Find the difference quotient of f; that is, find f(x+h)−f(x)/h, h≠0, for the following function.
f(x) = 7x + 1

f(x+h)−f(x) / h =

Answer:38

Step-by-step explanation:

Answer:

600.00

Step-by-step explanation:

Understanding :

600.00 is the actual price of the electric cooker.

Answer:

The standard deviation of the residuals calculates how much the data points spread around the regression line. The result is used to measure the error of the regression line's predictability.

Step-by-step explanation:

STDEV. S(errors) = (SQRT(1 minus R-squared)) x STDEV. S(Y). So, if you know the standard deviation of Y, and you know the correlation between Y and X, you can figure out what the standard deviation of the errors would be be if you regressed Y on X.

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

Answer:

(r - c)(4), is the profit made in George's new store after 4 months which is $4,500

Step-by-step explanation:

The given parameters for George's store are;

The amount of revenue George makes each month, r(x) = x² + 6·x + 10

The expenses each month, c(x) = x² - 4·x + 5

Where;

x = The number of months the store has opened the doors

r(x) and c(x) are measured in hundreds of dollars

The amount of profit from the store, P = Revenue - Expenses

Therefore, the profit made on a given month, x, is P(x), which is found as follows;

P(x) = r(x) - c(x) = (r - c)(x)

Therefore, (r - c)(4) = P(4), is the profit realized from George's new store, after 4 months

(r - c)(4) = 4² + 6·4 + 10 - (4² - 4·4 + 5) = 45

Answer:

The new store will have a profit of $4500 after its fourth month in business.

Step-by-step explanation:

I took the quiz

Answer:

The formula for the area of a circle is:

A = πr^2

where A is the area and r is the radius.

In this case, we are given that the area is 4π cm². Solving for the radius, we get:

4π = πr^2

r^2 = 4

r = 2

So the radius of the circle is 2 cm.

The formula for the circumference of a circle is:

C = 2πr

Plugging in the value for the radius, we get:

C = 2π(2) = 4π

Therefore, the circumference of the circle is 4π cm.

The total number of ways to line up 12 people are 479,001,600.  

We have 12 members of wedding party. We need to make arrangements for 12 people to line up for a photograph.

If we have total n objects and we need to arrange r objects then it can be done in \(^nP_r\) ways which is equivalent to =(n!/(n-r)!)

Now, here we have 12 members for photograph, we are free to choose any of members from 12 members.

So, this can be done in \(^1^2P_1_2\) ways which is equivalent to =(12!/(12-12)!)=12!/0!

We know that 0!=1

Therefore,12!/0!=12!=479,001,600

Hence, total number of ways are 479,001,600.

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To find the exponential model for the bat population in a certain Midwestern county, we use the given information that the population was 230,000 in 2012 and the observed doubling time is 31 years.

To find the exponential model n(t) = n0 * e^(rt), we need to determine the values of n0 and r. Given that the population was 230,000 in 2012, we have n0 = 230,000. Since the observed doubling time is 31 years, we can use this information to find the value of r. The doubling time formula is given by 2 = e^(r * doubling time). Substituting the values, we have 2 = e^(r * 31). Solving this equation for r, we find r ≈ 0.0223.

Therefore, the exponential model for the population t years after 2012 is n(t) = 230,000 * e^(0.0223t).

To find the exponential model n(t) = n0 * e^(rt) in the form n(t) = nge, we need to determine the value of ng. The population at time t years after 2012 can be represented as n(t) = 230,000 * e^(0.0223t). To find the value of ng, we substitute t = 0 (since we are looking for the population at the initial time) into the equation. Thus, n(0) = 230,000 * e^(0.0223 * 0) = 230,000 * e^0 = 230,000.

Therefore, the exponential model in the form n(t) = nge for the population t years after 2012 is n(t) = 230,000 * e^(0.0223t).

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Therefore , the solution of the given problem of inequality comes out to be the inequality is: 25g + 10l ≤ 250.

In mathematics, an inequality is a connection that does not have an equal sign between equations or values. Inequality precedes imbalance, therefore. When two numerical values are not equal, an inequality establishes a connection between them. Difference between equality and inequality Have used the not equal symbol, which is most often used, when values are not similar (). No issue how little or huge the values, variable inequalities are employed to contrast them.

Here,

Given:

Lacrosse balls cost $10 per pack

while golf balls price $25 per pack.

Total funds equal $250.

In order to create an inequality,

we must multiply g by the quantity of golf balls you bought and I by the quantity of lacrosse balls.

So, the inequality is:

25g + 10l ≤ 250

Therefore , the solution of the given problem of inequality comes out to be the inequality is: 25g + 10l ≤ 250.

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The Mae takes the absolute values of the forecast errors to ensure they don't cancel each other out.

By considering only the magnitude of the errors, the MAE (Mean Absolute Error) provides a measure of the average deviation between forecasts and actual values.

To ensure that forecast errors don't cancel each other out, the Mean Absolute Error (MAE) calculation involves taking the absolute values of the errors. The MAE is a commonly used metric to measure the accuracy of a forecasting model.

Forecast errors represent the differences between predicted values and actual values. These errors can be positive or negative, depending on whether the forecast overestimates or underestimates the actual value. By taking the absolute values, the direction of the error is disregarded, and only the magnitude of the deviation is considered.

By summing up the absolute values of all the forecast errors and dividing by the number of observations, the MAE provides an average measure of how far the forecasts deviate from the actual values. It allows for the evaluation of the average absolute magnitude of the errors without considering their direction.

In summary, the Mean Absolute Error (MAE) takes the absolute values of the forecast errors to ensure they don't cancel each other out. This approach allows for a measurement of the average deviation between forecasts and actual values by considering only the magnitude of the errors.

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Answer:

$2284.6

Step-by-step explanation:

Given data

Principal= $200

Rate= 7%

Time= 1980-2016= 36 years

The expression for the exponential model is given as

A= P(b)^t

b=1+r-----------because will are dealing with increase

A= P(1+r)^t

A=200(1+0.07)^36

A= 200(1.07)^36

A= 200*11.423

A=$2284.6

The value of the card is $2284.6

Answer:

13, 11

Step-by-step explanation:

common difference=-2

15+(-2)=13

13+(-2)=11

The instantaneous acceleration at any time t is given by 10t. The limit definition of a derivative is true because it allows us to find the instantaneous rate of change of a function at a specific point.

To use the limit definition of a derivative to calculate instantaneous acceleration, we need to find the derivative of the velocity function with respect to time. The derivative of velocity gives us acceleration.

The limit definition of a derivative is given by:

f'(x) = lim (h→0) [f(x+h) - f(x)] / h

To calculate instantaneous acceleration, we substitute the velocity function, v(t), into the limit definition. Let's say v(t) = 5t^2.

Using the limit definition, we have:

a(t) = lim (h→0) [v(t+h) - v(t)] / h

Substituting v(t) = 5t^2, we get:

a(t) = lim (h→0) [5(t+h)^2 - 5t^2] / h

Expanding and simplifying:

a(t) = lim (h→0) [10th + 5h^2] / h

Now, we can cancel out the h term:

a(t) = lim (h→0) 10t + 5h

Taking the limit as h approaches 0, we get:

a(t) = 10t

Therefore, the instantaneous acceleration at any time t is given by 10t.

The limit definition of a derivative is true because it allows us to find the instantaneous rate of change of a function at a specific point. By taking the limit as the change in input approaches zero, we are able to approximate the exact rate of change at that point. This concept is fundamental to calculus and is used in various applications such as physics, engineering, and economics.

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Answer:

x=2 is the answer.

Step-by-step explanation:

10+2x+6x=26

10+8x=26

Subtracting 10 on both sides to find out the value of x

10-10+8x=26-10

8x=16

Dividing 8 on both sides

8x/8=16/8

x=2

Hope it will help ^_^

Answer:

Step-by-step explanation: I hope it helps :)

\(10 + 2x + 6x = 26\\\\\mathrm{Add\:similar\:elements:}\:2x+6x=8x\\10+8x=26\\\\\mathrm{Subtract\:}10\mathrm{\:from\:both\:sides}\\10+8x-10=26-10\\\\Simplify\\8x=16\\\\\mathrm{Divide\:both\:sides\:by\:}8\\\frac{8x}{8}=\frac{16}{8}\\\\Simplify\\x =2\)

Answer:

Step-by-step explanation:

The loop will run an infinite number of times

Answer:

For 100 miles he uses 3.571 gallons of gasoline.

In equation form it is y/x*100

Step-by-step explanation:

Unitary Method

He travels 28 miles per gallon of gasoline.

For 1 mile he uses  1/28 gallons

For 100 miles he uses 1/28 * 100= 100/28= 3.571 gallons of gasoline.

Let x be the miles and y be the gallons of gasoline used to travel x miles.

Then for 1 mile  the gallons of gasoline used will be y/ x gallons.

For 100 miles  the gallons of gasoline used will be y/x *100 gallons.

In equation form it is y/x*100 gallons for 100 miles where x is the number of miles and y is the amount of gallons.

Answer:

You forgot the rest of the function, but if x is -2, then the function is represented by f(x)=-2x

If you supply more information the equation would be different.

Step-by-step explanation:

The equation of the tangent to the curve y = x^2 + 1 at the point (1,2) is y = 2x - 1.

To find the equation of the tangent line at a point (x0, y0), the first step is to calculate the slope of the tangent line at this point. This can be done using the derivative of the function at the point: Slope = dy/dx = 2x0

Since the point (x0, y0) is (1,2) in this case, the slope of the tangent line is:
Slope = dy/dx = 2(1) = 2
y1 = mx1 + b
We can substitute in the values we have already calculated:
2 = 2(x1) + b

Now, we can solve for b:
2 = 2x1 + b
2 - 2x1 = b
b = 2 - 2x1

Now, we can substitute in the values for x0 and b to get the equation of the tangent line:
y = 2x - (2 - 2x1)
y = 2x - 1
Therefore, the equation of the tangent to the curve y = x2 + 1 at the point (1,2) is y = 2x - 1.

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Answer:

27) 4.2

28) D

Step-by-step explanation:

Answer:

27. A 4.2ft

28. D

Step-by-step explanation:

27. Since this is a right triangle, we can use a^2 + b^2 = c^2

3.1^2 + b^2 = 5.2

b = sqrt(5.2^2 - 3.1^2)

b = 4.2ft A

28. sqrt(10^2 + 50^2) does not equat 54, this is not a right triangle.

Answer: 33.81<=w<=33.91

Step-by-step explanation:

w=weight in ounces

33.86-0.05<=w<=33.86+0.05 ==> 0.05 weight difference form 33.86, the ideal weight.

33.81<=w<=33.91

Answer:

a) Label the points given (give the ordered pair).

b) What is the unit rate?

c) Plot and label the point whose ordered pair represents the unit rate.

d) What are the coordinates of that point?

e) Explain what the point that you plotted means in this context of this problem.

f) Write an equation for this graph. ​

Answer:

it's B. y = x + 3

You can test it by putting the values of x in the equation.

The integral of (42³ - 2r + 7) dz is equal to (42³ - 2r + 7)z + C.

To integrate the function (42³ - 2r + 7) dz, we treat r as a constant and integrate with respect to z. The integral of a constant with respect to z is simply the constant multiplied by z:

∫ (42³ - 2r + 7) dz = (42³ - 2r + 7)z + C

where C is the constant of integration.

Note: The integral of a constant term (such as 7) with respect to any variable is simply the constant multiplied by the variable. In this case, the variable is z.

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Given:

The function is,

a) The graph of the given function us,

Answer: option B)

b) f(1) and f(5) is,

Answer:

c) the domain of the function is,

Answer:

$13.01 per student

Step-by-step explanation:

Answer:

Amount to be raised=$592.61

Amount available = $345.42

Amount remaining = $592.61-$345.42=$247.19

Each student will raise $247.19/19 = $13.01

Step-by-step explanation:

the coordinate for P is (-3,6)

The range for this function is (0,800].

What is a geometric progression?

It is a sequence of terms in which the succeeding term is can be found out by multiplying with a constant non zero value.

here the first term is 800 as it is the initial price. We can see that the common ratio is less than 1 which is 0.82, hence its a decreasing progression.

so the maximum value in range is 800

as x tends to infinity the equation tends to 0

hence the funtion apporaches 0

so the range will be (0,800]

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Using geometric progression, the range for this function is (0,800].

A mathematical sequence known as a geometric progression (GP) is one in which each following phrase is generated by multiplying each preceding term by a fixed integer, or "common ratio."

This progression is sometimes referred to as a pattern-following geometric sequence of numbers.

Here the first term is 800 as it is the initial price. We can see that the common ratio is less than 1 which is 0.82.

Hence it's a decreasing progression.

So, the maximum value in the range is 800.

As x tends to infinity the equation tends to 0.

Hence, the function approaches 0

So the range will be (0,800].

Therefore, using a geometric progression, the range for this function is (0,800].

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The dimensions 36 x 27 inches are too small to allow a 48-inch piece of glass to fit through it.

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