the Following table shows alexandra's investment options over the course of three years. Her initial investment was $1,000 . write one function for each option to describe the value of the investment f(n), in dollars, after n years.
Answers
The pattern in the given series of amount in the account are in the form of
arithmetic and geometric progression.
The function for Option 1 is; [tex]\underline{ f(n) = 1,100 + (n - 1) \cdot 100}[/tex]The function for Option 2 is; [tex]\underline{f(n) = 1,100 \times 1.1^{(n - 1)}}[/tex]Reasons:
The given table of values is presented as follows;
[tex]\begin{tabular}{c|c|c|c|}Number of years&1&2&3\\Option 1 (Amount in dollars)&1,100&1,200&1,300\\Option 2 (Amount in dollars)&1,100&1,210&1,331\end{array}\right][/tex]
In Option 1, the amount in dollars for each year has a common difference of d = 100
The first term, a = 1,100
Therefore;
The Option 1 can be represented as an arithmetic progression , A.P. in the
form, tₙ = a + (n - 1)·d as follows;
For the Option 1, we have;
The amount in dollars after n years, [tex]\underline{ f(n) = 1,100 + (n - 1) \cdot 100}[/tex]For Option 2, it is possible to find;
1,331 ÷ 1,210 = 1,210 ÷ 1,100 = 1.1
Therefore;
The terms in the Option 2 have a common ratio of r = 1.1
The Option 2 is a geometric progression, G.P.
The first term in Option 2 is a = 1,100
Which gives, the nth term, tₙ = a·r⁽ⁿ ⁻ ¹⁾
Therefor;
The function for the Option 2 is; [tex]\underline{f(n) = 1,100 \times 1.1^{(n - 1)}}[/tex]Learn more about arithmetic and geometric progression here:
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Related Questions
The graph of y = f(x) is the solid black graph below. Which function represents the
dotted graph?
Submit Answer
O y = f(x + 3) - 5
O y = f(x - 3) - 5
O y = f(x - 3) + 5
O y = f(x + 3) + 5
Answers
Answer:First option, y=f(x+3)+5
Step-by-step explanation:
analyse the transformation first
From the dotted function, when compared to the solid black line, is moved 3 units to the left, and moved upwards by 5 unitsInput transformation
In graphing, when a value is shifted horizontally, its transformation is equal to: -(x2-x1), and in this instance, we end up with a value of +3so, f(x+3) is the first componentWhen a function is shifted horizontally, it is proportiante to the distance it moves, so (y2-y1)in this instance, it is 0 - -5=5so the transformation vertically is +5Final answer, when all values are added is y=f(x+3)+5
There are 40 slices of pizza at the party that are shared equally between 8 people. Peter ate 3 slices of pizza before he came to the party. How many slices of pizza did Peter eat in all?
Answers
Answer:
that depends if it's taken in consideration the pizzas that he ate were from the 40 slices or not
Answer:
he ate 5 slices
Step-by-step explanation:
40/8=5 you would thinks you are timeing the answer29. Martin has some dollar notes. 20% of the notes are $10 notes, 40% of
the remainder are $5 notes and the rest are $2 notes. He has a total
of $1026. How many notes does Martin have altogether?
Answers
Answer:
225 notesStep-by-step explanation:
Let the number of notes is x.
20% of notes is:
0.2x40% of the remainder is:
40% of 0.8x, so it is 0.8x*0.4 = 0.32xRemaining notes are:
x - 0.2x - 0.32x = 0.48xTotal of the notes:
0.2x*10 + 0.32x*5 + 0.48x*2 = 10262x + 1.6x + 0.96x = 10264.56x = 1026x = 1026/4.56x = 225Help me please tha is a practice but is I pass it will make me not fail math
Answers
Answer:
x = 21 The angles are 85°, 58°, 69°, and 148°
Step-by-step explanation:
The sum of the interior angles of a 4 sided figure formula :
Sum of the interiors = (n - 2) 180°
Sum of the interiors = (4 - 2) 180
Sum of the interiors = (2)180° = 360°
Now : 85° + (x + 37)° + 69° + (6x + 22)° = 360°
213 + 7x = 360
7x = 360 - 213
7x = 147
x = 21 the angles are 85°, (21 + 37)° = 58°; 69°; (6·21 +22)°= 148°
Answer:
The degrees inside the quadrilateral are 85, 148, 69, and 58.
Step-by-step explanation:
The interior of the quadrilateral equals 360 degrees.
All the degrees inside need to add up to 360. You need to find out what x is so you can do that.
First, add all the degrees you know, then solve for x.
85 + 69 = 154.
Now, add in the other angles.
154 + (6x + 22) + (x + 37)
Add like terms together.
154 + 22 + 37 = 213 degrees 6x + x = 7x.
7x + 213 needs to equal 360.
Subtract 213 from both sides to get 7x alone.
7x = 360 - 213
7x = 147
Now, you need to solve for x. You do this by dividing both sides by 7.
7x/7 = 147/7
x = 21
To find the degrees of the two unknown angles, substitute 21 back in where x is.
6(21) + 22 = 126 + 22 = 148
and 21 + 37 = 58
85 + 148 + 69 + 58 = 360 degrees.
i know the pythagorean theorem
Answers
Answer:
I know the pythagorean theorem
Step-by-step explanation:
ok
heres a list of numbers 8,7,12,7,11,10,7,12Find median,mean,range and mode
Answers
Answer:
There it gose
Step-by-step explanation:
Jake earns $9.85 per hour working at a software company. He wants to earn at least $300 a week. How many full hours must he work to earn the money?
Answers
Answer:
30.4 hours
Step-by-step explanation:
300 divided by 9.85
This gives you 30.4
Find the slope of the line through each pair of points. (5, −5) (0, −1)
Answers
Answer:
slope = - [tex]\frac{4}{5}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (5, - 5 ) and (x₂, y₂ ) = (0, - 1 )
m = [tex]\frac{-1-(-5)}{0-5}[/tex] = [tex]\frac{-1+5}{-5}[/tex] = [tex]\frac{4}{-5}[/tex] = - [tex]\frac{4}{5}[/tex]
At the end of the day, a bakery had 6/7 of a pie left over. Louie, Duey and Huey split the pie, with each taking home the same amount of leftover pie. How much pie did Louie take home?
Answers
because 2/7 * 3 = 6/7
Answer:
2/7 of the pie
Step-by-step explanation:
6/7 / 3 = 2/7
What is 1+1 equal? Explain in paragraph form! 5 or more sentences!
Answers
I hope this helps give you a start
How many solutions does this system have?
y=2/3x + 32x - 3y = -9
A. One Solution
B. Two Solutions
C. No Solutions
D. Infinitely Many Solutions
Answers
Answer:
No solutions since they are two variables and it supposed to be solved simultaneously
Noah drove 480km in 5 hours. About how far did he drive in 2 hours?
Answers
Answer:
192km
Step-by-step explanation:
480/5 = x/2
5x = 960
/5 /5
x = 192
Answer:
If Noah's driving was at a constant rate, he drove 192 km in 2 hours
Step-by-step explanation:
In order to find the answer to this question then we can set up two equations with x meaning the km/h he is going and y as our answer.
Noah drove 480km in 5 hours can be set up as:
480 = 5x
Dividing both side by 5:
x=96
and we want to find the number of km he drove in 2 hours:
y = 2 x
because we know x=96 from the first equation
y = 196 so, therefore, Noah drove 192 km in 2 hours
Find the coordinates of the points D (4,-4) and E (5,-5) after the transformation (x,y) →
(x+ 3. y -5)
Answers
D = (7, -9)
E = (8, -10)
hope this helps!
In how many ways can you arrange six trophies on a shelf?
Answers
Answer:
720 ways
Step-by-step explanation:
Assuming order doesn't matter, there are [tex]6!=6*5*4*3*2*1=720[/tex] ways to arrange six trophies on a shelf.
46. An olympic athlete has just completed a four mile run. His average time was 6 minutes per mile. If he ran the first and last mile in 5 minutes, and the other 2 were the same time as each other, what was the average time for the 2 miles in the middle
Answers
Answer:
7 minutes
Step-by-step explanation:
average time = 6 minutes per mile
sum = average * count = 6 minutes / mile * 4 miles = 24 minutes
first + last mile = 5 + 5 = 10 minutes
first + second + third + last mile = sum = 24 minutes
second + third = sum - first - last = 24 - 5 - 5 = 24 - 10 = 14 minutes
average of 2 miles in the middle = sum / count = 14 minutes / 2 = 7 minutes
nth term of 5,8,13,20,29
Answers
Answer:
nth term = 4 + n^2
Step-by-step explanation:
Sorry if the answer is long but I'm hoping my explanation can help.
In order to understand the issue, we should try to find the pattern between the terms given.
The terms given were 5, 8, 13, 20 and 29.
Between the first term and second term, the difference is 3.
Between the second and third term, the difference is 5.
The pattern goes on and we find out that the difference between the (n-1)th term and the nth term is
2n - 1.
Hence, we can determine the pattern of the numbers is
nth term = (n-1) term + 2n - 1
We can use this to find term 0 (before term 1) by plugging in the values for term 1
5 = 0th term + 2 (1) - 1
5 = 0th term + 1
Hence the 0th term = 4
If we expand on the summation,
We can find the nth term
nth term = 4 + 2 (1) - 1 + 2(2) - 1 + ... + 2(n-1) - 1 + 2n - 1
As we can see, the number 1 has been subtracted n times (excluding the -1 in 2(n-1)). Hence, we can split combine all of the subtracted ones into -n.
We can rewrite it as
nth term = 4 + 2 (1) + 2(2) + ... + 2(n-1) + 2n - n
Now, we will move 4 and n to one side.
nth term = 4 - n + 2 (1) + 2(2) + ... + 2(n-1) + 2n
We can factorize 2 out from every term to the right of -n. This would give out
nth term = 4 - n + 2 (1 + 2 + ... + (n-1) + n)
The term (1 + 2 + ... + (n-1) + n) can actually be rewritten by using the triangular formula.
The triangular formula is stated such that
Tn = (n*(n+1))/2
This heavily simplifies the equation into
nth term = 4 - n + 2 [(n*(n+1))/2]
This equation becomes
nth term = 4 - n + n^2 + n.
Now, we can finally simplify into the final equation
nth term = 4 + n^2
plssssssssssssssssssssssss
Answers
Y = x^2 -3
y = (x-3)(x+3)
For x-intercepts, y = 0
Therefore (x-3)(x+3) = 0
x intercepts are (3,0) and (-3,0)
The line of symmetry is x = 3+(-3) = 0
Vertex is on the line of symmetry
When x = 0, y = -1
Vertex = (0,-1)
Answer:
The answer is equal to 0
Step-by-step explanation:
Explanation in the picture.
solve similar triangles (advanced)
Answers
Answer:
Step-by-step explanation:
There are 2 similar triangles.
EDA and CBA
From that we can get the following proportion.
ED / CB = AD / AB
Filling in the letters we get
6/x = (4 + 3)/3 Combine
6/x = 7/3 Cross Multiply
7x =6*3
7x = 18 Divide by 7
x = 2.57
Use the figure below to determine the relationship between _DBE and BED
Answers
Third option
The opposite angle to the side DE=5 is the The opposite angle to the side BD= 12 is the angle< BED
The side DE= 5
please help i need now
thank youu
Answers
Answer:
B
Step-by-step explanation:
if you cannot recognize the right equation, just start evaluating some points... try 5, 6, 4
4 more to go-2 + (-2) × -2 + (-2) ÷ -2
Answers
Let's se
-2+(-2)(-2)+(-2)/(-2)-2+(-2)^2+1-1+21Done!
How can you represent a proportinoal relationship with an equation
Answers
Answer:
Just be yourself
Step-by-step explanation:
As a car owner/lessee, it is not a requirement to have minimum coverage auto insurance.
T or F
Answers
Answer: False
Step-by-step explanation:
Given below, if Xy and are congruent, what is the measure of
A. 140°
B. 280°
C. 100°
D. 80°
(it’s A. 140°)
Answers
Answer:
holi , cómo estás espero que bien bueno déjame te digo que está facil soy de México pero voy a clases de inglés y ya me la hicieron esa pregunta y es la D hojala te ayude mucho
what's the answer? and how did you get it??
Answers
Answer:
97
Step-by-step explanation:
A straight horizonal line is 180 degrees, so you subtract 83 from 180 to get 97, which is the measure of angle JKL
Mr. Jones spent $156 to attend a college football game.
- Twenty percent of this cost was for a parking pass.
- He spent the remainder of the money on two tickets for the game.
What was the price per ticket?
Answers
Answer: $62.40
Step-by-step explanation:
what is 20% of 156 ? 31.20
what is 156 - 31.2 ? 124.80
what is 124.8 / 2 ? 62.40
each ticket cost 62.40 dollars
an auto dealership got a new shipment of 33 cars. Of these, two are red , 6-cylinder 4 door sedans; one is a red 4-door, but not a 6-cylinder sedan. There are four 6-cylinder 4-door sedans that are not red, and three red 6-cylinder sedans that are not 4-door sedans. Altogether, 19 of the 33 cars are 6-cylinder sedans and 12 of the 33 are 4-door sedans. How many of the 33 cars are red but neither 6-cylinder nor 4-door sedans?
Answers
Answer:
2
Step-by-step explanation:
If you take 19 6-cylinder sedans and add 12 4-door sedans you get 31, therefore making 2 red and neither 6-cylinder nor 4-door sedans. Hope this helps!
Solve: 67 x 104. 67,000 6,700 670,000 6,700,000
Answers
Answer: 67 x 104 = 6968
Step-by-step explanation:
Answer:
7303
Step-by-step explanation:
I just calculated 67x109 and it gave me 7303
HOPE THAT HELPS YOU MARK ME BRINILYLIST
Solve.
4 Joe solved (2x + 4) > 2(2x + 8) + 1 as shown at the
right. What error did Joe make? Solve the inequality.
(8)
Answers
Answer:
Step-by-step explanation: 2x+4+=
Please help it’s due in an hr
Which of these functions has a y-intercept that is
greater than that of the linear function
represented by the table of values below, and
why?
х
у
2
19
4
13
17
6
7
19
9
23
A. y = x + 9, because the y-intercept of the function
represented by the table of values is 2
B. y=x+9, because the y-intercept of the function
represented by the table of values is 5
C. y = 8x+1, because the y-intercept of the
function represented by the table of values is 2
D. y = 8x + 1, because the y-intercept of the
function represented by the table of values is 5
Answers
y = x+9 because the y-intercept of the function represented by the table is 5.
============================================================
Explanation:
Let's focus on the first two rows of the table. Plug those coordinates into the slope formula below.
m = (y2-y1)/(x2-x1)
m = (13-9)/(4-2)
m = 4/2
m = 2
The slope is 2.
Then we'll use something like (x,y) = (2,9) along with the slope we found to determine the y intercept b
y = mx+b
y = 2x+b
9 = 2*2+b
9 = 4+b
9-4 = b
5 = b
b = 5
The equation for the table is y = 2x+5
We can check this by seeing that x = 6 leads to y = 2*x+5 = 2*6+5 = 17. I'll let you check the other x values of the table.
Because y = 2x+5 has a y intercept of 5, we're going to aim for answer choice B. The y intercept of y = x+9 is 9 which is larger than what we just found.