An equation was created for the line of best fit from actual enrollment data. It was used to predict the dance studio enrollment values shown in the table below:

Enrollment
Month
January
February
March
April
May
June
Actual
500
400
550
550
750
400
Predicted
410
450
650
650
600
450
Residual
90
−50
−100
−100
150
−50
Analyze the data. Determine whether the equation that produced the predicted values represents a good line of best fit. (1 point)

Group of answer choices
No, the equation is not a good fit because the sum of the residuals is a large number.

No, the equation is not a good fit because the residuals are all far from zero.

Yes, the equation is a good fit because the residuals are not all far from zero.

Yes, the equation is a good fit because the sum of the residuals is a small number.

Answer:

-10x

Step-by-step explanation:

Answer:

Use the bodmas rule and do..

Solve in this order

B=bracket

O=of (multiply)

D=divison

M=multiplication

A=addition

S=subtraction

Step-by-step explanation:

U should remember this, it is very important and useful:))

Answer:

3÷4 = 0.75

Step-by-step explanation:

We are to find:

3÷ 4

3÷4 =

= 3 ÷ 4

= 3 × 1/4

= 3 × 0.25

= 0.75

Answer:

85%

Step-by-step explanation:

900-6000 divided by 6000

multiply your answer by 100

that will give you your answer

The discount rate is kept above the federal funds rate because the Fed prefers that banks borrow reserves from each other in order to maintain a stable and competitive interbank lending market.

The discount rate is kept above the federal funds rate because the Fed prefers that banks borrow reserves from each other. So, the correct answer is option C) above; banks borrow reserves from each other. This is because the Federal Reserve wants to encourage banks to borrow from each other in the open market, which promotes stability and liquidity within the banking system.

                                  This helps to ensure that banks have access to necessary funds and can lend to customers at reasonable rates. Therefore, option D is incorrect and the correct answer is A) below; banks borrow reserves from each other.
                          The discount rate is kept above the federal funds rate because the Fed prefers that banks borrow reserves from each other.

                            So, the correct answer is option C) above; banks borrow reserves from each other. This is because the Federal Reserve wants to encourage banks to borrow from each other in the open market, which promotes stability and liquidity within the banking system.

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Answer:

Step-by-step explanation:

45÷8 = 5.625

Since none of the 13 classmates had been given math homework between the original survey and Kelly's second survey, the sum of the values in the second data set is the same as the sum of the values in the original data set. Therefore, the change in the means can be determined without calculating the mean of either data set by considering the number of data points in each set.

Since both data sets have the same number of data points, the change in the means will be zero. This is because the mean is calculated by dividing the sum of the values by the number of data points, and since the sum of the values is the same in both data sets, the means will also be the same.

In other words, if the mean of the first data set is x, then the sum of the values in the first data set is 13x (since there are 13 classmates), and the sum of the values in the second data set is also 13x (since none of the values have changed). Therefore, the mean of the second data set will also be x, and the change in the means will be zero.

A second-order linear homogeneous differential equation has the general formula y"+py'+qy=0. By using this formula, we can calculate the solution of the given initial value problem:y"+14y'+49y=0

An initial value problem is used to find the value of the function at a certain point given its derivative and the function's value at that point. Similarly, the initial value problem for the differential equation y"+14y'+49y=0 specifies the function's values at the point x=1 and its derivative at that point.

We can solve the differential equation by applying the general formula y"+py'+qy=0. By using this formula, we can get the auxiliary equation which is m^2+14m+49=0. After factoring this equation, we can derive the solution y(x)=e^(-7x)(c1+c2x).

Here, c1 and c2 are constants that depend on the initial conditions of the problem. By applying the initial conditions y(1)=0 and y'(1)=1, we can calculate the values of c1 and c2. We find that c1=e^7 and c2=-e^7. By substituting these values in the equation for the solution, we get the final answer y(x)=xe^7+e^(-7x)(1+x)e^7. Therefore, we have solved the initial value problem for the given differential equation.

The differential equation y"+14y'+49y=0 has been solved by using the general formula y"+py'+qy=0. The solution to the differential equation is y(x)=e^(-7x)(c1+c2x) which can be determined by finding the auxiliary equation. The values of the constants c1 and c2 can be calculated by applying the initial conditions y(1)=0 and y'(1)=1. Finally, we can substitute the values of c1 and c2 in the equation for the solution to get the final answer y(x)=xe^7+e^(-7x)(1+x)e^7.

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The percentage change in frequency is 0%.Hence, the natural frequency of torsional vibration of the custen is given by f = 25.7 / L₀^(1/2) and the percentage change in frequency is 0%.

We are given that:

Total moment of inertia of moving parts = I = 1 kgm²

Moment of inertia of air-screw = I = 18 kgm²

Outer diameter of hollow shaft = D₀ = 80 mm

Inner diameter of hollow shaft = Dᵢ = 35 mm

Length of hollow shaft = L = 0.30 m

Stiffness of the crank-throw = K = 2.5 × 10⁴ Nm/rad

Shear modulus of elasticity = G = 83000 N/mm²

We need to calculate the natural frequency of torsional vibration of the custen.

The formula for natural frequency of torsional vibration is: f = (1/2π) [(K/L) (J/GD)]^(1/2)

Where, J = Polar moment of inertia

J = (π/32) (D₀⁴ - Dᵢ⁴)

The formula for equivalent length of hollow shaft is given by:

q₁ = q₁₁ + q₁₂

Where, q₁₁ = (π/32) (D₀⁴ - Dᵢ⁴) / L₁q₁₂ = (π/64) (D₀⁴ - Dᵢ⁴) / L₂

L₁ = length of outer diameter

L₂ = length of inner diameter

For the given shaft, L₁ + L₂ = L

Let L₁ = L₀D₀ = D = 80 mm

Dᵢ = d = 35 mm

So, L₂ = L - L₁= 0.3 - L₀...(1)

For the given crank-throw, q₁ = (π/32) (D⁴ - d⁴) / L, where D = 80 mm and d = 80 mm

Hence, q₁ = (π/32) (80⁴ - 35⁴) / L

Therefore, q₁ = (π/32) (80⁴ - 35⁴) / L₀...(2)

From the formula for natural frequency of torsional vibration, f = (1/2π) [(K/L) (J/GD)]^(1/2)

Substituting the values of K, J, G, D and L from above, f = (1/2π) [(2.5 × 10⁴ Nm/rad) / (L₀) ((π/32) (80⁴ - 35⁴) / (83000 N/mm² (80 mm)³))]^(1/2)f = (1/2π) [(2.5 × 10⁴ Nm/rad) / (L₀) (18.12)]^(1/2)f = 25.7 / L₀^(1/2)...(3)

Now, if we assume that the air-screw mass is infinite, then the moment of inertia of the air-screw is infinite.

Therefore, the formula for natural frequency of torsional vibration in this case is:

f = (1/2π) [(K/L) (J/GD)]^(1/2)Substituting I = ∞ in the above formula, we get:

f = (1/2π) [(K/L) (J/GD + J/∞)]^(1/2)f = (1/2π) [(K/L) (J/GD)]^(1/2)f = 25.7 / L₀^(1/2)

So, in this case also the frequency is the same.

Therefore, the percentage change in frequency is 0%.Hence, the natural frequency of torsional vibration of the custen is given by f = 25.7 / L₀^(1/2) and the percentage change in frequency is 0%.

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Answer:

.5 or 1/2

Step-by-step explanation:

Answer:

V = 276.32 ft^3

Step-by-step explanation:

Volume of a cylinder is

V = pi r^2 h

The diameter is 4 so the radius is d/2 = 4/2 = 2

V = (3.14) ( 2)^2 * 22

V = 276.32 ft^3

Answer:

Yes, will be

\((3x - 2)2 = 6x - 2 = 4x\)

Because the 4x it doesn't t affect the 6x and the 6x is

\(6 \times x\)

So the result will be 4x

Answer:

-9x^2 + 16x - 4

Step-by-step explanation:

The transformation represented by the rule (x, y) → (-x, -y) is a reflection across the origin.

The rule (-x, -y) reflects each point (x, y) across both the x-axis and the y-axis simultaneously. When a point is reflected across the x-axis, its y-coordinate changes sign, and when a point is reflected across the y-axis, its x-coordinate changes sign. Therefore, the rule (-x, -y) reflects a point (x, y) across both axes, resulting in the point (-x, -y).

A reflection across the origin involves reversing the sign of both the x-coordinate and the y-coordinate. This means that the transformation takes each point (x, y) and maps it to the point (-x, -y), effectively reflecting it across the origin (0, 0).

Thus, the given rule represents a reflection across the origin, and it can also be described as a rotation of 180° about the origin.

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Answer:

$34

-----------------------

The cost of direct labor per unit is $5.628 per apple.

To calculate the cost of direct labor per unit, we need to determine the total labor hours required to produce one unit of output and then multiply it by the wage rate.

Let's denote the labor hours required for the first resource as "L₁" and the labor hours required for the second resource as "L₂".

The first resource has a capacity of 2.1 apples per hour, and the demand is 1.6 apples per hour. Therefore, the labor hours required for the first resource per unit of output are:

L₁ = 1 apple / (2.1 apples/hour) = 0.4762 hours/apple (rounded to 4 decimal places)

The second resource has a capacity of 4.4 apples per hour, and the demand is 1.6 apples per hour. Therefore, the labor hours required for the second resource per unit of output are:

L₂ = 1 apple / (4.4 apples/hour) = 0.2273 hours/apple (rounded to 4 decimal places)

Now, let's calculate the total labor hours required per unit:

Total labor hours per unit = L₁ (first resource) + L₂ (second resource)

= 0.4762 hours/apple + 0.2273 hours/apple

= 0.7035 hours/apple (rounded to 4 decimal places)

Finally, to calculate the cost of direct labor per unit, we multiply the total labor hours per unit by the wage rate:

Cost of direct labor per unit = Total labor hours per unit * Wage rate

= 0.7035 hours/apple * $8/hour

= $5.628 per apple (rounded to 3 decimal places)

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Answer:

x=30

Step-by-step explanation:

You have to use intercept theorem, also known as Thales's theorem to slvoe this.

Answer:

0.0000889

Step-by-step explanation:

Conversion : -

1 mg = 0.00001 hg

8.90 mg

Multiply 8.90 with 0.00001 to convert to hg,

8.90 x 0.00001

= 0.000089 hg

Answer:

The point of intersection is located at approximately (1.75,7.75), which means both planes will be at an altitude of about 7,750 feet after approximately 1.75 minutes, or 1 minute, 45 seconds.

This is what the graph looks like:

Step-by-step explanation:

The intersection of the lines will be (1.692, 7.769). Then the graph of the lines is drawn below.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Plane A is plummeting toward the neighborhood air terminal at a pace of 2,500 feet/minute. It is right now at an elevation of 12,000 feet. Plane B is climbing from a similar air terminal at a pace of 4,000 feet/minute. It is at present at an elevation of 1,000 feet. This arrangement of conditions models what is happening, where x addresses the time in minutes and y addresses the elevation in a large number of feet:

y = 12 − 2.5x              ...1

y = 1 + 4x                  ...2

From equations 1 and 2, we have

1 + 4x = 12 - 2.5x

6.5x = 11

x = 1.692

Then the value of 'y' will be given as,

y = 12 - 2.5 (1.692)

y = 7.769

The intersection of the lines will be (1.692, 7.769). Then the graph of the lines is drawn below.

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Answer:

The second week had 10 more golfers than the first week.

Step-by-step explanation:

The graph clearly shows that the second week golfer are more than the first week. The median for week 2 is greater than the median of week 1. The graph of week 2 shows that number of golfers had increased and their age is between 60 to 80 years of age. The median of week 2 is 79 where as median of week 1 is 75.

Answer:

3 classmates

Step-by-step explanation:

1/9 = 0.111111...

27 x 1/9 = 3

Answer:

19/0.8 23,75 or 23 3/4

and go to elementary school

Answer:

23.75

Step-by-step explanation:

You need to isolate for x. To do that divide both sides by 0.8 to leave only x on the left side and 19/0.8 on the right side. Then simplify the right side to get 23.75

The sales tax rate is 8%.

The correct option is (b).

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Jenny bought scrapbooking supplies for $145.00.

She paid $11.60 in sales tax.

let the tax rate be x%.

So, the price without sales tax = 145 - 11.6 = $133.4

Thus, x% of 133.4 = 11.6

133.4 x = 1160

x = 8.65%

x= 8%

Hence, the tax rate is 8%.

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24 different seatings are possible when five people are to be seated around a circular table such that two seatings are considered the same if one is a rotation of the other.

A rule used to count the entire number of alternative outcomes in a circumstance is known as the fundamental counting principle. It asserts that if there are n ways to do something and then m ways to do something else, then there are nm methods to do both of these acts. The Fundamental Principle of Counting assists in determining how selection is made based on available options. The Fundamental Principle of Counting streamlines the method to choosing by taking into account all of the available options and their combinations in order to calculate the Probability.

Here,

Since there are 5 peoples,

let us fix the first person and remaining will be set according to that.

this can be arranged in,

(5-1)!=4!

=24 ways

When five persons are sitting around a circular table, 24 distinct seatings are available, with two seatings regarded the same if one is a rotation of the other.

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Answer:

2^(3/7)

Step-by-step explanation:

For these types of questions, what is inside the root is the numerator, and what is on top is the denominator.

3 is in the root, so it is the numerator

7 is outside the root, so it is the denominator

Therefore, The answer is 2^(3/7)

Answer:

$421.72

Step-by-step explanation:

Compounded Monthly Interest Rate Formula: A = P(1 + 4/12)^12t

Simply plug in our known variables:

A = 120(1 + 0.06/12)²¹⁽¹²⁾

A = 120(1.005)²⁵²

A = 120(3.51437)

A = 421.724

Solve for dy/dx:   dy/dx = (-2x) / (2y) = -x / y which gives the slope of tangent line using implicit differentiation

To find the slope of a tangent line using implicit differentiation, follow these steps:

1. Start with the given equation that represents the relationship between x and y in the form of an equation involving both variables, for example: F(x, y) = 0.

2. Differentiate both sides of the equation with respect to x using the chain rule whenever necessary. Treat y as a function of x and apply the derivative rules accordingly.

3. After differentiating, have a resulting equation involving both x, y, and their derivatives (dy/dx). Rearrange the equation if necessary to isolate dy/dx on one side.

4. Solve for dy/dx to find the derivative of y with respect to x. This will give the slope of the tangent line at any given point on the curve defined by the implicit equation.

Note: The resulting expression for dy/dx may involve both x and y variables. To find the slope of the tangent line at a specific point, substitute the coordinates of that point into the expression for dy/dx.

Here's an example to illustrate the process:

Given the implicit equation: \(x^2 + y^2 = 25\)

1. Start with the equation: \(x^2 + y^2 = 25.\)

2. Differentiate both sides with respect to x:

  2x + 2y * (dy/dx) = 0

3. Rearrange the equation to isolate dy/dx:

  2y * (dy/dx) = -2x

4. Solve for dy/dx:

  dy/dx = (-2x) / (2y)

         = -x / y

Now, have the expression for the slope of the tangent line in terms of x and y. To find the slope at a specific point, substitute the coordinates of that point into the expression.

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The possible values of a are 1,2, and 4 from quadratic equation

Given a quadratic 4x^2 + bx + c, Jimmy successfully factors it as (ax + b)(cx + d), where a, b, c and d are integers. We are to determine the possible values of a

To find the value of a, we first need to multiply (ax + b)(cx + d). This gives

(ax + b)(cx + d) &= acx^2 + (ad + bc)x + bd \\&= 4x^2 + bx +c

Comparing the coefficients of x^2, we get ac = 4

Since a and c are integers, the only possible values of a and c are a = 1, c = 4or a = 2, c = 2 or a = 4, c = 1.

Comparing the constant terms, we get bd = c and so b and d are factors of c.

Therefore, the possible values of a are 1,2 and 4

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The value of the definite integral of f(x) over the interval [10, 12] is approximately 1.899.

To integrate f(x) = 1² - √x over the interval [10, 12], we can use the definite integral formula:

∫[a,b] f(x) dx = [F(b) - F(a)]

where;

First, let's find the antiderivative of f(x):

∫(1² - √x) dx = ∫1 dx - ∫√x dx

= \(x - \frac{2}{3} x^{3/2} + C\)

where;

Now, we can evaluate the definite integral over [10, 12]:

[F(12) - F(10)] = [(12 - (2/3)(12)^(3/2)) - (10 - (2/3)(10)^(3/2))]

= [12 - (2/3)(12)^(3/2) - 10 + (2/3)(10)^(3/2)]

≈ 1.899

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The complete question is below:

integrate f(x) = 1² - √x, over the interval [10, 12].

The chicken will weigh 3 pounds when it is 10,000 miles from the earth's center.

There are two types of proportions.

1) Direct Proportion - shows the direct relationship between two quantities. It can be represented by the equation y = kx. As one quantity increases, the other quantity also increase.

2) Inverse Proportion - describes the indirect relationship between two quantities.  It can be represented by the equation y = k/x. As one quantity increases, the other quantity decreases.

According to the problem, a body’s weight varies inversely with the square of its distance from the center of the earth.

y = k/x

let y = a body's weight

x = square of its distance from the center of the earth

Solving for the proportionality constant, k.

y = k/x

12 = k / (5000^2)

k = 12 x 25, 000, 000

k = 300, 000, 000

The equation for the relationship in the problem can now be represented by:

y = 300,000,000/x

where

y = a body's weight

x = square of its distance from the center of the earth

Evaluating the new equation where x = square of 10,000:

y = 300,000,000/x

y = 300,000,00/(100,000,000)

y = 3

Hence, the chicken will weigh 3 pounds when it is 10,000 miles from the earth's center.

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The decimal expansion of 7/8 is also a repeating decimal, starting with 0.8 7 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...

In summary, the decimal expansions of the given rational numbers are:

- 7/15 = 0.4 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 ...
- 7/9 = 0.7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 ...
- 7/10 = 0.7
- 7/8 = 0.8 7 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...

To convert a rational number to a decimal expansion, we need to divide the numerator by the denominator.
Let's start with 7/15. To find its decimal expansion, we can use long division:

     0.4 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 ...
   ------------------------
15 | 7.000 000 000 000 000 ...
       6 0
       ------
         10
          9
         ---
           10
            9
           ---
             10
              9
             ---
               10
                9
               ---
                 10

As we can see, the decimal expansion of 7/15 is a repeating decimal that starts with 0.4 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 ...

Next, let's look at 7/9. We can again use long division:

      0.7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 ...
   ------------------------
9  | 7.000 000 000 000 000 ...
       6 3
       ------
         10
          9
         ---
            10
             9
            ---
              10
               9
              ---
                10

So the decimal expansion of 7/9 is a repeating decimal that starts with 0.7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 ...

Moving on to 7/10, we can simply divide 7 by 10:

7 ÷ 10 = 0.7

Therefore, the decimal expansion of 7/10 is simply 0.7.

Finally, let's look at 7/8. Using long division:

      0.8 7 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...
   ------------------------
8  | 7.000 000 000 000 000 ...
       6 4
       ------
         30
         24
         ---
          60
          56
          ---
           40
           32
           ---
            80
            72
            ---
             80
             72
             ---
              80

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