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The three quantities needed are the mean of X, the mean of Y, and the slope

The y-intercept of a linear regression is calculated using:

\(a = \bar y - a\bar x\)

Where:

Hence, the three quantities needed are the mean of X, the mean of Y, and the slope

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Charlotte's average rate of change is 58 pages per hour.

To find the average rate of change in Charlotte's reading progress, we can use the formula:

The average rate of change = (Change in pages) / (Change in time)

Let's calculate the change in pages and change in time first:

Change in pages = 201 - 85 = 116 pages

Change in time = 4 - 2 = 2 hours

Now we can calculate the average rate of change:

The average rate of change = (Change in pages) / (Change in time)

= 116 pages / 2 hours

= 58 pages per hour

Therefore, Charlotte's average rate of change is 58 pages per hour.

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Answer:

9.7%

Step-by-step explanation:

Given:

Observed score value = 8.5

Actual score value = 7.75

Required:

Percent error to the nearest tenth

SOLUTION:

Percent error = \frac{Value_{observed} - Value_{actual}}{Value_{actual} * 100 \)

Percent error = \frac{8.5 - 7.75}{7.75} * 100 \)

Percent error = \frac{0.75}{7.75} * 100 \)

Percent error = \frac{75}{7.75} \)

Percent error = 9.7 \) (nearest tenth)

Answer:

10) 64

14) 40

Hopes this helps:)

Answer:

6558879790645768543

Step-by-step explanation:

The income level that results in the maximum test score is approximately $45.63.. The correct answer is not provided among the given options.

To find the income level that results in the maximum test score, we need to determine the maximum point of the function represented by the equation: 607.3 + 3.85Income - 0.0423Income^2.

To find the maximum point, we can take the derivative of the function with respect to Income and set it equal to zero. Then we solve for Income.

Let's differentiate the function:

d/dIncome (607.3 + 3.85Income - 0.0423Income^2) = 3.85 - 2 * 0.0423 * Income

To find the maximum point, we set the derivative equal to zero:

3.85 - 2 * 0.0423 * Income = 0

Simplifying:

3.85 = 2 * 0.0423 * Income

Dividing both sides by 2 * 0.0423:

Income = 3.85 / (2 * 0.0423)

Income ≈ 45.63

Therefore, the income level that results in the maximum test score is approximately $45.63.

Among the given answer choices:

A. 607.3 is the constant term in the equation and does not represent an income level.

B. 91.02 is not the income level that results in the maximum test score.

C. 45.50 is close to the correct answer, but the correct approximation is $45.63.

D. The correct answer has been determined using calculus.

So, the correct answer is not provided among the given options.

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In order to make 4.5 gallons of orange juice, she will need 12 cartons of concentrated orange juice.

So,

The orange juice concentrate to water ratio is 12:36.

Now, let's call 'x' the amount of concentrated orange juice in 4.5 gallons of orange juice and 'y' the amount of water in the 4.5 gallons of orange juice we have;

We can conclude the following from equations (1) and (2):

x = 1.125 gallons of concentrated orange juice in 4.5 gallons of orange juice:

y = 3.375, the amount of water in 4.5 gallons of orange juice.

As a result, we have;

The number of fluid ounces in a carton is 12 ounces.

In 4.5 gallons of orange juice, x = 1.125 gallons = 144 fluidounces = 12 cartons of concentrated orange juice

Therefore, in order to make 4.5 gallons of orange juice, she will need 12 cartons of concentrated orange juice.

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Answer: Griffin charge $79.854 to his credit card when he bought the sneakers.

Step-by-step explanation:

Griffin ordered a pair of sneakers online.

Value of each credit point = 1 cent

Then , value of 16 credit points = 16 cents = $0.16 [1$ = 100 cents]

Cost of shoes = Rs $80

Charge to credit card = (Cost of shoes) - (Value of 16 credit points)

= $(80-0.16)

= $79.84

Hence, Griffin charge $79.854 to his credit card when he bought the sneakers.

The correct statement is Most of the songs were between 3 minutes and 3.8 minutes long.

Based on the given information from the graph, we can determine the following:

The graph shows an upward trend from 2.8 to 3.4 on the horizontal axis.

Then, there is a downward trend from 3.4 to 4 on the horizontal axis.

From this, we can conclude that most of the songs played during the one-hour interval were between 3 minutes and 3.8 minutes long. This is because the upward trend indicates an increase in length from 2.8 to 3.4, and the subsequent downward trend suggests a decrease in length from 3.4 to 4.

Therefore, the correct statement is:

Most of the songs were between 3 minutes and 3.8 minutes long.

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Answer:

A

Step-by-step explanation:

Given :

Price per folder = $2.15 .

Price per notebook = $4.60 .

The supply budget for this meeting is $150.

To Find :

Inequality represents the constraint on the number of folders f and notebooks n the office administrator can purchase.

Solution :

Let, number of folders and notebooks is f and n.

So, price of buying f and n number of folders and notebooks are :

P = 2.15f + 4.60n

Now, it is given that P ≤ $150 .

So,

2.15f + 4.60n ≤ 150

Hence, this is the required solution.

\(2.15f+2.5n\leq 150\) inequality will represent the constraint on the number of folders f and notebooks n the office administrator can purchase.

Given information:

An office administrator will be purchasing supplies for an upcoming meeting.

Staff will purchase folders, which are $2.15 each, and notebooks, which are $4.60 each.

The supply budget for this meeting is $150.

Let f be the number of folders purchased and n  be the number of notebooks purchased.

Now, the total amount spent on the whole purchase should not be greater than $150 which is the budget of the shopping.

In the form of inequality, the given condition can be written as,

\(2.15f+4.6n\leq 150\)

The total amount spent is less than equal to 150.

Therefore, \(2.15f+4.6n\leq 150\) inequality will represent the constraint on the number of folders f and notebooks n the office administrator can purchase.

For a graphical representation of the inequality, see the image attached.

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Answer:

0.98 ≤ x ≤ 2.9

Step-by-step explanation:

use graphing calculator

Answer:

Nah its odd negative

Step-by-step explanation:

Rises to the left and falls to the right.

The final answer is the probability that the boat is overloaded because the mean weight of the 70 passengers is greater than 143lb is 1.0000.

A normal distribution is a continuous data distribution with a bell-shaped curve. The normally distributed random variable X has mean \($\mu$\) and standard deviation \($\sigma$\).

In addition, the standard normal distribution represents a normal curve with a mean of zero and a standard deviation of one.

The number of standard deviations an element deviates from the mean is indicated by a standardized Z-score.

What is the theorem of the central limit?

\(z=\frac{\bar{x}-\mu_{x}}{\frac{\sigma}{\sqrt{n}}}\)

\($$\begin{aligned}P(\bar{X} > 143) &=P\left(\frac{\bar{X}-\mu}{\sigma / \sqrt{n}} > \frac{143-171}{37.7 / \sqrt{70}}\right) \\&=P(Z > -6.21) \\&=1-P(Z < -6.21) \text { (Use the Excel function NORMSDIST(-6.21)) } \\&=1-0.0000 \\&=1.0000\end{aligned}$$\)

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Use the formula shown C = 2PIr

r is the radius which is given as 3 and you are told to use 3 for pi:

C = 2(3)(3) = 18

The circumference = 18

The volume V of solid S is e - 1 cubic unit.

What is Volume?

Volume refers to the measure of three-dimensional space occupied by an object or a region. It quantifies the amount of space enclosed by the boundaries of an object or contained within a given region. In mathematical terms, volume is often calculated by integrating the cross-sectional areas of the object or region along a particular axis. Volume is typically expressed in cubic units, such as cubic meters (m^3) or cubic centimeters (cm^3). It is an essential concept in geometry, physics, engineering, and other scientific fields where the measurement of three-dimensional space is involved.

To find the volume of solid S, we need to integrate the areas of the cross sections perpendicular to the x-axis along the interval \([e, \infty).\)

The area of each square cross-section is equal to the square of the side length, which in this case is \(y = \sqrt{\ln(x)}.\)

Therefore, the volume V of solid S can be calculated as:

\(V = \int_{e}^{\infty} (\sqrt{\ln(x)})^2 dx\)

To evaluate this integral, we can simplify the expression:

\(V = \int_{e}^{\infty} \ln(x) dx\)

Using integration by parts, we let \(u = \ln(x)\)and dv = dx:

\(du = \frac{1}{x} dx\\v = x\)

Applying the integration by parts formula:

\(V = [uv] - \int v du= [x \ln(x)] - \int x \left(\frac{1}{x}\right) dx= x \ln(x) - \int dx= x \ln(x) - x + C\)

Evaluating the definite integral:

\(V = [x \ln(x) - x]_{e}^{\infty}= (\infty \cdot \ln(\infty) - \infty) - (e \cdot \ln(e) - e)= \infty - 0 - (1 - e)= e - 1\)

Therefore, the volume V of solid S is e - 1 cubic unit.

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The simplify value of numeric expression, 3 + 2, after adding 3456 then subtracting 45 and then dividing by 20 is equals the 17.8.

We have an expression of numbers, 3 + 2 we have to apply some arithematic operations on it and determine the final simplfy value. Let the expression be x = 3 + 2, add 3456 in it

=> x = 3 + 2 + 3456

Substracts 45 from above expression

=> x = 3 + 2 + 3456 - 45

Dividing the above expression of x by 20

=>

\(\frac{ x } {20} = \frac{ 3 + 2 + 3456 - 45}{20}\)

\(= \frac{3416}{20}\)

= 17.8

Hence, required simplify value is 17.8.

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To proof if a triangle is a right angled triangle, Pythagoras theorems must be obeyed

Pythagoras theorem states that

nows, lets test the triangle with pythagoras theorem

longest side, c = 97, a = 65, b = 72

Answer:

Step-by-step explanation:

You want the value of the piecewise function for various values of x.

The first step in evaluating a piecewise function is determining which domain is applicable to the value of x you have. Then you use the corresponding function, evaluating it in the usual way.

For x = -5, the applicable domain is x < -3, so the function is ...

  h(-5) = -4(-5) -18 = 20 -18

  h(-5) = 2

For x = 0, the applicable domain is -3 ≤ x < 1, so the function is ...

  h(0) = 1

For x = 1 or 4, the applicable domain is x ≥ 1, so the function is ...

  h(1) = 1 +2 = 3

  h(4) = 4 +2 = 6

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Answer:

a₄ = - 2

Step-by-step explanation:

to calculate a term in the sequence subtract 5 from the previous term

give first term a₁  = 13 , then

a₂ = a₁ - 5 = 13 - 5 = 8

a₃ = a₂ - 5 = 8 - 5 = 3

a₄ = a₃ - 5 = 3 - 5 = - 2

2x - 3y = -6

Solve for y:

-3y= -6-2x

y= (-2x-6) /-3

y= 2/3x+2

Slope intercept form:

y= mx+b

Where:

m= slope (2/3)

b= y-intercept (2)

So, to graph the function, we have to draw a line that crosses the y axis at 2, and for every 3 units moved to the right along the x-axis it goes up 2 units along the y-axis.

Jutin chooses a function J(x) = 3x - 1 that when he uses the number 7 as an input, then the output is 20.

As per the given data, Jutin chooses a function in which he uses the number 7 as an input, then the output is 20.

Here we have to determine which function Jutin has to use.

Now we have to substitute the value that x = 7 in all the given functions.

First function:

F(x) = 2\(x^{5}\)

F(7) = 2 \((7)^{5}\)

F(7) = 2 (16807)

F(7) = 33614 which is not equal to 20.

Second function:

G(x) = \(x^{2}\) - 19

F(7) = \((7)^{2}\) - 19

F(7) = 49 - 19

F(7) = 30 which is not equal to 20.

Third function:

H(x) = 13 - x

H(7) = 13 - 7

H(7) = 6 which is not equal to 20.

Fourth function:

J(x) = 3x - 1

J(7) = 3(7) - 1

J(7) = 21 - 1

J(7) = 20

The correct function is J(x) = 3x - 1

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Answer:

Option C is the correct option.

Step-by-step explanation:

Let the points be A and B

A ( -2 , 7 ) -----> ( x1 , y1 )

B ( 2 , 3 )-------> ( x2 , y2)

Now, let's find the slope:

Slope = \( \frac{y2 - y1}{x2 - x1} \)

plug the values

\( = \frac{3 - 7}{2 - ( - 2)} \)

Calculate the difference

\( = \frac{ - 4}{2 - (2)} \)

When there is a ( - ) in front of an expression in parentheses, change the sign of each term in the expression

\( = \frac{ - 4}{2 + 2} \)

Add the numbers

\( = \frac{ - 4}{4} \)

Any expression divided by its opposite equals -1

\( = - 1\)

Hope this helps..

Best regards!!

Answer:  The area = 234 \(cm^{2}\)

Step-by-step explanation:

Breadth = 13cm

Length = Breadth + 5cm = 13cm + 5cm = 18cm

Area = Length x Breadth

Area = 13 x 18 = 234\(cm^{2}\)

Answer:

Step-by-step explanation:

Here, the breadth is 5 cm less than the length of the rectangle.

Let, the length = x cm

 So, the breadth = (x-5) cm

given,

         x - 5 = 13

 or,  x = 18 cm

so the length = 18 cm

Area = length × breadth

         = 18 × 13

         = 234 cm²

Therefore, The area of the rectangle = 234 cm²

Answer:

$1920

Step-by-step explanation:

to find a percent of a number, divide the percent by 100 then multiply by the value:

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 900\\ P=\textit{initial amount}\dotfill &700\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ t=years\\\ \end{cases} \\\\\\ 900 = 700(1 + 0.06)^{t} \implies 900=700(1.06)^t\)

Answer:

70 miles per hour

Step-by-step explanation:

a) The probability that all 4 purchased games are rated mature is approximately 0.0009.

b) The probability that at least one purchased game is rated mature is approximately 0.8250.

c) The probability that none of the purchased games are rated mature is approximately 0.1750.

a) To find the probability that all 4 purchased games are rated mature, we can multiply the probability of a single game being rated mature by itself four times (assuming independence):

P(all 4 games are rated mature) = (0.141)^4

≈ 0.0009

b) To find the probability that at least one purchased game is rated mature, we can calculate the complement of the probability that none of the games are rated mature:

P(at least one game is rated mature) = 1 - P(none of the games are rated mature)

To find the probability that none of the games are rated mature, we can calculate the complement of the probability that a single game is rated mature, and then raise it to the power of 4 (assuming independence):

P(none of the games are rated mature) = (1 - 0.141)^4

≈ 0.1750

Finally, we can calculate the probability that at least one game is rated mature:

P(at least one game is rated mature) = 1 - P(none of the games are rated mature) ≈ 1 - 0.1750

≈ 0.8250

c) The probability that none of the purchased games are rated mature has been calculated in part b) as approximately 0.1750.

a) The probability that all 4 purchased games are rated mature is approximately 0.0009.

b) The probability that at least one purchased game is rated mature is approximately 0.8250.

c) The probability that none of the purchased games are rated mature is approximately 0.1750.

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Answer:

15 pieces :)

Step-by-step explanation: 30 percent of 50 is 15

Answer:

35 pieces of candy.

Step-by-step explanation:

30 percent of 50 is 15. 50 minus 15 is 35.

The company that has a lower minimum and find the minimum value will be B- f(x) at (16, 536)

The following function represents the production cost f(x), in dollars, for x number of units produced by company 1:

f(16) = 0.25(16)^2 - 8(16) + 600 = 536

So, the minimum value of f(x) is 536, and it occurs at x = 16.

In conclusion, the correct option is B.

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