The height of the triangle is √(115) - 1 inches and the width is (1 + √(115)) / 6 inches.
Let's begin by assigning variables to the height and width of the triangle. We'll use h for height and w for width.
From the problem statement, we know that the area of the triangle is 184 square inches:
Area = (1/2) * base * height
where the base is equal to the width. We can rearrange this formula to solve for the height:
height = 2 * Area / base
Since the area is given as 184 square inches and the base is equal to the width, we can write:
h = 2 * 184 / w
We also know that the height is two less than six times the width. Writing this as an equation, we have:
h = 6w - 2
Now we can substitute the expression for h from the second equation into the first equation:
2 * 184 / w = 6w - 2
Multiplying both sides by w gives:
2 * 184 = w * (6w - 2)
Expanding the right side gives:
2 * 184 = 6w² - 2w
Simplifying further gives:
6w² - 2w - 368 = 0
This is a quadratic equation that we can solve using the quadratic formula:
w = (-b ± √(b² - 4ac)) / 2a
where a = 6, b = -2, and c = -368. Plugging in these values gives:
w = (2 ± √(2² - 4 * 6 * (-368))) / 2(6)
Simplifying further gives:
w = (1 ± √(115)) / 6
Taking the positive value gives:
w = (1 + √(115)) / 6
Plugging this value back into either equation for h gives:
h = 6w - 2 = 6((1 + √(115)) / 6) - 2 = 1 + √(115) - 2 = √(115) - 1
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y= +- 3/5 is equivalent to?
The equivalent value of the expression is y = + 3/5 and y = -3/5
Given data ,
Let the expression be represented as A
Now , the value of A is
y = ±3/5
On simplifying the equation , we get
y = +3/5
And, y = -3/5
Now , the decimal values of y are
y = ±0.6
Hence , the expression is y = ±0.6
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Write the equation of a line perpendicular to y = −5/9x + 4 and that passes through point (-5,-4) in slope intercept form.
Answer: y = (9/5)x + 5.
Step-by-step explanation:
The slope of the given line is -5/9. The slope of a line perpendicular to it would be the negative reciprocal of -5/9, which is 9/5. Using the point-slope form of a line, we can write the equation of the line as y - (-4) = (9/5)(x - (-5)). Simplifying this equation gives y + 4 = (9/5)x + 9. Solving for y, we get y = (9/5)x + 5. This is the equation of the line in slope-intercept form.
In summary, the equation of a line perpendicular to y = −5/9x + 4 and that passes through point (-5,-4) is y = (9/5)x + 5.
Find m/_U. Write your answer as an integer or as a decimal rounded to the nearest tenth.
The measure of angle U = 41.83 degree.
In the given right angle triangle
VW = 6
UV = 9
Since sinΘ = (opposite side)/(hypotenuse)
Therefore,
sin U = VW/UV
= 6/9
= 0.667
Take inverse of sin both sides
∠U = arcsin(0.667)
= 41.83
Hence ∠U = 41.83 degree
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For the function value f(−9)=6, write a corresponding ordered pair.
Answer:
(-9, 6) This ordered pair is used to find the function value f(-9)=6
or the given function value, write a corresponding ordered pair.
Step-by-step explanation:
For the given function value, write a corresponding ordered pair.
f(-9) = 6
The ordered pair of each function can be written as (x,y).
For any function, for example, g(x)= 10x, the input is x, and the output y is 10x. So ordered pair is (x,10x)
The given function value is: f(-9) = 6
Here input x=-9 and y value is 6
So, he corresponding ordered pair is (-9, 6)
What does the circled portion represent in the confidence interval formula?
p±z.
O Sample proportion
O Margin of error
p(1-p)
n
Confidence interval
O Sample Size
The circled portion in the confidence interval formula p ± z represents the Margin of Error, which plays a crucial role in interpreting the range of plausible values for the population parameter.
In the confidence interval formula p ± z, the circled portion represents the Margin of Error.
The Margin of Error is a critical component of a confidence interval and quantifies the level of uncertainty in the estimate.
It indicates the range within which the true population parameter is likely to fall based on the sample data.
The Margin of Error is calculated by multiplying the critical value (z) by the standard deviation of the sampling distribution.
The critical value is determined based on the desired level of confidence, often denoted as (1 - α), where α is the significance level or the probability of making a Type I error.
The Margin of Error accounts for the variability in the sample and provides a measure of the precision of the estimate.
It reflects the trade-off between the desired level of confidence and the width of the interval.
A larger Margin of Error indicates a wider confidence interval, implying less precision and more uncertainty in the estimate.
Conversely, a smaller Margin of Error leads to a narrower confidence interval, indicating higher precision and greater certainty in the estimate.
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PLSSS HELP AND PLEASE SHOW WORK ASWELL
Collin has 100 feet of fencing to enclose a pen for his puppy. He is
trying to decide whether to make the pen
circular or square. He plans to use all of the
fencing.
Part A.) If Collin uses all of the fencing, what
would be the area of each pen? Use 3.14
for pie. Round to the nearest hundredth if
necessary.
Part B.) To have the largest possible area for the pen, which pen should Collin build?
Answer:
A.
circular: ≈ 795.77 square feet
square: 625
Step-by-step explanation:
the circular pen would have a larger area.
Solving for the radius, we have:
r = 100 / (2 × 3.14) = 15.92 feet (rounded to two decimal places)
Therefore, the area of the circular pen would be:
Area = πr^2 = 3.14 × (15.92 ft)^2 ≈ 795.77 square feet
For a square pen with side length s, the perimeter is given by:
4s = 100
s = 25
The area of a square pen with side length s is given by:
A = s^2 = 25^2 = 625
limit x->oo (sqrt(x^2-9x+1)-x)=?
I solved it up until -9x+1/((√x^2-9x+1)+x) but I don't know what to do after this.
Note that the limit of the expression as x approaches infinity is 1/2.
How did we arrive at this conclusion ?start by multiplying both the numerator and denominator by the conjugate expression
√ (x ² - 9x + 1) + x,
this will eliminates the root in the numerator
lim x->∞ [(√(x ² - 9x + 1) - x) * (√(x² - 9x + 1) + x)] / (√(x² - 9x + 1) + x)
Expanding the numerator
lim x- >∞ [(x² - 9x + 1) - x^2] / (√(x² - 9x + 1) + x)
Simplifying further:
lim x->∞ [(1 - 9/x + 1/ x²)] / (√(1 - 9/x + 1 /x²) + 1)
we can see that the 1/x ² term approaches zero, and the expression simplifies to
lim x->∞ [(1 - 0)] / (√(1 - 0) + 1)
= 1/2
So it is correct to state that the limit of the expression as x approaches infinity is 1/2.
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On a sample tray, 3 out of 6 cake samples are chocolate.
What is the probability that a randomly selected piece of cake will be chocolate?
Write your answer as a fraction or whole number.
The probability that a randomly decided piece of cake maybe chocolate is 1/2 or half of or 0.
The proportion of chocolate cakes to all other cakes can be used to calculate the probability that a person will pick a chocolate cake from the pattern tray.
In this case, there are 3 chocolate cakes out of a total of 6 cakes.
So the probability of selecting a chocolate cake is:
3/6 = 1/2 (Dividing the numerator and denominator by their greatest common factor, in this case, 3 will simplify the fraction 3/6.)
Therefore, the probability of selecting a chocolate cake is 1/2 or 0.5 when expressed as a decimal.
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real-estate agent conducted an experiment to test the effect of selling a staged home vs. selling an empty home. To do so, the agent obtained a list of 10 comparable homes just listed for sale that were currently empty. He randomly assigned 5 of the homes to be "staged," meaning filled with nice furniture and decorated. The owners of the 5 homes all agreed to have their homes staged by professional decorators. The other 5 homes remained empty. The hypothesis is that empty homes are not as appealing to buyers as staged homes and, therefore, sell for lower prices than staged homes. The mean selling price of the 5 empty homes was $150,000 with a standard deviation of $22,000. The mean selling price of the 5 staged homes was $175,000 with a standard deviation of 35,000. A dotplot of each sample shows no strong skewness and no outliers.
Real-estate agent tested the effect of staging on home sale prices. Out of 10 comparable homes, 5 were staged. Staged homes sold for $15k more on average, with no skewness or outliers.
Based on the information given, the real-estate agent conducted an experiment to test the effect of selling a staged home vs. selling an empty home.
The hypothesis is that empty homes sell for lower prices than staged homes. The agent randomly assigned 5 empty homes to be staged and obtained a list of 10 comparable homes.
The mean selling price of the 5 empty homes was $150,000 with a standard deviation of $22,000. The mean selling price of the 5 staged homes was $175,000 with a standard deviation of 35,000. There was no strong skewness or outliers in the dot plots of the two samples.
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what are the answers to these questions?
The height and radius that minimize the amount of material needed to manufacture the can are both approximately 6.39 cm.
The total surface area of the can is therefore:
A = 2πr² + 2πrh
We know that the volume of the can is 810 cm³, which is given by:
V = πr²h
We can solve this equation for h to get:
h = V/(πr²)
Substituting this expression for height h into the equation for the surface area, we get:
A = 2πr² + 2πr(V/(πr²))
Simplifying, we get:
A = 2πr² + 2V/r
Now we have an equation for the surface area of the can in terms of the radius, r.
To minimize the surface area, we need to take the derivative of this equation with respect to r, set it equal to zero, and solve for r.
dA/dr = 4πr - 2V/r² = 0
Solving for radius r, we get:
[tex]r = (810/\pi)^1^/^3[/tex]
r=∛810/3.14
r=6.35 cm
Now find h:
h = 810/πr²
h=810/3.14×6.35²
h=810/126.6
h=6.39 cm
Hence, the height and radius that minimize the amount of material needed to manufacture the can are both approximately 6.39 cm.
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uppose that you are told that the Taylor series of f(x)=x3ex2
about x=0
is
x3+x5+x72!+x93!+x114!+⋯.
Find each of the following:
ddx(x3ex2)∣∣∣x=0=
d7dx7(x3ex2)∣∣∣x=
a. Using Taylor series d(x³eˣ²)/dx about x = 0 is x⁴.
b. Using Taylor series d⁷(x³eˣ²)/dx⁷ about x = 0 is x¹⁰.
What is a Taylor series expansion?A Taylor series is a polynomial expansion of a function about a given point. It is given by f(x - a) = ∑(x - a)ⁿfⁿ(x - a)/n! where
a = point where f(x) is evaluated fⁿ(a) = nth derivative of f(x) about a and n is a positive integerGiven that the Taylor series of the function f(x) = x³eˣ² about x = 0 is
f(x) = x³ + x⁵ + x⁷/2! + x⁹/3! + x¹¹/4!, (1) we proceed to find the given variables
a. To find d( x³eˣ²)/dx about x = 0, the Taylor series expansion about x = 0 is given by
f(x - a) = ∑(x - a)ⁿfⁿ(a)/n!
f(x - 0) = ∑(x - 0)ⁿf(0)/n!
f(x) = ∑xⁿf(0)/n!
f(x) = x⁰f(x)/0! + xf(x)/1! + x²f(x)/2! + x³f(x)/3! + ....
f(x) = f(x) + xf¹(x) + x²f²(x)/2! + x³f³(x)/3! + ....(2)
Since fⁿ(x) is the nth derivative of f(x), and we desire f¹(x) which is the first derivative of f(x). Comparing equations (1) and (2), we have that
x⁵ = xf¹(x)
f¹(x) = x⁵/x
= x⁴
So, d( x³eˣ²)/dx about x = 0 is x⁴.
b. To find d⁷( x³eˣ²)/dx⁷ about x = 0, the Taylor series expansion about x = 0 is given by
f(x - a) = ∑(x - a)ⁿfⁿ(a)/n!
f(x - 0) = ∑(x - 0)ⁿf(0)/n!
f(x) = ∑xⁿf(0)/n!
f(x) = x⁰f(x)/0! + xf(x)/1! + x²f(x)/2! + x³f(x)/3! + ....
Expanding it up to the 8 th term, we have that
f(x) = f(x) + xf¹(x) + x²f²(x)/2! + x³f³(x)/3! + x⁴f⁴(x)/4! + x⁵f⁵(x)/5! + x⁶f⁶(x)/6! + x⁷f⁷(x)/7!.....(3)
Now expanding equation (1) above to the 8th term by following the pattern, we have that
f(x) = x³ + x⁵ + x⁷/2! + x⁹/3! + x¹¹/4! + x¹³/5! + x¹⁵/6! + x¹⁷/7!.....(4)
Since fⁿ(x) is the nth derivative of f(x), and we desire f⁷(x) which is the seventh derivative of f(x). Comparing equations (3) and (4), we have that
x⁷f⁷(x)/7! = x¹⁷/7!
f⁷(x) = x¹⁷/x⁷
= x¹⁰
So, d⁷( x³eˣ²)/dx⁷ about x = 0 is x¹⁰.
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Andy has $100 in an account. The interest rate is 6% compounded annually.
To the nearest cent, how much will he have in 2 years?
The amount that will be in Andy's account in 2 years after the addition of interest is $112.36
How to calculate the amount in Andy's account after 2 years ?Andy has $100 in an account
An interest rate of 6% is compounded annually
The amount that will be present in the account after 2 years can be calculated as follows
= 100(1+ 6/100)²
= 100(1 + 0.06)²
= 100(1.06)²
= 100(1.1236)
= 112.36
Hence the amount that will be present in the account after 2 years with the addition of interest is $112.36
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PLEASE SOMEONE HELP ME DO THIS MATH PROBLEM
i am having a mental breakdown rnn :(.
Check the picture below.
combine like terms 6x^2 - 10x + 21x - 35 = 6x^2 + 11x - 35
Answer:
Step-by-step explanation:
6x² - 10x + 21x - 35 = 6x² + 11x - 35
6x² - 6x² + 11x - 11x - 35 + 35 = 0
0 = 0
The equation is an identity. Its solution set is {all real numbers}.
Find the measure of EB
The measure of angle subtended by the arc EB is 96 ⁰.
What is the measure of arc angle EB?The measure of angle subtended by the arc EB is calculated by applying the following formula.
Based on the angle of intersecting chord theorem, the theory states that, the angle formed by the intersection of two chords at the circumference of a circle is equal to half of the difference between the arc angles of the two chords.
We will have the following equation;
m∠ECB = ¹/₂( 7x + 6 - (4x + 16))
25 x 2 = 7x + 6 - 4x - 16
50 = 3x - 10
60 = 3x
x = 60/3
x = 20
The measure of arc angle EB is calculated as follows;
m∠EB = 4x + 16
m∠EB = 4(20) + 16
m∠EB = 96 ⁰
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PLEASE HELP WITH THE IMAGE!! DUE TOMORROW!!!
The calculations of the down payments, monthly income or payments are as follows:
Part 1:
Annual income = $226,000
Federal Tax = $62,582
State Tax = $16,385
Local Tax = $5,537
Healthcare = $4,520
Yearly income = $136,976
Monthly income = $11,414.67.
Part 2:
Down payment = $150,000
The amount to borrow (Mortgage loan) = $600,000
Estimated interest = $810,000
Total installment payments = $1,410,000
Monthly payment = $3,916.67.
Part 3:
Down payment = $2,902.50
Mortgage loan = $16,447.50
Estimated interest = $3,700.69
Interest + Mortgage loan = $20,148.19
Monthly payment = $335.80.
Part 1:
Annual income = $226,000
Federal Tax:
25% of $89,350 = $22,337.50
28% of $97,000 = $27,160.00
33% of $39,650 = $13,084.50
Total federal tax = $62,582
State Tax = 7.25% of $226,000 = $16,385
Local Tax = 2.45% of $226,000 = $5,537
Healthcare = 2% of $226,000 = $4,520
f) Total of Federal, State, Local, and Healthcare = $89,024
Yearly income = $136,976 ($226,000 - $89,024)
Monthly income = $11,414.67 ($136,976 ÷ 12)
Part 2:
a) House price = $750,000
b) Down payment = 20%
= $150,000 ($750,000 x 20%)
c) Mortgage loan = $600,000 ($750,000 - $150,000)
d) Interest rate = 4.5%
Number of mortgage years = 30 years
Mortgage period in months = 360 months (30 x 12)
Estimated interest = $810,000 ($600,000 x 4.5% x 30)
Interest + Mortgage loan = $1,410,000 ($600,000 + $810,000)
Monthly payment = $3,916.67 ($1,410,000 ÷ 360)
Part 3:
Price of car = $19,350
Down payment = 15%
= $2,902.50 ($19,350 x 15%)
Mortgage loan = $16,447.50 ($19,350 - $2,902.50)
Number of years = 5 years
Mortgage period in months = 60 months (5 x 12)
Estimated interest = $3,700.69 ($16,447.50 x 4.5% x 5)
Interest + Mortgage loan = $20,148.19 ($16,447.50 + $3,700.69)
Monthly payment = $335.80 ($20,148.19 ÷ 60)
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3.4 MIXED FACTORING
1. Utilize all of the strategies for factoring in order to factor the following polynomials.
Reminder: Combine like-terms prior to factoring.
a. x² - 4x-2x+8
Answer:
(x -2)(x -4)
Step-by-step explanation:
You want to factor x² - 4x -2x +8.
Factor by groupingWe recognize that the product of the coefficients of the two linear terms is equal to the contant, so this is more easily factored by not combining like terms prior to factoring.
Grouping the terms in pairs, we find we can factor each pair:
(x² -4x) + (-2x +8)
= x(x -4) -2(x -4) . . . . . these terms have a common factor of (x -4)
= (x -2)(x -4) . . . . . . . factored form of the expression
Express the following probability as a simplified fraction and as a decimal.
If one person is selected from the population described in the table, find the probability that the person is or .
Note that the following probability as a simplified fraction and as a decimal is: 0.88617886178 and 109/123
How is this so?Note that the key phrase here is “given that this person is a man.”
This means that all we are interested in is the row labeled Male.
Married Never Div Widowed Total
Male 69 40 11 3 123
We are asked to find the probability that the person was either Married or Never. So the fraction you want is (69 + 40) / 123.
⇒ (69 + 40) / 123.
⇒ 109/123
or 0.886179
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Full Question:
Although part of your question is missing, you might be referring to this full question:
Express the following probability as a simplified fraction and a decimal.
if one person is selected from the population described in the table, find the probability that the person has never been married or is married, given that this person is a man.
Married Never Married Divorced Widowed Total
Male 69 40 11 3 123
Female 67 33 20 5 125
Total 136 73 31 8 248
Question 1.Express the probability as a simplified fraction
At 10.30 a.m, a van left Town X travelling at an average speed of 64 Km/h.
At 11.15 a.m., a car left Town X, travelling on the same road at an average speed of
80 Km/h.
a) At what time did the car catch up with the van?
b) How far from Town X did each vehicle travel when they passed each other?
Answer:
a) 2:15 pm
b) 240 km
Step-by-step explanation:
You want to know the time and place where a car leaving at 11:15 a.m. at 80 km/h catches up with a van leaving at 10:30 a.m. at 64 km/h.
Head startThe van travels for 11:15 -10:30 = :45, or 3/4 hour, before the car starts. This gives it a distance advantage of (3/4 h)(64 km/h) = 48 km.
Closing speedThe speed at which that distance is reduced is the difference between the car speed and the van speed:
80 km/h -64 km/h = 16 km/h
Closing timeThe time it takes for the head-start distance to be reduced to zero is ...
time = distance/speed
time = (48 km)/(16 km/h) = 3 h
a) Meeting timeThree hours after the car leaves, it will catch up with the van. That time is ... 11:15 +3:00 = 14:15 = 2:15 p.m.
b) Meeting distanceIn 3 hours, the car travels (3 h)(80 km/h) = 240 km.
Note that the van has been traveling 3 3/4 hours, so will have also traveled (3 3/4 h)(64 km/h) = 240 km. The two vehicles need to be in the same place at the same time if they are to pass each other.
__
Additional comment
The attached graph shows the two vehicles will have traveled 240 km when they mean at 2:15 pm. The horizontal axis is hours after midnight. The vertical axis is kilometers from town X. The relation graphed is distance = speed × time.
Samantha gets paid $18.50 for each soccer game she referees. If she is a referee for 12 games and spends $59.99 for a new pair of cleats, how much money
does she have?
Answer:
$162.01
Step-by-step explanation:
amount of money she earns: 12($18.50) = $222
spends $59.99
amount of money after her purchase: $222-$59.99=$162.01
Cami cut 17 1\2
inches off a rope that was 50 inches long. How is the length of the remaining rope in inches written in decimal form?
After Cami cut 17¹/₂ inches of a rope that was 50 inches long, the length of the remaining rope in inches, written in decimal form, is 32.5 inches.
How is the remaining length of the rope determined?To determine the remaining length of the rope, we apply subtraction operation.
However, since the cut rope was expressed in fractions, we can convert it to decimals before the subtraction.
The total length of the rope = 50 inches
The cut portion of the rope = 17¹/₂ inches
The remaining portion = 32¹/₂ inches or 32.5 inches (50 - 17¹/₂)
Thus, the remaining portion of the rope after Cami cut 17¹/₂ inches is 32.5 inches.
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What is 0.08% written as a decimal?
b/8 < 8 help me please I also need the graphic
The solution of the inequality given is b < 64
the graph is attached
How to solve for bIn the equation, let us replace b with x
To solve the inequality x/8 < 8 for x, we need to isolate x on one side of the inequality.
We can do this by multiplying both sides of the inequality by 8, which will cancel out the 8 in the denominator on the left side:
Therefore, the solution to the inequality x/8 < 8 is x < 64.
This means that any value of x that is less than 64 will make the inequality true.
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Here are five spinners with orange and white sectors. Each spinner is divided into equal sectors. A a) b) a) For one of the spinners, the probability of spinning orange is Which spinner is this? B A b) For two of the spinners, the probability of spinning orange is more than 40%. Which two spinners are these?
Spinner B is the spinner that has a probability of 1/3 of spinning orange.
How to find the he probability of spinning orange is more than 40%a) For one of the spinners, the probability of spinning orange is 1/3. To identify which spinner this is, we need to find the spinner that has exactly one orange sector out of three total sectors.
From the given spinners, Spinner B is the only spinner that has one orange sector out of three, so Spinner B is the spinner that has a probability of 1/3 of spinning orange.
b) For two of the spinners, the probability of spinning orange is more than 40%. To find these spinners, we need to look for the spinners that have at least three orange sectors out of a total of eight sectors (since 3/8 is greater than 40%).
From the given spinners, Spinner A and Spinner C both have three orange sectors out of eight total sectors, so they are the two spinners for which the probability of spinning orange is more than 40%.
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer: C {m | m > 2}
Step-by-step explanation:
write the number in exponential form with the base of 2
2^3m-4 > 2^2
compare the exponents = 3m-4 >2
move the constant to the right and then change the sign
3m> 2+4 add
3m>6 divide
m>2
A bug crawls 5 1/2 feet in 28.6 seconds. At that pace, how many seconds does it take the bug to crawl one foot?
Answer:
5.2 seconds
Step-by-step explanation:
To get one foot, we need to divide by 5.5
Set up a proportion:
[tex]\frac{5.5}{5.5}=\frac{28.6}{5.5}[/tex]
Solve:
[tex]1ft.=5.2secs.[/tex]
y + 6 < 10 or 2y - 3> 9
Answer:
2y - 3> 9 it is not y + 6< 10
Sketch the graph of the following function. Describe how
the graph can be obtained from the graph of the basic
exponential function ex.
f(x) = 2 (4-ex)
Use the graphing tool to graph the equation.
someone help pls, im not sure what to put in the little box for the vertical shift and vertical shrink
The vertical shift and vertical shrink of the exponential function are 2 and 1/2 respectively and the graph of the function is attached below
An exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.
The vertical shift and vertical shrink of the function f(x) = 1/2(4 - eˣ) are 2 and 1/2
The vertical shift = 2
vertical shrink = 1/2
Kindly find the attached graph below
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A card is drawn from a deck of 52 cards. What is the probability that it is a 3 or a spade?
Answer:
P = 4/13 = 0.308
Step-by-step explanation:
3 cards 3
13 spade cards (includes the card 3 of spades)
[tex]P=(3+13)/52= 16/52 = 4/13=0.308[/tex]
Hope this helps.
I have no idea how to solve this problem.
(a) The domain of f of g is {1, 8}.
(b) The range of f of g is {0, 1}.
What is the domain and range of f of g?The domain of f of g consists of all the inputs in the domain of g that are also in the domain of f.
(a) Domain of f of g:
The inputs in the domain of g that are also in the domain of f are 1, and 8. Therefore, the domain of f of g is {1, 8}.
To find the range of f of g, we need to apply the function composition f(g(x)) to each input in the domain of f of g, and collect all the outputs.
(b) Range of f of g:
The range of f of g consists of all the outputs obtained by applying f(g(x)) to each input in the domain of f of g.
We have:
f(g(1)) = f(8) = 0
f(g(4)) = f(2) = 1
f(g(8)) = f(0) = 1
Therefore, the range of f of g is {0, 1}.
Thus, in set notation, the domain of f of g is {1, 8}, and the range of f of g is {0, 1}.
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