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
6) solve the equation for m
Answers
Answer:
m=48
Step-by-step explanation:
m/3=18-2
m/3=16
m=16x3
m=48
Answer:
m=48
Step-by-step explanation:
Subtract 2 from both sides
2+m/3-2=18-2
Simplify
m/3=16
Multiply both sides by 3
3m/3=16*3
simplify
m=48
What is the volume of the pyramid?
Answers
Answer: 484
Step-by-step explanation:
12x11x11=1,452
1,452/3=484
WILL GIVE BRAINLIEST AND 20 POINTS!
A circular, inlaid-wood design for a dining table cost $35 per square foot to build. If the radius of the design is 18 in, find the cost to build the design. Use 3.14 for . Round to the nearest dollar. Hint: 144 in2 = 1 ft2.
Answers
Area of design= pi*r^2
= 3.14*324
= 1017.36 sq. in
1017.36/144
= 7.065 sq. ft
7.065*35
= 247.275
Therefore, the cost of building the design costs $247.275 to make
Given the Standard Form equation y - 6x = 4
What is the slope and y intercept?
someone plz explain
Answers
Answer: 6 is the slope and 4 is the y-intercept.
Step-by-step explanation:
Based on the question, I feel this is the best way to answer your question. I'm assuming you are in a basic graphing class.
The best, most useful thing for you right now would be to learn slope-intercept form, y = mx + b, where m and b are constants.
Simply add 6x to both sides to get into this form
y = 6x + 4.
In slope-intercept form, m is the slope, and b is the y-intercept. Thus, 6 is the slope and 4 is the y-intercept.
Hope it helps and lmk if you need more <3 :)
(40 POINTS) Let x = price of a standard ticket, y = price of a matinee ticket, and z = price of a senior ticket.
150x + 80y + 12z = 2,466
380x + 95y + 48z = 5,419
210x + 130y + 60z = 3,960
220x + 225y = 4,445
540x + 270y = 8,370 → y = −2x + 31
x = 11
The solutions to the system mean:
A.) Eleven tickets were sold on Friday. Nine tickets were sold on Saturday. Eight tickets were sold on Sunday.
B.) Eleven standard tickets were sold. Nine matinee tickets were sold. Eight senior tickets were sold.
C.) The price of a standard ticket is $11. The price of a matinee ticket is $9. The price of a senior ticket is $8.
Answers
Answer:
C. The price of a standard ticket is $11. The price of a matinee ticket is $9. The price of a senior ticket is $8.
Answer:
The answer is C
Step-by-step explanation:
Determine whether AB is a median,altitude,or neither
Answers
Line AB is neither a Median nor an Altitude.
What is angle Bi-sector?In geometry, an angle bisector is a line that divides an angle into two equal angles. The term "bisector" refers to a device that divides an item or a form into two equal halves. An angle bisector is a ray that divides an angle into two identical segments of the same length.
Given, A triangle in that there is an angle bisector AB.
Since,
Median:
A median of a triangle is a line segment that joins a vertex to the mid-point of the side that is opposite to that vertex.
In our case, it is not specified if AB bisects the opposite line
Altitude:
The altitude of a triangle is the perpendicular drawn from the vertex of the triangle to the opposite side. Also, known as the height of the triangle, the altitude makes a right-angle triangle with the base.
In our case, it is not specified if AB makes a Right triangle or not.
Therefore, Line Ab is neither a Median nor an Altitude.
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What is the square root of x to the 10 power
Answers
Answer:
x^5
Step-by-step explanation:
A. (−13)+(−7)= b. (−15)− (−15)= c. (2)∙ (−13)= d. (−44)÷ (11)= e. (−3)+(−5)+(8) +(25)= f. 3+4=4
Answers
Answer:
See answer below
Step-by-step explanation:
In this case, this is just sum, substraction and divisions using the properties or the signus. This is just basic operations using the negative and positive numbers.
To do this easily you just have to remember the following:
1. Numbers with same sign, must be summed and put the sign that have either number.
2. Numbers with different sign, must be substracted and then put the sign of the highest number.
3. If you have a multiplication or division:
- Same signs multiplied or dividied (Either positive or negative), result always positive.
- Different signs multiplied or dividied (positive and negative), result always negative.
Following this simple rules, you'll be able to solve almost any exercise of this.
Now, according to the rules above, let's solve the exercises:
A. (-13) + (-7)
In this case, you have two negative numbers, and one positive sign between them. Apply the 3rd rule. The negative sign remains and then:
-13 - 7
Now 1st rule applied, sum the numbers and let the same sign:
-13 - 7 = -20.
B. (-15) - (-15) = 0.
Applying 3rd rule and then 2nd rule, we have a subtration of -15 + 15.
C. (2) * (-13) = -26
Applying the 3rd rule, we have positive and negative, result always negative.
D. (-44) / 11 = -4
3rd rule applied.
E. (-3) + (-5) + 8 + 25 = 31
Applied 3rd and 1st rule.
I don't understand the f, but you can use the rules here and get the final answer of that one.
Hope this helps
Alis needs 10 strips of ribbon each 2 and 1/2 feet. how much ribbon in all is needed
Answers
Answer:
She needs 25 feet
Step-by-step explanation:
10 * 2.5 = 25
Answer: There are 3 strips that can be cut from the roll of ribbon.
mutilply 2 3/5 x 1 3/7
Answers
Answer:3.71428571429
Step-by-step explanation:
If a hexagon is worth 5 and a triangle is worth 3, what is a circle
Answers
Answer:
6
Step-by-step explanation:
Call pentagon p, circle c and triangle t
We have 2c + 2p = 2p + 2t + c
p = 5, t = 3 so
2c + 2(5) = 2(5) + 2(3) + c
2c + 10 = 10 + 6 + c
2c = 6 + c
c = 6
6 answer
Call pentagon p, circle c and triangle t
We have 2c + 2p = 2p + 2t + c
p = 5, t = 3 so
2c + 2(5) = 2(5) + 2(3) + c
2c + 10 = 10 + 6 + c
2c = 6 + c
c = 6
The polygons are similar. Find the scale factor from ABCD to EFGH.
Answers
Answer:
2.5
Step-by-step explanation:
45/18 = 2.5
35/24 = 2.5
40/16 = 2.5
i just want to know if this is correct if not Plss correct me (ZOOM IN TO SEE FULL PIC)
Answers
Answer:
A correct
B is 15 not 17
C correct
D correct
E correct
F is 10 not 3.5
Step-by-step explanation:
Answer:
Step-by-step explanation:
They are all correct except the last one f.
12.5^2-7.5^2=100
So the missing side should be 10 not 3.5
Please help I really need it I will be giveing 15 points to whoever can help me
Answers
Answer:
the slope is: -1/2
y-intercept: (0,-f)
hopefully that makes sense
...................help
Answers
omg it's so hard what is 2 + 2 (yes)
Answers
Answer:
5
Step-by-step explanation:
graph the image of M (–10,–7) after a rotation 180° counterclockwise around the origin.
Answers
Answer and Step-by-step explanation:
The point will be (7, 10).
#teamtrees #WAP (Water And Plant)
The image of the point M is M' = (10, 7) as shown in the graph below.
What is Coordinate Geometry?One of the most intriguing ideas in mathematics is called coordinate geometry. By using graphs with curves and lines, coordinate geometry (also known as the analytic geometry) explains how geometry and algebra are related.
As per the given data:
Coordinates of point M = (-10, -7)
Rotation to be given = 180° (counter - clockwise)
For drawing the image of point M (-10, -7):
Step 1: Create a line connecting the origin to the point M (-10, -7) and extending across the third and first quadrants.
Step 2: Modify the x and y coordinates signs to reflect the 180° rotation, then mark the point in the first quadrant.
The image of the point M is M' = (10, 7) as shown in the graph below.
Hence, the image of the point M is M' = (10, 7).
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Solve the equation for x, and enter your answer in the box below.
12x = 36
Answers
Answer:
x = 3
Step-by-step explanation:
Step 1:
12x = 36 Equation
Step 2:
x = 36 ÷ 12 Divide by 12 on both sides
Answer:
x = 3
Hope This Helps :)
I need help !! This is being timed
Answers
Divide the number of people who bought tickets by total people in the seats:
15 / 22 = 0.681818
The 8181 part continues forever, so there will be a line above the 81.
The answer is the first one.
Kayla is a basketball CHAMP!!! She sits at her desk and throws garbage into the trash can! Last week, she took 30 shots and made 24 of them. What percentage of her shots did Kayla make? (PLEASE HELP!)
Answers
Answer:
80
Step-by-step explanation:
30 = 100
24 = 80
6 x 5 = 30
6 x 4 = 24
5 = 20 because 5 x 8 = 80.
which graph models the solution of the Inequality -6 ≤ -3x
Answers
First make x the subject which would be -6/-3 ≤ x
Which is 2 ≤x and that is represented in B
We know that graph (B) models the solution of the given inequality -6 ≤ -3x.
What are graphs?Drawing the curve that represents a function on a coordinate plane is known as graphing a function. Every point on the curve will satisfy the function equation if the curve (or graph) represents the function.Line graphs, bar graphs, pie charts, scatter plots, and histograms are examples of common graph types. Graphs are a fantastic tool for displaying statistics and visualizing data. To depict numerical data that is unrelated to one another, a bar graph or chart may be utilized.So, in the given inequality:
-6 ≤ -3xWe know that:
Make x subject: -6/-3 ≤ xWhich is 2 ≤ x, represented in a graph (B).Therefore, we know that graph (B) models the solution of the given inequality -6 ≤ -3x.
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Solve the inequality. HELPPP ME PLZZ
3/4x − 2/3 ≤ 5/6
Choose the solution that is graphed on this number line.
A. x < 2
B. x > 2
C. x ≤ 2
D. x ≥ 2
Answers
c
Step-by-step explanation:
if you look at the graph, if there is a closed circle, that means x can be equal to whatever number the circle is on. if the circle is open, that means you don't include that number, which is in this case two. a closed circle means that x can be equal to 2. since the arrow is going from 2 to the left, x can be anything from two to any real numbers to the left. therefore, since to the left goes to numbers smaller than 2, x can either be equal to or less than two.
The solution of the inequality 3/4 x - 2/3 ≤ 5/6 which is graphed on given number line is x ≤ 2.
Here inequality is given as;
3/4 x - 2/3 ≤ 5/6
What is inequality?
A statement of an order relationship; less than, greater than, greater than or equal to, less than or equal to, between two algebraic expression is known as inequality.
Now,
3/4 x - 2/3 ≤ 5/6
3/4 x - 2/3 + 2/3 ≤ 5/6 + 2/3
3/4 x ≤ 7/3
Now multiply both side by 4/3;
[tex]\frac{3}{4} x *\frac{4}{3} \leq \frac{7}{3} *\frac{4}{3} \\x\leq \frac{28}{9} \\x\leq 3.11\\[/tex]
Hence, The solution of the inequality 3/4 x - 2/3 ≤ 5/6 which is graphed on given number line is x ≤ 2.
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Find the difference: 4.9 - 2.46
Answers
Answer:
The answer is 2.44
Step-by-step explanation:
4.9 - 2.46 = 4.90 - 2.46
4.90 - 2.46 = ?. 44
4. 90 - 2.46 = 2.44
Simultaneous equations:
1) 3x + 2y = 23
2x - y = 6
2) 3x - 3y = 9
2x + y = 12
3) 4x + 2y = 34
3x + y = 21
(if you could answer with workings out that would be great)
Answers
Answer:
1)x=5 y=4
2)y=2 x=5
3)y=12 x=3
Step-by-step explanation:
hope that helps!
Write a rule for the linear function in the table.
i need help
x f(x)
0
3
6
9
f(x)
3
15
27
39
f(x) = 4x + 3
f(x) = –4x – 3
f(x) = [tex]\frac{1}{4}[/tex]x + 3
f(x) = x + 3
Answers
Answer:
i'm gonna go with A. f(x) = 4x + 3
Step-by-step explanation:
i hope this is the right answer.. i can't find this answer anywhere.. i can't remember the answer from a week ago :(
Which PERCENT is represented by the shaded area? (This is urgent!!)
Answers
Answer:
47%
Step-by-step explanation:
hope this helps
Answer:
47%
Step-by-step explanation:
47 blocks out of 100 were shaded, which makes it 47%
34.98×104= -------------
because the number 10 to the 4th power has
------------- zeros when it is written without an exponent.
brainliest if right easy question
Answers
Answer:
349,800.0 because the number 10 to the 4th power has four zeros when it is written without an exponent.
Step-by-step explanation:
34.98 x 10^4 = 349,800.0 = 349,800
34.98×10⁴ = 349,800.0 because the number 10 to the 4th power has four zeros when it is written without an exponent.
Here, we have,
given that,
the term is: 34.98 x 10⁴
now, we have to find the result of multiplication without an exponent.
so, we get,
34.98 x 10⁴
=34.98 x 10000
= 349,800.0
= 349,800
Hence, 34.98×10⁴ = 349,800.0 because the number 10 to the 4th power has four zeros when it is written without an exponent.
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each piece of paper is a memo pad is a square. The length of of each side is 2 3/4 inches. What is the area of one piece. please and thank you
Answers
Answer:
approximately 7.5265in
Step-by-step explanation:
Area = length x width
2.75 x 2.75 = 7.5265in
Find the slope of the line that passes through
(7,-1) and (9,0)
Answers
Answer:
1/2 or 0.5
Step-by-step explanation:
so to find the slope of two points you use the slope formula which is rise over run, y2-y1/x2-x1. so that would be -1-0/7-9. leading to -1/-2. so the slope is 1/2 or 0.5.
A principal of $480 earns $108 interest in 5 years . what rate of interest was being paid?
Answers
Answer:
4.5%
Step-by-step explanation:
Solving our equation
r = 108 / ( 480 × 5 ) = 0.045
r = 0.045
converting r decimal to a percentage
R = 0.045 * 100 = 4.5%/year
The interest rate required to
accumulate simple interest of $ 108.00
from a principal of $ 480.00
over 5 years is 4.5% per year.