Using an exponential function, it is found that the value of David's Investment will be at least $415 after a period of 20 years.
What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.In this problem, the initial value and the growth rate for his investment are given by:
A(0) = 230, r = 0.03.
Hence, the value after t years is given by:
[tex]A(t) = 230(1.03)^t[/tex]
Then, the value will be of at least $415 when:
[tex]A(t) \geq 415[/tex]
[tex]230(1.03)^t \geq 415[/tex]
[tex](1.03)^t \geq \frac{415}{230}[/tex]
[tex]\log{(1.03)^t} \geq \log{\frac{415}{230}}[/tex]
[tex]t\log{1.03} \geq \log{\frac{415}{230}}[/tex]
[tex]t \geq \frac{\log{\frac{415}{230}}}{\log{1.03}}[/tex]
[tex]t \geq 20[/tex]
More can be learned about exponential functions at https://brainly.com/question/25537936
#SPJ1
Which of the following is a point on the plane curve defined by the parametric equations?
x=3t
y=18t^2+12t+2
The ANSWER is (-1,0) ---- PLEASE EXPLAIN!!! THANK YOU x1000000!!!
By eliminating the parameter t and evaluating the function at x = -1 we conclude that the parametric equations contains the point (x, y) = (-1, 0).
How to determine that point belongs to a set of parametric functions
In this case we must determine if a point in rectangular format belongs to a set formed by two parametric functions. The functions are parametric as they are based in a parameter t. A quick approach consist in reduce the number of equations by eliminating the parameter.
The first equation is represented below:
t = x/3
And the parameter is substituted in the second equation:
y = 18 · (x/3)² + 12 · (x/3) + 2
y = 2 · x² + 4 · x + 2
If we know that x = -1, then the y-value is:
y = 2 · (- 1)² + 4 · (- 1) + 2
y = 0
By eliminating the parameter t and evaluating the function at x = -1 we conclude that the parametric equations contains the point (x, y) = (-1, 0).
Remark
The statement is incomplete, the complete definition is presented below:
Which of the following is a point on the plane curve defined by the parametric equations?
x = 3 · t, y = 18 · t² + 12 · t + 2
A. (-1, 0)
B. (-3, -28)
C. (-1, 8)
D. (-3, 128)
To learn more on parametric equations: https://brainly.com/question/12718642
#SPJ1
PRECISION In November 2010 the average cost of 5 gallons of regular unleaded gasoline in the United States was $14.46. What was the average cost for 16 gallons of gasoline?
Answer:
46.272 or 46 34
125
Explains :
Let see :
Based on the given conditions, formulate: 16×14.46÷5
Calculate the product or quotient:231.36
5
Convert decimal to fraction:23136
100
5
Divide a fraction by multiplying its reciprocal:23136 × 1
100 5
Write as a single fraction:23136
100×5
Cross out the common factor:5784
25×5
Calculate the product or quotient:5784
5784 125
get the result: 46.272 or 46 34
125
Answer: 46.272 or 46 34
125
Please help quickly! and Correctly. :)
There are 30 homes in Neighborhood A. Each year, the number of homes increases by 20%. Just down the road, Neighborhood B has 45 homes. Each year, 3 new homes are built in Neighborhood B.
Part A: Write functions to represent the number of homes in Neighborhood A and Neighborhood B throughout the years. (4 points)
Part B: How many homes does Neighborhood A have after 5 years? How many does Neighborhood B have after the same number of years? (2 points)
Part C: After approximately how many years is the number of homes in Neighborhood A and Neighborhood B the same? Justify your answer mathematically. (4 points)
(10 points)
Answer:
We know that:
Neighbourhood A = 30 homes and the number increases by 20% each year
Neighbourhood B = 45 homes, and each year 3 new homes are built.
A.
Neighbourhood A and B are as follows:
For neighbourhood A: f(x) =
For neighbourhood B: f(x) = 45 + 3x
B.
Over five years:
Neighbourhood A has =
Neighbourhood A =
Neighbourhood A = 74.65 homes
Neighbourhood B: = 45 + 3(5)
Neighbourhood B: = 45 + 15
Neighbourhood B: = 60 homes
C.
To determine how many years the number of homes are the same for neighbourhood A and B, we need to equate both together.
So x= 3.3
so, hence after 3.3 years, the number of homes will be the same.
Step-by-step explanation:
Hope this helped, good luck
Help please give answer please
The mean is 8 gerbils and the MAD is 4.29.
What is the mean?Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number
Mean = sum of the numbers / total number
(0 + 3 + 6 + 9 + 11 + 13 + 14) / 7 = 8
What is the MAD?
MAD = ∑ l x - m(x) l
| (0 - 8) + (3 - 8) + (6 - 8) + (9 - 8) + (11 - 8) + (13 - 8) + (14 - 8)| / 7 = 4.29
To learn more about mean, please check: https://brainly.com/question/25842202
#SPJ1
Evaluate P(4, 2)
O 24
O 12
06
If the assessment rate is 46% and the tax rate is $37.84 per $1,000 of assessed value, the property tax on a house with a market value of $170,000 is
The property tax on a house with a market value of $170,000 is $2,959.09.
What is property tax?Property tax is a tax levied on the assessed value of property owned by an individual or a corporation.
Data and Calculations:Assessment rate = 46%
Tax rate = $37.84 per $1,000
Market value of house = $170,000
Assessed value = $78,200 ($170,000 x 46%)
Property tax = $2,959.09 ($78,200 x $37.84/$1,000)
Thus, the property tax on a house with a market value of $170,000 is $2,959.09.
Learn more about property taxes at https://brainly.com/question/25844719
#SPJ1
A town on the coast is building a lighthouse that is 27 meters tall. Determine the area of the circular base of the lighthouse if the radius of the base is 35 meters. Use 22/7 for pi. WILL GIVE BRAINLIEST
A. 220 m2
B, 3,830 m2
C.103,950 m2
D.15,400 m2
Answer:
B. 3850 m²Step-by-step explanation:
Use the equation of area of circle:
A = πr²Substitute π with 22/7 and r with 35 m as per question.
Find the area:A = 35²*(22/7) = 3850 m²Correct choice is B (with slight difference)
Answer:
B. 3850 m²
Step-by-step explanation:
The area of the base of the lighthouse can be modeled as a circle.
Area of a circle
[tex]\textsf{A}=\pi r^2 \quad \textsf{(where r is the radius)}[/tex]
Given:
r = 35 mπ = 22/7Substitute the given values into the formula and solve for A:
[tex]\implies \sf A=\dfrac{22}{7} \cdot 35^2[/tex]
[tex]\implies \sf A=\dfrac{22}{7} \cdot 1225[/tex]
[tex]\implies \sf A=\dfrac{26950}{7}[/tex]
[tex]\implies \sf A=3850\:\:m^2[/tex]
Therefore, the area of the circular base of the lighthouse is 3850 m²
Put the following equation of a line into slope-intercept form, simplifying all fractions. 5x+6y=42
Answer:
[tex]y=-\frac{5}{6} + 7[/tex]
Step-by-step explanation:
Slope-intercept formula requires us to isolate the y variable. We can do this in just a couple of steps.
1) Move 5x from the left to the right side by subtracting 5x from both sides. This cancels out the 5x on the left side, and remember, what we do to one side we must do to the other to keep the equation balanced.
[tex]6y=-5x+42[/tex]
2) Divide both sides by 6. Again, we are cancelling out the 6 on the left but we must also divide on the right. This would mean dividing -5 and 42 by 6 to get:
[tex]y=-\frac{5}{6} + 7[/tex]
An angle turns through 2/8 of the circle.what is the measure of this angle
Answer:
90°
Step-by-step explanation:
note that [tex]\frac{2}{8}[/tex] simplifies to [tex]\frac{1}{4}[/tex]
There are 360° in one turn of the circle , then
[tex]\frac{1}{4}[/tex] × 360° = 360° ÷ 4 = 90°
A recipe uses 5 eggs to make 11 omelettes.
Find the amount of eggs required to make 32 omelettes
Answer:
14 and a half
Step-by-step explanation:
5 eggs - 11 omlets
x eggs - 32 omlets
11x = 5x32
x = 160/11 = 14.5454...
Type the correct answer in each box. a race car is driven by a professional driver at 99 . what is this speed in and ? 1 mile = 1.61 kilometers 1 hour = 60 minutes express the answers to the correct number of significant figures. the speed is equivalent to , or .
The speed of the car in kilometres per minutes is 2.6565 km/minutes
How to find speed in km/minutes?The car speed is 99 miles per hours.
Therefore,
1 miles = 1.61 km
99 miles = ?
cross multiply
distance = 159.39 km
Therefore,
1 hour = 60 minutes
Hence,
speed = 159.39 / 60
speed = 2.6565
speed = 2.6565 km/minutes
learn more on speed here: https://brainly.com/question/17096123
#SPJ1
big test, 70% of my grade, PLS HELP.
will give brainly to first CORRECT answer :)
Answer:
Lines J and K are parallel :)
Step-by-step explanation:
Parallel: (of lines, planes, surfaces, or objects) side by side and having the same distance continuously between them.
It would be Lines J and K are parallel because they never cross and the other statements are incorrect :)
Have an amazing day!!
Please rate and mark brainliest!!
Tammy said the product of 5/7 and 1 1/4 is 1 3/4.
Answer:
Tammy is incorrect
Step-by-step explanation:
The product of 5/7 and 1 1/4 is,
(5/7) x (1 1/4)
turn the mixed number to a whole number.
1 1/4= 4/4 + 1/4 = 5/4
(5/7) x (5/4) = 25/28 which is approximately 0.8929
Tammy believes it equals 1 3/4
1 3/4 = 4/4 + 3/4 = 7/4 which is 1.75
0.8929 does not equal 1.75
The thousand islands are located along the border between new york and canada. the adventure club wants to place a stone marker on 684 of the islands. the club has 36 members. if every club member goes to the same number of islands, how many islands will each member have to visit? a. 720 islands b. 648 islands c. 19 islands d. 24,624 islands
Using proportions, it is found that the number of islands that each member will have to visit is given by:
c. 19 islands.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, there are 684 islands, and 36 members, hence the number of islands per member is given by:
n = 684/36 = 19.
Which means that option c is correct.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
pls answer, will mark brainliest
Answer:5200-0.0005x=2800+0.0003x
Step-by-step explanation: Ignore the supply and demand stuff. Just focus on what value of x will make the two equations equal, which is all the question is asking.
5200-0.0005x=2800+0.0003x
solve for x
This is now a very simple one variable equation, try to solve this yourself and message me if you still need help.
Brainliest if you give correct answer + explanation
Answer:
x = 8
Step-by-step explanation:
Perimeter :
2(Length + Width) = 44 2x + 3 + x - 5 = 22 3x - 2 = 22 3x = 24 x = 8Multiplying by which number is equivalent to finding 2%?
You buy 100 file folders for 7.72. how much are you paying for each file folder?
Each folder would cost 0.0772.
What is Rate?Rate is used to express the change in a quantity with respect to a standard quantity.
Analysis:
If 100 file folders cost 7.72, then each folder will cost 7.72/100 = 0.0772
Learn more about rate: brainly.com/question/24304697
#SPJ1
Answer: 0.8 or whatever has 8 last since i forgot sorry!, but it was correct for me!
Step-by-step explanation:
I dont know if its right for you but its right for me
C. If f(4x+5)=12x+18 then find f¹(x).
If f¹ is supposed to say f⁻¹ : rewrite f(4x + 5) as an "obvious" function of 4x + 5, then replace 4x + 5 with x. By "obvious", I mean make it clear how 4x + 5 is the argument to f.
[tex]f(4x+5) = 12x+18 = 3 (4x + 6) = 3 (4x + 5 + 1) = 3 (4x + 5) + 3[/tex]
Then swapping out 4x + 5 for x gives
[tex]f(x) = 3x + 3[/tex]
The inverse of f(x), if it exists, is a function f⁻¹(x) such that
[tex]f\left(f^{-1}(x)\right) = x[/tex]
Evaluate f at f⁻¹ and solve for f⁻¹ :
[tex]f\left(f^{-1}(x)\right) = 3 f^{-1}(x) + 3 = x \implies \boxed{f^{-1}(x) = \dfrac{x-3}3}[/tex]
If f¹ instead means f' (as in the first derivative of f) : earlier we found f(x) = 3x + 3, and differentiating this is trivial.
[tex]f(x) = 3x+3 \implies f'(x) = 3[/tex]
When Famke charges her phone, it gains 2 percentage points each minute. When Famke uses her phone, it loses 5 percentage points each minute. Once, Famke used her phone for some time, and then charged it for twice the amount of time she used it. In the end, her phone lost 10 percentage points. How long did Famke use her phone and how long did she charge it?
Justine and Meagan played a trivia game. Justine answered a question incorrectly and lost 7 points. Then Meagan answered correctly and got the opposite score. Which is the correct way to represent that “the opposite of Justine’s score was equal to Meagan’s score”? –7 = 7 –(–7) = –7 –(7) = –7 –(–7) = 7
Answer:
the opposite of the Justine score (-7) = Meghan score (7)
-(-7)=7
Step-by-step explanation:
Please help me on this.
Answer: B; 4
Explanation: The squares means that's how many numbers there are.
The example : -- There's 4 of 4. = 16. 6 of 2. = 12.
All of them add up to 64.
There are 16 numbers.
The mean means adding up all the numbers then divide by how many numbers are there.
64 / 16 = 4.
What is true about the completely simplified sum of the polynomials 3x2y²-2xy and -3x²y² + 3xy?
The picture are the answer choices and i only have 20 mins left so please help!
The sum is a binomial with a degree of 6 after adding like terms, and the sum is -2xy⁵ + 3x⁴y option fourth is correct.
What is polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have two polynomials:
3x²y² - 2xy⁵ and -3x²y² + 3x⁴y
Adding two polynomials:
= (3x²y² -2xy⁵) + (-3x²y² + 3x⁴y)
= -2xy⁵ + 3x⁴y
The expression represents a binomial with degree 6(1+5) because it has two terms.
Thus, the sum is a binomial with a degree of 6 after adding like terms and the sum is -2xy⁵ + 3x⁴y option fourth is correct.
Learn more about Polynomial here:
brainly.com/question/17822016
#SPJ1
please answer this question!
How do I solve and find x?
Answer:
x = 76.5
Step-by-step explanation:
[tex]\frac{x}{4.5}[/tex] = 22 - 5
[tex]\frac{x}{4.5}[/tex] = 17
x = 17 x 4.5
x = 76.5
Which of the following best describes AD?
A. Angle bisector
OB. Perpendicular bisector
OC. Median
OD. Altitude
17
D
17
C
Answer:
C. median
Step-by-step explanation:
AD is median because it's dividing BC in two equal parts.
John and Elijah are both driving from New York City to Richmond. John leaves
at 7:20 and averages 60 mph (miles per hour) on the way. Elijah leaves at 7:30
and averages 62 mph on the way. The situation is modeled by this system,
where x is the number of hours after Elijah leaves and y is the distance each
will travel.
y = 60x+10
y = 62x
How long after Elijah leaves will he pass John, and how far will they each
have traveled?
OA. Elijah will pass John after 4 hours, and they each will have traveled
248 miles.
OB. Elijah will not pass John, because he will never catch up with him.
C. Elijah will pass John after 5 hours, and they each will have traveled
310 miles.
D. Elijah will pass John after 2 hours, and they each will have traveled
128 miles.
2
5-
Elijah will pass John after 5 hours, and they each will have traveled 310 miles. Then the correct option is C.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
Speed = Distance/Time
John and Elijah are both driving from New York City to Richmond.
John leaves at 7:20 and averages 60 mph (miles per hour) on the way.
Elijah leaves at 7:30 and averages 62 mph on the way.
The situation is modeled by this system, where x is the number of hours after Elijah leaves and y is the distance each will travel.
y = 60x + 10 ...1
y = 62x ...2
The time is taken by Elijah to cross John will be
62x = 60x + 10
2x = 10
x = 5 hours
The distance traveled in 5 hours will be
y = 62 (5)
y = 310 miles
Elijah will pass John after 5 hours, and they each will have traveled 310 miles.
Then the correct option is C.
More about the speed link is given below.
https://brainly.com/question/7359669
#SPJ1
Answer:
c
Step-by-step explanation:
i took the quiz
what is the equation of the function y=3/x translated 4 units up and three units to the left
Using translation concepts, it is found that the equation of the function after the changes is given by:
[tex]y = \frac{3}{x + 3} + 4[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the parent function is given by:
[tex]y = \frac{3}{x}[/tex]
Then, these following changes happened:
Shift left of 3 units, which means that x -> x + 3.Shift up of 4 units, which means that y -> y + 4.Hence, the equation of the function after the changes is given by:
[tex]y = \frac{3}{x + 3} + 4[/tex]
More can be learned about translation concepts at https://brainly.com/question/4521517
#SPJ1
If P(x)=6+9x−5x^2 represents the profit in selling x thousand Boombotix speakers, how many speakers should be sold to maximize profit?
The number of speakers that should be sold to maximize profit is 0.9
Vertex of a quadratic equationGiven the function that represents the profit made in selling x thousand Boombotix speakers expressed as:
P(x)=6+9x−5x^2
In order to maximize the profit, p'(x) = 0, hence;
P'(x) =9 - 10x
0 = 9 - 10x
x = 9/10
Hence the number of speakers that should be sold to maximize profit is 0.9
Learn more on vertex here: https://brainly.com/question/21191648
#SPJ1
PLEASE HURRY! What is the value of x in this triangle? The triangle is labeled 5, 20 & x
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
x =
°
Answer:
[tex]x = 14.04[/tex]°
Step-by-step explanation:
[tex]\text{tan(x) = Opposite / Adjacent}\\tan(x) = 5/20\\tan(x) = 0.25\\x = 14.04[/tex]