The money in the account at the end of 5 years is 2208.16
Compound interestThe formula for calculating the compound interest is expressed according to the formula:
Compound interest = P(1+r)^t
Given the following parameters
Principal = 2000
rate = 2 % = 0.02
time = 5 years
Substitute
A = 2000(1+0.02)^5
A = 2000(1.02)^5
A = 2208.16
Hence the amount of money that will be in that account at the end of 5 years is 2208.16
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The function h (x) = startfraction 1 over x squared 1 endfraction is the result of the composition f(g(x)). if g(x) = x2 1, what is f(x)? f (x) = startfraction 1 over startroot x endroot f (x) = startfraction 1 over x 1 endfraction f (x) = startfraction 1 over x squared 1 endfraction
This means that function of (x²+ 1) will give 1/(x²+ 1). To get f(x), we will simply replace x²+ 1 in the function f(x²+ 1) with x to give;
f(x) = 1/x
How do you define a function?
A technical definition of a function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given h(x) = 1/(x²+ 1) and g(x) = x²+ 1. If h(x) = f(g(x)) then;
1/(x²+ 1) = f(x²+ 1)
f(x²+ 1) = 1/(x²+ 1)
This means that function of (x²+ 1) will give 1/(x²+ 1). To get f(x), we will simply replace x²+ 1 in the function f(x²+ 1) with x to give output ;
f(x) = 1/x
Hence the function of x i.e f(x) is 1/x
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An online streaming service that offers TV shows, documentaries, and movies charges an initial fee of $20.25 and an additional monthly membership fee of $3.75. The total cost, N(t), for a member after t months can be expressed with the function N(t) = 3.75t + 20.25. What is the range of the function in the context of the problem?
ℝ
[0, ∞)
[3.75, ∞)
[20.25, ∞)
The range of the function N(t) is [20.25, ∞). The correct option is D.
What is the range of the function?A function's range is the set of possible output values. For example, the range of the function f(x)=x² on the domain of all real numbers (xR) is the non-negative real numbers, which can be written as f(x)0 (or [0,] in interval notation).
In this question, we have been given that an online streaming service that offers TV shows, documentaries, and movies charges an initial fee of $ 20.25 and an additional monthly membership fee of $3.75.
The total cost, N(t), for a member after t months can be expressed with the function N(t) = 3.75t + 20.25
As t is the number of months, t can take values from 0 to infinity.
For t = 0 years,
N(0) = 3.75(0) + 17.25
N(0) = 0 + 17.25
N(0) = $17.25
For x tends to ∞, the value of function would be ∞. The range will be (20.25,∞).
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The ACT is a college entrance exam taken by high school students. The maximum score that can be earned is 36. The average score in the United States was 21.2 during a recent year. The average score for Vermont students that year was 7.5% higher than the national average. What was the average ACT score for Vermont students? Round your answer to the nearest tenth.
If the average score in the United States was 21.2 during a recent year. The average score for Vermont students that year was 7.5% higher than the national average. The average ACT score for Vermont students is: 22.80.
Average ACT scoreUsing this formula to determine the average ACT score
Average ACT score = Average score in the United states + ( Average score in the United States × Average score for Vermont students)
Let plug in the formula
Average ACT score = 21.2 + ( 21. 2 × 7.5%)
Average ACT score = 21.2 + 1.59
Average ACT score = 22.79
Average ACT score = 22.80 (Approximately)
Therefore we can conclude that the average score is 22.80.
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Please help me to wrap my head around #22please included the Subjects I need to work on for (HW).
chaperones/students; 1/7 = x/45
7x = 45
x = 6.43
the min amount would be 7, as there can not be .43 of a chaperone. It cannot also be 6 because 6 x 7 would be 42 < 45.
hilda bought 10 7/20 she left with 21 1/4 using decimal form
The pounds of pork that Hilda bought based on the information illustrated is 10.9 pounds.
How to calculate the value?From the information, Hilda bought 10 7/20 lb of beef and some pork and she left with 21 1/4 of meat.
The pounds of pork that she bought using the decimal form will be:
= Total meat - Pounds of beef
= 21 1/4 - 10 7/20
= 21.25 pounds - 10.35 pounds
= 10.9 pounds.
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Hilda bought 10 7/20 lb of beef and some pork. She left with 21 1/4 of meat. Express the pounds of pork that she bought using decimal form
this is not a question im giving you all the answers!!!! I did miss like one question though sorry
Answer Key
Question 1 (Worth 1 points)
(03.03 MC)
The annual growth of Noah's worm collection is represented by the table. What does the f(x) = 4 represent?
x 0 2 4
f(x) 4 16 64
The number of new worms each year
The number of worms Noah started with
The common ratio of worm growth
The average rate of change of worm growth each year
Points earned on this question: 1
Question 2 (Worth 1 points)
(03.03 MC)
A talent competition on television had five elimination rounds. After each elimination, only one-third of the contestants were sent to the next round. The table below shows the number of contestants in each round of the competition:
x 1 2 3 4 5
f(x) 243 81 27 9 3
Compute the average rate of change of f(x) from x = 1 to x = 4, and describe what it represents.
−78 contestants per round, and it represents the number of contestants who will reach the final round
−234 contestants per round, and it represents the number of contestants who will reach the final round
−234 contestants per round, and it represents the average rate at which the number of contestants changed from the first round to the fourth round
−78 contestants per round, and it represents the average rate at which the number of contestants changed from the first round to the fourth round
Points earned on this question: 1
Question 3 (Worth 1 points)
(03.03 MC)
The table represents a continuous exponential function f(x).
x 2 3 4 5
f(x) 9 3 1 one-third
Graph f(x) and identify the y-intercept.
9
15
36
81
Points earned on this question: 0
Question 4 (Worth 1 points)
(03.03 MC)
Terrance invested money in a technology stock whose growth is modeled by the function f(x) = 0.01(2)x, where x represents number of days. Find the approximate average rate of change from day 3 to day 8.
0.496
2.016
2.48
5
Points earned on this question: 1
Question 5 (Worth 1 points)
(03.03 MC)
Does the function f of x equals 4 times the quantity 1 over 3 end quantity to the x power represent growth or decay? What is the y-intercept of f(x)?
Growth; (0, 4)
Growth; 0 comma one-third
Decay; (0, 4)
Decay; 0 comma one-third
Points earned on this question: 1
Question 6 (Worth 1 points)
(03.03 LC)
Which of the following options results in a graph that shows exponential decay?
f(x) = 0.6(2)x
f(x) = 3(0.7)x
f(x) = 0.4(1.6)x
f(x) = 20(3)x
Points earned on this question: 1
Question 7 (Worth 1 points)
(03.03 LC)
The number of members, f(x), in Joe's health club increased by 25% every year over a period of x years. The function below shows the relationship between f(x) and x:
f(x) = 15(1.25)x
Which of the following graphs best represents the function?
graph of exponential function going up from left to right through the point 0 comma 1 and approximately 6 tenths comma 6
graph of exponential function going up from left to right through the point 0 comma 15 and approximately 5 comma 45
graph of exponential function going up from left to right in quadrant 1 through the point 0, 0 and continuing toward infinity
graph of exponential function going up from left to right through the point 0 comma 1 and approximately 4 comma 3
Points earned on this question: 1
Question 8 (Worth 1 points)
(03.03 MC)
A bacteria is growing by a factor of 2 every hour from 1 p.m. to 11 p.m. The function below shows the number of bacterial cells, f(x), after x hours from 1 p.m.:
f(x) = 20(2)x
Which of the following is a reasonable domain for the function?
All positive integers
1 ≤ x ≤ 11
0 ≤ x ≤ 20
0 ≤ x ≤ 10
Points earned on this question: 0
Question 9 (Worth 1 points)
(03.03 MC)
Enrollment at a golf academy has grown exponentially since the academy opened. Below is a graph depicting this growth. Determine the average rate of change from x = 0 to x = 4.
An exponential graph has time in years on the x axis and enrollments on the y axis. An upward rising curve begins at zero comma fifteen and passes through four comma seventy five.
0.067
4
15
75
Points earned on this question: 1
Question 10 (Worth 1 points)
(03.03 MC)
The number of subscribers, f(t), to a newspaper after t years is shown by the equation below:
f(t) = 75(0.95)t
Which conclusion is correct about the number of subscribers to the newspaper?
It increased by 75% every year.
It decreased by 75% every year.
It increased by 5% every year.
It decreased by 5% every year.
Points earned on this question: 1
What's your question? This is already your submitted quiz on FLVS, I took it earlier today. After you've submitted it and try to resubmit, it will give you different questions with different answers...
Answer:
none of the answers showed up!it’s jut a useless list of questions!
PLEASE HELP
if f(x)=3x-2 and g(x)=x+2/3, find f(g(x))
PHOTO ATTACHED
Answer:
g(x)= 1
f(x) = 1
f(g(x)) = 1
Step-by-step explanation:
7/9 - 1/3 divided by 3/4
Answer:
16/27
Step-by-step explanation:
simplifying
(7/9−1/3)/3/4=16/27
Answer:
Step-by-step explanation:
7/9 - 1/3
= 7/9 = 3/9
= 4/9
4/9 / 3/4
= 4/9 * 4/3
= 16/27 Answer.
Zachary purchased a computer for $1,800 on a payment plan. Three months after he purchased the computer, his balance was $1,365. Four months after he purchased the computer, his balance was $1,220. What is an equation that models the balance y after x months?
Use the slopes of lines A and B to show that
they are perpendicular
to each other.
The line A and line B are perpendicular to each other.
What is defined as the perpendicular lines?Perpendicular lines are defined in geometry as two lines which meet or intersect at right angles (90°). The term "perpendicular" is derived from the Latin phrase "perpendicularis," which means "a plumb line."The following are the two important properties of perpendicular lines.These lines are always at right angles when they intersect.If two lines seem to be perpendicular to each other, they are parallel and will never intersect.For the given ques, the graph of line A and line B are given.
The relation of slope of two perpendicular lines is their product of slope is -1.
Line A: select two point lying on the line A.
(2, 3) and (1, 1)
slope = m = (2 - 1)/(3 - 1)
m₁ = 1/2
Line B: select two point lying on the line B.
(8, 0) and (0, 4)
slope = m = (0 - 4)/(8 - 0)
m₂ = -4/8
m₂ = -1/2
Now, multiply both slopes.
m₁ x m₂ = 1/ 2 x -1/2
m₁ x m₂ = - 1
Thus, the line A and line B are perpendicular to each other.
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Randy planted a small pine tree in his yard. When he bought the tree it was 6 inches tall and grew at a rate of 2 inches weekly. Write a function of height, h, in terms of weeks, w.
Answer:
h = 2w + 6
Step-by-step explanation:
2 is the rate of change and 6 is the starting value.
hi please help me!!!!!!!!!!!!!!
Answer:
10, 9, 8, -3, -8
Step-by-step explanation:
from top to bottom highest lowest
10
9
8
-3
-8
Can someone help me ASAP please!!!!
Answer:
18 ft
Step-by-step explanation:
a=wl (3)(4) = 12
1/2bh 1/2(3)(4) = 6
12+6 = 18
One pound of grout is enough to grout a tiled area that is 110 sq. ft. Alyssa’s kitchen counter is made up of two rectangular segments. One is 10.3 ft by 2.5 ft, and the other is 3.1 ft by 2 ft. Which expression represents the number of pounds of grout Alyssa will need?
By taking the quotient between the area that one pound covers and the area of the kitchen, we conclude that Alyssa will need 0.29 pounds of grout.
How many pounds will Alyssa need?We know that one pound of grout covers a total of 110 square feet.
Alyssa's kitchen is made of two rectangular segments, one that measures 10.3ft by 2.5 ft, then the area of this rectangle is:
10.3ft*2.5ft = 25.75 ft²
The other rectangle has dimensions of 3.1ft by 2ft, so the area is:
3.1ft*2ft = 6.2ft²
The total area is:
25.75 ft² + 6.2ft² = 31.95 ft²
Now, with one pond of grout, they can cover 110 ft², then the number of pounds that Alyssa needs is:
N = 31.95 ft²/110 ft² = 0.29
Alyssa will need 0.29 pounds of grout.
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Every year, santiago's grandmother knits him a cozy wool sweater for his birthday. santiago's favorite color is red, so she plans to buy 700 yards of red thick wool for his sweater this year. she chooses a wool that is sold in 420-foot skeins. how many skeins should she buy?
Santiago's grandmother should buy 5 skeins to knit the sweater for his birthday.
Firstly converting the required amount of wool in foot. As per the known fact, 1 yard = 3 feet
So, required amount of wool = 700 × 3
Performing multiplication to find the required amount of wool
Required amount of wool = 2100 feet
Amount of wool in 1 skein = 420 feet
Number of skeins = 2100÷420
Performing division to find the number of skeins to be bought for knitting sweater for birthday
Number of skeins = 5
Therefore, Santiago's grandmother should buy 5 skeins of wool.
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The perimeter of a pool is 116 feet. If the length of the pool is 3 times its width,
what is the width of the pool?
(Show work)
Answer:
The perimeter P of a rectangular is given by formula P=2l+2w where l is the length and w is width of rectangle.Given that perimeter is 56 meters and length's 16 meters. Substituting values in formula,subtract 32 from both sides -⇒24=2w w=12width of rectangular pool is 12 meters.Hence, the answer is 12.Answer:
Perimeter = 2(l+b)
Perimeter = 116
width = x
length = 3x
116 = 2(3x+ x)
116 = 6x+2x
116 = 8x
x = 116/8
x = 14.5
You can verify answer by inputing value of x to see if perimeter is = 116 :
perimeter = 2(l+b)
116 = 2(3(14.5) + 14.5)
116 = 2(43.5 + 14.5)
116 = 87 + 29
116 = 116
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She starts with $100 and plans to add $50 each week. write an equation she can use to calculate the amount of money she will have after any number of weeks. how much money will she have after 1 year?
Main Answer:
2700 dollars
Explanation:
Let x be the number of weeks and y be the total amount of money, then the equation can be written as,
[tex]y=50x+100[/tex] -------(1)
In a year there are 52 weeks.
Money she will have after 1 year is found out by putting x = 52 in the equation (1), we get
[tex]y=50(52)+100[/tex]
[tex]y=2600+100[/tex]
∴[tex]y=2700[/tex]
Therefore, the money she have after 1 year is 2700 dollars.
what is the answer to this equation.
Answer:
a = 10
Step-by-step explanation:
9 + a/10 = 10
we are going to be multiplying everything by 10
90 + a = 100
100-90=10
so a =10
The circumference of a circle is 7 ft. What is the area, in square feet? Express your
answer in terms of
Answer:
3.9ft²
Step-by-step explanation:
Hence circumference of the circle =2π(7)=2⋅722⋅7=2⋅22=44 cm.
Complete the statement. Justify your answer If 11m=3n, then m/n=?
[tex]11m = 3n \\ \frac{11m}{11 \times n} = \frac{3n}{11 \times n} \\ \frac{m}{n} = \frac{3}{11} [/tex]
ATTACHED IS THE SOLUTION
B. Fill in the correct angle measurement.
7)
What is the complement of an 11° angle?
8)
What is the supplement of a 92° angle?
9)
What is the complement of a 56° angle?
For #10-12, use the diagram to the right.
10) m/ 2 =
11) m/3 =
12) m/4=
||·|
41°
3
2
Answer:
see solution
Step-by-step explanation
complementary means that both the angles add up to 90 and supplementary means both the angles add up to 180.
7) 90-11 = 79 degrees
8) 180-92 = 88 degrees
9) 90-56 = 34 degrees
You have not shown the diagram which questions 10 to 12 requires so I cant solve that
molly and kali are selling fruit for a school fundraiser. customers can buy small boxes of grapefruit and large boxes of grapefruit. molly sold 12 small boxes of grapefruit and 5 large boxes of grapefruit for a total of $200. kali sold 4 small boxes of grapefruit and 10 large boxes of grapefruit for a total of $200. what is the cost of one small box of grapefruit and one large box of grapefruit?
The cost of one small box is $10 and the cost of one large box of grapefruit is equal to $16.
This type of problem can be solved using linear equations.
If we consider x to be the cost of one small box and y to be the cost of one large box of fruit, the linear equations can be given as;
12x + 5y = 200
4x + 10y = 200
Multiplying the second equation by 3
12x + 5y = 200
12x + 30y = 600
Now by subtracting both equations we get;
-25y = -400
y = -400 / -25
y = 16
Now adding this value of y = 16 in the first equation;
12x + 5y = 200
12x + 5(16) = 200
12x + 80 = 200
12x = 200 - 80
12x = 120
x = 120 / 12
x = 10
Therefore, $10 is the cost of one small box and $16 is the cost of one large box of grapefruit.
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You have a budget of $300 to order shirts for a math club. The equation. 10x + 12y = 300 models the total cost, where x is the number of short-sleeved shirts and y is the number of long-sleeved shirts.
a. Interpret the terms and coefficients in the equation.
b. Graph the equation. Interpret the intercepts.
c. Find three possible solutions in the context of the problem.
The x-intercept is at point (30,0) and the y-intercept is at point (0,25). The graph of the equation is attached below.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that Short-sleeved shirts cost $10 each.
The Long-sleeved shirts cost $12 each.
The total budget is $300.
The given equation is 10x + 12y = 300
where x is the number of short-sleeved shirts and y is the number of long-sleeved shirts.
We have, 10x + 12y = 300
Substitute the value x = 0
10(0) + 12y = 300
12y = 300
y = 25
So, the y-intercept will be at 0,25).
Substitute y = 0
10x + 12(0) = 300
10x = 300
x = 30
So, the x-intercept is at point (30,0).
The x-intercept is at point (30,0), that means the number of short-sleeved shirts is 30. The y-intercept is at point (0,25), that means the number of long-sleeved shirts is 25.
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18.) Find the average speed if you walk 6.2 miles in 90 minutes.
A) 14.52 miles per minute
B) .067 miles per minute
C) .069 miles per minute
D) 15 minutes per mile
If 5x + 3y = 31 and 6x + 4y = 39 using elimination,
what is the value of x + y?
Answer:
x=3.5,y=4.5
lets check if our answer is correct
let's use equation 1
5x+3y=31
5(3.5)+3(4.5)=31
17.5+13.5=31
31=31
Step-by-step explanation:
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Mai biked 6\frac{3}{4} miles today, and Noah biked 4\frac{1}{2} miles.
How many times the length of Noah’s bike ride was Mai’s bike ride?
The length of Noah’s bike ride was 1 1/2 of Mai’s bike ride
How to determine the number of times?From the question, the given parameters are
Distance covered by Mai = 6 3/4 milesDistance covered by Noah = 4 1/2 milesThe number of times the length of Noah’s bike ride was Mai’s bike ride is calculated as
Number of times = Distance covered by Mai/Distance covered by Noah
Substitute the known values in the above equation
So, we have the following equation
Number of times = (6 3/4)/(4 1/2)
Evaluate the quotient in the above equation
Number of times = 1 1/2
Hence. the number of times is 1 1/2 times
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What is the vertex of the graph of y = x^2 + 8x + 23?
VERTEX
The point on an angle where the two sides intersect.
So, The vertex of y = x^2 + 8x + 23 is (-4, 7).
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Describe one example of a human right that you think is essential for everyone to have throughout the world. Why is this right essential? (
An example of a human right that I think is essential for everyone to have throughout the world is the right to life.
This right is essential because we all should live and no one should deny others the right.
Whet are human rights?All people have the same basic legal rights, regardless of their gender, color, nationality, ethnicity, language, religion, or any other distinction. Human rights cover a wide range of rights, such as the freedom from slavery and torture, the right to life and liberty, the freedom of speech, the right to a job and an education, among many more. Human rights, which are usually protected by both domestic and international law, are moral principles or rules for particular standards of human behavior.
Human rights cover a wide range of rights, such as the freedom from slavery and torture, the right to life and liberty, the freedom of speech, the right to a job and an education, among many more. These rights apply to everyone without exception. The idea that a creature has the right to survive and, in particular, shouldn't be killed by another entity, is known as the right to life.
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REASONING You can paint 75 square feet of a surface every 45 minutes. Determine how long it takes you to paint a wall with
the given dimensions.
8 ft x 5ft
It will take you
minutes to paint the wall.
It will take you approximately 24 minutes to paint a 8ft x 5ft wall.
Lets find the area of the given wall,
Area of the wall (A) = 8ft x 5ft
A = 40sq ft.
It takes 45 minutes to paint a 75 square feet wall, i.e.,
45min = 75 sq. ft.
So, in one min we can paint,
1 min = 75/45sq.ft. = 1.67sq.ft.
Therefore, the time taken to paint the given wall,
= 40sq.ft./1.67sq.ft.
= 24 mins (approx.)
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You roll a fair 6-sided die twice. Find the probability of getting the same number.
Answer:2/12
Step-by-step explanation:6x2 is 12 and the chance of getting is 2/12.
Answer: 1/6
Step-by-step explanation:
When you roll a dice, you will get a number from 1-6. It could be any number.
However, to roll a dice and get that same number, out of the 6 numbers, is 1/6.