The required function that gives [tex]f(g(x))[/tex] that represents the total amount of money Raul earned is
[tex]f(g(x)) = 10x^{3}+16[/tex]
What is a function?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
Mostly functions are written as f(x) where x is the input of the function.
Given,
[tex]f(x) = 2x^{2}+16[/tex]
[tex]g(x)[/tex] = [tex]\sqrt{5x^{3} }[/tex]
If [tex]f(x)[/tex] represents amount of money Raul earns per ticket and [tex]g(x)[/tex] represents number of tickets Raul sells per hour, where x is the number of hours he works, then,
[tex]f(g(x))[/tex] represents the total amount of money Raul earned in a day.
To find [tex]f(g(x))[/tex], substitute value of [tex]g(x)[/tex] in the place of x in function [tex]f(x)[/tex] .
[tex]f(g(x))[/tex] = [tex]f[/tex]([tex]\sqrt{5x^{3} }[/tex])
= 2( [tex]\sqrt{5x^{3} }[/tex])² +16
= 10x³ + 16
Therefore the required function is [tex]f(g(x)) = 10x^{3}+16[/tex].
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Can someone help me please? Picture attached
Answer:
Step-by-step explanation:
A^2 + B^2 = C^2
12^2 + B^2 = 18^2
144 + B^2 = 324
Subtract 144 from both sides
B^2 = 324 - 144
B^2 = 180
[tex]\sqrt{180}[/tex] = 13.416
B^2 = 13.4
The table shows the heights y (in centimeters) of a plant after x weeks. Use the table to complete the statements.
x 0
4
8
y 17 29 41
Which tatement correctly compare the meaure of center of the data in the dot plot
A statement that correctly compares the measures of center in the two sets of data is: Both the mean and median are greater for Plot A than for Plot B.
The correct answer is an option (A)
Consider plot A.
The data value represented on the dot plot:
3, 4, 4, 5, 5, 6, 6, 7, 7, 10
Using the formula of mean, the mean of Plot A would be:
mean = (3 + 4 + 4 + 5 + 5 + 6 + 6 + 7 + 7 + 10) / 10
mean = 57/10
mean = 5.7
The middle value of the data is: 5, 6
So, the median is:
Median = (5 + 6)/2
= 11/2
= 5.5
Consider plot B.
The data value represented on the dot plot:
3, 4, 4, 5, 5, 5, 6, 6, 6, 7
mean = (3 + 4 + 4 + 5 + 5 + 5 + 6 + 6 + 6 + 7)/10
mean = 51/10
mean = 5.1
The middle value of the data is: 5, 6
So, the median is:
Median = (5 + 5)/2
= 5
Hence, both the mean and median are greater for Plot A than for Plot B.
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The complete question is:
Which statement correctly compares the measures of center in the two sets of data? Both the mean and median are greater for Plot A than for Plot B. Both the mean and median are greater for Plot B than for Plot A. Plot A has a greater median than Plot B, but Plot B has a greater mean. Plot B has a greater median than Plot A, but Plot A has a greater mean.
Tickets for all of the described charity raffle games cost $2 per game. James wants to choose three raffles that will give him the best chance of winning. Identify the games that james should play and the games he shouldn’t.
Answer:
C,A, and F
Step-by-step explanation:
the ones that basically give him a chance is the very first one on the left side and the 3rd one down on the left side and the 2nd column the 2nd one hope this helps
What are the coordinates of point (x,y) when it is reflected across the line y=−x?
The coordinate of the reflection is (-y, -x)
How to determine the coordinate of the reflectionFrom the question, we have the following parameters that can be used in our computation:
Point = (x, y)
Reflection: Across the line y=−x
Using the above as a guide, we have the following:
The reflection of a point over the line y = -x implies that, the x-coordinate and y-coordinate change places Then they are negated (the signs are changed)So, we have
Image = (-y, -x)
Hence, the image is (-y, -x)
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What is the coefficient in this expression?
12 - x + 3
The coefficient is -1
5. The population of Haleyville, Alabama was 4,403 in 2010. Haleyville has been experiencing a population decline of 0.6% per year since 2000. What will be the projected population of Haleyville in 2020?
The projected population of Haleyville in 2020 is 4139.
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,
Population in 2010 = 4403
The decline in population per year = 0.06%
Now,
The population in 2020.
There are 10 years between 2010 and 2020.
The function used to find the population after x years.
= 4403 x [tex]0.994^x[/tex]
Now,
x = 10
= 4403 x [tex]0.994^{10}[/tex]
= 4403 x 0.94
= 4139
Thus,
The population in 2020 is 4139.
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' I did he heard diamster of 76 ice. Whidh meekureman it dosef to the draunference of the
Since the diameter of this circle is 76 inches, a measurement which the circumference of this circle has include the following: C. 238.64 inches.
How to calculate the circumference of a circle?Mathematically, the circumference of a circle can be calculated by using this mathematical expression:
C = 2πr or C = πD
Where:
C represents the circumference of a circle.D represents the diameter of a circle.r represents the radius of a circle.Substituting the given parameters into the circumference of a circle formula, we have;
Circumference of circle, C = πD
Circumference of circle, C = 3.14 × 76
Circumference of circle, C = 238.64 inches.
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Complete Question:
The diameter of a circle is 76 inches. Which measurement does the circumference of this circle have?
A. 123.45 inches.
B. 438.65 inches.
C. 238.64 inches.
D. 338.64 inches.
As n ranges over the positive integers, what is the maximum possible value for the greatest common divisor of 11n 3 and 2n 1
The maximum possible value for the greatest common divisor (GCD) of 11n + 3 and 2n + 1 as n ranges over the positive integers is 1.
The GCD of two integers is the largest integer that divides both integers without leaving a remainder. We can use the Euclidean algorithm to find the GCD of two numbers.
The Euclidean algorithm states that for two integers a and b, we can find the GCD of a and b by repeatedly applying the following steps:
Divide a by b to get a quotient q and a remainder r
Replace a with b and b with r
Repeat the process until r is 0
If we apply this algorithm to 11n + 3 and 2n + 1, we get the following:
GCD(11n+3, 2n+1)
As 11n + 3 = 3(2n + 1) + 5n
= GCD(2n+1, 5n )
As 2n + 1 = (2/5)(5n) + 1
= GCD(5n, 1)
= GCD(1, 0)
= 1
So as n ranges over the positive integers, the maximum possible value for the GCD of 11n + 3 and 2n + 1 is 1.
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Similar figures review
The width for the second rectangle which is HIJK will be A. 24 inches.
How to illustrate the relationship?From the diagram, it should be noted that rectangle ABCD is similar to rectangle HIJK. Therefore it should be noted that the relationship between the width and length is expressed as:
= Width / Length
= 12/16
= 3/4
Therefore, the width for the second rectangle will be:
= 3/4 × 3.2
= 2.4
In conclusion, the correct option is A.
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What are the 4 quadrants called?
The 4 quadrants are called as Quadrant I, Quadrant II, Quadrant III and Quadrant IV.
The term quadrant in math is also known as the coordinate grid, cartesian coordinate system, or Cartesian plane, are basically constructed by taking a vertical axis, or the y-axis and setting it against a horizontal axis, or the x-axis and it creates a grid with four quadrants.
According to the cartesian system, here the coordinate plane is divided into four equal parts by the intersection of the x-axis and the y-axis such as the vertical number line.
Here the four quadrants are written as,
Quadrant I that is placed upon the upper right quadrant is the first quadrant, denoted as Quadrant I and the value on the x-axis and the y-axis both have positive numbers.
Next one is Quadrant II which is placed on the upper left quadrant is the second quadrant, denoted as Quadrant II and the value of the x-axis has negative numbers and the y-axis has positive numbers.
Third one is Quadrant III placed on the bottom left quadrant is the third quadrant, denoted as Quadrant III and the value of both the x-axis and the y-axis have negative numbers.
Final one is Quadrant IV which is placed on the bottom right quadrant is the fourth quadrant, denoted as Quadrant IV and here the value of the x-axis has positive numbers and the y-axis has negative numbers.
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Jupiter is about 5. 2 Astronomical Units (AU) from the Sun. Neptune is about 30. 1 AU from the sun. How many times as far from the Sun is Neptune as Jupiter? First answer gets brainliest
If Jupiter is about 5.2 Astronomical Units (AU) from the Sun and Neptune is about 30.1 AU from the Sun, Neptune is about 5.79 times far from the Sun as Jupiter.
Therefore the answer is 5.79.
To find how many times as far from the Sun Neptune is as Jupiter, we need to divide the distance from the Sun to Neptune by the distance from the Sun to Jupiter.
Neptune is about 30.1 AU from the Sun and Jupiter is about 5.2 AU from the Sun, so:
= Distance from the Sun to Neptune / Distance from the Sun to Jupiter
= 30.1 / 5.2
= 5.79
So, Neptune is about 5.78 times as far from the Sun as Jupiter.
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what is 1 half of 2 thirds
A rectangular school banner has a length of 21 inches and a perimeter of 66 inches. A sign is made that is similar to the school banner and has a length of 7 inches. What is the perimeter of the sign?
The perimeter of the sign is 22 inches.
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
A rectangular school banner has a length of 21 inches and a perimeter of 66 inches.
Let the perimeter of the sign for the length of 7 inches of the banner = x
So, By definition of proportion, we get;
⇒ 21 / 66 = 7 / x
Solve for x;
⇒ x = 7 × 66 / 21
⇒ x = 22
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Select all questions that depicts one of the properties of exponents
Answer: 1st, 4th, and 5th choices
Mr. Hurd buys a trampoline for his kids. The cost of the trampoline is $699.99. He gets the items for $429.99. What is the percent of discount? Round to the nearest percent.
Answer:
Mr. Hurd received a discount of 57% on the trampoline. The cost of the trampoline was $699.99 and he got it for $429.99, resulting in a discount of 57% when rounded to the nearest percent.
Step-by-step explanation:
Find the ratio of the volume of the cone to the volume of the cylinder. Express your answer as a common fraction.
The ratio of the volume of the cone to the cylinder is 1:3.
A cone has a circular base and the base is made of a radius and diameter.
The volume of a cone is defined as the amount of space a cone occupies. The formula of the volume of a cone is given as one-third the product of the area of the circular base and the height of the cone. If the radius of the cone is "r" and the height is "h", the volume of a cone is given as V = (1/3)πr²h.A cylinder is a three-dimensional solid shape that makes of two parallel bases linked by a curved surface.
Thus, the volume (V1) of a right circular cylinder, using the above formula, is,V1= πr²h
Here,
'r' is the radius of the cylinder
'h' is the height of the cylinder
π is a constant whose value is 22/7.
The ratio of the volume of the cone to the cylinder is
= (1/3)πr²h : πr²h
= 1 : 3
So, the ratio is - 1:3.
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Marius buys computers for £915.00 each and sells them for £2081.00 each. What is his total profit on the sale of 13 computers?
Answer:
£15158.00
Step-by-step explanation:
The profit on the sale of 1 computer is the difference between the selling price and the buying price.
Profit on 1 computer:
£2081.00 - £915.00 = £1166.00
The profit on 13 computers is 13 times the profit on 1 computer.
13 × £1166.00 = £15158.00
Answer: £15158.00
PLEASE HELP ME WITH PROBLEM C
1) The Magnolia trees purchased for planting at the school are 3 feet tall. Research shows that these types of trees grow at an average rate of 3/4 feet per year.
a) Write an equation in Slope-Intercept form to represent the growth of the trees over time. Let x represent the number of years and let y represent the height (in ft.) of the tree.
Y=3/4x+3
b) What does the y-intercept represent in your equation
Y=3. 3 stands for feet tall
c) Determine the height of the tree in 3 years.
a) To write an equation in slope-intercept form to represent the growth of the Magnolia trees over time, we can use the formula y = mx + b, where x represents the number of years, y represents the height of the tree in feet, m represents the slope (or rate of growth) of the tree, and b represents the y-intercept (or the height of the tree at x = 0).
In this case, the slope (m) of the tree is 3/4 feet per year and the y-intercept (b) is 3 feet, as the trees are initially 3 feet tall when they are purchased. Plugging these values into the formula gives us:
y = (3/4)x + 3
This equation represents the growth of the Magnolia trees over time.
b) The y-intercept of an equation in slope-intercept form represents the value of y when x is equal to 0. In this case, the y-intercept of the equation y = (3/4)x + 3 is 3 feet. This means that when x is equal to 0 (when no years have passed), the height of the tree is 3 feet.
c) To determine the height of the tree in 3 years, we can substitute 3 for x in the equation y = (3/4)x + 3 and solve for y. This gives us:
y = (3/4)(3) + 3
= 9/4 + 3
= 21/4
= 5.25 feet
Therefore, the height of the tree in 3 years is approximately 5.25 feet.
Is x 3 a factor of the polynomial x^3 3x^2 4x 12?
(x - 3) is a factor of the polynomial f(x) = x³ - 3x² + 4x - 12 since f(3) = 0.
To solve the problem, recall the factor theorem.
Factor Theorem states that if we have a polynomial f(x) and if (x - a) is a factor of f(x), then f(a) = 0
The given function is:
f(x) = x³ - 3x² + 4x - 12
To see whether x - 3 is a factor of f(x) = x³ - 3x² + 4x - 12, we need to find f(3).
Substitute x = 3 into f(x):
f(3) =3³ - 3(3)² + 4(3) - 12
f(3) = 27 - 27 + 12 - 12
f(3) = 0
Since f(3) = 0, then x -3 is a factor of x³ - 3x² + 4x - 12
Your question is incomplete, but most probably your question was:
Is x - 3 a factor of the polynomial x³ - 3x² + 4x - 12?
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The cost of an online newspaper is 7. 99 per month. If you buy a one year subscription the cost is 89. 88. How much do you pay each month if you choose the one year subscription
If we chosen the one year subscription we have to pay 7.49 per each month.
What is Linear Equation ?
Linear Equation can be defined as the equation in which the highest degree of the variable is one.
Given,
The cost of an online newspaper is 7.99
And if we bought the one year subscription the cost is 89.88
Let the the cost of the each month if we bought the one year subscription be x .
for one year the cost is 89.88
for one month could be
that is, x = 89.88/12
x = 7.49
Hence , If we chosen the one year subscription we have to pay 7.49 per each month.
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Josh exercises no less than 40 minutes per day.
Use t to represent Josh's amount of exercise (in minutes per day).
Answer
x ≥ 40
Step-by-step explanation:
Since Josh only exercises more or equal to 40 min, this is how you would represent this problem.
How much money should be put into a savings account now that earns 6.0% a year compounded weekly if you want to have 70000 in 15 years?
If you want to have $70,000 in 15 years, you need start saving money now in a savings account that earns 6.0% annually compounded weekly.
How does compound interest work?When you earn interest on your interest earnings as well as the money you have saved, this is known as compound interest.Compounding is effective for both promised and unguaranteed products. All or part of your money could be lost.
Use the compound interest formula and enter the figures you are familiar with. Then find a solution for the unknown number.
A = P(1 +r/n)^(nt)
where A represents the balance of the account, P represents the amount invested, r represents the yearly rate, n represents the number of times per year interest is compounded, and t is the number of years.
Filling in the given values, we have ...
70000 = P( 1 + 0.06/52)^(52*15) = P(2.4583)
P = 70000/2.4583 = 28474.96
You would need to deposit 28474.96 in order to have 70000 in 15 years.
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Find the area of the figure shown.
6
8
20
The area of the figure given is 49 square feet's.
What is area?The area is a two - dimensional region enclosed by a single - dimensional entity. We can write area as -∫dA = ∫∫F(x, y) dx dy
A = ∫∫F(x, y) dx dy
Given is a figure as shown in the image attached.
We can write the area of the figure as -
A = A{T} + A{R}
A = (4 x 10) + (1/2 x 6 x 3)
A = 40 + 9
A = 49 square feet's
Therefore, the area of the figure given is 49 square feet's.
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If the radius of a circle is x cm, what is the measure of its circumference? write.
Answer:
2 pie over r
Step-by-step explanation:
Step-by-step explanation:
the circumference is given by:
[tex]2\pi(radius)[/tex]
in this case x is the radius hence the circumference would be:
[tex]2\pi(x)[/tex]
hope this helps :)
maz changes 30 dollars back into pounds how many pounds will he get
Answer:
24.90 pound
1 dollar equivalent to 0.8301 pound
so 30 dollar will be 30 multiply by 0.8301
which equals 24.903 pounds
Use the graph of the equation to answer the question.
What is the domain of the equation?
What is the range of the equation?
As per the graph, there is no restrictions for the domain but the range has a minimum value at y = - 4.
The domain is any real number:
x ∈ ( - ∞, + ∞)The range is any real number not less than - 4:
y ∈ [ - 4, + ∞)PLEASEE HELP PICTURE ATTACHED
if m/P = (12x + 7);, m Q = (6x - 7), and LP
and /Q are complementary angles, find m /Q.
On solving the provided question, we can say that - the valuye os the complementary angle is 83.0000000004.
what is complementary angles?When two angles add up to 90 degrees, they are said to be complimentary. When two angles add up to 180 degrees, they are said to be subservient. . When the sum of two angles equals 90 degrees, they are called complementary angles. For example, 30 and 60 degrees are supplementary angles. A supplementary angle is two angles that add up to 180 degrees, and a supplementary angle is two angles that add up to 90 degrees. of 30 and 60 degrees are supplementary. A supplementary angle is two angles combined to make a 180 degree angle, while a supplemental angle is two angles combined to make a 90 degree angle. Two angles are referred to as complimentary if their total is 90 degrees. Alternatively said, a right angle is created by the complementary angles (90 degrees).
here we have
(12x + 7) = 90
12x = 83
x= 6.9166666667
12x = 83.0000000004
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caleb earned 15 dollars on monday and 25 dollars on saturday when he raked his neighbors yard. on sunday he gave 10 percent in the offering at church. how much did he give away.
15 + 25 = 40
10% of 40 = 4
Therefore, Caleb gave $4 to the church!
Hope this helps :D
What is the relationship between multiplying and factoring?
You multiply numbers or expressions to produce a
[Select]
numbers or [Select]
produce it.
✓. You factor a product into the
✓that were multiplied to
Polynomial factoring is the opposite of polynomial multiplication. A polynomial's leftover will be 0 if it is divided by its factors after factoring.
What do "multiply" and "factor" mean?A multiple is a number that is the result of multiplying the provided number by other numbers, as opposed to a factor, which divides the given number perfectly without leaving a remainder.
What connection exists between the factor theorem and the division of polynomials?When a polynomial f(x) is divided by (x - c), and (x - c) is a factor of the polynomial f(x), the remainder of the division is simply equal to 0. Therefore, if the remainder of a division like the ones mentioned above equals zero.
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