George has opened a new store and he is monitoring its success closely.

He has found that this store’s revenue each month can be modeled by r(x)=x2+6x+10 where x represents the number of months since the store opens the doors and r(x) is measured in hundreds of dollars.

He has also found that his expenses each month can be modeled by c(x)=x2−4x+5 where x represents the number of months the store has been open and c(x) is measured in hundreds of dollars.



What does (r−c)(4) mean about George's new store?



Responses

The new store will have a profit of $2300 after its fourth month in business.
The new store will have a profit of $2300 after its fourth month in business.

The new store will sell 4500 items in its fourth month in business.
The new store will sell 4500 items in its fourth month in business.

The new store will sell 2300 items in its fourth month in business.
The new store will sell 2300 items in its fourth month in business.

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

The statement is examined using the equation to find that

1. False

2. False

3. True

4. False

The given equation is

f(x) = 32 / ( 1 + e⁰°⁵ˣ)

Evaluating the first statement by substituting

For x = 3, f(3 ) gives 5.84

For x = 6, f( 6) gives  1.52

5.82 - 1.52 is not equal to 9 ft hence the statement is False

Evaluating the second statement by substituting

when x = 0, the function gives 16 which is against 2 ft hence False

Evaluating the third statement by substituting

For x = 1, f(1) = 12.08 this is less than 16 ft hence a decline hence this is True

fourth statement

The trees maximum height, captured should be 16 ft not 35 ft hence False

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The first term of GP is  a₁ = -4.

Given that,

Sum of five terms of GP = s₅ = -16.3804

Common ratio = 9/10  which is less than 1

Number of terms = n = 5

We know that,

Sum of nth term of GP when common ration is less than 1,

s₅ = a₁(1-[tex]r^{n}[/tex])/(1-r)

Substituting the values,

⇒ -16.3804 = a₁(1-0.9⁵)/(1-0.9)

⇒             a₁ = -16.3804/4.0951

⇒             a₁ = -4

Hence, the value of  a₁ is -4.

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If the volume of an open rectangular object or space is 24.3m³ with a height of 2.7m, the surface area is 9m.

The surface area can be determined by dividing the volume by the height.

This is because the product of the surface area and the height gives the volume.

The surface area is a product of the length and width, while the volume is the product of the length, width, and height.

Volume = 24.3m³

Height = 2.7m

Surface area = 9m (24.3m³ ÷ 2.7)

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Given that this is an isosceles triangle, then the lengths of the sides opposite the two 45º angles have to be the same length.

For this reason, x = 8.

And since x = 8 and there's only one answer with x=8, the first option must be the answer.

You can calculate the value of y using the Pythagorean Theorem.  

   [tex]y^2 = 8^2+8^2[/tex]
which will lead you to [tex]y=8\sqrt{2}[/tex].  

The term (100 C 15) represents the number of ways to choose 15 defective screws out of 100 packs.

In a scenario where there are 2 defective screws out of 100 packs, each containing 500 screws, we can calculate the probability of obtaining 15 defective screws. Let's assume that each pack is independent of the others.

The probability of a single screw being defective is 2/500, as there are 2 defective screws out of 500 in each pack.

Conversely, the probability of a screw being non-defective is 498/500.

To find the probability of obtaining exactly 15 defective screws, we can use the binomial distribution formula. The probability (P) can be calculated as follows:

P = (100 C 15) * (2/500)^15 * (498/500)^85

The term (100 C 15) represents the number of ways to choose 15 defective screws out of 100 packs.

By plugging these values into the formula and performing the calculations, the probability of obtaining exactly 15 defective screws can be determined. However, I am unable to perform the calculation for you within the given word limit.

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The total volume is the one in option C, 708 cubic centimeters.

We know that this prism can be divided into two prisms, and remember that the volume of a prism is equal to the product between its dimensions.

Then the volume of the first prism is:

V = 8cm*6cm*13cm = 624 cm³

And the volume of the second prism is:

v' = 3cm*4cm*7cm = 84 cm³

Adding that we will get:

total volume =  624 cm³+  84 cm³ = 708 cm³

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"The correct option is (C) $25w < $168." This means that Joe needs to save for at least 7 weeks (since he can't save for a fraction of a week) to afford the hoverboard.

The hoverboard costs $168 and Joe earns $25 each week. To determine if Joe can afford the hoverboard, we need to determine how many weeks he needs to save to reach the cost of the hoverboard.

Let's represent the number of weeks Joe needs to save as "x". Each week, he earns $25, so the total amount he will have after "x" weeks is 25x. In order to buy the hoverboard, he needs to have saved $168. Thus, we can write the inequality:

25x ≥ 168

This inequality represents the fact that the amount of money Joe earns after "x" weeks must be greater than or equal to $168, the cost of the hoverboard, for him to be able to afford it. Simplifying this inequality, we get:

x ≥ 6.72.

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A higher credit score reduces your fixed costs because you will pay lower interest rates. That is option A.

A higher credit score is one of the factors that are being considered by banks or lenders before one is being viewed as being legible to borrow money.

This is soo because a higher credit score will reduce the lending interest rates of the individual because it shows such will pay back the borrowed money as soon as possible.

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9. The ball returns to 98.00% of its previous height after each bounce Option B

10. It will take 183 bounce until the ball bounces back to a height less than 3 inches.  Option B

To solve for k% of previous height after each bounce, we say

10×(k/100)⁵ = 9.04

k = [tex](9.04/10)^{1/5}[/tex]×100

k = 98.00

To find out how many bounces it takes for the ball to bounce back to a height less than 3 inches (or 0.25 feet), we use the inequality

10 × (0.961)ⁿ < 0.25

The logarithm of both sides gives

n × log(0.961) < log(0.025)

n > log(0.025) / log(0.961)

n > 182.593

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Answer:

C. Through a given point not on a given line, there is exactly one line parallel to the given line.

Step-by-step explanation:

hope i helped

Answer:

Look down

Step-by-step explanation:

Thanks for reaching out for assistance! Based on the context you provided, it seems like the correct answer is C. Playfair's axiom states that there is exactly one line parallel to a given line that can be drawn through a point not on it. I hope this helps! Let me know if there's anything else I can do for you.

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The compound interest is solved and the amount in her account in 2047 is given by A = $ 1315.46

Given data ,

To determine how much money Carly has in her account after 37 years, we need to substitute the value of t as 37 into the equation:

P = 600(1.0375)^t

P = 600(1.0375)^37

P ≈ 600(1.0375)^37 ≈ 600(2.19243) ≈ $ 1315.46

Therefore , Carly has approximately $1315.46 in her account after 37 years.

To calculate the growth rate, we need to find the rate of change between the initial and final amounts over the given time period.

Regarding how long it takes for Carly's account to reach $750, we'll assume you mean when the account reaches or exceeds $750. Let's set up the equation and solve for t:

750 = 600(1.0375)^t

Dividing both sides by 600, we get:

1.25 = 1.0375^t

Taking the logarithm of both sides (base 1.0375):

log(1.25) = t * log(1.0375)

t ≈ log(1.25) / log(1.0375) ≈ 8.5 years

Hence , it takes approximately 8.5 years for Carly's account to reach or exceed $750

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Answer: 8000

Step-by-step explanation:

The mean absolute deviation for the data-set in the table is given as follows:

1.52 million.

The mean for the data-set in this problem is given as follows:

(1.5 + 3.8 + 1.3 + 1.6 + 2.9 + 1.4 + 0.9 + 2.3 + 8.4 + 1.3)/10 = 2.54.

The deviations are given as follows:

Hence the mean absolute deviation is given as follows:

(1.04 + 1.26 + 1.24 + 1.06 + 0.46 + 1.14 + 1.64 + 0.24 + 5.86 + 1.24)/10 = 1.52 million.

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Answer:

dwdaddaw

Step-by-step explanation:

ad plus devide

Answer: 2/13.86

Step-by-step explanation:

A lines rate of change is equal to it's slope

Slope is rise over run (Y/X)

The point is up 2 on the Y axis and over 13.86 on the X axis

The slope is= 2/13.86

A type of transportation is LEAST likely to take more than 30 minutes include the following: d. train.

In order to determine the type of transportation that is least likely to take more than 30 minutes for Conrad to get to an appointment at the other end, we would have to compare the median minute for each data set (type of transportation) that is represented on the box-and-whisker plot shown above.

By critically observing the box-and-whisker plot, we can reasonably infer and logically deduce that a train is the type of transportation that is least likely to take more than 30 minutes because its median minute is the lowest compare to the other data set (type of transportation) that is represented on the box-and-whisker plot shown above.

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Answer:

If it can be exactly 150, then 50.

there’s not exactly enough info for me to solve.

The measure of value of ∠5 is 83°.

Now, It is given that;

Two Lines m and n are parallel with each other and l is the transversal crossing the two given parallel lines.

And, m∠6 = 97°,

Since, Two rays combined into an angle have a single terminal. The point is known as the vertex of the angle, while the rays are known as its sides, occasionally as its legs, and occasionally as its arms.

Hence, Then by using the property of liner pair angles, we have

⇒ m∠5 + m∠6=180°

(Because they form a linear pair angles.)

⇒ m∠5 + 97 = 180

Subtract 97 both side, we get;

⇒ m∠5 + 97 - 97 = 180 - 97

⇒m∠5 = 180 - 97

⇒m∠5 = 83°.

Therefore, the value of the measure of ∠5 is,

⇒ ∠5 = 83°.

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The symmetric equations for the line are:

(36x + 40y - 28z - 100) / 0 = (x-5) / -6 = (y-8) / -5 = (z+2) / 7

To find the parametric equations for the line passing through A(5, 8, -2) and B(-1, 3, 5), we can use the vector equation:

r = A + t(B-A)

where r is the position vector of any point on the line, t is a scalar parameter, and A and B are the given points. Substituting the values, we get:

r = (5, 8, -2) + t((-1)-5, 3-8, 5-(-2))

r = (5, 8, -2) + t(-6, -5, 7)

The parametric equations for the line are:

x = 5 - 6t
y = 8 - 5t
z = -2 + 7t

To find the symmetric equations, we can use the fact that any point on the line is equidistant from points A and B. Thus, the distance from a point (x, y, z) to A must be the same as the distance from the same point to B. Using the distance formula, we get:

√[(x-5)² + (y-8)² + (z+2)²] = √[(x+1)² + (y-3)² + (z-5)²]

Squaring both sides and simplifying, we get:

36x + 40y - 28z - 100 = 0

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Answer: If the number is placed on the X as in (X,Y) the X value will rise but the Y value will stay the same, but if the number is played on the Y, the Y value will go up, and the X value will stay the same

The solution is it's hard to say which company would be cheaper to hire based on the information provided, but it's recommended to check the warranty, prices of parts, and reputation of both companies, and to get a second opinion or quote from both companies before making a decision.

Here,

we can see that the function C(x) = 25x + 75 represents the labor cost (in dollars) for Bob's Auto Repair to replace your alternator, where x is the number of hours. We can use this function to find the cost of replacing an alternator that is estimated to take 5 hours of labor.

C(5) = 25(5) + 75 = 125 + 75 = 200

We also have the labor cost for the main competitor, Budget Auto Repair, in a table format.

Hours Cost

1          $90

2         $130

3         $170

We can see that the cost of labor increases as the number of hours increases. From the information provided it's hard to say which company would be cheaper to hire, however the company with the function C(x) = 25x + 75 would be cheaper if the alternator takes more than 4 hours of labor, otherwise Budget Auto Repair would be cheaper.

It's important to check the warranty, prices of parts, and reputation of both companies. If a company has a good reputation and a good warranty, it may be worth paying a little more for labor.

It's also a good idea to get a second opinion or ask for a quote from both companies before making a decision.

In conclusion, it's hard to say which company would be cheaper to hire based on the information provided, but it's recommended to check the warranty, prices of parts, and reputation of both companies, and to get a second opinion or quote from both companies before making a decision.

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complete question:

19) The function C(x) = 25x+75 represents the labor cost (in dollars) for Bob's Auto Repair to replace

your alternator, where x is the number of hours. The table below shows sample labor costs from its main

competitor, Budget Auto Repair. The alternator is estimated to take 5 hours of labor. Which company

would you hire? Explain.

Hours 1,2,3

Cost

$90 $130 $170

The size tray of plants which is the best value for money is large tray.

A small tray of 10 plants costs £2.50

Cost per unit = Total cost / number of plants

= £2.50 / 10 plants

= £0.25 per plant

A medium tray of 40 plants costs £8.40

Cost per unit = Total cost / number of plants

= £8.40 / 40 plants

= £0.21 per plant

A large tray of 90 plants costs £12.60

Cost per unit = Total cost / number of plants

= £12.60 / 90 plants

= £0.14 per plant

Hence, the large tray of 90 plants costs £12.60 is the best buy for your money.

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The number of terms n of the geometric progression is n = 12

Given data ,

Let the geometric progression be represented as A

Now , the value of A is

10 + 30 + 90 + .... = 2657200

And , let the number of terms be n

common ratio r = 30 / 10 = 3

where sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )

On simplifying , we get

2657200 = 10 ( 3ⁿ - 1 ) / ( 2 )

Divide by 5 on both sides , we get

3ⁿ - 1 = 5,31,440

Adding 1 on both sides , we get

3ⁿ = 5,31,441

Taking log on both sides , we get

n = 12

Hence , the number of terms of GP is n = 12

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Using the secant-secant theorem, the possible values of x are x = 6 and x = -10. -10 cannot be a value of x because length cannot be negative.

From the question, we are to determine the value of x in the given diagram.

The Secant-secant theorem states that

"Given two secant segments which share an endpoint outside of the circle, the product of one secant segment and its external segment is equal to the product of the other segment and its external segment"

Thus,

We can write that

5 × (5 + 7) = x × (x + 4)

Simplifying

5 × 12 = x² + 4x

60 = x² + 4x

x² + 4x - 60 = 0

Solve the quadratic equation

x² + 4x - 60 = 0

x² + 10x - 6x - 60 = 0

x(x + 10) - 6(x + 10) = 0

(x - 6)(x + 10) = 0

x - 6 = 0 or x + 10 = 0

x = 6 or x = -10

Since x cannot be negative,

x = 6

Hence, the value of x is 6

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Step-by-step explanation:

To find the slope of the line between two points, you can use the formula:

slope (m) = (y2 - y1) / (x2 - x1)

Plugging in the given coordinates, we have:

m = (-4 - (-2)) / (2 - (-2))

m = (-4 + 2) / (2 + 2)

m = (-2) / (4)

m = -1/2

The slope of the line through the points (-2, -2) and (2, -4) is -1/2.

Answer:14/165

Step-by-step explanation:

its a fraction i did the same qestion and got it right