Answers
Part 1) Finding the inverse
Let x = r and y = H(r)
We have the equation y = 6240(1 + x/100)^t which is the same as saying y = 6240(1 + 0.01x)^t since 1/100 = 0.01
From here, swap x and y to get the equation x = 6240(1+0.01y)^t
Let's solve for y
x = 6240(1+0.01y)^t
6240(1+0.01y)^t = x
(1+0.01y)^t = x/6240
1+0.01y = (x/6240)^(1/t)
0.01y = (x/6240)^(1/t)-1
100*0.01y = 100*((x/6240)^(1/t)-1)
y = 100*((x/6240)^(1/t)-1)
y = 100*(x/6240)^(1/t) - 100
This becomes r = 100*(H/6240)^(1/t) - 100 after we replace y with r and x with H. Note the r and H swapped places, just like x and y did. Earlier we had H isolated on the left, but now r is isolated on the left.
We could write r(H) = 100*(H/6240)^(1/t) - 100 to mean the same thing.
So what exactly does this inverse function do? Well the original function tells us the number of households for any given growth rate, which is r.
The inverse function swaps things around to allow us to find the growth rate if we know how many households there are. We're working backwards. In both cases, t is held to some constant fixed value.
===========================================================
Part 2) Finding the growth rate if the number of households is 7800 after 3 years.
We're going to plug in H = 7800 and t = 3 into the inverse function we found to determine the value of r, or r(H)
r(H) = 100*(H/6240)^(1/t) - 100
r(7800) = 100*(7800/6240)^(1/3) - 100
r(7800) = 7.72173450159419
You'll need your calculator to get this approximate value. After rounding to two decimal places, we get r(7800) = 7.72
Since r = 7.72, this means the growth rate is 7.72%
Related Questions
dvd: $15; 35% markup
Answers
Answer:
35% of 15=35/100×15=21/4=5.25
Solve the inequality for x.
22 >x-5
Answers
Answer:
x < 27
Step-by-step explanation:
22 > x - 5
Subtract x from both sides.
-x + 22 > -5
Subtract 22 from both sides.
-x > -27
Divide both sides by -1. Remember that when you multiply or divide an inequality by a negative number, the inequality sign changes direction.
x < 27
The equation C(l) = l3 – l2 + l + 2.5 models the cost to mail a package as a function of its length. To the nearest quarter inch, approximately what is the length of a package that costs $11.00 to mail? Enter your answer as a decimal.
Answers
Answer:
2.25
Step-by-step explanation:
Given the cost model:
C(l) = l3 – l2 + l + 2.5
l = Length fo package
The length of a package that cost $11.00
11 = l³ - l² + l + 2.5
From the table given :
Length of mail which cost $11 will just be slightly greater Than 2 as the cost of 2 length mail cost 8.50
Taking l as 2.20
2.2^3 - 2.2^2 + 2.2 + 2.50 = 10.508
Taking a slightly higher value :
Put l = 2.25
2.25^3 - 2.25^2 + 2.25 + 2.50 = 11.078
Ww can conclude that the length of mail would be 2.25
Answer:
2.75
Step-by-step explanation:
Camillo is making gourmet peanut butter and jelly sandwiches for a food challenge. What is the unit price of a loaf of bread at each store? Store A: Store B: Store C: Store D:
Answers
Answer:
The answer is below
Step-by-step explanation:
A 2-column table with 4 rows. Column 1 is labeled Store with entries A, B, C, D. Column 2 is labeled Advertised Bread Prices with entries 3 loaves for 5 dollars and 94 cents, 4 loaves for 7 dollars and 80 cents, 5 loaves for 10 dollars and 5 cents, 6 loaves for 12 dollars and 12 cents.
Camillo is making gourmet peanut butter and jelly sandwiches for a food challenge.
PLS HELP ASAP!!What is the unit price of a loaf of bread at each store?
Store A:
Store B:
Store C:
Store D:
Solution:
The unit price of an item is the price for a single unit of measure of that item. It is measured in price / unit measure.
unit price of a loaf of bread at each store = cost of the loaf of bread / number of loaves
For store A, unit price = $5.94 / 3 loaves = $1.98 per loaf
For store B, unit price = $7.80 / 4 loaves = $1.95 per loaf
For store C, unit price = $10.50 / 5 loaves = $2.10 per loaf
For store D, unit price = $12.12 / 6 loaves = $2.02 per loaf
Answer:
yup the person above me is right but for C its $2.01 :>
Step-by-step explanation:
Hope this helps!!
Mayra bought x grams of rice.
Anika bought 5
more than Mayra bought.
Select ALL of the equations that represent the relationship
between the amount of rice that Mayra bought, x, and the
amount of rice that Anika bought, y.
(Select all that apply)
Answers
Answer:
[tex]y = 5 + x[/tex]
[tex]y - x = 5[/tex]
[tex]x = y - 5[/tex]
Step-by-step explanation:
No options were given but the question can still be solved
Given
From the first statement, we have:
[tex]Maria = x[/tex]
From the second, we have:
[tex]Anika = 5\ more[/tex]
Required
Determine the relationship between the amount of rice they bought
5 more means 5 + Maria.
So, [tex]Anika = 5\ more[/tex] becomes
[tex]Anika = 5 + Maria[/tex]
Substitute x for Maria
[tex]Anika = 5 + x[/tex]
For proper expression, let Anika be y
[tex]y = 5 + x[/tex]
Subtract x from both sides
[tex]y - x = 5[/tex]
Make x the subject
[tex]x = y - 5[/tex]
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! WILL MARK THE BRAINLIEST! 20 PTS!
A rectangular prism has a volume of 198 cm³. A rectangular pyramid has the same height as the rectangular prism and a base that is congruent to the base of the rectangular prism. What is the relationship between the volume of the rectangular prism and the rectangular pyramid?
a. The volume of a rectangular pyramid is 3 times the volume of a rectangular prism. The volume of the rectangular pyramid is 594 cm3.
b. The volume of a rectangular pyramid is 13 the volume of a rectangular prism. The volume of the rectangular pyramid is 66 cm3.
c. The volume of a rectangular pyramid is 12 the volume of a rectangular prism. The volume of the rectangular pyramid is 99 cm3.
d. The volume of a rectangular pyramid is 2 times the volume of a rectangular prism. The volume of the rectangular pyramid is 396 cm3.
Answers
Answer:
i need an answer to have you figured it out yet
Step-by-step explanation:
Answer:
B - (Probably)
Step by step explanation:
the Volume of the Pyramid = Volume of Prism / 3
198cm^3 / 3 = 66cm^3
help pls i’ll mark as brainliest if correct
Answers
Answer:
B
Step-by-step explanation:
Sandra wrote the sequence shown:
7, 14, 25, 40, 59
Complete each of the 2 activities for this Task.
Activity 1 of 2
What explicit expression can be used to find the nth term of this sequence?
Answers
Answer:
2n^2 + n + 4.
Step-by-step explanation:
7, 14, 25, 40, 59
The differences are 7, 11, 15, 19 which is arithmetic sequence so the given sequence is quadratic.
Compile a table:
n 1 2 3 4 5
term 7 14 25 40 59
Diff: 7 11 15 19
Diff: 4 4 4 - this indicates that first part is 2n^2.
2n^2 2 8 18 32 50
term-2n^2 5 6 7 8 9
- the nth term for the last sequence is 5+ (n - 1)d =
= 5 + (n - 1)* 1
= n + 4.
So nth term for the original sequence is 2n^2 + n + 4.
I think of a number. I multiply it by 2 and my answer is 24. What was my number?
Need help trying to solve
Answers
Answer:
12
Step-by-step explanation:
Brainliest plz trying to level upJared measured a house and its lot and made a scale drawing. The scale of the drawing was 5 millimeters : 3 meters. The actual length of the front lawn is 69 meters. How long is the lawn in the drawing?
Answers
Answer:
115mm
Step-by-step explanation:
5/x = 3/69
5/x = 1/23
5*23 = x
115 = x
Please help. Pleaaseeeeeee :))
Answers
Answer:
H:Median
Step-by-step explanation:
We know that Median means the middle, and we know that lines AB or in the middle of the page.
-9.b = 45
b =
What is the answer I need to know the answe
Answers
Answer:
b=-5
Step-by-step explanation:
Divide by -9 to eliminate the -9 on -9b
(Since -9b is the same thing as -9 times b we can use the inverse of multiplication which is division to eliminate the -9 from b but we need to do it on both sides to make it balance)
-9b/-9=45/-9
b=-5
Help !! I need to do this fast !!!!!
Answers
Answer:
3 and 6
Step-by-step explanation:
can i get brainliest please? thanks!
hope this helps!
please help.[tex]\frac{4}{x+2} +\frac{8}{x+5} -\frac{8}{x+3} -\frac{4}{x+6}[/tex]
Answers
A cell phone plan costs $200 to start. Then there is a $50 charge each
month. What is the total cost (start-up fee and monthly charge) to use the
cell phone plan for 3 months? *
O $150
$200
O $350
$750
Answers
Answer:
750
Step-by-step explanation:
200+50=250
250x3+750
Step by step explanation:
plz help ill give brainliest for best answers
Answers
Answer:
The least they will have to pay is 235 dollars.
They will have to pay 15 more dollars next year. (250 dollars)
Step-by-step explanation:
25x3=75
40x4=160
75+160=235
25x2=50
40x5=200
50+200=250
Can anyone help me pls???
Answers
Answer:
It's
Step-by-step explanation:
9a-3b
because 3×3a is 9a and 3×-b is -3b hope this helps
Answer:
8) A 9) B
Step-by-step explanation:
For question 8 just combine like terms, combine the numbers that have the same variables. Number 9, distribute the 3 to the rest of the equation.
Hope this helped :)
A car travels 825 miles in 15 hourso How many
miles does the can
travel in
I hour. Helps
ASAP
Answers
add x³-2x²y+4xy²-y³,2x³-5xy²+3x²y-4y³
Answers
Step-by-step explanation:
the answer is x times (x^2 +xy-y^2 - x^2 y^32)
911÷406 con operaciones
Answers
Answer:
2.24384236453
Step-by-step explanation:
division/división
Answer:
Step-by-step explanation:
2.24384236453 divicion y divicion
Function 1 is defined by the equation p= --3/2r - 5. function 2 is defined by the following table. Which function has a greater y-intercept. A: Function 1 B: Function 2 C: The functions have the same y-intercept.
Answers
The y-intercept of function 1 is -5.
The y-intercept of function 2 is -5.
Option C is the correct answer.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
Consider the function to be in the form of p = mr + c
Where x is the y-intercept.
Function 1.
p = (-3/2)r - 5 _______(1)
y-intercept = -5
Function 2.
Let p = mr + c
Take two pairs from the table.
(0, -5) and (1, -6.5)
m = (-6.5 + 5) / (1 - 0) = -1.5
(0, -5) = (r, p)
-5 = -1.5 x 0 + c
c = -5
Now,
p = -5x - 5 ______(2)
y-intercept = -5
From (1 ) and (2)
Both have the same y-intercept.
Thus,
Function 1 and Function 2 have the same y-intercept.
Learn more about functions here:
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In a right angled triangke abc the perpendicular and the base measure 3 cm find hypotenus and three trignometrice ratios
Answers
Given:
In a right angled triangle ABC the perpendicular and the base measure 3 cm.
To find:
The hypotenuse and three trigonometric ratios.
Solution:
Pythagoras theorem:
[tex]Hypotenuse^2=Perpendicular^2+Base^2[/tex]
Use Pythagoras theorem in triangle ABC.
[tex]Hypotenuse^2=(3)^2+(3)^2[/tex]
[tex]Hypotenuse^2=9+9[/tex]
[tex]Hypotenuse=\sqrt{18}[/tex]
[tex]Hypotenuse=3\sqrt{2}[/tex]
The three trigonometric ratios are
[tex]\sin \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]\sin \theta=\dfrac{3}{3\sqrt{2}}[/tex]
[tex]\sin \theta=\dfrac{1}{\sqrt{2}}[/tex]
Similarly,
[tex]\cos \theta=\dfrac{Base}{Hypotenuse}[/tex]
[tex]\cos \theta=\dfrac{3}{3\sqrt{2}}[/tex]
[tex]\cos \theta=\dfrac{1}{\sqrt{2}}[/tex]
And,
[tex]\tan \theta=\dfrac{Perpendicular}{Base}[/tex]
[tex]\tan \theta=\dfrac{3}{3}[/tex]
[tex]\tan \theta=1[/tex]
Therefore, the hypotenuse is [tex]3\sqrt{2}[/tex] cm and three trigonometric ratios are [tex]\sin \theta=\dfrac{1}{\sqrt{2}}, \cos \theta=\dfrac{1}{\sqrt{2}}, \tan \theta=1[/tex].
Tory read her book and rate of 4/5 of a chapter her 2/3 of an hour. How many chapters can she read in one hour
Answers
Answer: She can read 1.2 chapters of her book in one hour.
Step-by-step explanation:
When we have a relation of: "doing something" in a given "amount of time"
The rate at which you can do that activity per unit of time is:
R = (how much you did)/(time it took)
In this case, we know that
"Tory reads 4/5 of a chapter in 2/3 of an hour"
Then the rate, in this case, could be calculated as:
R = (4/5 chapters)/(2/3 hour) = 1.2 chapter per hour.
This means she can read 1.2 chapters of her book in one hour.
PLEASE HELP, I need this test done and something not failed. I dont understand.
Answers
Answer:
XVW and WVT
Step-by-step explanation:
Two angles are supplementary angles when the sum of their measures is equaled to 180 degrees.
180 degrees = a line.
YVZ and WVU are Vertical Angles
YVZ and ZVT are not straight lines together.
XVW and WVU are on the same straight line but you have to add UVT in order to get 180.
XVW and WVT are the only ones that look like they can add up to 180 degrees.
XVW and WVT should be the answer, I really hope this helps!
Is the function represented by the table non-linear?
х
у
6
4
7
2
8
0
9
-2
Answers
Answer:
the top answer
Step-by-step explanation:
Select all the expressions that are equivalent to 24x + 12.
2(12x + 6)
–6(–4x – 2)
–3(8x – 4)
12(1 + 2x)
–4(–6 – 3x)
Answers
Answer:
2(12x + 6)
-6(-4x - 2)
12(1 + 2x)
The expressions that are equivalent to 24x + 12 are:
2(12x + 6)
-6(-4x - 2)
12(1 + 2x)
Let's go through each expression and simplify them to determine if they are equivalent to 24x + 12.
2(12x + 6):
We can use the distributive property to simplify this expression:
2 * 12x + 2 * 6 = 24x + 12
This expression is equivalent to 24x + 12.
–6(–4x – 2):
Again, using the distributive property, we simplify:
–6 * –4x + –6 * –2 = 24x + 12
This expression is equivalent to 24x + 12.
–3(8x – 4):
Once again, applying the distributive property:
–3 * 8x + –3 * –4 = –24x + 12
This expression is not equivalent to 24x + 12.
12(1 + 2x):
Using the distributive property:
12 * 1 + 12 * 2x = 12 + 24x = 24x + 12
This expression is equivalent to 24x + 12.
–4(–6 – 3x):
Applying the distributive property:
–4 * –6 + –4 * –3x = 24 + 12x = 12x + 24
This expression is not equivalent to 24x + 12.
To know more about expressions click here :
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A bakery uses 44 cups of flour to make 10 loaves of bread. How many cups of flour are there per loaf?
Answers
Answer: 4.4
Step-by-step explanation:
44 divided by 10
Answer:
4.4 cups of flour
Step-by-step explanation:
You would have to divide 44(cups of flour) by 10(loaves of bread) to get the amount of cups of flour for each loaf. 44/10=4.4
Help pls I don’t know
Answers
Answer:
z-7
Step-by-step explanation:
hope this helped!
Given RS = 6, ST = 3, and SL = 4, find the required measure. (Part of the answer is provided for you.)
KT =
Answers
Answer:
https://brainly.com/question/1593288
Step-by-step explanation:
This was answered previously on here
Answer:
Square root of 61
Step-by-step explanation:
It was correct on my assignment
9+(-14)
What is the answer
Answers
Answer:
9+(-14)=-5
Step-by-step explanation:
9+(-14)
9-14
=-5
Answer:
-5
Step-by-step explanation:
the answer is negative 5