have to write a system of equations:

Leas's cost: 11 h + 7 g = 69

Elisa’s cost: 10h + 7g = 64

Where h is the price of one hosta and g is the price of one geranium.

Subtracting Elisa's cost to Leas's cost:

11 h + 7 g = 69

-

10h + 7g = 64

____________

h = $5

Replacing h in one equation:

11 (5) + 7 g = 69

55 +7g =69

7g = 69-55

7g= 14

g= 14/7

g= $2

The three angle bisector of a triangle intersect at a single point that point of concurrency of the angle of bisectors is called the incenter.

Given:

the 3 angle bisectors of a triangle intersect.

when three angle bisector of a triangle intersect then that point of concurrency is called incenter.

Incenter:

The incenter of a triangle is the intersection point of all the three interior angle bisectors of the triangle. In other words, it can be defined as the point where the internal angle bisectors of the triangle cross. This point will be equidistant from the sides of a triangle, as the central axis’s junction point is the center point of the triangle’s inscribed circle.

Incenter formula:

= (ax1+bx2+x3 / a+b+c  , ay1+by2+y3 / a+b+c).

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Answer: 25°

Step-by-step explanation: Notice that in this figure, we are given two triangles and to find the value of x, we first need to find the missing angle measure in the big triangle.

Since all the interior angles of a triangle add up to 180 degrees, we know that the missing angle of the big triangle is 180° - 94° - 41° or 45°.

Now we know all the angles of the big triangle and we know two of the angles of the smaller triangle, so we can find the value of x.

The missing angle of the smaller triangle will be 180° - 110 - 45° or 25°

So we know that the missing angle is 25°.

Answer: I believe those would be opposite angles (aka vertically opposite angles).

Where k is a constant

When y = 36 , x = 3 , z=3

The value of y is 40

Answer:

-2

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

Answer:

f(x)=1.25x

Step-by-step explanation:

It goes up at a constant rate of 1.25, meaning it's a linear equation. The formula for a linear equation is:

f(x)=mx+b

M = The average rate of change

B = The initial value

And since the initial value of this data starts at 0 on the x intercept, if you subtract 1.25 from 1.25 you get 0. The average rate of change is 1.25 so you would format the equation as:

f(x)=1.25x

And there is no need to add +0, which means instead of the equation being f(x)=1.25x+0, it is much simpler as f(x)=1.25x.

I hope this was helpful!

The required function to model this data is,

f(x)=1.25x.

A mathematical expression, rule, or law that specifies the relation between an independent variable and a dependent variable (the dependent variable).

The property that every input is related to exactly one output defines a function as a relation between a set of inputs and a set of permissible outputs.

It goes up at a constant rate of 1.25, meaning it's a linear equation. A linear equation is written as:

f(x)=mx+b

M = The average rate of change

B = The initial value

And since the initial value of this data starts at 0 on the x intercept, if you subtract 1.25 from 1.25 you get 0. The average rate of change is 1.25 so you would format the equation as:

f(x)=1.25x

Additionally, there is no need to include 0,

which means instead of the equation being f(x)=1.25x+0,

it is much simpler as f(x)=1.25x.

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Answer: 16, 17, and 18.

Step-by-step explanation: What I'll do I'll just let explain how to solve it and that will instantly solve your question!

The first case of business to make things easier would be to try and put this on a linear equation so...

Let the first integer be x.

Then the next consecutive two integers will be x + 1 and x + 2

x + (x + 1) + (x + 2) = 51 [Sum of the 3 consecutive integers is 51]

-> 3x + 3 = 51

-> 3x = 51 - 3

-> 3x = 48

-> x = 48/3

-> x = 16,

Thus, x + 1 = 17, x + 2 = 18

Therefore, the three consecutive integers are 16, 17, and 18.

Hope it helps ^^

First subtract the weight of the suitcase from the total weight they case can weigh when full:

50 - 5.7 = 44.3 pounds

This means she can put 44. 3 pounds of books in the suitcase.

Now find the number of books:

Divide the total Weight of what she can fit in the suitcase by the weight of each book:

44.3 / 2.4 = 18.458

Because the answer has a decimal you round down to the whole number, because if you rounded up it would weigh more than allowed.

The answer is she can carry 18 books