Answers
The composite functions when solved accordingly gives us;
(f ° g)(x) = 75x³ + 140x²+ 87x + 18
(f ÷ g)(x) = 3x + 2
How to solve composite functions?Composite functions are formed when the output of one function is used as the input of another.
Now, we are given the functions as;
f(x) = 15x² + 19x + 6
g(x) = 5x + 3
Let us factorize f(x) to get;
f(x) = 15x² + 19x + 6 = (5x + 3)(3x + 2)
(f ° g)(x) simply means; f[g(x)]
Thus, we have;
f.g(x) = (15x² + 19x + 6)(5x + 3)
f.g(x) = 75x³ + 95x² + 30x + 45x² + 57x + 18
f.g(x) = 75x³ + 95x² + 45x²+ 30x + 57x + 18
f.g(x) = 75x³ + 140x²+ 87x + 18
(f ÷ g)(x) = ((5x + 3)(3x + 2))/(5x + 3)
(f ÷ g)(x) = 3x + 2
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Related Questions
Can you say this number: 15,130,000,000? (Write it out in words.)
List as many possible ways that you can think of to write this number. (Ex. 15,130 x 1,000,000) What is the shortest way you can think of for writing this number?
Answers
Answer:
Word form:
Fifteen billion and one hundred thirty million.
The shortest way of writing this would be:
1,513 + 10 to the seventh power.
Step-by-step explanation:
Hope it helps!
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100
POINTS!!!!!!!!!!
Answers
Answer:
Step-by-step explanation:
a) correct
b) incorrect, its actually approximately 94cm^3
c) correct
d) correct
e) incorrect, its actually around 188cm^3
i tried, i hope this works :)
When drawing a card from a deck of 52 cards, (13 clubs, 13 hearts, 13, spades, and 13 diamonds with each kind having A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, O, k) what is the probability of drawing a Heart or a Seven?
Answers
Answer:
There are 52 cards in a deck, and 13 of them are hearts. Therefore, the probability of drawing a heart is 13/52, or approximately 0.25.
There are also four sevens in a deck (one of each suit), so the probability of drawing a seven is 4/52, or approximately 0.08.
To find the probability of drawing either a heart or a seven, we need to add the probabilities of these two events together. Therefore, the probability of drawing a heart or a seven is 0.25 + 0.08, or approximately 0.33. This can also be written as a fraction as 13/52 + 4/52, which simplifies to 17/52.
Overall, the probability of drawing a heart or a seven from a standard deck of cards is approximately 0.33, or 17/52.
An art project has an area of 63.6 square inches what is the width in inches of the project
Answers
The art project with an area of 63.6 square inches and length of 12 inches, have a width of is 5.3 inches.
How to solve an equationAn equation is an expression that shows the relationship between two or more numbers and variables.
Area is the amount of space occupied by a two dimensional shape or object.
Let x represent the width and y represent the length
Let us assume that the art project is a rectangle with a length of 12 inches, since the area is 63.6 square inches, hence:
Area = length * width
63.6 = xy
63.6 = x(12)
x = 5.3 in
The width of the project is 5.3 inches.
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GIVING BRAINLY
During our trip, we keep a constant rate of 55 miles per hour traveled. How many hours will it take us to travel 500 miles?
Use coordinates to solve the real-world problems
involving ratio and rates
If u answer the question u get 5 stars and brainly
I Need it before 2:00 pm and 2:30 pm
Answers
Answer: 3hr 16min
I hope this answers your Question
I’ll give BRAINLIEST if correct
Answers
Answer:
I think ifs y<5 I did this question last year but if not I'm sorry I tried sorry if I'm late
Answer:
x <= 5
Step-by-step explanation:
1st step: Observe the line
The line drawn is vertical.
Hence, it must be in the form x = k , where k is a constant.
2nd step: The line passes through the coordinate (5, 0) along the x axis.
Hence, k is this case is 5.
The shaded region of the graph includes values of x lesser than or equal to 5. (left part of the graph)
Hence, the inequality satisfied by the shaded region is x <= 5. (y can be of any value)
The data set below shows a city's high temperature for 11 days in degrees Fahrenheit. 56,60,60,60,62,64,64,66,66,90,95. Which is the most reasonable measure of central tendency for the data set?
Answers
The measure of central tendency of the data set that has a mode of 60, and median of 64 is the mean, 67.[tex]\overline{54}[/tex]
What is a measure of central tendency?A measure of central tendency is a descriptive statistics that describes the location of the center of a set of data.
Measure of central tendencies includes the mean, the mode, and the median.
The mean is the average value of the data set
The mode is the value of the most frequent data of the data set
The median is the value at the middle of the dataset, when the data is arranged in order of their increasing values.
The values in the data set are;
56, 60, 60, 60, 62, 64, 64, 66, 66, 90, 95
The mean of the data = (56 + 60 + 60 + 60 + 62 + 64 + 64 + 66 + 66 + 90 + 95) ÷ 11 ≈ 67.[tex]\overline{54}[/tex]
The mode of the data = 60
The median of the data = 64
The value of the measure of central tendency that most accurately describes the set of data is 67.[tex]\overline{54}[/tex], which is the mean.
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Find A given that (3, 1, -1) || (A, -4, 4)
Answers
Answer: A=-12
Step-by-step explanation:
-4/1 is -4
4/-1 is also -4
Then multiply 3 by -4 to get -12
a taguchi loss function implies that the loss to company as the process output varies on either side of the process mean remains constant regardless of how far the output varies from this mean.T/F
Answers
The given statement "A Taguchi loss function suggests that regardless of how much the output deviates from the process mean on either side, the loss to the company remains constant" is TRUE.
What is the Taguchi loss function?The Japanese business statistician Genichi Taguchi created the Taguchi loss function, a graphical representation of loss, to describe a phenomenon that affects the value of a company's products.
It clarified the idea that quality does not suddenly decline when, for example, a machinist exceeds a strict plan tolerance, which was praised by Dr. W. Edwards Deming, the business guru of the e American quality movement in the 1980s.
Instead, the value of the "loss" grows over time as the deviation from the anticipated condition rises.
This was seen as a milestone in describing the quality and contributed to the growth of the continuous improvement movement.
According to the Taguchi loss function, as process variation drifts further and further from the mean, the loss to the organization grows.
Therefore, the given statement "A Taguchi loss function suggests that regardless of how much the output deviates from the process mean on either side, the loss to the company remains constant" is TRUE.
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Which number sentence shows one way to find the sum of 4 and 5?
4 +4+5 = 13
4 + 5 +5 = 14
4 + 4 +4 = 12
4+4+1=9
Answers
The number sentence 4 + 4 + 1 = 9 shows one way to find the sum of 4 and 5.
What is sum of numbers?
By adding the digits of a number, we can find the sum of digits. To determine the digit sum, we can disregard the place values of the digits. For instance, 1 + 8 + 5 or 14 is the digit sum of 185.
We have to find Which number sentence shows one way to find the sum of 4 and 5.
Since, the sum of 4 and 5 equal to 9.
4 + 4 + 1 = 4 + 5
Given:
No. 1 - 4
No. 2 - 5
way 1. 4 + 5 = 9
2. 4 + 4 + 1 = 9
3. 4 + 3 + 1 + 1 = 9
4. 4 + 2 + 1 + 1 + 1 = 9
5. 4 + 1 + 1 + 1 + 1 + 1 = 9
Hence, the last option 4 + 4 + 1 is correct.
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A line passes through the points (-2, 9) and (1, 3).
Click “show your work” and provide work for calculating the slope and y-intercept. Then, write the equation for the line in slope-intercept form. Please write your answers on the lines provided on the whiteboard.
Answers
The slope is 4.
The y-intercept is 17.
The slope-intercept form is y = 4x +17
How to write the equation of a line in slope-intercept form?The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system
The slope-intercept form of the equation of a line is y = mx+b,
where m is the slope and b is the y-intercept
The line passes through points (-2, 9) and (1, 3).
m = (y₂-y₁)/(x₂-x₁)
where (x₁, y₁) = (-2, 9)and (x₂, y₂) = (1, 3)
m = (3-(-9)) / (1-(-2)) = 12/3 = 4
Using y = mx + b with (-2, 9) to find b:
9 = 4(-2) + b
9 = -8 + b
b = 9 + 8
b = 17
Thus, the equation of the line is y = 4x + 17
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Find g(x), where g(x) is the translation 6 units left of f(x) = x².
Write your answer in the form a(x - h)+k, where a, h, and k are integers.
Answers
The function g(x) can be expressed as g(x) = a(x - h) + k, where a is the coefficient of x (which is 1 for f(x) = x^2), h is the horizontal shift, and k is the vertical shift.
To translate a function 6 units left, we need to shift it horizontally by -6 units. So, h = -6.
Since the function g(x) is a translation of f(x), a and k will have the same values as in f(x). In this case, a = 1 and k = 0.
Therefore, the function g(x) that represents the translation 6 units left of f(x) is:
g(x) = a(x - h) + k
= 1(x - (-6)) + 0
= 1(x + 6) + 0
= x + 6
the answer is: g(x) = x + 6
There are 26 children in a class, 16 brown-haired and 10 black-haired. Two students are randomly selected for a stage performance. What is the probability of two brown-haired students being selected?
A: 61.5%
B: 36.9%
C: 35.5%
D: 13.8%
Answers
The probability of selecting brown-haired children is 61.5%. The correct option is A.
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favourable outcomes / Number of samples
Given that there are 26 children in a class, 16 are brown-haired and 10 are black-haired. Two students are randomly selected for a stage performance.
The probability will be calculated as,
Probability = 16 / 26
Probability = 0.615 x 100
Probability = 61.5%
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through: (1,1), slope =5
Answers
Answer:
y = 5x - 4
Step-by-step explanation:
For this question, use the slope-intercept formula: y=mx+b
y=mx+b ==> 1 = (5)(1) + b ==> plugin point (x=1, y=1) and m=5; m is the slope
1 = 5 + b ==> solve for b
-4 = b ==> subtract 5 on both sides
y = 5x + (-4) ==> plugin -4 for b in the equation y=mx+b
y = 5x - 4 <== simplified equation
Answer:
The line is y = 5x - 4-----------------------------------
The line has a slope of 5 and passes through the point (1, 1).
Use point-slope form:
y - y₁ = m(x - x₁)Substitute coordinates:
y - 1 = 5(x - 1)Convert the equation into slope-intercept form:
y - 1 = 5x - 5y = 5x - 5 + 1y = 5x - 4Question 2 (Multiple Choice Worth 1 points)
(06.02 MC)
Three friends, Nakobe, Mikah, and Ashton, are saving up money to buy microphones for their podcast. The total cost of the microphones is represented by the expression 9 x^2-3 x+4
The friends have already saved the following amounts:
Nakobe x^2
Mikah x-12
Ashton: 3x+4
Which expression represents the amount of money the friends still need to buy the microphones?
8x^2-7 x-4
8x^2-7 x+12
4x^2+5 x+4
x^2+4 x-8
Answers
An expression which represents the amount of money the friends still need to buy the microphones include the following: B. 8x² - 7x + 12.
What is a quadratic function?In Mathematics, a quadratic function can be defined as a mathematical expression which defines and represent the relationship that exists between two or more variable on a graph, with a maximum exponent of two (2).
Generally speaking, the standard form of a quadratic function is given by;
ax² + bx + c = 0
Next, we would determine the total amount of money that has been saved by these three friends, Nakobe, Mikah, and Ashton as follows;
Total amount of money saved = x² + x - 12 + 3x + 4
Total amount of money saved = x² + 4x - 8
Now, we can determine the total amount of money that is still needed for the purchase of the microphones:
Total amount of money remaining = 9x² - 3x + 4 - (x² + 4x - 8)
Total amount of money remaining = 9x² - 3x + 4 - x² - 4x + 8
Total amount of money remaining = 8x² - 7x + 12.
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Answer:
B: 8x² − 7x + 12
Place parentheses and brackets in the expression below so that it equals 18
2³ x 4/2 +2
Answers
The value of the equation A = ( 2³ x 4 ) / 2 + 2 = 18
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A = 18
Substituting the values in the equation , we get
A = ( 2³ x 4 ) / 2 + 2 be equation (1)
On simplifying the equation , we get
2³ = 8
A = ( 8 x 4 ) / 2 + 2
A = 32/2 + 2
A = 16 + 2
The value of A = 18
Therefore , the value of A = 18
Hence , the equation is A = ( 2³ x 4 ) / 2 + 2
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Please help!! Thank you so much if you do :)
Answers
The area of the triangle ABD is 45 inches², the area of the triangle ADC is 30 inches², and the area of the triangle ABC is 75 inches².
What is triangle?One of the fundamental shapes in geometry is represented by the symbol Δ and consists of three connected vertices, known as a triangle.
Given:
The measure of sides CD = 6 inches, BD = 9 inches, AD = 10 inches,
Calculate the area of ABD and ADC as shown below,
The area of ABD = 1 / 2 × BD × AD
The area of ABD = 1 / 2 × 9 × 10
The area of ABD = 45 inches²
The area of ADC = 1 / 2 × AD × CD
The area of ADC = 1 / 2 × 6 × 10
The area of ADC = 30 inches²
The area of Δ ABC = 1 / 2 × BC × AD
The area of Δ ABC = 1 / 2 × 15 × 10
The area of Δ ABC = 75 inches²
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the equation of a line is y+4=6x+13
what is the value of y at the point where the line crosses the y-axis?
Answers
y = 9
The y-axis is the vertical axis in a coordinate system, and a point on the y-axis has an x-coordinate of 0. The equation of a line is a mathematical expression that describes the relationship between the x- and y-coordinates of points on the line.
To find the value of y at the point where the line crosses the y-axis, we need to substitute x=0 into the equation of the line and solve for y. This will give us the value of y at the point where the line intersects the y-axis.
For the given equation y+4=6x+13, substituting x=0 gives us:
y + 4 = 6*0 + 13
y + 4 = 13
y = 9
Therefore, the value of y at the point where the line crosses the y-axis is 9. This means that the point where the line intersects the y-axis has coordinates (0,9).
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Use the distributive property with factoring to find the equivalent expression.
21x + 39z = (7x + z)
Answers
The equivalent expression is 14x + 38z = 0.
What is an expression?We have to note that an expression has to do with a mathematical statement. According to the distributive property, we can be able to open up the brackets over the values that we have in the question.
As such we would have;
21x + 39z = (7x + z)
Removing the brackets;
21x + 39z = 7x + z
Then we collect the like terms;
21x - 7x = z - 39z
14x = -38z
14x + 38z = 0
This is the expression that is equivalent to the one given above.
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URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100
POINTS!!!
Answers
Word blanks are:
Blank 1: The Pythagorean Theorem
Blank 2: √91.
Blank 3: a leg
Blank 4: The hypotenuse.
Blank 5: 10.34
What is Pythagoras theorem?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.
From the diagram:
To find the length of the diagonal from point A (front/bottom/left) to point G (back/top/right):
You would first use the Pythagorean Theorem on the bottom of the box rectangle to find the diagonal AC = √91
Then use CG as a leg of the triangle ACG, with AG being the hypotenuse.
AG is approximately = 10.34
Word blanks are:
Blank 1: The Pythagorean Theorem
Blank 2: √91.
Blank 3: a leg
Blank 4: The hypotenuse.
Blank 5: 10.34
Therefore, the blank words are given above.
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If 40% of a number is 56, what was the original number?
Answers
Hope this helps!
he profit for a production process is equal to $2,000
minus two times the number of units produced. The
mean and variance for the number of units produced
are 500 and 900, respectively. Find the mean and variance of the profit.
Answers
Answer:I don’t know
Step-by-step explanation:
if 24 is not an even number, then 6 is divisible by 3
Answers
Graph the solution to this inequality on the number line.
x+3<-6
First select the correct ray. Then select the location of the endpoint to plot the inequality on the number line.
Answers
The solution set for the inequality given in the task content as required is; x < -9.
The graph of the inequality on the number line is such that it includes all points to the left of -9 on the number line.
What is the graph of the inequality; x + 3 < -6?It follows from the task content that the graph of the inequality x + 3 < -6 as required is to be determined.
Since the given inequality is; x + 3 < -6.
The inequality can be solved by first subtracting 3 from both sides of the inequality; subtractive proper of inequalities;
x + 3 - 3 < -6 - 3
x < -9.
On this note, the correct ray is that which points leftwards with an open ring (indicating the < sign).
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A 12 year old child has been prescribed tofranil at bedtime for enuresis a typical adult maintenance dose of tofranil is 100 mg daily the medication is available in 10 25 and 50 mg tablets what is the approximate maintenance dose that can be administered to the child based on this information
Answers
Based on this information the approximate maintenance dose that can be administered to the child to achieve 100 mg daily of the medication is as follows for:
10 mg (10 tablets)25 mg (4 tablets) 50 mg ( 2tablets)SolutionThe question states that the 12-year-old child be administered 100 mg daily the medication is available in 10, 25 and 50 mg tablets.
For the administration of 10 mg tabletsto achieve 100 mg daily dose
1 tablet = 10 mg
10 mg *10tablets = 100 mg
For the administration of 25 mg tabletsto achieve 100 mg daily dose
1 tablet = 25 mg
10 mg *4tablets = 100 mg
For the administration of50 mg tabletsto achieve 100 mg daily dose
1 tablet = 50 mg
10 mg * 2tablets = 100 mg
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A city requires that smoke detectors be installed in all houses. There is concern that too many houses are still without detectors, so a costly inspection program is being considered. Let p be the proportion of all houses that have a detector. A random sample of 25 houses is selected. If the sample strongly suggests that p < 0.80 (less than 80% have detectors), as opposed to p ≥ 0.80, the program will be implemented. Let x be the number of residences among the 25 that have a detector, and consider the following decision rule: Reject the claim that
p ≥ 0.8
and implement the program if x ≤ 17. (Round your answers to three decimal places.)
Answers
The probability that the claim is rejected when the actual value of p is 0.8 = P(X ≤ 17) = 0.10912
How to solve binomial probability distribution?A binomial experiment is defined as one in which the probability of success doesn't change with every run or number of trials.
The outcome of each trial of a binomial experiment is independent of one another.
Binomial distribution function is represented by the formula;
P(X = x) = ⁿCₓ pˣ (1 - p)ⁿ⁻ˣ
Where;
p is the true proportion.
n is sample size
x is number of successes
a) We want to find the probability that the claim is rejected when the actual value of p is 0.8 = P(X ≤ 17)
We are given that the claim is that 80% of houses have smoke detectors is rejected if in a sample of 25 houses, not more than 15 houses have smoke detectors.
Thus;
Sample size; n = 25
Number of successes required = 17
Probability of success; p = 0.80
Thus;
P(X ≤ 17) = Sum of probabilities from P(X = 0) to P(X = 17)
Using online binomial probability calculator gives us;
P(X ≤ 17) = 0.10912
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What are the dimensions of a rectangle if the area is 103ft²
Answers
The dimensions of the rectangle are 25 by 4.12 feet
How to determine the dimensions of the rectangleFrom the question, we have the following parameters that can be used in our computation:
Rectangle area = 103 square feet
The area of a rectangle is calculated as
Area = Length * Width
Assume the length is 25
So, we have
Area = 25 * Width
Substitute the known values in the above equation, so, we have the following representation
25 * Width = 103
Divide both sides by 25
Width = 4.12
Hence, the dimensions are 25 by 4.12 feet
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An online music club offers individual songs for one price or entire albums
for another Kendrick pays $14.90 to download 5 individual songs and
1 album Geoffrey pays
s $21.75 to download 3 individual songs a
s and 2 albums.
S
a. How much does the music club charge to download a song?
b. How much does the music club charge to download an entire album?
Answers
Answer:
To solve for the price of a single song, we can set up the following equation:
Kendrick paid $14.90 for 5 songs + 1 album = $x for a single song
We can solve for x by dividing both sides of the equation by 5:
$14.90 / 5 = $x / 5
This simplifies to:
$x = $2.98
So the music club charges $2.98 to download a single song.
To solve for the price of an entire album, we can set up the following equation:
Geoffrey paid $21.75 for 3 songs + 2 albums = $y for an entire album
We can solve for y by subtracting the cost of the songs from both sides of the equation:
$21.75 - $2.98 * 3 = $y - $2.98 * 3
This simplifies to:
$12.79 = $y
So the music club charges $12.79 to download an entire album.
Step-by-step explanation:
Answer:
$1.15 and $9.15
Step-by-step explanation:
let s represent the cost of a song and a represent the cost of an album , then
5s + a = 14.9 → (1)
3s + 2a = 21.75 → (2)
multiplying (1) by - 2 and adding to (2) will eliminate a
- 10s - 2a = - 29.8 → (3)
add (2) and (3) term by term to eliminate a
- 7s + 0 = - 8.05
- 7s = - 8.05 ( divide both sides by - 7 )
s = 1.15
substitute s = 1.15 into either of the 2 equations and solve for a
substituting into (1)
5(1.15) + a = 14.9
5.75 + a = 14.9 ( subtract 5.75 from both sides )
a = 9.15
(a) the charge for downloading a song is $1.15
(b) the charge for downloading an album is $9.15
pls solveee (correct answers only and explaintion)
Answers
Stephanie is playing a board game and rolls two number cubes. Let A = {the sum of the number cubes is 7}, and let B = {the second number cube shows an even number}. Are events A and B independent?
Answers
They are independent since the sum of the number cubes is 7 B = the second number cube shows an even number.
How to illustrate the information?From the information, Stephanie is playing a board game and rolls two number cubes. Let A = {the sum of the number cubes is 7}, and let B = {the second number cube shows an even number}.
If the occurrence of one event does not change the likelihood that the other event will also occur, two events A and B are said to be independent. The two events are said to be dependent if the occurrence of one event affects the likelihood that the other event will also occur.
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