A sequence has its first term equal to 8, and each term of the sequence is obtained by adding 6 to the previous term. If f(n) represents the nth term of the sequence, which of the following recursive functions best defines this sequence?

Answers

Answer 1

A recursive formula for an arithmetic sequence is:

a(n)=a(n-1)+d, where n=term number and d=common difference.

Since we are told that d=6:

a(n)=a(n-1)+6, a1=8

They may want:

f(n)=f(n-1)+6, a1=8

I never understood why they teach this instead of explicit formulas because the above is pretty useless if you simply want say the 1031st term, you would need to do a lot of calculations to find it. :P. The explicit function is:

a(n)=a+d(n-1), here a=8 and d=6 so

a(n)=8+6(n-1)

a(1031)=8+6(1031-1)=6188

Try finding the 1031st term with the recursive formula :D

Answer 2

Answer:

f(1) = 8 and f(n) = f(n − 1) + 6; n > 1

Related Questions

The balance in Beth's checking account is $75. She must deposit enough money in her account to be able to pay the electric bill, which is $110. How much should she deposit?

Answers

75+d=110 subtract 75 from both sides

d=$35

So she needs to deposit at least $35 to be able to pay the electric bill.

Answer:

She should deposit $35.00 in her account.

Step-by-step explanation:

The balance in Beth's checking account = $75.00

She must deposit enough money in her account to be able to pay the electric bill, which is = $110.00

So we have to subtract 75 from 110 to get how much more money she needs to deposit the electric bill.

$110.00 - $75.00= $35.00

She should deposit $35.00 in her account.

How many ways are there to arrange the first five letters of the alphabet?

Answers

In probability, problems involving arrangements are called combinations or permutations. The difference between both is the order or repetition. If you want to arrange the letters regardless of the order and that there must be no repetition, that is combination. Otherwise, it is permutation. Therefore, the problem of arrange A, B, C, D, and E is a combination problem.

In combination, the number of ways of arranging 'r' items out of 'n' items is determined using n!/r!(n-r)!. In this case, you want to arrange all 5 letters. So, r=n=5. Therefore, 5!/5!(505)! = 5!/0!=5!/1. It is simply equal to 5! or 120 ways.

Answer:

120 ways

Explanation:

Since there are no repeating letters, and there are 5 total letters, there are 5!= 120 ways to arrange them. In other words, there are 5 slots to place the first letter in, then 4 slots for the second letter, 3 for the third, 2 for the fourth, and then the last letter goes in the 1 slot that is left.

I hope this is correct and if it is I hope it helps. I hope you have a great day and remember it doesn't matter what other people say or think about you, you are still and always will be strong, smart, and an amazing person. Have a wonderful day.

I am happy to help with anything.

Pythagoras is planting a rose garden in the center of his rectangular yard, which is 20 feet long and 8 feet wide. He wants to dig up an area in the shape of an equilateral triangle with sides 5 feet each. After he digs up the rose-bed section, approximately how much grass will be left? Round to the nearest foot.

Answers

The remaining area that the grass will cover will be given by:
Area=[area of rectangle]-[area of the triangle]
area of rectangle will be:
A1=length*width
=20*8
=160 square feet

The area of the triangle will be:
A2=1/2absin theta
since the triangle is equilateral, all the angles are equal and the size of each angle is 60°. Thus the area will be:
A2=1/2*5*5sin 60
=18.3
thus the remaining area of the grass will be:
Area=160-18.3
=149.7 square feet

Answer:

The approximate remaining grass area is 144 square feet.

Explanation:

To find the area of the rectangular yard, we use the formula:

Area of rectangle [tex]= \text{length} \times \text{width} \)[/tex]

Given that the length is 20 feet and the width is 8 feet, we have:

Area of Rectangle [tex]= 20 \times 8 = 160 \text{ square feet} \)[/tex]

Next, we find the area of the equilateral triangle. Since we know the length of each side (5 feet) and an equilateral triangle can be divided into two congruent 30-60-90 triangles, we can use the formula for the area of an equilateral triangle:

Area of equilateral triangle [tex]= \frac{\sqrt{3}}{4} \times (\text{side length})^2 \)[/tex]

Plugging in the value of the side length (5 feet), we get:

Area of equilateral triangle [tex]= \frac{\sqrt{3}}{4} \times (5)^2 \)[/tex]

Area of equilateral triangle [tex]= \frac{\sqrt{3}}{4} \times 25 \)[/tex]

Area of equilateral triangle [tex]= \frac{25\sqrt{3}}{4} \text{ square feet} \)[/tex]

Now, to find the remaining grass area after Pythagoras digs up the rose-bed section, we subtract the area of the equilateral triangle from the total area of the rectangle:

Remaining grass area [tex]= \text{Area of rectangle} - \text{Area of equilateral triangle} \)[/tex]

Remaining grass area [tex]= \ 160 - \frac{25\sqrt{3}}{4} \)[/tex]

Using a calculator, we find:

Remaining grass area [tex]\approx 144.3 \text{ square feet} \)[/tex]

Rounded to the nearest foot, the approximate remaining grass area is 144 square feet.

Evaluate the expression:
the difference of 26 and 22
Select one:
a. 48
b. 91
c. 4
d. 13/11

Answers

H̲̅ᴇ̲̅ʏ̲̅!̲̅ Hope that I can help!
To do this, all you have to do is subtract 22 from 26. 26-22=4.

Answer: C.) 4
If you were helped by my answer, remember that I worked really hard on it. Please click the [ ♥ ᴛʜᴀɴᴋs ] button below and give me a rating of ★★★★★ to show your appreciation.

Write the equation of a hyperbola with vertices (0, -4) and (0, 4) and foci (0, -5) and (0, 5).

Answers

check the picture below. So, more or less looks like so.

notice, the center is clearly at the origin, and notice how long the "a" component is, also, bear in mind that, is opening towards the y-axis, that means the fraction with the "y" variable is the positive one.

Also notice, the "c" distance from the center to either foci, is just 5 units.

[tex]\bf \textit{hyperbolas, vertical traverse axis }\\\\ \cfrac{(y-{{ k}})^2}{{{ a}}^2}-\cfrac{(x-{{ h}})^2}{{{ b}}^2}=1 \qquad \begin{cases} center\ ({{ h}},{{ k}})\\ vertices\ ({{ h}}, {{ k}}\pm a)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{{{ a }}^2+{{ b }}^2} \end{cases}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \begin{cases} h=0\\ k=0\\ a=4\\ c=5 \end{cases}\implies \cfrac{(y-{{ 0}})^2}{{{ 4}}^2}-\cfrac{(x-{{ 0}})^2}{{{ b}}^2}=1\implies \cfrac{y^2}{16}-\cfrac{x^2}{b^2}=1 \\\\\\ c=\sqrt{a^2+b^2}\implies c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \\\\\\ \sqrt{5^2-4^2}=b\implies \boxed{3=b} \\\\\\ \cfrac{y^2}{16}-\cfrac{x^2}{3^2}=1\implies \boxed{\cfrac{y^2}{16}-\cfrac{x^2}{9}=1}[/tex]

solve the equation 14.50-p=53 please help

Answers

Hello there!

14.50 - p = 53

To solve for this, we need to isolate p and see what else may need to be done afterwards.

First, isolate p by subtracting 14.50 from both sides (what you do to one side of the equation you must do to the other).

14.50 - 14.50 = 0
53 - 14.50 = 38.50

-p = 38.50

We need to solve for p, so divide both sides by -1 to get rid of the negative sign.

-p / -1 = p
38.50 / -1 = -38.50

P = -38.50

I hope this helps!

If $10,000 is invested in an account at the rate of 6.25% compounded monthly, then the amount after 15 years is approximately

Answers

The formula is
A=p (1+r/k)^kt
A future value?
P present value 10000
R interest rate 0.0625
K compounded monthly 12
T time 15 years
A=10,000×(1+0.0625÷12)^(12×15)
A=25,473.84

Final answer:

The amount after 15 years is approximately $26,971.67.

Explanation:

To calculate the amount after 15 years, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:

A = the final amountP = the principal amount (initial investment)r = annual interest rate (in decimal form)n = number of times interest is compounded per yeart = number of years

In this case, P = $10,000, r = 0.0625 (6.25% as a decimal), n = 12 (monthly compounding), and t = 15. Substituting these values into the formula:

A = $10,000(1 + 0.0625/12)^(12*15) = $26,971.67 (approximately).

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There are exactly four positive integers $n$ such that \[\frac{(n + 1)^2}{n + 23}\] is an integer. Compute the largest such $n$.

Answers

Final answer:

To find the largest positive integer $n$ such that $rac{(n + 1)^2}{n + 23}$ is an integer, we need to find the largest perfect square that is less than or equal to $n + 23$. The largest such $n$ is $41$.

Explanation:

To find the largest positive integer $n$ such that $rac{(n + 1)^2}{n + 23}$ is an integer, we can start by considering the numerator. The expression $(n + 1)^2$ is a perfect square, so it will always be divisible by $n + 23$ if $n + 23$ is also a perfect square. Therefore, we need to find the largest perfect square that is less than or equal to $n + 23$.

Let's consider some examples. If $n + 23 = 25$, then $n = 2$. If $n + 23 = 36$, then $n = 13$. If $n + 23 = 49$, then $n = 26$. If $n + 23 = 64$, then $n = 41$. Therefore, the largest value of $n$ such that $rac{(n + 1)^2}{n + 23}$ is an integer is $41$.

There are no positive integers $n$ that satisfy the given condition, and we cannot compute the largest such $n$.

To find the largest positive integer $n$ such that $\frac{(n + 1)^2}{n + 23}$ is an integer, we need to consider the factors of the numerator and denominator.

Let's expand the numerator, $(n + 1)^2$, using the binomial expansion formula:

$(n + 1)^2 = n^2 + 2n + 1$

Now, we divide this expression by $n + 23$ and express the result as an integer:

$\frac{n^2 + 2n + 1}{n + 23}$

We can use polynomial long division to divide $n^2 + 2n + 1$ by $n + 23$:

- (n - 21)
__________
n + 23 | n^2 + 2n + 1
- (n^2 + 23n)
_____________
-21n + 1
- (-21n - 483)
_____________
484

We obtain a remainder of 484. In order for the fraction to be an integer, the remainder must be 0. However, in this case, the remainder is not 0, which means that $\frac{(n + 1)^2}{n + 23}$ is not an integer for any positive integer $n$.

Therefore, there are no positive integers $n$ that satisfy the given condition, and we cannot compute the largest such $n$.

Complete question :-

There are exactly four positive integers $n$ such that \[\frac{(n + 1)^2}{n + 23}\] is an integer. Compute the largest such $n$.

find the slope of the line through points (1,8) and (2,7). write the answer in simplest form.

Answers

The slope formula is (y2-y1)/(x2-x1). By plugging this in, you get (7-8)/(2-1) = -1/1 = -1
So, the slope is -1.

(X1, Y1) (X2, Y2)

Y2-Y1/X2-X1

so the answer is -1

Given the function g(x) = 4(3)x, Section A is from x = 1 to x = 2 and Section B is from x = 3 to x = 4.

A) Find the average rate of change of each section. (4 points)

Answers

g(x)=4* 3^(x)
g(2)=4*9=36
g(1)=4*3=12
36-12/2-1=24
g(4)=4*81=324
g(3)=4*27=108
324-108/4-3=216

A bag contains 5 apples and 3 oranges. if you select 4 pieces of fruit without looking, how many ways can you get 4 apples?

Answers

Every time (the four times) that you select a fruit it has to be an apple: the first piece be an apple, so as the second, the third and the fourth pieces.

That is becasue if you do not select an apple on any of the selections then you will not have selected 4 apples, so you do not have any chance to select a different fruit.

Now, given that there are 5 apples, you can combine them in 5C4 ways:

5C4 = 5! / [(4!) (5-4)! ] = 5! / [4! * 1!] = 5 * 4! / 4! = 5

Answer: 5 ways.

Answer:

5 ways

Step-by-step explanation:

I got it correct on founders edtell

A student reader is making $5.90 per hour and gets a $0.52 raise. what is the percent increase? (round to the nearest tenth of a percent.)

Answers

Does it give you answers ??

What is the value for B, after the equation A=3/7(B-25) is rearranged?

Answers

To find B in terms of A (i hope this is what you want!) you can first multiply 3/7(B-25) by the reciprocal of 3/7, that being 7/3. You now have 7/3A=B-25, and through adding 25 on both sides, you have B=7/3A+25.

Hope this helps!

Answer:

[tex]B=\frac{7A}{3}+25[/tex]

Step-by-step explanation:

We have been given an equation [tex]A=\frac{3}{7}(B-25)[/tex]. We are asked to find the value of B for our given equation.

Upon multiplying both sides of our equation by [tex]\frac{7}{3}[/tex], we will get:

[tex]\frac{7}{3}*A=\frac{7}{3}*\frac{3}{7}(B-25)[/tex]

[tex]\frac{7}{3}*A=B-25[/tex]

[tex]\frac{7A}{3}+25=B-25+25[/tex]

[tex]\frac{7A}{3}+25=B[/tex]

[tex]B=\frac{7A}{3}+25[/tex]

Therefore, the value of B is [tex]\frac{7A}{3}+25[/tex].

What is the area the shaded triangle?

Answers

Answer:

Step-by-step explanation:

The area of the shaded triangle will be 96 mm² so option (B) is correct.

What is a triangle?

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

As per the given two inscribed triangles.

The bigger one is the right-angle triangle.

The area of the right-angle triangle will be as,

A = 1/2 x 8 x (6 + 24)

A = 4 x 30= 120 mm².

The area of the smaller right-angle triangle,

a = 1/2 x 8 x 6 = 24 mm²

The area of the shaded triangle = 120 - 24 = 96 mm².

Hence "The area of the shaded triangle will be 96 mm²".

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Evaluate the following expression using the values given: Find 3x − y − 3z if x = −2, y = 1, and z = −2. −13 −1 1 13

Answers

3(-2) - 1 - 3(-2) = -6 - 1 + 6 = -1

The correct answer is -1

Katie earned $54.30 in interest from two accounts. One account Paid 4.1% apr and the other paid 3.2% apr. if she had a total of $1500 in the two accounts, How much was in each account?

Answers

0.032x+0.041 (1500-x)=54.3
Solve for x
0.032x+61.5-0.041x=54.3
0.032x-0.041x=54.3-61.5
-0.009x=-7.2
X=7.2/0.009
X=800 invested at 3.2%

1500-800=700 invested at 4.1%

What is the sum of the measures of the exterior angles of any convex polygon

Answers

Answer:

360 degrees is sum of the measures of the exterior angles of any convex polygon.

Step-by-step explanation:

Convex Polygon:

A convex polygon is a polygon with all its interior angle less than 180 degrees.Thus, all the vertices of the polygon will be away from the interior of the polygon.If all the angles are not less than 180 degrees then it becomes concave polygon.Example: Triangle is a convex polygon with three sides.

Exterior angle sum Property:

If we extend the side of the polygon, then the angle formed by the extended side and polygon side is an exterior angle.The sum of all the exterior angles if a convex polygon is 360 degrees.If this convex polygon is a regular polygon, then the sum is 360 degrees and each exterior angle is equal to [tex]\frac{360}{n}[/tex], where n is the number of sides in regular polygon.

The sum of the measures of the exterior angles of any convex

polygon is 360°.

What is a Convex polygon?

This is the polygon that is the boundary of a convex set and has

all the interior angles to be less than 180°.

The interior angles is 180(n-2) degrees and each exterior angle

is supplementary to its interior angle thereby resulting in the

sum of the exterior angles to be 360°.

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Angle x is an acute angle in a triangle. If cos x=4/5, then the sin x=

Answers

The answer is 3/5 because u need to find the missing side in order to find sin

Answer:

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

Step-by-step explanation:

Angle x is an acute angle in a triangle.

The measure of cosine angle is given to be :

[tex]\cos x = \frac{4}{5}[/tex]

Now, we need to find the measure of the sine angle for the same triangle.

[tex]\cos x = \frac{Base}{Hypotenuse}[/tex]

⇒ Base = 4 units and Hypotenuse = 5 units

So, Length of perpendicular = 3 units ( By using Pythagoras theorem)

[tex]\sin x=\frac{Perpendicular}{Hypotenuse}\\\\\implies\bf \sin x =\frac{3}{5}[/tex]

Evaluate [(30 + 6) − 3^2] ÷ 9 ⋅ 2

Answers

[(30 + 6) − 3^2] ÷ 9 ⋅ 2
=
[(30 + 6) − 3^2] ÷ 18
=
[(30 + 6) − 9] ÷ 18
=
[36 − 9] ÷ 18
=
[27] ÷ 18
=
3/2
=
1.5
=
1 1/2

hope that helps

At what angle do the angle bisectors of two same side interior angles intersect in construction with two parallel lines and a transversal?

Answers

Same-side interior angles are a pair of angles on one side of a transversal line, and on the inside of the two parallel lines being intersected.

The sum of same-side interior angles is equal to 180 degrees.

A transversal line is a line that intersects other lines.

Parallel lines are lines that run alongside each other that never intersect.

An angle bisector is a line that divides an angle into two equal parts.

Given that the sum of same side interior angles is equal to 180 degrees, then the sum of the angle formed by the angle bisector is equal to 90 degrees.
Thus the angle bisectors intersect at an angle 90 degrees.

Therefore, the angle bisectors of two same side interior angles in construction with two parallel lines and a transversal intersect at angle 90 degrees.

Complete the solution of the equation. find the value of y when equals -7

-3x+6y=-21

Answers

if x = -7 then
-3x+6y=-21
-3(-7) +6y = -21
21 + 6y = -21
6y = -42
y = -7

The value of y when equals -7 would be equal to -7.

What does it mean to solve an equation?

An equation represents equality of two or more mathematical expression.

When someone asks you to solve an equation, then they usually mean to find the values of the unknowns for which that equation would be true

Solutions to an equation are those values of the variables involved in that equation for which the equation is true.

We are given the equation as-3x+6y=-21

if x = -7 then we get;

-3x+6y=-21

Substitute;

-3(-7) +6y = -21

21 + 6y = -21

6y = -42

y = -7

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what is the correct name for the angle shown

Answers

Angle s is the correct one

Answer: The correct name is (B) ∠S.

Step-by-step explanation: We are given to find the correct name for the angle shown in the figure.

We can see in the figure that the rays RS and ST are intersecting at the point S. Therefore, RS and ST are making an angle at the point 'S'.

So, the name of the angle will be ∠S or ∠RST or ∠TSR.

First option is ∠R. This is not correct.

Second option is ∠S. This is the correct option.

Third option is ∠RTS. This is also not correct.

Fourth option is ∠SRT. This is not correct.

Thus, the correct option is (B) ∠S.

Find the directrix of the parabola y = (1/8)(x – 5)2 - 3.

Answers

I have no idea. Quick question for you though since we are working on similar stuff. How do I write this equation in graphing form: y=2x^2-12x+19

Answer:

y= -5

Step-by-step explanation:

rewrite as standard form [tex]4.2(y-(3-))=(x-2)^{2}[/tex]

(h.k) = (2, -3), P=2

y= -3 -P

y= -3 -2

y= -5

If ABCDE is translated 3 units to the right and 4 units down, what will happen to the polygon?

Answers

If the polygon ABCDE is translated to the right 3 units and 4 units down, it's great to not that translation never affects the shape and size of the image, the image will be congruent to the pre-image in every way possible. Therefore the answer to our question is :
B] It will move but won't change shape or size.

Final answer:

When polygon ABCDE is translated 3 units to the right and 4 units down, its shape and size remain unchanged, but its position on the coordinate plane changes, maintaining the same orientation and angles.

Explanation:

If a polygon ABCDE is translated 3 units to the right and 4 units down, the shape and size of the polygon will remain the same, but its position will change. Each vertex (point) of the polygon will move 3 units to the right on the x-axis and 4 units down on the y-axis. This type of transformation is known as a translation, which is a slide of the entire figure in a specific direction. As a result, the translated polygon will maintain the same orientation and angles; it will simply be in a different location on the coordinate plane.

Rewrite in simplest radical form 1/x^3/6.
Can anyone solve this.

Answers

[tex]\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad \sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\\\\ -------------------------------\\\\ \cfrac{1}{x^{\frac{3}{6}}}\implies \cfrac{1}{x^{\frac{1}{2}}}\implies \cfrac{1}{\sqrt{x}}\impliedby \textit{now, rationalizing the denominator} \\\\\\ \cfrac{1}{\sqrt{x}}\cdot \cfrac{\sqrt{x}}{\sqrt{x}}\implies \cfrac{\sqrt{x}}{x}[/tex]

If f(x)=5x-7 and g(x)√x-2 which statement is true?
-5 is in the domain or
-5 is not in the domain

Answers

Final answer:

-5 is in the domain of the function f(x)=5x-7, but not in the domain of the function g(x)√x-2. The domain of a function is the set of all acceptable input values.

Explanation:

The question is asking whether -5 is in the domain of the given functions, f(x)=5x−7 and g(x)√x−2. The domain of a function is the set of all permissible inputs or arguments, i.e. x-values that can be inserted into the function.

In the case of f(x)=5x-7, the domain is all real numbers, as we can substitute any real number into 'x' and obtain a valid result. Hence, -5, indeed, is in the domain of the function f(x). However, for the function g(x)√x-2, the domain is all non-negative real numbers since we can't take the square root of a negative number in the real number system, hence -5 is not in the domain of g(x).

Thus, the statement '-5 is not in the domain' would be true if we are referring to g(x). However, if we are referring to f(x), the statement would be false because -5 is in the domain.

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Classify the variable as discrete or continuous. weights of backpacks of first graders on a school bus

Answers

The weights of their backpacks would be discrete

How do i graph the line y=2/3x+ 490 using the slope intercept method?

Answers

Find 490 on the y-axis. Remember the slope-intercept formula: y = mx + b where m = slope and b = y intercept.
slope = rise/run. With the point 490 on the y-axis, move 3 units to the left and two units upward, and mark another point there. Draw a straight line through it, and make sure the line is rising (left to right) because the slope is positive.

Hope this helped!

Graph of the line [tex]y = \frac{2}{3} x+490[/tex] is drawn with slope [tex]m = \frac{2}{3}[/tex] and y-intercept 490 and x-intercept = -735.

What is slope?

"Slope of the line is defined as the ratio of difference in the increment in y coordinates to the difference in increment in x-coordinates."

Formula used

standard equation of line

y = mx + c

m = slope of the line

c = y- intercept

According to the question,

Given equation of line,

[tex]y = \frac{2}{3} x+490[/tex]

Compare it with standard equation of line y = mx + c we get,

Slope [tex]m = \frac{2}{3}[/tex]

y-intercept = 490

Calculate x-intercept by putting y=0

x-intercept = -735

Now plot it on the graph as shown and join the points with slope [tex]m = \frac{2}{3}[/tex]

Hence, graph of the line [tex]y = \frac{2}{3} x+490[/tex] is drawn with slope [tex]m = \frac{2}{3}[/tex] and y-intercept 490 and x-intercept = -735.

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WILL GIVE A BRAINLIEST ANSWER IF UR 100% CORRECT!!

Which of the following expressions is not equal to p^2?

A.
p^-3 * p^5 * p^-2 * p^2
B.
p^-9 * p^0 * p^2 * p^5
C.
p^-3 * p^-1 * p * p^5
D.
p^-5 * p^9 * p^-2 * p^0

Answers

remember [tex](x^m)(x^n)=x^{m+n}[/tex]
so since they're all being multiplied, just add the exponents and see which one doesn't add to 2

A. -3+5-2+2=2+0=2, yep

B. -9+0+2+5=-9+7=-2, nope

C. -3-1+1+5=-4+6=2, yep

D. -5+9-2+0=4-2=2, yep

answer is B

Option B, [tex]p^{-9} *p^{0} * p^{2} *p^{5}[/tex] is not equal to [tex]p^{2}[/tex].

Here,

We have to find the expression is not equal to p^2.

What is Property of addition in power of number?

This property states that when multiplying two powers with the same base, we add the exponents.

Now,

Let an expression [tex]x^{a} x^{b}[/tex]

Then it can be written as, [tex]x^{a} x^{b} = x^{a+b}[/tex]

So, Option B is given as,

[tex]p^{-9} *p^{0} * p^{2} *p^{5} = p^{-9+0+2+5} = p^{-2}[/tex]

Which is not equal to [tex]p^{2}[/tex].

Similarly, we check all options.

We get only option B is not equal to [tex]p^{2}[/tex].

Hence,

Option B, [tex]p^{-9} *p^{0} * p^{2} *p^{5}[/tex] is not equal to [tex]p^{2}[/tex].

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Jessica plots the data points relating the amount of money she needs to repay a loan and the number of months she has been making payments.

She calculates two regression models. Which is true?

A.) The linear model better represents the situation because the amount she owes is decreasing by about the same amount every 6 months.

B.) The linear model better represents the situation because according to the exponential model, the repayment amount will never be 0.

C.) The exponential model better represents the situation because the amount she owes decreases by about the same amount every 6 months.

D.) The exponential model better represents the situation because according to the linear model, the repayment amount will eventually be negative.

Answers

The difference between the linear model and the exponential model is the degree of difference of consecutive points. If their difference is constant, then it is more appropriate for the linear model. If their difference is increasing at a very fast rate, then that follows an exponential model. With that being said, let's look at the differences at every 6 month-intervals.

2700-2110 = 590
2110-1500 = 610
1500-870 = 630
870-220 = 650

Their differences are about the same having a mean of 620. Thus, this is a linear model. To check,you can see visually that the points are more fitted to the line than the curve. The answer is A.

The regression models used by Jessica is such that A.) The linear model better represents the situation ... owes is decreasing by about the same amount every 6 months.

What regression model is best?

The linear regression model is best for a situation where there is a constant rate of change while the exponential model is for situations where change isn't constant.

Jessica's data shows that there is a constant rate of reduction in the amount to repay because the amounts are quite similar to each other as shown by the graph.

In conclusion, option A is correct.

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