Rebecca buys a new couch for $1,200. She plans on making a monthly payment of $75 on the balance, starting the month
after she buys the couch. Which recursive function models the amount of money Rebecca still has to pay for the couch?

Answers

Answer 1

The recursive function is A(t + 1) = A(t) - 75

Where;

A(t) = 1,200 - 75×t

The known parameter are;

The amount Rebecca buys the new couch = $1,200

The amount she plans to make as monthly payment = $75

The time she plans to start paying = The month after she buys the couch

Strategy;

Define a recursive function that models the amount of money Rebecca still has to pay

Definition

A recursive function is one which has its own process as an input in the process of its implementation

A recursive function that models the amount of money Rebecca still has to pay for the couch is found as follows;

The amount left for her to pay in the present month = The amount left to pay in the previous month - $75

Let A(t + 1) represent the amount left for her to pay in the present month and let A(t) represent the amount left to pay in the previous month, we get;

A(t) = 1,200 - 75×t

A(t + 1) = 1,200 - 75×t - 75 = A(t) - 75

The recursive function is A(t + 1) = A(t) - 75

The function is recursive because, the function, A(t), is called in as an input to the execution of the function

Learn more about recursive functions here;

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Answer 2

Answer:

f(1) = 1,200

f(n) = f(n-1) -75 for n > 2

Step-by-step explanation:

Since the initial loan amount is $1,200, f(1) =1200.

And since $75 is deducted from the balance each month starting with n >2 , the common difference, d, is  -75 .

Use the general recursive function for an arithmetic sequence,f(n)= f (n - 1 ) +d , for n > 2 to write the recursive function models Rebecca’s situation:


Related Questions

y _minus 7 equal 10.find y​

Answers

Answer:

y=17

Step-by-step explanation:

y-7=10

transpose 7

y=10+7

y=17

Please I need a step by step explanation ASAP.
Calculate the perimeter and area of the shape below: ​

Answers

Answer:

38.6 cm

Step-by-step explanation:

add all of the sides up to get your perimeter

a soft drink vendor at a popular beach analyzes his sales recods and finds that if he sells x cans of soda pop in one day, his profit (in dollars) is given by

Answers

Complete Question:

A soft-drink vendor at a popular beach analyzes his sales records, and finds that if he sells x cans of soda pop in one day, his profit (in dollars) is given by P(x) = -0.001x² + 3x - 1800.

a. What is his maximum profit per day?

b. How many cans must be sold in order to obtain the maximum profit?

Answer:

a. $450

b. 1500 cans

Step-by-step explanation:

Given the following quadratic function;

P(x) = -0.001x² + 3x - 1800  ......equation 1

a. To find his maximum profit per day;

Since P(x) is a quadratic equation, P(x) would be maximum when [tex] x = \frac {-b}{2a} [/tex]

Note : the standard form of a quadratic equation is ax² + bx + c = 0  ......equation 2

Comparing eqn 1 and eqn 2, we have;

a = -0.001, b = 3 and c = -1800

Now, we determine the maximum profit;

[tex] x = \frac {-b}{2a} [/tex]

Substituting the values, we have;

[tex] x = \frac {-3}{2*(-0.001)} [/tex]

Cancelling out the negative signs, we have;

[tex] x = \frac {3}{2*0.001} [/tex]

[tex] x = \frac {3}{0.002} [/tex]

x at maximum = 1500

Substituting the value of "x" into equation 1;

P(1500) = -0.001 * 1500² + 3(1500) - 1800

P(1500) = -0.001 * 2250000 + 4500 - 1800

P(1500) = -2250 + 2700

P(1500) = $450

b. Therefore, the soft-drink vendor must sell 1500 cans in order to obtain the maximum profit.

Assume that in the absence of immigration and emigration, the growth of a country's population P(t) satisfies dP/dt = kP for some constant k > 0.

a. Determine a differential equation governing the growing population P(t) of the country when individuals are allowed to immigrate into the country at a constant rate r > 0.
b. What is the differential equation for the population P(t) of the country when individuals are allowed to emigrate at a constant rate r > 0?

Answers

Answer:

[tex](a)\ \frac{dP}{dt} = kP + r[/tex]

[tex](b)\ \frac{dP}{dt} = kP - r[/tex]

Step-by-step explanation:

Given

[tex]\frac{dP}{dt} = kP[/tex]

Solving (a): Differential equation for immigration where [tex]r > 0[/tex]

We have:

[tex]\frac{dP}{dt} = kP[/tex]

Make dP the subject

[tex]dP =kP \cdot dt[/tex]

From the question, we understand that: [tex]r > 0[/tex]. This means that

[tex]dP =kP \cdot dt + r \cdot dt[/tex] --- i.e. the population will increase with time

Divide both sides by dt

[tex]\frac{dP}{dt} = kP + r[/tex]

Solving (b): Differential equation for emigration where [tex]r > 0[/tex]

We have:

[tex]\frac{dP}{dt} = kP[/tex]

Make dP the subject

[tex]dP =kP \cdot dt[/tex]

From the question, we understand that: [tex]r > 0[/tex]. This means that

[tex]dP =kP \cdot dt - r \cdot dt[/tex] --- i.e. the population will decrease with time

Divide both sides by dt

[tex]\frac{dP}{dt} = kP - r[/tex]

Please helps me out !!!

Answers

Answer:

x = 74.2

Step-by-step explanation:

Recall: SOH CAH TOA

Reference angle (θ) = 70°

Angle opposite reference angle = x

Adjacent side = 28

Since we have Adjacent side and opposite side, we would apply the trigonometric ratio, TOA:

Tan θ = Opp/Adj

Substitute

Tan 70 = x/27

27*Tan 70 = x

x = 74.2 (nearest tenth)

If you make $11.25/hour, how many hours will you need to work to earn $416.25? Please explain how you figured this out.

Answers

37 hours, you divide 11.25 by 416.25

Answer:

37 hours.

Step-by-step explanation:

Since you need $416.25 start with that. Then divide by $11.25 to see how many hours you need to work. 416.25 divided by 11.25 is 37.

What is the ratio of the area of the inner square to the area of the outer square?

Answers

Answer:

Step-by-step explanation:

If we are looking for the ratio of the area of the inner square to the area of the outer square, that means that we need the areas of each of these squares, and we need to find the areas without any numbers. But that's ok; the answer they want is not a number answer. The answer will have a's and b's in it instead of numbers.

First the area of the inner square. Here we go:

Look at the triangle in the lower left corner of this coordinate plane. It is a right triangle. The height of it is b. That's because the height is a "y" thing and the y-coordinates of each of those sets of coordinates is b and 0. The height is then b - 0 = b.

The length of the base is a - b. That's because the length is an "x" thing and the x-coordinates of each of those sets of coordinates is (a - b) and 0. The length is then a - b - 0 = a - b.

Now we need the length of the hypotenuse which also serves as one of the sides of the inner square. Using Pythagorean's Theorem, we can find the length of the hypotenuse, which I will label as "?":

[tex]?^2=b^2+(a-b)^2[/tex] and

[tex]?^2=b^2+a^2-2ab+b^2[/tex] and

[tex]?^2=a^2-2ab+2b^2[/tex] so

?, the length of the hypotenuse, is

[tex]?=\sqrt{a^2-2ab+2b^2}[/tex] and now we can use that to find the area of the inner square. The formula for a square's area is

[tex]A=s^2[/tex] so

[tex]A=(\sqrt{a^_2}-2ab+2b^2})^2[/tex] which gives us finally:

[tex]A=a^2-2ab+2b^2[/tex] **

Now for the outer square. Those blue triangles you see are all congruent. We can use the side lengths for the triangles we found above to find the length of a side of the outer square. One side of the outer square is made up of one base length of these triangles and one height. We found the base length to be (a - b) and the height to be b; therefore, the length of one side of the outer square is b + (a - b) which is just "a". That's is, just a length of "a". The area is found by multiplying this side length by itself, so the area of the outer square is

A = a²

The ratio of the area of the inner to the outer is:

[tex]\frac{A_i}{A_o}:\frac{a^2-2ab+2b^2}{a^2}[/tex] and that does not reduce.

Answer:

A

Step-by-step explanation:

Edmentum

For a standard normal distribution, find:

P(z > -1.6)
Express the probability as a decimal rounded to 4 decimal places.

Answers

Answer:

P(z > -1.76) = 1 - P(z < -1.76) = 1 - 0.0392 = 0.960

Find x on this triangle

Answers

Answer:

3 sqrt(3) =x

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adj / hyp

cos 30 = x/6

6 cos 30 = x

6 ( sqrt(3)/2) = x

3 sqrt(3) =x

f(x) = 2x2 + 4x - 5
g(x) = 6x3 – 2x2 + 3
Find (f + g)(x).

Answers

Answer:

4x-5=4x-5

(f+g) (x)=6x³+3

Step-by-step explanation:

Seventy-two percent of all observations fall within one standard deviation of the mean if the data is normally distributed. a. True b. False

Answers

Answer:

I think this answer is A.

Hii guys if you have time plz help me

Answers

Answer:

[tex]5 {x}^{2} + 21 + 5x[/tex]

Step-by-step explanation:

TOTAL AMOUNT earned = Tim money + Melina money

[tex]5 {x}^{2} - 4x + 8 + (9x + 13)[/tex]

[tex] = 5 {x}^{2} - 4x + 8 + 9x + 13[/tex]

[tex] = 5 {x}^{2} + 21 + 5x[/tex]

Mikita is painting a spherical model of a human cell for a science fair. She uses 452.16 square inches of paint to evenly cover the outside of the cell with one coat of paint. What is the diameter of the cell model? (Use 3.14 for the value of π.)

6 in.
12 in.
24 in.
36 in.

Answers

Answer:

12

Step-by-step explanation:

Basically you have to divide 3.14 by 452.16 (the formula for area of circle is pi times r squared) and that will get you 144. The square root of 144 is 12 :)

APP
A set of quiz scores has a mean of 78 and a standard
deviation of 9. Using a common grading scale where 60
and above is a passing score, what percentage of the
students passed this test?
Explain your answer in terms of the 68-95-99.7 rule.

Answers

Answer:

The answer is "There are [tex]97.5\%[/tex] of the students pass in the test ".

Step-by-step explanation:

Since a normally distributed random variable, the practical rule states:

About 68% of the metrics are in the 1 default deviation

About 95% of metrics correspond to 2 standard deviations from the average.

About 3 standard deviations of the average represent 99.7% of the measurement.

We have the following in this problem:

Average of 78, the average 9 default.

 Calculating the percentage of students that passed the test.

[tex]Above 60\\\\60 = 78 - 2\times 9[/tex]

Therefore 60 is under the average for two standard deviations.

Its normality test is symmetric, so 50% of such observations are below mean and 50% below mean.

Everything was cleared of the 50 percent above.

Of the 50% below, 95% (within 2 known mean deviations) succeeded.

therefore

[tex]p=0.5+0.5 \times 0.95=0.975[/tex]

Determine if the triangles are similar. If they are, state the theorem.

Answers

9514 1404 393

Answer:

  ΔGHF ~ ΔMLF by AA theorem

Step-by-step explanation:

The height h of water in a cylindrical container with radius r = 5 cm is equal to 10 cm. Peter needs to measure the volume of a stone with a complicated shape and so he puts the stone inside the container with water. The height of the water inside the container rises to 13.2 cm. What is the volume of the stone is cubic cm

Answers

Answer:

We first find the volume of water without the stone.

V1 = 10 *(π * 52) = 250 π , where π = 3.14

The volume of water and stone is given by

V2 = 13.2 *(π * 52) = 330 π

The volume of the stone is given by

V2 - v1 = 330 π - 250 π = 80 π

= 251.1 cm3

Solve for f(-2)
PLEASE HELPPPPP

Answers

Answer:

5/9

Step-by-step explanation:

f(x) = 5 * 3^x

Let x = -2

f(-2) = 5 * 3^-2

We know a^-b = 1/a^b

     = 5 * 1/3^2

    = 5/9

F(-2) means the value of x is -2

Replace x with -2 and solve:

3^-2 = 1/9

5 x 1/9 = 5/9

Answer: D.5/9

What is the common difference in this sequence: 3, 11, 19, 27,35?
1
ОА.1/8
O B. 3
O C. 8
O D. 12

Answers

Answer:

8

Step-by-step explanation:

To determine the common difference, take the second term and subtract the first term

11-3 = 8

Check with the other terms in the sequence

19-11= 8

27-19 = 8

35-27=8

The common difference is 8

Answer:

C. 8

Step-by-step explanation:

There is a common difference between them and that’s 8.

3 + 8 = 11

11 + 8 = 19

19 + 8 = 27

27 + 8 = 35

In the picture the exponent says 5/3

Answers

Answer:

the answer is B

Step-by-step explanation:

[tex] {{ (- 2)}^{3}}^{5 \div 3} = { ( - 2)}^{5} = - 32[/tex]

write -8 form of 2 on up and complete other steps

Find the exact length of the curve. x=et+e−t, y=5−2t, 0≤t≤2 For a curve given by parametric equations x=f(t) and y=g(t), arc length is given by

Answers

The length of a curve C parameterized by a vector function r(t) = x(t) i + y(t) j over an interval a ≤ t ≤ b is

[tex]\displaystyle\int_C\mathrm ds = \int_a^b \sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2} \,\mathrm dt[/tex]

In this case, we have

x(t) = exp(t ) + exp(-t )   ==>   dx/dt = exp(t ) - exp(-t )

y(t) = 5 - 2t   ==>   dy/dt = -2

and [a, b] = [0, 2]. The length of the curve is then

[tex]\displaystyle\int_0^2 \sqrt{\left(e^t-e^{-t}\right)^2+(-2)^2} \,\mathrm dt = \int_0^2 \sqrt{e^{2t}-2+e^{-2t}+4}\,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^2 \sqrt{e^{2t}+2+e^{-2t}} \,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^2\sqrt{\left(e^t+e^{-t}\right)^2} \,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^2\left(e^t+e^{-t}\right)\,\mathrm dt[/tex]

[tex]=\left(e^t-e^{-t}\right)\bigg|_0^2 = \left(e^2-e^{-2}\right)-\left(e^0-e^{-0}\right) = \boxed{e^2-\frac1{e^2}}[/tex]

The exact length of the curve when the parametric equations are x = f(t) and y = g(t) is given below.

[tex]e^2 -\dfrac{1}{e^2 }[/tex]

What is integration?

It is the reverse of differentiation.

The parametric equations are given below.

[tex]\rm x=e^t+e^{-t}, \ \ 0\leq t\leq 2\\\\y=5-2t, \ \ \ \ \ 0\leq t\leq 2[/tex]

Then the arc length of the curve will be given as

[tex]\int _0^2 \sqrt{(\dfrac{dx}{dt})^2+(\dfrac{dy}{dx})^2}[/tex]

Then we have

[tex]\rm \dfrac{dx}{dt} = e^t-e^{-t}\\\\ \dfrac{dy}{dt} = -2[/tex]

Then

[tex]\rightarrow \int _0^2 \sqrt{(\dfrac{dx}{dt})^2+(\dfrac{dy}{dx})^2}\ \ dt\\\\\rightarrow \int _0^2 \sqrt{(e^t-e^{-t})^2 + (-2)^2} \ dt\\\\\rightarrow \int _0^2 \sqrt{(e^t+e^{-t})^2} \ dt\\\\\rightarrow \int _0^2 (e^t+e^{-t}) \ dt\\\\\rightarrow (e^2-e^{-2}) \\\\\rightarrow e^2 - \dfrac{1}{e^2}[/tex]

More about the integration link is given below.

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F(x)=3/4x-5, find the slope

Answers

Answer:

slope = 3/4

Step-by-step explanation:

Slope 3/4 Yeah so this is the answer I just need to wait 20 more characters but I don’t know what to write

Select the correct answer.
Simplify the following expression. Classify the resulting polynomial.

3x(x − 3) + (2x + 6)(-x − 3)


quadratic monomial

quadratic binomial

quadratic trinomial

linear binomial

Answers

Answer:

quadratic trinomial

Step-by-step explanation:

3x(x − 3) + (2x + 6)(-x − 3)

Distribute

3x^2 -9x  + (2x + 6)(-x − 3)

FOIL

3x^2 -9x   + -2x^2 -6x -6x -18

Combine like terms

x^2-21x-18

This has 3 terms so it is a trinomial

The highest power of x is 2 so it is quadratic

9514 1404 393

Answer:

x² -21x -18quadratic trinomial

Step-by-step explanation:

Eliminating parentheses, we get ...

  = (3x)(x) -(3x)(3) +(2x)(-x -3) +6(-x -3)

  = 3x² -9x +(2x)(-x) +(2x)(-3) +(6)(-x) +(6)(-3)

  = 3x² -9x -2x² -6x -6x -18

  = x²(3 -2) +x(-9-6-6) -18

  = x² -21x -18

The highest power is 2, so this is a quadratic.

There are 3 terms, so this is a trinomial.

Select the correct answer.
What is this equation rewritten in exponential form?
log7 343 = 3

Answers

Answer:

b.,............................

Step-by-step explanation:

correct answer.

The equation which is rewritten of [tex]log_{7}[/tex] (343) = 3 will be 7³ = 343 which means the option (B) will be correct.

What is a logarithm?

The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.

In another word, a logarithm is a different way to denote any number.

By log property of  [tex]log_{a}[/tex] b = x ⇒ [tex]a^{x}[/tex] = b

So  [tex]log_{7}[/tex] (343) = 3 ⇒ 7³ = 343 will be the correct answer to the question.

For more about logarithm

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can someone help me out with this question??? ​

Answers

Answer:

a

Step-by-step explanation:

If there is a 65% chance you will make a free throw, what percent of the
time you will miss? *

Answers

Given:

There is a 65% chance you will make a free throw.

To find:

The percent of the time you will miss.

Solution:

If p is the percent of success and q is the percent of failure, then

[tex]p+q=100\%[/tex]

[tex]q=100\%-p[/tex]         ...(i)

It is given that there is a 65% chance you will make a free throw. It means the percent of success is 65%. We need to find the percent of the time you will miss.  It means we have to find the percent of failure.

Substituting p=65% in (i), we get

[tex]q=100\%-65\%[/tex]

[tex]q=35\%[/tex]

Therefore, there is a 35% chance you will miss the free throw.

WILL MAKE BRAINLIEST

Answers

Answer:

x=3

Step-by-step explanation:

The ratios need to be the same

AB             CB

---------- = ----------

AD             ED

3           x

-----  = ---------

3+9       12

3           x

-----  = ---------

12          12

X must equal 3

ABCD is
square forces 1,2,3,4 and
2.828427125newtons act at
a point in directions
AB, BC, CD, DA and AC.find the resultant.

Answers

9514 1404 393

Answer:

  0

Step-by-step explanation:

Force AC resolves to 2 N in the AB direction and 2 N in the BC direction. Directions AB and CD are opposite, as are directions BC and DA. So, the sum of forces in the AB direction is ...

  AB -CD +part of AC = 1 -3 +2 = 0

The sum of forces in the BC direction is ...

  BC -DA +part of AC = 2 -4 +2 = 0

The resultant of these 5 forces is 0. There is no net force in any direction.

If you have two six sided die each labelled one throgh six. Which set of independent events has a higher probability?

Answers

Answer : Four sides (1, 2, 3, 4) are less than 5. The probability is 4 out of 6, or 2/3 or 0.6667.

The solution is, the correct answer is B. comparing all the probabilities, the set of independent events with the highest probability is the event of You land on an odd number or you roll a 6.

What is probability?

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

We will consider all the sets of probabilities, the one with the highest probability is the right answer.

a) You roll an odd number and roll a 5: the probability is calculated thus:

1/6 * 3/6

=0.0833

b) You land on an odd number or you roll a 6: the probability is calculated thus:

3/6 +1/6

= 0.6667

c) You roll a six and roll a 4: the probability is calculated thus:

1/6 * 1/4

= 0.0417

d) You roll a 3 and roll an old number: the probability is calculated thus:

1/6 * 3/6

=0.0833

Now, comparing all the probabilities, the set of independent events with the highest probability is the event of You land on an odd number or you roll a 6.

Therefore the correct answer is B.

To learn more on probability click:

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(a+b)^2 hihhhhhhhhhhhhhhhhhhhh

Answers

Answer:

a^2 + 2ab + b^2

Answered by Gauthmath

HELP PLZ<3

An international company has 28,300 employees in one country. If this represents 34.1% of the company's employees, how many employees does it have in
total?
Round your answer to the nearest whole number.

Answers

Answer:

82991 employees

Step-by-step explanation:

One way to solve this would be to solve for 1% of the company's employees and use that value to solve for 100% (100%=the whole part, or the total). We know that

28300 = 34.1%

If we divide a number by itself, it turns into 1. Dividing both sides by 34.1, we get

829.912 = 1%

Then, we know that anything multiplied by 1 is equal to itself. We want to figure out 100%, or the whole part, so we can multiply both sides by 100 to get

100% = 82991

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