PLEASEEEEE HELP…
In Exploration 3.1.2 you went through a procedure that helped you see how a formula
with n compounds per year relates to the formula for compounding continuously. Select
the appropriate answers to model what you did in the exploration.
Annual growth Rate
A (t) = P(1 + r)
n compounds per year
nt
A () = (1+ a)
a =
[Select]
n
let z = -
7
A (t) = P(1 + [b])"
b = (Select)
let n = ar
Ict
C =
[Select)
A (0) P(1)
110) - P{(x - 2)
+
2
Answers
The growth amount is given by the growth rate the duration of the growth
and how the rate is applied to each period.
The correct selections are;
a = n[tex]\displaystyle b = \frac{1}{x}[/tex]c = x·r[tex]\displaystyle \lim_{x \to \infty} \left(1 + \frac{1}{x} \right)^x \to 1[/tex]Reasons:
First part;
The given formula for the annual growth rate is; [tex]A(t) = \mathbf{P \cdot \left(1 + r)^t}[/tex]
[tex]\displaystyle A(t) = \mathbf{P \cdot \left (1 + \frac{r}{[a]} \right)^{n \cdot t}}[/tex]
Where;
P = The principal
r = The rate per period
n = The number of compounding per period
t = The number of periods
In the above formula, we have that the number of compounding per periods = n
Therefore;
a = nWhich gives the fraction of the interest applied to each period as [tex]\displaystyle \frac{r}{n}[/tex]
Which gives;
[tex]\displaystyle A(t) = \mathbf{P \cdot \left (1 + \frac{r}{n} \right)^{n \cdot t}}[/tex]
Second part;
When [tex]x = \displaystyle \frac{n}{r}[/tex], we have; [tex]A(t) = \mathbf{P \cdot \left(1 + [b])^{n \cdot t}}[/tex]
[tex]\displaystyle A(t) = P \cdot \left (1 + \frac{r}{n} \right)^{n \cdot t}[/tex]
Therefore;
[tex]\displaystyle b=\frac{r}{n}[/tex]
[tex]\displaystyle \frac{1}{x} = \frac{1}{\left(\frac{n}{r} \right)} =\frac{r}{n}[/tex]
Which gives;
[tex]\displaystyle b=\frac{r}{n} = \mathbf{\frac{1}{x}}[/tex]
[tex]\displaystyle \underline{ b = \frac{1}{x} }[/tex]
Third part;
Where, n = x·r, and [tex]\displaystyle A(t) = \mathbf{P \cdot \left (1 + \frac{1}{x} \right)^{[c] \cdot t}}[/tex]
We have;
[tex]\displaystyle x= \frac{n}{r}[/tex]
[tex]\displaystyle \frac{1}{x}=\frac{r}{n}[/tex]
[tex]\displaystyle A(t) = P \cdot \left (1 + \frac{1}{x} \right)^{[c] \cdot t} = \mathbf{P \cdot \left (1 + \frac{r}{n} \right)^{[c] \cdot t}}[/tex]
Which gives;
c = n = x·r
c = x·rFourth part;
If x is a really large number, we have; [tex]\displaystyle \mathbf{\left(1 + \frac{1}{x} \right)^x}[/tex]
Where x approaches ∞, we have;
[tex]\displaystyle \frac{1}{\infty}=0[/tex]
Which gives;
[tex]\displaystyle \displaystyle \left(1 + \frac{1}{x} \right)^x= \left(1 + \frac{1}{\infty} \right)^\infty = \displaystyle \left(1 + 0\right)^\infty = 1 ^\infty = 1[/tex]
[tex]\displaystyle \underline{\lim_{x \to \infty} \left(1 + \frac{1}{x} \right)^x \to 1}[/tex]Learn more about growth rate formula here:
https://brainly.com/question/2284816
Related Questions
The janitor at a school discovered a leak in a pipe. The janitor found that it was leaking at a rate of 21 fl oz per hour. How fast was the pipe leaking in gallons per day?
Answers
Answer:
3.9375 gallons per day or 4 gallons if you want to round up
3.9375
Explanation:
21 x 24 = 504
504 fl oz = 3.9375 gallons
What is the distance between −93 and 114 on a number line?
Answers
Answer:
207
Step-by-step explanation:
By counting the amount of numbers to get from -93 to 114, you count a total of 207. This means it takes 207 steps to get from -93 to 114.
When finding the distance between negative and positive numbers you can also add the numbers together to get the total distance between the numbers.
Answer: what ever u said on the answer to one of my questions got deleted lol
Step-by-step explanation:
Mrs. Wong has placed together 60% of the pieces of a jigsaw puzzle She has placed 570 pieces of the puzzle together How many pieces are there in the whole puzzle? Explain whether or not it is possible to determine how many pleces there are in the whole puzzle using the given information. If so, show the calculations to find the total pieces in the puzzle If not explain why not Type the answer in the response area below
Pls help ASAP
Answers
Here is a list of five numbers.98^53 98^64 98^73 98^88 98^91Find the lowest common multiple of these five numbers.
Answers
Answer:
98^91
Step-by-step explanation:
Since the base of all the numbers is 98,
the LCM is simply the one with the greatest exponent
example
98^53 * 98^38 = 98^91
A cube has volume 1331cm3. Calculate the length of one edge of the cube.
Answers
Answer:
answer=11 cm.
Step-by-step explanation:
Step-by-step explanation:
V = Volume of cube
a = edge
Formula of volume of cube:
V = a³
[tex]1331 = {a}^{3} \\ \sqrt[3]{1331} = a \\ a = 11[/tex]
The length of each edge is 11 cm.
Give me some tips for the Shsat that is tomorrow.
Answers
Answer:
1. Sleep well
2. Eat a proper meal to increase your energy
3. Do the ones you are good at first. Skip the harder questions
4. There are 2 parts. One is ELA while the other is math. Do the one that you are good at first so you wouldn't be annoyed.
5. When you are finished filling out the test slip double-check your work that way you could see which one you got wrong.
6. Have faith in yourself. :)
Step-by-step explanation:
find the length of segment AB
Answers
Answer:
26
Step-by-step explanation:
AB=CB so
3x+8=7x-16
-4x=-24
x=6
then plug that x value into the length which is 3x+8
so 3(6)+8=18+8=26
A color printer prints 10 pages in 3 minutes.
How many minutes does it take per page?
Answers
Answer:
3.3 secs
Step-by-step explanation:
divide the pages by the minutes
Simplify 7-2 + 2(4 divide 1/2)
Answers
Answer:
21
Step-by-step explanation:
5 + 16 = 21
Answer:
21
Step-by-step explanation:
hope it helps
PLS HELP ASAP ILL GIVE BRAINLKEST THANKS
Answers
Answer:
n > 8/3
Step-by-step explanation:
Divide both sides of the equation by 3 to make n the only variable left, n> 8/3
pls help me with these 2 questions
Answers
Answer:
x(2x-1)=0
3x-1x=0
2x=0
x=0/2
x=0
Step-by-step explanation:
LCM
first term =3x
=3×x
second term = 4x²y
=2×2×x×x×y
third term =x(x+1)
LCM=x
Answer:
djeuiiuhjjjcjffvgbftvkrfjjjjjrjrjrjjnnrnrf
Find the first six nonzero multiples of 9.
Answers
Answer: 9,18,27,36,45, and 54
Step-by-step explanation: the first 6 multiples of 9 don't have zeros in them.
spilled $40 into the ratio of 3:7
Answers
Answer:
$12/$28
Step-by-step explanation:
Let x and y represent the two amounts of money adding up to $40.
Assume that x is the smaller amount. Then:
x 3
----- = ----- Remembering that x + y = $40, we get x = $40 - y
y 7
amd sp we have
$40 - y 3
-------------- = ------ which, after cross-multiplication, is $280 - $7y = 3y
y 7
Simplifying this, we get $280 = 10 y, so that y must be $28. If y = $28, x must be $40 - $28, or $12.
$12
Then $40, split in the ratio 3/7, is the ratio ----------------
$28
Check: Note that $12 + $28 = $40, as required, and that $12/$28 = 3/7.
Part 1: Celebration!
You and three friends will be going out to eat at your favorite restaurant!
Each of you will order three items of your choice. You will also need to leave a tip. If you split the bill evenly among all four of you, how much will each person need to contribute?
Locate a menu for your favorite restaurant and pick three items for yourself and each friend. Make sure all or some of the items differ for each person.
List the restaurant name, items, and prices in a table like the one below.
In the column labeled Subtotal, determine the cost of each person’s order.
The customary tip is 20% of the total bill. In the column labeled Tip, calculate the amount of tip each person should leave.
In the column labeled Total Bill, determine the total of each person’s order, including the tip.
Restaurant name:
Names Item 1 Price Item 2 Price Item 3 Price Subtotal Tip Total Bill
Your name
Friend #1
Friend #2
Friend #3
Part 2: Questions
Answer the following questions, showing all work:
What is the total cost of the entire bill (all four meals), including tip?
Write an expression using fractions to show how to determine the amount that each person will pay. Then calculate each person's contributions showing all steps in long division.
If each person paid an equal amount, who would save the most money? Explain your reasoning using at least two complete sentences.
Answers
Answer: All four friends would have to share paying the tip and the total so all of them would pay 1/4 of the bill and 1/4 of the tip
Step-by-step explanation: divide the bill and tip between the 4 friends and you get 1/4 which is how much of the bill and tip that all you and the friends have to pay
REWARDING BRAINLIEST!
What is the value of x?
Enter your answer in the box.
x =
Answers
Answer:
7
Step-by-step explanation:
5/45 = 3/2x+13
C+3/8=1 1/3
(3/8 Is a fraction, and so is 1/ 13)
(Solve for C)
Answers
Answer:
see below
Step-by-step explanation:
c+9/24=32/24 so c=23/24
Answer:
C = 23/24
Step-by-step explanation:
Step 1: Convert 1 1/3 to an improper fraction.
[tex]C + \frac{3}{8} = 1 \frac{1}{3}[/tex] [tex]C + \frac{3}{8} = \frac{4}{3}[/tex]Step 2: Change the denominator of 3/8 and 4/3 to a common denominator: 24.
[tex]C + \frac{9}{24} = \frac{32}{24}[/tex]Step 3: Subtract 9/24 from both sides.
[tex]C + \frac{9}{24}-\frac{9}{24}=\frac{32}{24} - \frac{9}{24}[/tex] [tex]C = \frac{23}{24}[/tex]Therefore, C = 23/24.
Simplify: 7.2 x10^4/3.0 x 10^2
Answers
Answer:
240
Step-by-step explanation:
If the height of a cone is 7.5 cm and the radius is 2 cm, find the approximate volume of the cone.
Answers
Volume: (7.5) • pi (2)^2
Volume: 94.247796
Just round to your teacher’s liking
Answer:
The volume of the cone is approximately 31.43 cm³Step-by-step explanation:
We know that:
Volume of cone: πr²h/3h = 7.5r = 2Work:
πr²h/3=> π x r² x h/3=> 22/7 x 2² x 7.5/3=> 22/7 x 4 x 2.5=> 22/7 x 10=> 220/7=> 31.43 (Rounded to nearest hundredth.)Hence, the volume of the cone is approximately 31.43 cm³
Hoped this helped.
[tex]BrainaicUser1357[/tex]
Factorise:
a) 22y -33z b) ax + bx –ay – by
Answers
(b) (a+b)(x-y)
…………………………………
Ed is on a road trip. He has already traveled 229 miles and is driving at a rate of 68 miles per hour. Which equation could be used to find how many hours, x, Ed has left in his road trip if he is traveling 647 total miles?
A.
68x + 647 = 229
B.
229x + 647 = 68
C.
68x + 229 = 647
D.
229x + 68 = 647
Answers
Step-by-step explanation:
THE ANSWER IS D BUT ME 8S NOT SURE
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Answers
The number of comic books is an illustration of a linear function
The complete equations are: [tex]\mathbf{8b + 17 =65}[/tex] and [tex]\mathbf{b =6}[/tex]The value of b has increased by 4She had 17 comic books already.
So, we have:
[tex]\mathbf{Base\ Amount = 17}[/tex]
Her order of 65 books contains 8 comic books per collection.
So, we have:
[tex]\mathbf{Rate = 8}[/tex]
[tex]\mathbf{Total = 65}[/tex]
This is represented as:
[tex]\mathbf{Rate \times b + Base\ Amount =Total}[/tex]
So, we have:
[tex]\mathbf{8\times b + 17 =65}[/tex]
Rewrite as:
[tex]\mathbf{8b + 17 =65}[/tex]
Subtract 17 from both sides
[tex]\mathbf{8b =48}[/tex]
Divide both sides by 8
[tex]\mathbf{b =6}[/tex]
Assume she has 97 books in her collection, then the equation would be represented as:
[tex]\mathbf{8b + 17 = 97}[/tex]
Subtract 17 from both sides
[tex]\mathbf{8b = 80}[/tex]
Divide both sides by 8
[tex]\mathbf{b = 10}[/tex]
The values of b are 6 and 10.
The difference between 6 and 10 is 4
Hence, the value of b has increased by 4
Read more about linear equations at:
https://brainly.com/question/11897796
.
Christian pays $15 to join a music streaming service. He also pays $0.99 for each song he downloads from the same service.
Which function can be used to find, y, the the amount of money Christian spends for x downloaded songs?
y = 0.99x + 15
y = 15x + 0.99
y = 15x
y = 0.99x
Answers
The total amount of money Christian spends to download x xongs is y = 15 + 0.99x.
Christian initially pays $15 to join the music service.
Also, he pays $0.99 for each song he downloads from the service.
If he downloads x songs, the amount extra he pays per song he downloads is price per song × number of songs = $0.99 × x = $0.99x.
This amount is added to the initial $15 he pays to join the service. So, the total amount of money he pays is y = initial amount + extra per song = $15 + $0.99x = $0.99x + $15
So, the total amount of money Christian spends to download x xongs is y = 15 + 0.99x.
Learn more about linear equations here:
https://brainly.com/question/11767839
CAN SOMEONE HELP ME PLEASE ASAP!
Answers
Step-by-step explanation:
the same factor of one dimension or one line applies then for all dimensions or lines.
the length goes from 16 to 32 cm. that means it doubles.
so, we need to double also the width :
10.5 × 2 = 21 cm
therefore, the first answer option is correct.
What is -x-y=5 in function form solving for y
Answers
Answer:
f(x) = - x - 5
Step-by-step explanation:
- x - y = 5 ( multiply through by - 1 )
x + y = - 5 ( subtract x from both sides )
y = - x - 5 , that is
f(x) = - x - 5
Let f(x)=cosx. Determine the x-value(s) where the function has a maximum or minimum value on [0,2π).
Answers
Answer:
can u say what subject is that
(0, 1) is a local maxima and (π, −1) is a local minima of the given function.
The given function is f(x)=cos(x).
What is a function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Graph the trigonometric function using the amplitude, period, phase shift, and vertical shift.
Amplitude: 1
Period: 2π
Phase Shift: None
Vertical Shift: None
The coordinates to plot the graph are (0, 1), (π/2, 0), (π, -1),....
To find the x-intercept, substitute in 0 for y and solve for x.
To find the y-intercept, substitute in 0 for x and solve for y.
x-intercept(s): (π/2 +πn,0), for any integer n
y-intercept(s): (0,1)
Use the derivative to find the maximum and minimum.
(0, 1) is a local maxima and (π, −1) is a local minima
Therefore, (0, 1) is a local maxima and (π, −1) is a local minima of the given function.
To learn more about the function visit:
https://brainly.com/question/9554035.
#SPJ2
Which of the following is a like radical please answer asap
Answers
An electronics retailer sells a washing machine at cost price (how much the retailer paid for it) of $400 with a profit of 20%. What price does the customer pay?
Answers
Answer:
$480
Step-by-step explanation:
400 × .20 = 80
the retailer got an extra 20% or $80 for the machine.
$400 + $80 = $480
The customer paid $480 for the washing machine.
The coordinates of a point change as follows during a dilation:
(-6, 3) ----> (-2, 1)
What is the scale factor?
Answers
Answer:
The answer is D. (6,9)
Step-by-step explanation:
Glad to help
What expression is equivalent to tje alegbraic expression
2n-n
Possible Answers
n+2
2n+2
n²
n
3n
Answers
Answer:
n
Step-by-step explanation:
2n - n ← factor out n from each term
= n(2 - 1)
= n × 1
= n
please helpp and show your work pleasee
Answers
Answer:
[tex]b=27[/tex]
Step-by-step explanation:
[tex]\frac{b}{3} -7=2\\\\\frac{b}{3}=9\\\\b=27[/tex]
Invisible Steps:
Add 7 on each side of the equation:
[tex]\frac{b}{3}-7+7=\frac{b}{3}\\2+7=9[/tex]
Multiple 3 on each side of the equation:
[tex]\frac{b}{3}[/tex] · [tex]3=b[/tex]
[tex]9[/tex] · [tex]3=27[/tex]
