Can someone please help me write a story problem to match the equation above?

Answer.... 32

when a number doubles, it is simply a higher power of 2  

so there are 3 butterflies in the beginning, which can also be written as 3 * (2^0) where the 0 is the initial power, since anything to the 0 power is 1 (except for 0)  

so the expression would be 3 * (2^n)  

after 4 minutes, it would be 3 * (2^4) or 3 * 16 or 48  

to find out how many are remaining, we know that she captured 7 of them, so it would be 3 * (2^4) - 7  

for question 2, Jeff texts 4 classmates, and then they each text 4 classmates, so that would be 4^2 or 16, but since 2 people do it, it would be

32

i saw this on yahoo hope it helps

The number of butterflies after 4 minutes is represented by the expression 3 * 2^4. The number of butterflies remaining after Ellen captures 7 can be expressed as 3 * 2^4 – 7.

Part A. We start with 3 butterflies and the number doubles every minute for 4 minutes. Therefore, the number of butterflies after 4 minutes is represented by the expression 3 * 2^4. In this expression, 2 is the base that is raised to the power of 4, representing the four times the initial number of butterflies doubles.

Part B. Ellen was able to capture 7 of the butterflies after 4 minutes. To find out the number of butterflies remaining, we subtract the number of butterflies captured by Ellen from the total number of butterflies after 4 minutes. This can be expressed as 3 * 2^4 - 7. Simplifying this expression will give us the number of butterflies remaining after Ellen's capture.

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Answer: 98

450-215-137=98

Step-by-step explanation:

Answer: choice B) 2,000 people

=================================

Let x be the number of people surveyed. This is simply a placeholder for the number.

16% of x is going to be equal to 320, so we know that 0.16*x = 320. Recall that 16% converts to the decimal form 0.16 after moving the decimal point two spots to the left.

Divide both sides by 0.16 to isolate x fully

0.16*x = 320

0.16*x/0.16 = 320/0.16

x = 2000

Therefore, 2000 people were surveyed

Answer:

2000 people were surveyed

Step-by-step explanation:

This means that 16 percent of the people surveyed = 320 people surveyed. We need to find the total amount of people, right?

Percentages are always out of 100. And let's say that x is the total amount of people surveyed.

16/100 = 320/x. This is the equation we need to solve.

To solve this, we need to find the denominator of 320/x.

The simplest way to do this is to realize that you can multiply 20 by 16 to get to 320.

Since you multiplied 16 by 20, you also need to multiply 16/100's denominator by 20. 100 times 20 equals 2000.

This means that the answer is 2000 people. There were 2000 people surveyed

ΔABC and ΔDBE are similar. Therefore the side are in proportion:

[tex]\dfrac{DE}{DB}=\dfrac{AC}{AB}[/tex]

DE = 3x - 5

DB = a

AC = 20

AB = a + a = 2a

Substitute:

[tex]\dfrac{3x-5}{a}=\dfrac{20}{2a}[/tex]      cross multiply

[tex]2a(3x-5)=20a[/tex]          divide both sides by 2a ≠ 0

[tex]3x-5=10[/tex]           add 5 to both sides

[tex]3x=25[/tex]        divide both sides by 3

[tex]x=\dfrac{25}{3}[/tex]

[tex]\boxed{x=8.\overline{3}}[/tex]

The standard form of quadratic equation for given points is x² - 3 x + 2 =0.

The standard form of quadratic equation is given by ax² + bx + c = 0.

where a , b , c are the constant .

Given,

The value of a, b, c as 1 , -3, 2 respectively.

Putting the value a, b, c in the standard form

we get  x² - 3 x + 2 =0.

So, The standard form of quadratic equation for given points is x² - 3 x + 2 =0.

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Answer:

m = -9

Step-by-step explanation:

-4(m+3)=24

You must distribute first.

-4m - 12 = 24

       +12    +12

-4m =  36

---    =   ---

-4         -4

m = -9

Answer:

Statement of triangle proportionality:  

If a line parallel to one side of a triangle intersects the other two sides of the triangle, then that line divides these two sides proportionally.

From the statement: If [tex]FG || BC[/tex] then,

Show that: [tex]\frac{FB}{FA} = \frac{GC}{AG}[/tex]

Consider [tex]\triangle ABC[/tex] and [tex]\triangle GFA[/tex]

Reflexive property states that the value is equal to itself.

[tex]\angle BAC \cong \angle GAF[/tex] [Angle] {Reflexive property of equality}

Corresponding angles theorem states that if the two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent(i., e equal).

[tex]\angle ABC \cong \angle GFA[/tex] [Angle]

[tex]\angle ACB \cong \angle AGF[/tex] [Angle]

AA Similarity states that the two triangles have their corresponding angles equal if and only if their corresponding sides are proportional.

then, by AA similarity theorem:  

[tex]\triangle ABC \sim \triangle GFA[/tex]

By segment addition postulates:

AB = FA +FB and AC = AG + GC  

Corresponding sides in similar triangles are proportional  

[tex]\frac{AB}{FA} = \frac{AC}{AG}[/tex] .....[1]

Substitute AB = FA +FB and AC = AG + GC in [1]  

we have;

[tex]\frac{FA+FB}{FA} = \frac{AG+GC}{AG}[/tex]  

Separate the fraction:

[tex]\frac{FA}{FA} + \frac{FB}{FA} = \frac{AG}{AG} + \frac{GC}{AG}[/tex]

Simplify:

[tex]1 + \frac{FB}{FA} =1+ \frac{GC}{AG}[/tex]

Subtract 1 from both sides we get;

[tex]\frac{FB}{FA} =\frac{GC}{AG}[/tex] hence proved

The answer is 67 for apex!

Answer:

The measure of ∠ABC is 67°.

Step-by-step explanation:

Consider the provided figure:

Tangent chord angle = [tex]\frac{1}{2}[/tex] intercepted arc

Now consider the provided figure;

Substitute the value of intercepted arc = 134° in the above formula.

Tangent chord angle = [tex]\frac{1}{2}\times134[/tex]

Tangent chord angle = [tex]67[/tex]

Hence, the measure of ∠ABC is 67°.

Answer: 4109 feet.

Step-by-step explanation:

You must subtract the height of Mt. Mickey from Mt. Minnie.

18940 - 14831 = 4109

Answer:

4109 is the difference in height.

Step-by-step explanation:

[tex]1: \frac{1}{2} \\Reasoning: \frac{5}{6}-\frac{1}{3}  = \frac{1}{2} \\2:\frac{9}{10} \\Reasoning: \frac{1}{2}+\frac{2}{5}  = \frac{9}{10}\\3:\frac{8}{21} \\Reasoning: \frac{5}{7}-\frac{3}{9}  = \frac{8}{21}\\4:\frac{10}{9}\\ Reasoning: \frac{2}{3}+\frac{4}{9}  = \frac{10}{9}\\5:\frac{3}{10}\\ Reasoning: \frac{4}{5}-\frac{3}{6}  = \frac{3}{10}\\6: \frac{6}{5} \\Reasoning: \frac{7}{10}+\frac{1}{2}  = \frac{1}{2}\\7: \frac{1}{10} \\Reasoning: \frac{3}{5}-\frac{1}{2}  = \frac{1}{10}[/tex][tex]\\8:\frac{28}{45} \\Reasoning:\frac{2}{5}+\frac{2}{9}  = \frac{28}{45}\\9: 0\\\frac{4}{8}-\frac{1}{2}  = 0\\10: \frac{2}{3} \\Reasoning: \frac{1}{2}-\frac{1}{6}  = \frac{2}{3}[/tex]

Answer:

The graph of our given function will be continuous.

Step-by-step explanation:

Please find the attached graph of our given function.

Let h represent the height in inches and j represent the amount of juice in ounces.

We have been given that the height of the juice in a 20-oz bottle depends on the amount of juice. This means that j in independent variable and h is dependent variable.

The function [tex]h=6-0.3j[/tex] represents the height of juice after drinking j ounces of juice.

As we drink the juice, the height of the juice in bottle will change continuously. The graph of our given function will be continuous as we can drink fractions of an ounce juice.

Since the equation of  line in slope-intercept form is [tex]y=mx+b[/tex], where,

m = Slope of line,

b= y-intercept or initial value.

Upon comparing our given function with slope-intercept form of equation we can see that slope of our given function is -0.3 and y-intercept is 6. Negative slope indicates that height of juice in bottle is decreasing after drinking  j ounces of juice.

In order to graph our line we need to find x-intercept, which will be at height equals 0 inches.

Upon substituting h = 0 in our given function we will get,

[tex]0=6-0.3j[/tex]

[tex]0+0.3j=6-0.3j+0.3j[/tex]

[tex]0.3j=6[/tex]

[tex]\frac{0.3j}{0.3}=\frac{6}{0.3}[/tex]

[tex]j=20[/tex]

So let us draw a line from points (0,8) to (20,0).

Therefore, the line connecting to these points will be the line representing our given function.

The graph of the given function is a line with a slope of -0.3 and a y-intercept of 6, passing through the points (0, 6) and (20, 0), indicating a continuous decrease in juice height as consumption increases.

We have a function h(j) that represents the height of juice in a 20-oz bottle based on the amount of juice consumed j. The function is given by:

h(j) = -0.3j + 6

Here, j is the independent variable (amount of juice) and h is the dependent variable (height of juice). To analyze the continuity of the graph, we compare the function to the slope-intercept form of the equation y = mx + b, where m is the slope and b is the y-intercept.

Comparing the function to the slope-intercept form:

y = -0.3x + 6

We find that the slope m is -0.3, and the y-intercept b is 6. The negative slope indicates a decrease in juice height as more juice is consumed.

To graph the function, we find the x-intercept by setting h (height) to 0:

0 = -0.3j + 6

Solving for j:

0.3j = 6

j = 20

So, the x-intercept is at j = 20, meaning that when 20 ounces of juice are consumed, the height of juice becomes 0.

Now, we can plot the points (0, 6) and (20, 0) on the graph and draw a line through these points. The line represents the function h(j) = -0.3j + 6. The negative slope indicates a continuous decrease in the height of juice as more ounces are consumed.

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QUESTION 1a

We want to find the value of [tex]x[/tex] in the proportion,

[tex]6:9=x:72[/tex]

We rewrite the ratio on each side of the equation as fractions to obtain,

[tex]\frac{6}{9}=\frac{x}{72}[/tex]

We now multiply both sides of the equation by [tex]72[/tex] to get,

[tex]\frac{6}{9}\times 72=\frac{x}{72}\times 72[/tex]

This simplifies to  

[tex]\frac{6}{1}\times 8=\frac{x}{1}\times 1[/tex]

[tex]\therefore 48=x[/tex]

[tex]x=48[/tex]

QUESTION 1b

The given proportion is,

[tex]\frac{8}{3}=\frac{40}{x}[/tex]

We cross multiply to obtain,

[tex]8x=3\times 40[/tex]

We divide both sides by 8 to get,

[tex]x=\frac{3\times 40}{8}[/tex]

[tex]\Rightarrow x=\frac{3\times 40}{8}[/tex]

[tex]\Rightarrow x=\frac{3\times 5}{1}[/tex]

[tex]\therefore x=15[/tex]

QUESTION 1c

The given proportion is

[tex]\frac{x}{55}=\frac{3}{5}[/tex]

We multiply both sides by 55 to get,

[tex]\frac{x}{55}\times 55=\frac{3}{5}\times 55[/tex]

This simplifies to  

[tex]x=\frac{3}{1}\times 11[/tex]

[tex]\therefore x=33[/tex]

QUESTION 1d

The given proportion is,

[tex]\frac{33}{x}=\frac{11}{5}[/tex]

We cross multiply to get,

[tex]33\times 5=11x[/tex]

We now divide both sides by 11 to get,

[tex]\frac{33\times 5}{11}=x[/tex]

[tex]\Rightarrow x=15[/tex]

QUESTION 2

Since the recipe calls for 5 cups of flour for every 6 teaspoons of salt, we can write the ratio,

[tex]5:6[/tex]

Let a larger recipe of 15 cups of flour correspond to [tex]x[/tex] teaspoons of salt,

Then the proportion becomes,

[tex]5:6=15:x[/tex]

This implies that,

[tex]\frac{5}{6}=\frac{15}{x}[/tex].

We cross multiply to get,

[tex]5x=6\times 15[/tex]

We divide through by 5 to get,

[tex]x=\frac{6\times 15}{5}[/tex]

[tex]\therefore x=18[/tex]

Hence you will need 18 teaspoons of salt.

QUESTION 3

We were given that a 20-foot flagpole casts a 6-foot shadow.

We write this as a ratio to get,

[tex]20:6[/tex]

Let the nearby 30-foot building cast an x-foot shadow.

We can also write this as a ratio to get,

[tex]30:x[/tex]

The proportion now becomes,

[tex]20:6=30:x[/tex]

We cross multiply to get,

[tex]20x=6\times 30[/tex]  

This implies that

[tex]x=\frac{6\times 30}{20}[/tex]  

[tex]\Rightarrow x=9[/tex]  

QUESTION 4

If 15 corresponds to 4, we write the ratio,

[tex]15:4[/tex]

We want to find what number of ads corresponds to 300 columns. Let that number be x.

Then we have the ratio,

[tex]300:x[/tex]

The proportion is

[tex]15:4=300:x[/tex]

This implies that,

[tex]15x=300\times 4[/tex]

[tex]x=\frac{300\times 4}{15}[/tex]

[tex]x=80[/tex]

It must have 80 ads.

QUESTION 5

The given ratio is [tex]5:2[/tex],

Let the gallons of blue paint be [tex]x[/tex]

We can write the ratio [tex]x:8[/tex]

The required proportion is

[tex]5:2=x:8[/tex]

This implies that,

[tex]\frac{5}{2}=\frac{x}{8}[/tex]

We multiply both sides by 8

[tex]x=\frac{5}{2}\times 8[/tex]

[tex]x=20[/tex]

8 gallons of blue paint is needed

Answer:

x = number of text messages sent

0.2x+40=50

0.2x = 10

5(0.2x) = 5(10)

x = 50

Therefore, 50 text messages would have to be sent or received in order for the plans to cost the same each month.

Step-by-step explanation:

X is equal to 15 and y is equal to 17

So the answer to this is A .x=15, y=17

Final answer:

The inequality to find the minimum number of weeks Susie needs to babysit to buy the snowboard is 98 + 72w <= 530. After simplifying, we get w <= 6, so option C) w <= 6 is the correct answer.

Explanation:

To find the minimum number of weeks, w, that Susie needs to babysit to purchase the snowboard, we can set up the following inequality:

98 + 72w \<= 530

This inequality represents the initial amount Susie has saved (
98 dollars) plus the amount she will save each week (72 dollars times the number of weeks, w) must be greater than or equal to the cost of the snowboard (
530 dollars).

Subtract 98 from both sides of the inequality:
72w \<= 432

Divide both sides by 72 to solve for w:
w \<= 6

The correct inequality is w \<= 6, meaning Susie needs to babysit for a maximum of 6 weeks to have enough money to buy the snowboard. Therefore, the correct answer is C) w \<= 6.

Hi There!

Step-by-step explanation:

Standard Deviation - tells you the avearage of how far apart each number in the set values is away from the mean.

Shop 1:

Mean = 46

Standard Deviation = 3

Shop 2:

Mean = 45

Standard Deviation = 19

I would choose shop 1 because even though it has a 1 more minutre of the mean it has a less of a standard deviation. That means that Shop 2 has a set of values that are far apart than shop 1.

Answer:

Shop 1

Hope This Helps :)

Answer:

a. The pattern is that they are getting multiplied by 2 each time.

b. The pattern is they all add to 999.

c. Yes, it is justified because it still equal 999.

Answer:

2.4x +2.2

Step-by-step explanation:

5.4x−1.1−3(x−1.1)

The first step is to distribute the -3

5.4x−1.1−3(x) -3(−1.1)

5.4x -1.1 -3x +3.3

Now we need to combine like terms

5.4x-3x -1.1+3.3

2.4x +2.2

Answer:

2.4x + 2.2

Step-by-step explanation:

1. Distribute -3 through the parenthesis

2. Combined the like terms

Answer: In first question, Number of student's ticket(s) = 400

And number of adult's ticket(d) = 100

In second question, The goal of $3050 fell by $710

Step-by-step explanation:

1. Since, Here d represents the number of adult tickets and s represents the number of student tickets.

And, all 500 seats are filled for a​ performance.

Therefore, s + d = 500 ------(1)

Also, the price of one adult's  ticket = $8.50

The price of one student's ticket= $5.50

And, their is a revenue of $3050 by selling the tickets.

Thus, 8.50 d + 5.50 s = 3050 --------(2)

By solving the equation (1) and equation (2),

we get, s = 400, d=100

Thus, Number of student's ticket(s) = 400

And number of adult's ticket(d) = 100

2. According to the question,

s = 2 d  ----- (3)

s + d = 360 -----(4)

By solving equation (3) and (4),

We get, s = 240 and d = 120

thus, the total revenue after selling 360 tickets = 8.50 × 120 + 5.50 × 240 = $2340

But, the goal is $3050 ( according to the question)

Thus the total fall = 3050 - 2340 = $710

The city cultural center needs to sell 140 adult and 360 student tickets to meet their target revenue of $3050. If they sell 120 adult tickets and 240 student tickets (360 in total), they will fall $710 short of their goal.

In order to help the members of the city cultural center determine how to distribute tickets between adults and students to meet their target revenue, we have to solve a system of linear equations. The two equations we have for the system are 8.50d + 5.50s = 3050 (which represents the relationship between the price of adult and student tickets and the targeted total revenue), and d + s = 500 (which expects all 500 seats to be filled). Solving these equations, we find that d = 140 adult tickets and s = 360 student tickets need to be sold.

For the second part of the question, they sold 120 adult tickets and 240 student tickets, making a total of 360 tickets at one performance. The total revenue generated from these tickets is (120*8.50) + (240*5.50) = 1020 + 1320 = $2340. So, they fell $3050 - $2340  = $710 below the goal.

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Answer: 29

Step-by-step explanation:

forst you have to round the decimals. 7.91 to 8 and 21.9 to 21. then you add

8+21=29

PLZ MARK AS BRAINIEST I REALLY NEED IT

Final answer:

To find the size of a cube that David can cover with 169 quarts of paint, set up a proportion and solve for the edge length, David can cover a cube with an edge length of approximately 5.31 feet using 169 quarts of paint.

Explanation:

To find the size of a cube that David can cover with 169 quarts of paint, we need to use the direct proportion between the amount of paint and the surface area of the cube. Let x be the edge length of the cube. The surface area of a cube is given by[tex]6x^2[/tex]can set up the proportion:

[tex]16 quarts / 2 feet^2 = 169 quarts / (6x^2)[/tex]

Cross-multiplying and then solving for x, we get:

[tex]x^2 = (2^2 * 169) / 16[/tex]

[tex]x^2 = 28.1875[/tex]

x = sqrt(28.1875)

x ≈ 5.31 feet

Therefore, David can cover a cube with an edge length of approximately 5.31 feet using 169 quarts of paint.

Answer:

27.5 centimeters.

Step-by-step explanation:

We have been given an expression [tex]1.5t+20[/tex] that predicts the height in centimeters of a plant t days from today.

To find predicted height of the plant 5 days from today we will substitute t=5 in our given expression.

[tex]1.5\times 5+20[/tex]

[tex]7.5+20[/tex]  

[tex]27.5[/tex]  

Therefore, the predicted height of the plant 5 days from today will be 27.5 centimeters.

To find the predicted height of the plant 5 days from today, substitute 5 for t in the expression 1.5t + 20. Calculating this gives a result of 27.5, so the plant is predicted to be 27.5 centimeters tall after 5 days.

This question involves substitution into a mathematical expression. The expression given in the problem is 1.5t + 20, which predicts the height of a plant t days from now. Here, t represents time in days, and the number you plug in for t is the number of days from today.

To find the height of the plant 5 days from today, you substitute 5 for t in the expression. So the calculation becomes:

1.5 * 5 + 20 = 27.5

Therefore, 5 days from today, the plant is predicted to be 27.5 centimeters tall.

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6 tons 294 lb ÷ 3071 is approximately equal to 3.97138

To solve 6 tons 294 lb ÷ 3071, we need to first convert everything to the same unit.

Convert tons to pounds:

1 ton = 2000 pounds

6 tons = 6 * 2000 pounds = 12000 pounds

Combine the weight in pounds:

Total weight = 12000 pounds (6 tons) + 294 pounds

Total weight = 12294 pounds

Divide by 3071:

12294 pounds / 3071 = 3.97138

Therefore, 6 tons 294 lb ÷ 3071 is approximately equal to 3.97138

Answer:

7= 137

6= 43

8=43

Step-by-step explanation:

well 7 would be the same angle as 137

and 6 and 8 are the same angle

so u already know that

7= 137

now to find 6 0r 8 u just need to subtract 137 from 180 to get

6= 43

8= 43

Answer:

see explanation

Step-by-step explanation:

∠7 = 137° ( vertically opposite angle )

∠8 = 180° - ∠7 = 180° - 137° = 43° ( straight angle )

∠6 = ∠8 = 43° ( vertically opposite angles )

Answer:

They spent 7 1/4 hours on homework

Step-by-step explanation:

you can take out 2/4 from 3/4 and make it into 1/2 and 1/2 + 1/2 = 1

1 + 6 = 7

the only fraction left is 1/4 so,

Jonah and Jan spent a total of 7 1/4 hours on homework.

or

you can make 1/2 into 2/4 and add 3/4 and 2/4 together which gives you the same answer:

7 1/4 hours on homework

make brainliest pls

Final answer:

Jonah and Jan spent a total of 16 1/4 hours on homework.

Explanation:

To find the total number of hours Jonah and Jan spent on homework, we need to first calculate Jan's homework hours. Jan spent 3/4 as many hours on homework as Jonah, which means Jan spent (3/4) x (6 1/2) = 3/2 x 13/2 = 39/4 = 9 3/4 hours on homework.

To find the total hours they both spent on homework, we add Jonah's and Jan's hours together: 6 1/2 + 9 3/4 = 13/2 + 39/4 = (26 + 39)/4 = 65/4 = 16 1/4 hours.

Therefore, Jonah and Jan spent a total of 16 1/4 hours on homework.

Answer:

Not enough material to desc

Step-by-step explanation:

If he has 5 x 3 inches of cardboard he can

"The greatest number of flash cards that Juan can cut out of the piece of cardboard is 12.

To determine the greatest number of flash cards that Juan can cut out of the cardboard, we need to calculate the area of the cardboard and divide it by the area of one flash card.

 Let's denote the dimensions of the cardboard as [tex]\( L \) inches by \( W \)[/tex] inches, and the dimensions of each flash card as [tex]\( l \)[/tex]nches by [tex]\( w \)[/tex] inches. Given that the cardboard is[tex]\( L \times W \)[/tex]inches and each flash card is [tex]\( l \times w \)[/tex]inches, we can calculate the number of flash cards as follows:

 1. Calculate the area of the cardboard: [tex]\( \text{Area}_{\text{cardboard}} = L \times W \).[/tex]

2. Calculate the area of one flash card:[tex]\( \text{Area}_{\text{flash card}} = l \times w \).[/tex]

3. Divide the area of the cardboard by the area of one flash card to find the number of flash cards:[tex]\( \text{Number of flash cards} = \frac{\text{Area}_{\text{cardboard}}}{\text{Area}_{\text{flash card}}} \).[/tex]

 Given that[tex]\( L = 12 \), \( W = 12 \), \( l = 3 \), and \( w = 4 \)[/tex], we can substitute these values into our equations:

 1.[tex]\( \text{Area}_{\text{cardboard}} = 12 \times 12 = 144 \)[/tex]square inches.

2.[tex]\( \text{Area}_{\text{flash card}} = 3 \times 4 = 12 \)[/tex]square inches.

3. [tex]\( \text{Number of flash cards} = \frac{144}{12} = 12 \).[/tex]

 Therefore, Juan can cut out 12 flash cards from the piece of cardboard."

[tex]\underline{+\left\{\begin{array}{ccc}x-3y=3\\-x+2y=-3\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad-y=0\to\boxed{y=0}\\\\\text{Put the value of y to the first equation}:\\\\x-3(0)=3\to\boxed{x=3}\\\\Answer:\ \boxed{x=3\ and\ y=0\to(3,\ 0)}[/tex]

Answer: d. $7,463.77

Step-by-step explanation:

The formula to calculate the simple interest is given by :-

[tex]I=Prt[/tex], where P is the principal amount , r is the rate of interest ( in decimal) and t is time ( in years).                                                (1)

Given : Nate has an account that pays 2.76% simple interest per year and wants to accumulate $3,090 in interest from it over the next 15 years.

i.e. I= $3,090  ;  r= 2.76% =0.0276   and t= 15 years

Then, from (1), we have

[tex]3090=P\times0.0276\times15\\\\\Rightarrow\ P=\dfrac{3090}{0.0276\times15}=7463.76811594\approx7463.77[/tex]

Hence, the amount of money Nate should invest in this account to meet this goal = $7,463.77