consider the following functions which all have a value of 30 does each equation represent growth or decay
Answers
The general equation forms representing growth or decay is;
[tex]\begin{gathered} F=I(1+r)^{t\text{ }}orF=I(1-r)^t \\ F\text{ is future value} \\ I\text{ is initial value} \\ r\text{ is growth rate} \\ t\text{ is time} \\ (1-r)\text{ represents decay} \\ (1+r)\text{ represents growth} \end{gathered}[/tex]So let us consider the equations;
a) f(t) = 30(1.04)^t
f(t) = 30(1+0.04)^t
It is growth as it is greater than 1 and the growth rate is 0.04 = 4/100 = 4%
b) p(x) = 30(0.65)^x
P(x) = 30(1-0.35)^x
it is decay as it is less than 1
Growth rate is 0.35 = 35/100 = 35%
c) A(x) = 30(1.10)^x
A(x) = 30(1 + 0.1)^x
it is growth as it is greater than 1
0.1 = 10/100 = 10%
d) h(t) = 30(0.98)^t
h(t) = 30(1-0.02)^t
It is decay since it is less than 1
growth rate is;
0.02 = 2/100 = 2%
e) s(t) = 30(0.77)^t
s(t) = 30(1-0.23)^t
it is decay as it is less than 1
0.23 is growth rate = 23/100 = 23%
f) B(t) = 30(1.2)^t
B(t) = 30(1+0.2)^t
It is growth since it is greater than 1
0.2 = 20/100 = 20%
Related Questions
Select the correct answer from each drop menu Short answers only and this time also not a test
Answers
The parent function f(x) has a horizontal asymptote located at:
[tex]y=0[/tex]Since g(x) has the horizontal asymptote located at:
[tex]y=3[/tex]We can conclude that g(x) is the result of translate f(x) 3 units up, therefore:
[tex]g(x)=\frac{1}{x}+3[/tex]Answer:
k = 3
y = 5
2x − 4y = –10
( _ , _ )
Answers
PLUG 5 IN THE PLACE OF Y AND SOLVE FOR X
[tex]2x - 4(5) = - 10 \\ 2x - 20 = - 10 \\ 2x = - 10 + 20 \\ 2x = 10 \\ \frac{2x}{2} = \frac{10}{2} \\ x = 5[/tex]
SINCE WE FOUND THAT x=5
we have the pair
(5,5)
I want to learn mathematics
Answers
Answer:
take math class and watch stuff on kai academy
Answer:
use maths watch and get smart
Describe all numbers x that are at a distance of 4 from the number 7.Express this using absolute value notation.
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Describe all numbers x that are at a distance of 4 from the number 7.
Express this using absolute value notation.
Step 2:
The details of the solution are as follows:
Given:
Number x at a distance of 4 from the number 7.
Calculation:
The given statement is the numbers x are at a distance of 4 from the
number 7;
The number x at a distance of 4 is:
[tex]y\text{ = }\lvert{x}\rvert\text{ + 4}[/tex]x at a distance of 4 from the number 7;
[tex]y\text{ = }\lvert x-7\text{ }\rvert\text{ + 4}[/tex]CONCLUSION:
Thus, the absolue value equation is:
[tex]y\text{ = }\lvert{x-7}\rvert\text{ + 4}[/tex]A worker assembles 5.4 products per hour. At this rate how many products will she assemble in a year if she works 40 hours per week and gets two weeks of vacation each year? (Assume no holidays.) A) 432 products B) 2,700 products C) 5,400 products O D) 10,800 products
Answers
we have:
5.4 products per hour
1 year = 52 weeks
40 hours -----> 1 week
x hours -------> 50 weeks
[tex]\begin{gathered} x\times1=40\times52 \\ x=2000 \end{gathered}[/tex]she works 2080 hours per year
then,
5.4 products ----> 1 hour
y products -------> 2000 hours
[tex]\begin{gathered} y\times1=5.4\times2000 \\ y=10800 \end{gathered}[/tex]answer: D. 10,800 products
what is the first step when you do 3(19c+4)=12
Answers
3(19c + 4) = 12
1st step multiply the bracket (19c + 4) by 3
3(19c + 4) = 3(19c) + 3(4)
3(19c + 4) = 57c + 12
57c + 12 = 12
2nd step subtract 12 from both sides
57c + 12 - 12 = 12 - 12
57c = 0
3rd step divide both sides by 57 to find c
[tex]\frac{57c}{57}=\frac{0}{57}[/tex]c = 0
Hi I need help sketching the graphIts a domain and function
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
y = - 5 + √x
Step 02:
Domain:
x ≥ 0
[0 , oo)
Graph:
x-intercept = 25
(25 , 0)
y-intercept = -5
(0 , -5)
That is the full solution.
What is the domain of the function y = 2 StartRoot x minus 5 EndRoot?
x greater-than-or-equal-to negative 5
x greater-than-or-equal-to 2
x greater-than-or-equal-to 5
Answers
The domain of the function given; y = 2 StartRoot x minus 5 EndRoot is; x greater-than-or-equal-to 5.
What is the domain of the function given; y = 2√(x -5)?It follows from the task content that the domain of the square root function is to be determined.
Recall, that the domain of a function involving square roots includes all values of x except those which render the expression in the square root less than 0.
Hence, the domain of.the function given is;
x - 5 ≥ 0.
x ≥ 5.
Ultimately, the domain of the function is all values of x greater than or equal to; 5.
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4 in 3.2 in 7.5 in x x = [x] inches.
Answers
7.5in then 4in together next is 3.2in x and find
7.5" + 4" +3.2"x
Suppose your friend is trying to answer the following question:"How many centimeters are in 4.7 meters?"Your friend knows there are 100 cm in 1 m, exactly. Yet, when they solve the problem, they got an incorrect answer of "0.047 cm." Explain what they may have done wrong and how you could help them fix their mistake.
Answers
we know that
1 m=100 cm
so
to convert 4.7 meters to cm
Multiply 4.7 by 100
4.7*100=470 cm
Your friend instead of multiplying 4.7 by 100, divide 4.7 by 100
Find all the angles in the interval 0 to 360 degrees that satisfy the following condition. Round theanswer to the nearest hundredth of a degree.sin(x) = 5/14
Answers
Given the expression:
[tex]\sin (x)=\frac{5}{14}[/tex]to find the angle, we use the invers sine function to get x:
[tex]\begin{gathered} \sin (x)=\frac{5}{14} \\ \Rightarrow x=\sin ^{-1}(\frac{5}{14})=20.92 \\ x=20.92 \end{gathered}[/tex]therefore, the angle x = 20.92°
what is 3/5 as an equation or fraction?
Answers
Given,
[tex]\frac{3}{5}[/tex]In algebra, an equation is a mathematical statement consisting of an equal symbol between two algebraic expression
In the given, there is no equal symbol
Then the given value looks like a fraction format
so,
[tex]\frac{3}{5}[/tex]Is a fraction
Question in picture answer please
Answers
The expression in the image is:
a*(a + b + b) = a² + 2ab
So the correct option is the bottom left one.
Which expression is on the diagram?
The diagram is a rectangle that can be divided into smaller rectangles. We know that the area of the large rectangle will be equal to the sum of the areas of the smaller rectangles, then we can write:
area of the larger rectangle = a*(a + b + b)
While the addition of the areas of the smaller figures gives:
sum of areas: a² + a*b + a*b = a² + 2ab
Then the expression in the image is:
a*(a + b + b) = a² + 2ab
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1. There were 330 people at a play. the admission price was $3 for adults and $1 for children. the admission receipts were $650. how many adults and how many children attended? A) Children: 170, Adults: 60B) Children: 30, Adults: 300C) Children: 160, Adults: 170D) Children: 170, Adults: 160
Answers
Explanation
Step 1
Set the equations
let x represents the number of adults attended
let y represents the number of children attended
so
There were 330 people at a play:
it means the sum of adults and children is 330
[tex]x+y=330\Rightarrow equation(1)[/tex]and
if the admission price for $3 for adults, the money from the adult tickets is
[tex]3x[/tex]and $1 for children
[tex]1y[/tex]admission receipts were $650,hence
[tex]\begin{gathered} 3x+y=650\Rightarrow equation(2) \\ \end{gathered}[/tex]Step 2
solve the equations
[tex]\begin{gathered} x+y=330\Rightarrow equation(1) \\ 3x+y=650\Rightarrow equation(2) \\ \end{gathered}[/tex]a) isolate y in equation (1) and replace in equation (2)
[tex]\begin{gathered} x+y=330\Rightarrow equation(1) \\ \text{subtract y in both sides} \\ x+y-y=330-y \\ x=330-y \\ \text{Now , replace in equation (2)} \\ 3x+y=650\Rightarrow equation(2) \\ 3(330-y)+y=650 \\ 990-3y+y=650 \\ 990-2y=650 \\ \text{subtract 990 in both sides} \\ 990-2y-990=650-990 \\ -2y=-340 \\ divide\text{ both sides by -2} \\ \frac{-2y}{-2}=\frac{-340}{-2} \\ y=170 \end{gathered}[/tex]therefore
170 childrend attended
b) now, to find x, replace the y value in equation (1)
[tex]\begin{gathered} x+y=330\Rightarrow equation(1) \\ x+170=330 \\ \text{subtract 170 in both sides} \\ x+170-170=330-170 \\ x=160 \end{gathered}[/tex]Therefore,
160 adults attended
so, the answer is
[tex]D)\text{Children:}170\text{ , Adults :160}[/tex]I hope this helps you
in the design a regular hexagon is inscribed in a circle point q will map onto which point after a 120 degree clockwise rotation around the center
Answers
Given a regular hexagon
At first we should know that, the angle of rotation between any two consecutive two points will be 360/6 = 60
So,
So, the point q after rotation of 120 degree clockwise will be point S
The answer is option A. Point S
Can find the correct answer
Answers
Answer:
∠ QOR = 35°
Step-by-step explanation:
from the diagram
∠ POQ + ∠ QOR = ∠ POR , that is
24° + ∠ QOR = 59° ( subtract 24° from both sides )
∠ QOR = 35°
Options for the first box: 9.51, 9.75, 9.67, 9.59Options for the second box: 9.91, 9.99, 9.75, 9.83
Answers
We know that
• The mean is 9.75 meters per second.
,• The standard deviation is 0.08 meters per second.
According to the empirical rule, 95% of the data falls into 2 standard deviations below and above the mean, so we just have to subtract and add the standard deviation twice.
[tex]\begin{gathered} \bar{x}+2\sigma \\ \bar{x}-2\sigma \end{gathered}[/tex]Using the given information, we have
[tex]\begin{gathered} 9.75+2(0.08)=9.75+0.16=9.91 \\ 9.75-2(0.08)=9.75-0.16=9.59 \end{gathered}[/tex]Therefore, her next measurement will fall between the values of 9.59 and 9.91 meters per second.[tex]9.59Tomas is leaving a tip of 18% of his original bill. If the amount of the tip is $2.34, what is the amount of the original bill? Do not place a dollar sign as it will not be needed for this question.
Answers
Explanation
We are given the following information:
• Tomas is leaving a tip of 18% of his original bill.
,• The amount of his tip is $2.34.
We are required to determine the amount of the original bill.
This can be calculated as:
[tex]\begin{gathered} Tip=18\%\text{ }of\text{ }Original\text{ }bill \\ 2.34=18\%\times Original\text{ }bill \\ 2.34=0.18\times Original\text{ }bill \\ Original\text{ }bill=\frac{2.34}{0.18}=13 \end{gathered}[/tex]Hence, the amount of the original bill is $13.
OlialSlideAfrange Tools Add-ons HelpLast edit was 30 minutes ago२D PresentBackgroundLayoutThemeTransition56716. The Garcias are on their way to the beach. They are traveling ata rate of 30 miles per hour. Use the ordered pairs to graph thedistance traveled over time.Distance (miles)306090120150Time (hours)12345A15012090Distance (miles)60300Time (hours)GO ONGO ON
Answers
it is given that gracias travels 30 miles with speed of 30 miles per hour in a hour,
so (1 , 30)
the x cordinate is representing the time and y cordinate is representing the distance
so all the coordinates will be
(2, 60) & (3, 90) & (4, 120) & (5, 150)
mark these point on the graph
then draw the line that will meet these point.
i got it wrong twice ( c and b are incorrect)
Answers
You have to closely look at the values and figure out a pattern.
If you look at the right-hand column, you can see a pattern of powers of 3.
3^0 = 1
3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81
But the "power" doesn't correspond with nth term.
For example, when we have the power of "1", it is "2nd term", a_2.
Also, when we have the power of "3", it is the "4th term", a_4.
Hence,
the pattern suggests us that
the power is "1 less than" the nth term. In other words, the formula can be "a_(n-1) to the power 3" to incorporate this.
Looking at the choices,
A is correct.
Five thousand tickets are sold at $1 each for a charity raffle. Tickets will be drawn at random and monetary prizes awarded as follows: 1 prize of$500; 3 prizes of $100, 5 prizes of$20, and 20 prizes of $5. What is the expected value of this raffle if you buy 1 ticket?
Answers
As per the unitary method, the expected value of this raffle if you buy 1 ticket is $ 0.25.
Unitary method:
Basically, the word unitary refers to a single or an individual unit.
Therefore, this method aims at determining values in relation to a single unit.
Given,
Here we have that five thousand tickets are sold at $ 1 each for a charity raffle, and tickets are to be drawn at random and monetary prizes awarded as follows:
1 prize of $ 500,
3 prizes of $ 200,
5 prizes of $ 10, and
20 prizes of $ 5,
And here we need to determine what is the expected value of this raffle if you buy 1 ticket.
As per the given details, let us consider X be the expected value then we have written it as the equation like the following,
(500 + 3 x 200 + 5 x 10 + 20 x 5) / 5000 = X
When we simplify it then we get,
(500 + 600 + 50 + 100) / 5000 = X
After the addition operation we get the value,
1250/5000 = X
Then the value of X can be written as,
0.25 = X
Therefore, the expected value of this raffle per ticket is $ 0.25.
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Answer the following The sign of a is : a. positive B .Zero C.Negative The value of h is given by h The value of k is given by k
Answers
Since the function is concave up, the leading coefficient a must be positive.
Then: The sing of a is positive
The function is expressed in its canonical form, where h and k are the x and y coordinates of the vertex, respectively.
We can check in the graph that the vertex coordinates are (-5,-4).
Therefore, we have:
The value of h is given by h = -5
The value of k is given by k = -4
Cindy and Cora are going to a movie. Cindy forgot her money and is going to pay Cora back later. The cost of the two tickets is $16.50 and a bucket of popcorn is $3.66. What is the total cost that Cora will pay for two tickets and one bucket of popcorn?
Answers
Answer: I think 10.08
$16.50 and a bucket of popcorn is $3.66
$16.50 + $3.66 = 20.16
20.16/2= 10.08
Use the above (rounded) slope and y-value to write the equation of the tangent line to the graph of f(x)at x=3. Write your answer in mx+b format.
Answers
In order to calculate the slope of f(x) at x = 3, we can use the formula below:
[tex]m=\frac{f(x+h)-f(x)}{h}[/tex]For x = 3 and h = 0.001, we have:
[tex]\begin{gathered} m=\frac{f(3.001)-f(3)}{0.001} \\ f(3.001)=4.8\cdot3.001^2-4.6\cdot3.001=43.2288048-13.8046=29.4242048 \\ f(3)=4.8\cdot3^2-4.6\cdot3=43.2-13.8=29.4 \\ m=\frac{29.4242048-29.4}{0.001}=\frac{0.0242048}{0.001}=24.2 \end{gathered}[/tex]The value of f(3), as calculated above, is 29.4.
The tangent line has a slope of m = 24.2 and it passes through the point (3, 29.4), so let's calculate the value of b:
[tex]\begin{gathered} y=mx+b \\ 29.4=24.2\cdot3+b \\ 29.4=72.6+b \\ b=29.4-72.6 \\ b=-43.2 \end{gathered}[/tex]Therefore the equation of the tangent line is y = 24.2x - 43.2.
A group of 45 people attened a ball game.There were twice as many children as adults in the group, Set up a system of equations that represents the numbers of adults and children who attened the game and solve the system to find the number of children who were in the groupe as many children as adults in the group. set up a system of equations that represents the number of adults and children who attened the game and solve the system to find the number of children who were in the group
Answers
A system of equations representing the number of adults and children attending the game is x + 2x = 45, and the number of children who were in the group is 30.
What is an equation?An equation is a mathematical statement showing that two mathematical expressions are equal or equivalent.
Equations are represented using the equation sign (=).
The total number of people who attended the game = 45
Let the number of children, who were twice as many as adults, C = 2x
Let the number of adults, who attended the game, A = x
Therefore, the total number of attendees, T = x + 2x = 45
x + 2x = 45
3x = 45
x = 15
C = 2x
= 2(15)
= 30
Check:
x + 2x = 45
Substitute x with 15
15 + 2(15) = 45
15 + 30 = 45
45 = 45
Thus, from the system of equations, we can conclude that 30 children attended the game, which is twice the number of adults.
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A rectangular board is 1200 millimeters long and 800 millimeters wide. What is the area of the board in square meters? Do not round your answer. Be sure to include the correct unit in your answer.
Answers
Given:
shape: rectangle
length: 1200 mm
width: 800 mm
Find: area in square meters
Solution:
First, let's convert the given dimensions to meters.
Conversion rule is 1 m = 1000mm. Let's convert the length first.
[tex]1200\operatorname{mm}\times\frac{1m}{1000\operatorname{mm}}=1.2m[/tex]Length = 1.2 meters
Now, let's convert the width.
[tex]800\operatorname{mm}\times\frac{1m}{1000\operatorname{mm}}=0.8m[/tex]Width = 0.8 meters
Now that we are done converting the dimensions of the board to meters, let's solve for the area. The formula is:
[tex]Area=length\times width\text{ }[/tex]Let's plug in the converted dimensions to the formula.
[tex]Area=1.2m\times0.8m=0.96m^2\text{ }[/tex]Therefore, the area of the board is 0.96 square meters.
can you tell me in steps how to solve this quadratic formula problem?It's for an essay
Answers
3) cos X 2 37 12 35 35 B) ما را با را 35 12 C 35 D) 12
Answers
We get that
[tex]\cos x=\frac{35}{37}[/tex]According to historical records, the highest price for regular gas in Florida over the last ten years was just under $4.06 write an inequality to represent Florida's gas prices over the last ten years
Answers
We know that the regular gas over the last ten years was just under $4.06.
Also, it's important to keep in mind that the price must be more than zero.
Therefore, based on the given information, the inequality is
[tex]0Construct parametric equations describing the graph of the line passing through the following points.(20, -14) and (12, -12)If y = 1-5, find the parametric equation for x,
Answers
ANSWER :
x = -4t - 16
EXPLANATION :
From the problem, we have the points :
[tex](20,-14)\quad and\quad(12,-12)[/tex]Solve for the equation of the line using two-point formula :
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]That will be :
[tex]\begin{gathered} y-(-14)=\frac{-12-(-14)}{12-20}(x-20) \\ y+14=\frac{2}{-8}(x-20) \\ y+14=-\frac{1}{4}(x-20) \\ y+14=-\frac{1}{4}x+5 \\ y=-\frac{1}{4}x+5-14 \\ y=-\frac{1}{4}x-9 \end{gathered}[/tex]Next is to substitute the given paremetric equation for y :
[tex]y=t-5[/tex]That will be :
[tex]\begin{gathered} y=-\frac{1}{4}x-9 \\ y=t-5 \\ t-5=-\frac{1}{4}x-9 \\ t-5+9=-\frac{1}{4}x \\ t+4=-\frac{1}{4}x \\ 4t+16=-x \\ x=-4t-16 \end{gathered}[/tex]