2 This table shows the relationship between
the total weight, w, in pounds, of a crate
containing t textbooks.
B
t
W
1
2
0
4
8
20
What is the slope of the line that models
this situation?
A 2
16
36
C 4
D
24
52
4

Answers

Answer 1

The slope of the line that models this situation is equal to 2.

How to calculate the slope of a line?

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following data points on the line:

Points on x-axis = (0, 8).

Points on y-axis = (4, 20).

Substituting the given data points into the slope formula, we have the following;

Slope, m = (20 - 4)/(8 - 0)

Slope, m = 16/8

Slope, m = 2.

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2 This Table Shows The Relationship Betweenthe Total Weight, W, In Pounds, Of A Cratecontaining T Textbooks.BtW1204820What

Related Questions

What is the shape of the graph of the function? g(x)= 3/2 ​ ⋅( 2/3 ​ ) ^x

Answers

Answer:

Shape of the graph is exponentially decreasing

The horizontal asymptote is y = 0

The y intercept is at x = 0 and is at y = 3/2

Graph attached

Step-by-step explanation:

Not sure what exactly the question is asking for.

Here is what I figured out

Shape of the graph is exponentially decreasing

The horizontal asymptote is y = 0

The y intercept is at x = 0 and is at y = 3/2

We can also rewrite this equation as:

[tex]g(x) = \dfrac{3}{2} \cdot \dfrac{2}{3} \cdot \left(\dfrac{2}{3}\right)^{x-1}\\\\\\= \left(\dfrac{2}{3}\right)^{x-1}[/tex]

3. Utilizando el Teorema de Pitágoras encuentra el valor que falta. 12cm b= b 13cm 5.4 cm 7.2 cm​

Answers

The missing value is given as follows:

x = 11.3 cm.

What is the Pythagorean Theorem?

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

The parameters for this problem are given as follows:

The sides are 14 cm and x.The hypotenuse is of 18 cm.

Hence the missing value is obtained as follows:

14² + x² = 18²

x = sqrt(18² - 14²)

x = 11.3 cm.

Missing Information

We have a triangle in which:

The sides are 14 cm and x.The hypotenuse is of 18 cm.

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29 Transformations of linear functions C8G
Find g(x), where g(x) is the translation 1 unit right of f(x) = 7x + 4.
Write your answer in the form mx + b, where m and b are integers.
g(x) =
Submit

Answers

Step-by-step explanation:

please review the attachment

select the correct answer. what is the solution to this equation? 3^2x = 1/3

Answers

Answer:

x= 1/27

Step-by-step explanation:

the correct answer is : X = 1/27

Answer:

- 1/2

Step-by-step explanation:

To solve for x in the equation 3^2x = 1/3, we can start by taking the logarithm of both sides with base 3:

log3 (3^2x) = log3 (1/3)

Using the logarithmic property logb (a^n) = n * logb (a), we can simplify the left side:

2x * log3 (3) = log3 (1/3)

Since log3 (3) = 1, we can simplify further:

2x = log3 (1/3)

To find the value of the logarithm on the right side, we can use the definition of logarithms: logb (a) = c if and only if b^c = a. Since 1/3 = 3^-1, we have:

2x = log3 (3^-1) = -1

Finally, to solve for x, we divide both sides of the equation by 2:

x = -1/2

So the solution to the equation 3^2x = 1/3 is x = -1/2.

Longitude and latitude can be easily calculated by observing the direction that the fish are swimming.

True

False

Answers

Answer:

False.

Step-by-step explanation:

Longitude and latitude are geographical coordinates used to determine the location of a place on the earth's surface. They are not easily calculated by observing the direction that fish are swimming. Latitude is determined by observing the position of the sun relative to the earth's equator and longitude is determined by observing the position of the sun relative to the Prime Meridian. To accurately calculate latitude and longitude, one would need to use specialized instruments, such as a sextant, or rely on GPS technology. Observing the direction that fish are swimming would not provide enough information to accurately determine latitude and longitude.

False

the longitude and latitude can be easily calculated and determined with using a map not by observing the direction that the fish are swimming.

A brick path between two buildings is a rectangle 30.5m by 4.1m.Flowers grow in 4 square holes in the walkway.Each side of the holes is 1.2m.Calculate the area covered in brick.

Answers

119.39 is the amount covered in brick.

the full path has an area of 125.05 (4.1x30.5). each square has an area of 1.44 (1.2^2). there are 4 squares so the flowery area is 5.76 total. subtract the flowers from the brick (125.05-5.76) and get your answer of 119.39

Pls help thank you will mark the Brainliest

Answers

The exponential function from the decay function given is y = 30.5(0.7)ˣ

What is an exponential function

An exponential function is a mathematical function that models the growth of a quantity as a power of another quantity, typically as the exponent of a constant called the base. The general form of an exponential function is given by:

f(x) = a^x

where "a" is the base and "x" is the input. The value of "a" must be positive and greater than zero. When "a" is greater than 1, the exponential function grows very quickly, and when "a" is between 0 and 1, the exponential function decreases very quickly.

In this problem, we can find the exponential function by;

when x = 0

f(0) = 30.5

The function can be written as;

f(x) = 30.5(b)ˣ

To find the value of b,

We can take another point and solve;

f(0) = 30.5

f(1) = (21.35)

Looking at the graph, this is a decay function and we can easily find the value as 0.7.

The function is given as y = 30.5(0.7)ˣ

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V = Sp.v solve for v

Answers

Answer: Given the equation V = Sp.v, to solve for v, we need to divide both sides of the equation by Sp.

V / Sp = v

So v = V / Sp

Here, V is the volume of the item being sold, Sp is the price per unit, and v is the number of units being sold. By dividing V by Sp, we can find the number of units being sold (v) at a given price per unit.

Step-by-step explanation:

What is the value of the c when 5c + 23 = c -1

Answers

answer is

5(-1) = -5 +23 = 18

Jesse spends 12
of his pocket money on Monday. On Tuesday, he spends 23
of what is left. On Wednesday, he spends 14
of what remains. What fraction of the pocket money does he have left? Choose the most reasonable answer. CLEAR CHECK

13


43


66


18

Answers

The most reasonable answer for left pocket money to Jesse after spending it on Monday, Tuesday and Wednesday is 1/8.

Let's assume that the amount of pocket money Jesse has is "x".

On Monday, he spends 1/2 of his pocket money, so he has 1/2 of his pocket money left:

Amount left after Monday = x - (1/2)x = (1/2)x

On Tuesday, he spends 2/3 of what is left, which is 2/3 of (1/2)x:

Amount left after Tuesday = (1/2)x - (2/3)(1/2)x = (1/6)x

On Wednesday, he spends 1/4 of what remains, which is 1/4 of (1/6)x:

Amount left after Wednesday = (1/6)x - (1/4)(1/6)x = (1/8)x

Therefore, the fraction of the pocket money he has left is:

Amount left / Original amount = (1/8)x / x = 1/8

So, the most reasonable answer is 1/8.

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____The given question is incorrect, the correct question is given below:

Jesse spends 1/2 of his pocket money on Monday. On Tuesday, he spends 2/3 of what is left. On Wednesday, he spends 1/4 of what remains. What fraction of the pocket money does he have left? Choose the most reasonable answer.

The picture has the question

Answers

The exponential function for the given table will be y=0.01(2)ˣ where x=positive integer.

What exactly are exponential functions?

An exponential function is a mathematical function with the formula f (x) = aˣ, where "x" is a variable and "a" is a constant that is termed the function's base and must be greater than zero. The transcendental number e, which is approximately equal to 2.71828, is the most often used exponential function basis.

Growth that is exponential

The amount expands extremely slowly at first, then rapidly in Exponential Growth. The rate of change accelerates with time. As time passes, the pace of growth accelerates. The quick expansion is designed to represent a "exponential rise".

The exponential growth formula is: y = a (1+ r)ˣ, where r is the growth percentage.

Now,

as given in the table initial value = 0.01

and it is increasing into multiples of where x=positive integer

Then for the value of y for any value of x will be

y=0.01(2)ˣ where x=positive integer

Hence,

           The exponential function for the given table will be y=0.01(2)ˣ.

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Estimate ∫20(4x2−2x)dx= using a left Reimann Summ and 4 equal subintervals

Answers

The left Riemann Sum approximation for the integral of 20(4x² - 2x)dx over the interval [0, 20] with four equal subintervals is 165250.

In calculus, the integral is a mathematical tool that allows us to find the area under a curve. It is an important concept that is used in many fields of science and engineering. One way to estimate the value of an integral is by using a Riemann Sum, which involves dividing the region under the curve into small rectangles and adding up their areas.

In this case, we will be using a left Riemann Sum with four equal subintervals to estimate the integral of 20(4x² - 2x)dx.

To use a left Riemann Sum, we need to first divide the interval of integration into equal subintervals. In this case, we have four subintervals of width

=> (b - a)/n = (20 - 0)/4 = 5.

The left endpoint of each subinterval will be used as the height of the rectangle that represents the area under the curve in that subinterval.

Next, we need to evaluate the function 20(4x² - 2x) at the left endpoints of each subinterval. These values will be used as the heights of the rectangles. The left endpoints are 0, 5, 10, and 15, so we have:

f(0) = 20(4(0)² - 2(0)) = 0

f(5) = 20(4(5)² - 2(5)) = 1900

f(10) = 20(4(10)² - 2(10)) = 7200

f(15) = 20(4(15)² - 2(15)) = 15150

We can now find the area of each rectangle by multiplying its height by its width (5). The total area is the sum of these areas:

(0)(5) + (1900)(5) + (7200)(5) + (15150)(5) = 165250

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LaShawn designs websites for local businesses. He charges $25 an hour to build a websites and charges $15 an hour to update websites once he builds
them. He wants to earn at least $100 every week, but he does not want to work more than 6 hours each week. What is a possible number of hours LaShawn can
spend each week building websites x and updating websites y that will allow him to attain his goals? Write your answer as an ordered pair.


OA) (3.1.5)
OB) (3,3)
OC) (2,3)
OD) (5,2)

Answers

Answer:

B

Step-by-step explanation:

3+3 = 6 which is not more than 6 hours

3 x $25 = $75

3 x $15 = $45

$75 + $45 = $120

Determine if the side lengths 9, 9, and 17 form a triangle. If it is a triangle, classify it by its sides.

equilateral triangle
It's not a triangle.
scalene triangle
isosceles triangle

Answers

Answer:

It's not a triangle

Step-by-step explanation:

What you do is add the two smallest numbers and hope it's smaller than the longer side

9 + 9 = 18

The longest side is 17, which is LESS than 18. That means it's not a triangle

Answer:

It isnt a triangle

Step-by-step explanation:

I did the quiz and this was the answer.

What is the answer Which of the following equations have infinitely many solutions?
Choose all answers that apply:
Choose all answers that apply:

(Choice A)
A
-6x+35=-6x-35−6x+35=−6x−35minus, 6, x, plus, 35, equals, minus, 6, x, minus, 35

(Choice B)
B
6x+35=-6x-356x+35=−6x−356, x, plus, 35, equals, minus, 6, x, minus, 35

(Choice C)
C
-6x+35=-6x+35−6x+35=−6x+35minus, 6, x, plus, 35, equals, minus, 6, x, plus, 35

(Choice D)
D
6x+35=-6x+356x+35=−6x+35


I am still confused

Answers

-6x+35 = -6x+35 has the same thing on each side: , so this has infinite solutions. Option c is correct.

An equation will have infinite solutions if both sides of the equal sign are the exact same thing, for instance . (You can test this with any value of x and find that they all work!)

So to find the equations that have infinite solutions, we need to see which have the same exact sides.

(Choice A)

-6x+35 = -6x-35 have the different thing on each side: , so this has no solution.

(Choice B)

6x+35  = -6x-35 does not have the same thing on each side, so it doesn’t have infinite solutions (it has 1).

(Choice C)

-6x+35 = -6x+35 has the same thing on each side: , so this has infinite solutions.

(Choice D)

6x+35=-6x+35 And finally,  has the different thing on each side: , so it has one solution.

Hence , -6x+35 = -6x+35 has the same thing on each side: , so this has infinite solutions.

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what is the expression for a quadratic formula discriminatnt

Answers

The discriminant of a quadratic equation in standard form, [tex]ax^2 + bx + c = 0[/tex] , is given by the expression: [tex]b^2 - 4ac[/tex]

The expression gives the discriminant: [tex]b^2 - 4ac[/tex]

This expression is used to determine the nature of the roots of the quadratic equation. Specifically, if the discriminant is positive, then the equation has two real and distinct roots. If the discriminant is zero, then the equation has one real root with a multiplicity of 2. If the discriminant is negative, then the equation has two complex conjugate roots.

A quadratic equation is a second-degree polynomial equation in one variable, typically written in the form:

[tex]ax^2 + bx + c = 0[/tex]

where x is a variable and a, b, and c are constants. The coefficient "a" cannot be zero, since otherwise, the equation would become a linear equation.

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lindsey was the top scorer in a​ women's professional basketball league for the 2006 regular​ season, with a total of 862 points. The number of​ two-point field goals that lidnsey made was 71 less than double the number of​ three-point field goals she made. The number of free throws​ (each worth one​ point) she made was 21 less than the number of​ two-point field goals she made. Find how many free​ throws, two-point field​ goals, and​ three-point field goals lindsey made during the 2006 regular season.

Answers

Lindsey made 35 free throws, 143 two-point field goals, and 107 three-point field goals during the 2006 regular season.

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

Let's denote the number of two-point field goals Lindsey made by x, and the number of three-point field goals she made by y.

x + y + (x+y-71)/2 + (x+y-71)/2 - 21 = 862 (total points equation)

x = 2y - 71 (two-point field goals equation)

Simplifying the first equation and substituting the second equation, we get:

3x + 3y = 1964

Substituting x = 2y - 71 into this equation, we get:

3(2y-71) + 3y = 1964

Solving for y, we get:

y = 107

Substituting this value into the equation x = 2y - 71, we get:

x = 143

Now, (x + y - 71)/2 - 21 = (143 + 107 - 71)/2 - 21 = 35

Therefore, Lindsey made 35 free throws, 143 two-point field goals, and 107 three-point field goals during the 2006 regular season.

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10. Best Buy is having a 15% off sale on brands of computer regularly priced at $2250 How much does Jerome save on the computer the sales tax is 7. 5% what is the amount of on the computer How much is the total cost for the computer What would be the total price for the computer on sale

Answers

The total cost of the computer is $2418.75.

The total cost of the computer in sale $2,056.

The computer is regularly priced at $2250.

With the 15% discount, Jerome would save = $2250 × 15%

With the 15% discount, Jerome would save = $2250 × 15/100

With the 15% discount, Jerome would save = $337.50 on the computer

The sales tax is 7.5%.

So the tax on the computer would be = $2250 × 7.5%

The tax on the computer would bee = $2250 × 7.5/100

The tax on the computer would be = $168.75

The total cost for the computer on sale would be = $2250 - $337.50

The total cost for the computer on sale would be = $1,912.5

If the tax is 7.5% .

So he has to pay = $1,912.5 + $1,912.5 × 7.5% = $2,056

Therefore, the total price for the computer on sale would be $2,056,

The price of the computer not on sale = $2250 + $168.75 = $2418.75.

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Help meee
Which one is it?

Answers

Answer:

the number of shirts sold

Step-by-step explanation:

that's what the question is asking

barry wrote 6 different numbers, one on each side of 3 cards, and laid the cards on a table, as shown. the sums of the two numbers on each of the three cards are equal. the three numbers on the hidden sides are prime numbers. what is the average of the hidden prime numbers?

Answers

The average of the three hidden prime numbers is 5, as the sum of any two of the numbers is equal to 10, and since all three numbers are prime, the only possible values are 3, 5, and 7.

3 + 5 + 7 = 15

15/3 = 5

The average of the three hidden prime numbers is 5. This means that the sum of any two of the numbers on the cards must be equal to 10. Since all three numbers are prime,as the sum of any two of the numbers is equal to 10 the only possible values are 3, 5, and 7. Therefore, the three numbers on the hidden sides of the cards are 3, 5, and 7. To calculate the average, we add the three values together and divide by three. 3 + 5 + 7 = 15, and 15 divided by 3 is 5. Therefore, the average of the hidden prime numbers is 5.

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Subtract 7x²-x-1 from x²+3x+3

Answers

Answer: The answer is x²+2x-8

Step-by-step explanation:

BRAINLIEST AND 50 points At practice, Diego does twice as many push-ups as Noah, and also 40 jumping jacks. He does 62 exercises in total. The equation LaTeX: 2x+40=622 x + 40 = 62 describes this situation. What does the variable x represent?

Group of answer choices


The number of jumping jacks Diego does


The number of push-ups Diego does


The number of jumping jacks Noah does


The number of push-ups Noah does

Answers

If the equation describes the situation is 2x + 40 = 62, then the variable x represents the option (D) number of push ups Noah does

The given statements are

Diego does twice as many push ups as Noah

Therefore, if Noah does x push ups Diego does 2x push ups

Number of jumping jacks that Diego does = 40

Total number of exercises that he does = 62

The linear equation that represents the situation is

2x + 40 = 62

From the given equation

2x = 62 - 40

2x = 22

x = 22/2

x = 11

Here we can see that x is the number of push ups Noah does and 2x is the number of push ups Diego does

Therefore, the variable x is the number of push ups Diego does

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A baker initially makes 10 loaves of bread and sells 2 loaves each day.
What equation models the situation, where x is time in days and y is number of loaves?
Y=2x+10
Y=2x-10
Y=-2x+10
Y=-2x-10

Answers

Answer:

y = 2x + 10

Step-by-step explanation:

y = 2x + 10  

y is the total number of loaves of bread.

x is the number of days.

If the baker baked for ten days, he would have 30 loaves of bread

y = 2x + 10

y = 2(10) + 10

y = 20 + 10

y = 30

If he baked for 50 days, he would have baked 110 loaves

y = 2x + 10

y = 2(50) + 10

y = 100 + 10

y = 110

And so on and so on...

the value of a building is $180,000. the value is expected to increase by 3.5% each year. write a function that represents the value y (in dollars) of the building after x years. the predict the value after 10 years

Answers

3.5/100 = 0.035
$180,000 x 0.035 = $6,300 (the 3.5%)
6,300 x 10 = $63,000 the 3.5% after 10 years
$180,000 + $63,000 = $243,000
Therefore the building value after 10 years is $243,000.

Explain why 2. 8x0. 5 only one decimal place in the produc

Answers

Only one decimal place in the product of 8x0. 5 because the final zeros in the product do not change the value of the number.

One decimal place to the left of the decimal point is the ones place. One decimal place to the right of the decimal place is the tenths place.

This is a result of the rules of significant figures. These are the digits of the numbers that matter. For operations involving multiplication, the product should have the same significant numbers with the least significant numbers of the given data. In this case, that would be 0.5. Since 0.5 has one significant figure, then the product should be reported with one significant number. That should be 4.0.

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how would i get these answers ​

Answers

Answer:

just use the properties of the figure for rxample in number 3 they are equal as the oppositevangle are equal

Lin is shopping for a couch with her dad and hears him ask the salesperson, "How much is your commission?" The salesperson says that her commission is 6% of the selling price. How much commission will the salesperson earn by selling a couch for $495?

Answers

The commission amount the salesperson earn is $29.7.

What is a percentage?

The percentage formula is dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Selling price = $495

Commission = 6%

Now,

The amount of commission.

= 6% of 495

= 6/100 x 495

= 29.7

Thus,

The commission the salesperson earn is $29.7.

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In AJKL, if m ZJ is seven less than mZL and mZK is 21 less than twice mZL, find the measure
of each angle?

Answers

The measures regarding the angles of the triangle are given as follows:

x = 26.<P = 116º.<Q = 21º.<R = 43º.

How to obtain the angle measures?

The angle measures are defined as follows:

<P = 5x - 14.<Q = x - 5.<R = 2x - 9.

The sum of the measures of the internal angles of a triangle is of 180º, hence the value of x is obtained as follows:

5x - 14 + x - 5 + 2x - 9 = 180

8x = 208

x = 208/8

x = 26.

Then the measures are given as follows:

<P = 5(26) - 14 = 116º.<Q = 26 - 5 = 21º.<R = 2(26) - 9 = 43º.

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which of these statements about a normally distributed data set is true? a.) the smaller the standard deviation, the less concentrated the data will be. b.) the concentration of the data set is not related to the standard deviation. c.) the smaller the standard deviation, the more concentrated the data will be. d.) the greater the standard deviation, the more concentrated the data will be.

Answers

The Statement which is true is (c) the smaller the standard deviation, the more concentrated the data will be.

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.

A standard deviation close to zero indicates that data points are close to the mean, whereas a high or low standard deviation indicates data points are respectively above or below the mean.

The smallest possible value for the standard deviation is 0, and that happens only in contrived situations where every single number in the data set is exactly the same

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Find the area of the polygon in square units.

Answers

The area of the figure is solved to be

10 square units

What is the area of ta kite?

The area of a kite is solved using the formula

= P * q / 2

Where

p = length of long diagonal

q = length of short diagonal

Using the figure the length can be traced to be

p = 3 - -5 = 3 + 5 = 5

q = 6 - 2 = 4

Area of the figure

= 5 * 4 / 2

= 20 / 2

= 10 square units

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Given the point (,), write the coordinates of a point that is related by a reflection over the -axis. Write your answer with a comma and no spaces. Example 7,2 or -7,-2 you are considering buying a new house, and have found that a $100,000, 30-year fixed-rate mortgage is available with an interest rate of 7 percent. this mortgage requires 360 monthly payments of approximately $651 each. if the interest rate rises to 8 percent, what will happen to your monthly payment? instructions: enter your response rounded to the nearest dollar. do not round intermediate calculations. the monthly payment will be $ . instructions: enter your response rounded to the nearest tenth of a percent (one decimal place). do not round intermediate calculations. the change in the monthly payment will be percent while the change in the interest rate will be percent. The protests in Hong Kong center around the idea of keeping the ideals of democracy alive for the people of that city. You will now write letter to the editor of a newspaper for PT which number line shows the solution to x + 8 > 15 A 7.132 gram sample of an organic compound containing only C, H, and O is analyzed by combustion analysis and 11.88 g CO and3.891 g H0 are produced.In a separate experiment, the molar mass is found to be 132.1 g/mol. Determine the empirical formula and the molecular formulaof the organic compound. myofibrils is the sarcoplasm of a skeletal muscle fiber contains hundreds to thousands of long, cylindrical structures called that extend the length of the cell. true or false? An investor purchases one municipal bond and one corporate bond that pay rates of return of 8% and 9. 5%, respectively. If the investor is in the 20% tax bracket, his after-tax rates of return on the municipal and corporate bonds would be, respectively, _ _ _ _ _. A) 9. 60% and 7. 60%B) 8% and 9. 5%C) 8% and 7. 60%D) 6. 40% and 9. 5% What is the volume Calculate the area of a parallelogram which sides are 8cm 13cm and11cm Which term means a twisting of the intestine on itself that causes and obstruction Calculate the pH of a solution prepared by mixing 15.0 mL of 0.50 M NaOH and 30.0 mL of 0.50 M benzoic acid solution. (Benzoic acid is monoprotic; its dissociation constant is 6.5 x 10-5.) Whats the correct answer answer asap for brainlist Whats the correct answer answer asap for brainlist Why would one use basic dyes instead of acidic dyes for simple stains? Complete the sentence: Economies are the activities involved in producing, selling and buying products and _____ required for the basic needs. hint: missing word starts with an "s" suppose that the proportions of blood phenotypes in a particular population are as follows: a b ab o 0.42 0.14 0.05 0.39 assuming that the phenotypes of two randomly selected individuals are independent of one another, what is the probability that both phenotypes are o? (enter your answer to four decimal places.) the central idea of a speech is usually formulated before the specific purpose. true/false The points K (1,3), L(-4,-3), M (2,-8), and N (7,-2) form quadrilateral KLMN. Where would these points be on the graph? 13 25 4 8 17 21 A number is to be written on the blank card. The mode and median of all seven numbers are both the same. Find one possible number that can be written on the blank card. you are offered an investment that will pay you $200 in one year, $400 the next year, $600 in the third year, and $800 in the fourth year. you can earn 12% per year on similar investments. what is the most you would pay for this opportunity?