Qn2. Two functions f and g are defined as follows: f(x) = 2x – 1 and g(x) = x +4. Determine: i) fg(x) ii) value of x such that fg(x) = 20
Answers
The value of x such that fg(x) = 20 is 6.5.
Find the value of f(x)g(x) by substituting g(x) into f(x):f(x)g(x) = f(x)(x+4) = 2x(x+4) - 1(x+4) = 2x^2 + 8x - 4To find the composite function fg(x), we need to substitute the expression for g(x) into f(x), as follows:
fg(x) = f(g(x)) = f(x + 4) = 2(x + 4) - 1 = 2x + 7
So, fg(x) = 2x + 7
ii) To find the value of x such that fg(x) = 20, we can substitute fg(x) into the equation and solve for x, as follows:
fg(x) = 2x + 7 = 20
2x = 13
x = 6.5
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Related Questions
Marie said that the equivalent decimal amount for 7/12 is 0.583. Is she correct yes or no?
Answers
Answer:
Yes she is correct
Step-by-step explanation:
What are the domain and range of the function F(x) = |x| * 0.015, for x > 0 (sale)
F(x) = |x| *0.005, for x < (return)
Answers
Domain: For sales, x > 0 (positive values); for returns, x < 0 (negative values).
Range: F(x) ≥ 0 (non-negative values).
The given function is defined as follows:
For x > 0 (sale): F(x) = |x| * 0.015
For x < 0 (return): F(x) = |x| * 0.005
The domain of the function is the set of all possible input values, which in this case is all real numbers. However, due to the specific conditions mentioned, the domain is restricted to positive values of x for the "sale" scenario (x > 0) and negative values of x for the "return" scenario (x < 0).
Therefore, the domain of the function F(x) is:
For x > 0 (sale): x ∈ (0, +∞)
For x < 0 (return): x ∈ (-∞, 0)
The range of the function is the set of all possible output values. Since the function involves taking the absolute value of x and multiplying it by a constant, the range will always be non-negative. In other words, the range of the function F(x) is:
For x > 0 (sale): F(x) ∈ [0, +∞)
For x < 0 (return): F(x) ∈ [0, +∞)
In conclusion, the domain of the function F(x) is x ∈ (0, +∞) for sales and x ∈ (-∞, 0) for returns, while the range is F(x) ∈ [0, +∞) for both scenarios.
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QUESTION 4
You and a friend want to create a confidence interval for the proportion of undergraduates at a college who favor eliminating evening exams.
Your friend will choose a simple random sample of 250 students for their confidence interval.
If you choose a simple random sample of 1000 students, your interval will have
A. approximately the same estimate but a smaller margin of error.
OB. approximately the same estimate but a larger margin of error.
C. a smaller estimate and a smaller margin of error.
D. a larger estimate but a smaller margin of error.
E. a larger estimate but a larger margin of error.
Answers
Using a confidence interval of proportions, it is found that the correct option is:
A. approximately the same estimate but a smaller margin of error.
In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(\alpha\), we have the following confidence interval of proportions.
\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)
In which z is the z-score that has a p-value of \(\frac{1+\alpha}{2}\).
The margin of error is given by:
\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)
From this, it is taken that the margin of error is inversely proportional to the sample size, hence, increasing the sample from 250 to 1000 students, the margin of error will be smaller.The sample size has no bearing on the estimate, hence, it stays the same, and option A is correct.
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pooja's plant began sprouting 222 days before pooja bought it, and she had it for 989898 days until it died. at its tallest, the plant was 303030 centimeters tall. h(t)h(t)h, (, t, )models the height of pooja's plant (in centimeters), ttt days after she bought it. which number type is more appropriate for the domain of hhh?
Answers
If Pooja's plant began sprouting 2 days before Pooja bought it, and she had it for 98 days until it died , then the most appropriate for the domain of h is (c) -2 ≤ t ≤ 98 .
The term Domain is defined as the set of its possible inputs .
number of days before which the Pooja's plant sprouted = 2 days ,
the number of days Pooja had the plant is = 98 days ,
the height of the plant is denoted by the function ; h(t) .
where "t" is the number of days after she bought the plant .
From the above data , we can conclude that the domain for the function h(t) is -2 ≤ t ≤ 98 .
Therefore , the correct option is (c) -2 ≤ t ≤ 98 .
The given question is incomplete , the complete question is
Pooja's plant began sprouting 2 days before Pooja bought it, and she had it for 98 days until it died. at its tallest, the plant was 30 centimeters tall. h(t) models the height of Pooja's plant (in centimeters), t days after she bought it. Which number type is more appropriate for the domain of h ?
(a) 0 ≤ t ≤ 30
(b) 0 ≤ t ≤ 100
(c) -2 ≤ t ≤ 98
(d) 2 ≤ t ≤ 30
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Write the equation of the line, in
standard form Ax+By=C, that has a
slope of -4 and passes through the point
(1, -3).
(Do NOT put any spaces between terms
when you type in your answer below.)
Answers
Answer:
4x + y = 1
Step-by-step explanation:
Start with the familiar format of y=mx+b, where m is the slope and b is the y-intercept (the value of y when x = 0).
With a slope of -4, we can write:
y = -4x + b
We need to find a value for b that forces the line through point (1,-3). This is done by entering this point in the equation and solving for b:
y = -4x + b
-3 = -4*(1) + b
b = 1
The equation is y = -4x + 1, This can be rewritten as:
4x + y = 1
Se attached graph.
Tell whether the two ratios form a proportion. 120 baskets made in 3 days and 720 baskets made in 18 days.
Answers
Answer:
Yes they form a proportion.
Step-by-step explanation:
120:3 = 720:18 because:
3x6=18 so multiply 120 by 6 and you get 720. Which means the ratios are proportionate.
HELP!!
enter the terms and the coefficients of the expression.
-60+ 6p - 4z
The terms are
and___,___,____
The coefficients are
and___,____,___
Answers
Answer:
Step-by-step explanation:
Terms Coefficient
-60 -60
6p 6
-4z -4
Answer:
The terms of expression are −30, 6p, and −4z.
The coefficients are 6 and −4.
Find an equation of the tangent line to the curve y=8x at the point (2,64)
Answers
Equation of the tangent line to the curve y=8x is y = 8x + 48.
How do we need to find the slope of the tangent at that point?Derivative of the curve, we get:
dy/dx = 8
This means that the slope of the tangent line to the curve at any point is 8.
So, at the point (2,64), the slope of the tangent line is 8.
By point-slope form of a line, we will find the equation of the tangent line:
y - y1 = m(x - x1)
where m is the slope and (x1,y1) is the given point.
Plugging in the values, we get:
y - 64 = 8(x - 2)
Simplifying, we get:
y = 8x + 48
Equation of the tangent line to the curve y=8x at the point (2,64) is y = 8x + 48.
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1/5 (10x - 5)
whoever answers first and at least looks correct gets brainliest!!!
Answers
Answer:
2x - 1
Step-by-step explanation:
Simplify. Note that you cannot combine a term with a variable with a constant term. Divide 5 from both terms in the parenthesis:
1/5(10x - 5) = (10x - 5)/5
Divide 5 from both terms in the parenthesis:
10x/5 = 2x
-5/5 = -1
2x - 1 is your answer.
~
Answer:
1/5 (10x - 5)
\(taking common \: 5 \: from (10x - 5) \\ 1 \div 5 \times 5(2x - 1)\)
2x-1 is your answer
help plssss it’s timed ty
Answers
Answer:
A is the correct answer m8
Miriam took a taxi from her home to school. The taxi driver charged an initial fee of $4.50 plus $2 per mile. The total fare was $20.50. How many miles did she travel?
Answers
Answer:
8 miles
Step-by-step explanation:
$20.50-$4.50= $16
$16/$2= 8 miles
Hope this helped! :)
The response earned 6 points: 3 points in part (a), no points in part (b), 2 points in part (c), and 1 point in part (d). In part (a) the student uses the initial condition f (−2) with an appropriate definite integral ( ) 2 6 f x dx − − ′ ∫ to find f (− = 6 3. ) Thus, the student earned the first and second points. The student uses f (−2) again with an appropriate definite integral ( ) 5 2 f x dx − ′ ∫ to find f (5 10 2 . ) = − π The student earned the third point. In part (b) the student presents two intervals, [−6, 2) and (2, 5 .) Because f x ′( ) < 0 on (−2, 2 ,) f is decreasing on [−2, 2 .] The student is not eligible to earn any points because of the presence of an interval containing points where f x ′( ) < 0. Thus, the student did not earn any points. In part (c) the student investigates where f x ′( ) = 0 and identifies f ′(−2) and f ′(2 .) The student earned the first point for considering x = 2. The student identifies the absolute minimum value as 7 2. − π The student justifies by evaluating f x( ) at the critical values and endpoints. The student earned the second point. In part (d) the student identifies f ′′(−5) as the derivative of f x ′( ) at x = −5 and finds ( ) 1 5 . 2 f ′′ − =− The student earned the first point. The student states that f ′′(3) does not exist. The student uses two one-sided limits at x = 3. The student states that " f x( ) is not differentiable at x = 3, " which contradicts the given statement in the problem that f is differentiable on the closed interval [−6, 5 .] The student did not earn the second point.
Answers
The student earned a total of 6 points by correctly using definite integrals to find f(-2) and f(2), identifying the critical values and absolute minimum value of f(x) and finding f''(-5).
The student earned a total of 6 points in the problem. They earned 3 points in for using an appropriate definite integral to find f(-2), and another point for using a definite integral to find f(2). They did not earn any points.
In next part, they earned 2 points for identifying where f'(x) = 0, and identifying the absolute minimum value of f(x) at x=2. In part (d), they earned 1 point for finding f''(-5), but did not earn the second point due to a contradiction in their reasoning about the differentiability of f(x) at x=3.
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A pink gold bracelet weighs 60 g. It is made from 76% gold, 18% copper and 6% aluminium.
a What is the mass of the gold in the bracelet?
b What is the mass of the copper in the bracelet?
Answers
Answer:
m(Au)=45.6 [gr] ; m(Cu)= 10.8 [gr].
Step-by-step explanation:
the masses of gold (Au), copper (Cu) and aluminium (Al) are:
0.76*60=45.6 (gr); 0.18*60=10.8 (gr.) and 0.06*60=3.6 (gr).
(NEED ASAP PLEASE ILL MAKE YOU BRAINLIEST ANSWER)
Graph the line that represents a proportional relationship between d and t with the property that an increase of 3 units in t corresponds to an increase of 8 units in d.
What is the unit rate of change of d with respect to t (that is, a change of 1 unit in t will correspond to a changed of how many units in d?)
The unit rate of change is ____
Answers
Answer:
8/3 im pretty sure
Question 9 1 pts Bottles of cream have a normal distribution with mean 8 ounces. You would stop the process if the containers were being filled incorrectly. What is your alternative hypothesis? a.Ha: u not equal to 8 b.Ha: u > 8 c.Ha: u<8
d. None of the other answers is correct.
Answers
The correct alternative hypothesis in this case would be Ha: u not equal to 8, option a. This is because the null hypothesis in this scenario would be that the mean of the bottles of cream being filled is equal to 8 ounces.
The alternative hypothesis, on the other hand, is what we believe to be true if the null hypothesis is proven to be false. In this case, if we were to find evidence that the mean is not equal to 8 ounces, it would lead us to reject the null hypothesis and accept the alternative hypothesis that the mean is in fact different from 8 ounces. Therefore, the alternative hypothesis must be Ha: u not equal to 8, as we are not specifying a direction in which the mean could be different from 8 ounces.The alternative hypothesis for this scenario, where bottles of cream have a normal distribution with a mean of 8 ounces, and you would stop the process if the containers were being filled incorrectly, is:
a. Ha: u ≠ 8
This hypothesis suggests that there is a significant difference between the expected mean of 8 ounces and the actual mean of the filled bottles. If the alternative hypothesis is true, it indicates that the process is not working correctly and should be stopped to address the issue.
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Answer: c
Step-by-step explanation: i took the test and got it right sorry if it is wrong hope it helps
Using a number line, find both the intersection and the union of the following
intervals:
[1, 5] and (0,8]
pls help !
Answers
Answer:
The union of the intervals is (0,8]
The intersection of the intervals is [1,5]
Hope this helped!
Which of the following random variables is discrete? Select the correct response:
O the time spent waiting for a bus at
O the bus stop the number of heads tossed on four distinct coins
O the amount of water traveling over a waterfall in one minute
O the mass of a test cylinder of concrete
Answers
The number of heads tossed on four distinct coins is a discrete random variable.
A discrete random variable can be a count or a finite set of values. Out of the options given in the question, the random variable that is discrete is the number of heads tossed on four distinct coins.
The correct option is: The number of heads tossed on four distinct coins is a discrete random variable.
The time spent waiting for a bus at the bus stop is a continuous random variable because time can take on any value in a given range. The amount of water traveling over a waterfall in one minute is also a continuous random variable because the water can flow at any rate.
The mass of a test cylinder of concrete is also a continuous random variable because the mass can take on any value within a certain range.
The number of heads tossed on four distinct coins, on the other hand, is a discrete random variable because it can only take on certain values: 0, 1, 2, 3, or 4 heads.
Hence, the number of heads tossed on four distinct coins is a discrete random variable.
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BO and OC are the bisector of angle B and angle C of the triangle ABC. Find BOC if BAC = 70 degrees.
For reference please look at the photo above.
Answers
Answer:
BOC= 110 degrees
Step-by-step explanation:
you can refer the above explanation
Find a vector equation with parameter t for the line of intersection of the planes x y z=2 and x z=0.
Answers
The vector equation with parameter t for the line of intersection of the planes x + y + z = 2 and x + z = 0 is r(t) = <0, 2, 0> - t<1, -1, 0>.
To find a vector equation with parameter t for the line of intersection of the planes x + y + z = 2 and x + z = 0, we can solve the system of equations formed by the planes.
First, let's solve for y in terms of x and z from the equation x + y + z = 2. Rearranging the equation, we have y = 2 - x - z.
Now, substitute this expression for y in the equation x + z = 0. We have x + (2 - x - z) + z = 2, which simplifies to 2 - z = 2.
Solving for z, we find z = 0.
Substituting z = 0 into the equation x + z = 0, we have x = 0.
Now that we have the values of x, y, and z, we can form a vector equation for the line of intersection as follows:
r(t) = = <0, 2 - x - z, 0> = <0, 2, 0> - t<1, -1, 0>.
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15(x + 3)2
Box the exponent (s)
please help
Answers
Answer:
"2" is the exponent
Step-by-step explanation:
There is no exponent in your expression.
__
When the expression is typeset, the superscript text is considered to be an exponent:
\(15(x+3){\boxed{^2}}\)
When the expression is written in plain text, the exponent is indicated by a caret (^):
\(\textsf{15(x+3)\^\ \!\!\boxed{\textsf{2}}}\)
Answer:
\( {15x}^{2} + 90x + 135 \\ \)
Step-by-step explanation:
\(15 {(x + 3)}^{2} \\ 15(x + 3)(x + 3) \\ 15 |(x(x + 3) + 3(x + 3)| \\ 15( {x}^{2} + 3x + 3x + 9) \\ 15( {x}^{2} + 6x + 9) \\ {15x}^{2} + 90x + 135 \\ \)
HELP!! PLS
Find the values of x and y in parallelogram PQRS.
PT=y, TR= 2x + 1, QT=3y. TS = 3x +9
Answers
Step-by-step explanation:
In a parallelogram, opposite sides are equal and parallel. Therefore,
QT = PS = 3y ...(1)
PT + TR = PS
y + 2x + 1 = 3x + 9
2x - y = 4 .....(2)
PR = QT = 3y
PR = SQ = 3x + 9 ....(3)
From equations (1) and (3), we can see that:
3y = 3x + 9
y = x + 3
Substitute this value of y in equation (2):
2x - (x + 3) = 4
x = 7
To find the value of y, we can substitute x = 7 in equation (2):
2(7) - y = 4
y = 10
Therefore, x = 7 and y = 10.
circle $c$ has radius 10 cm. how many square centimeters are in the area of the largest possible inscribed triangle having one side as a diameter of circle $c$?
Answers
100 square centimeters are in the area of the largest possible inscribed triangle having one side as a diameter of circle.
What is the area?
A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface. In general, square units such as square inches, square feet, etc. are used as the standard unit of area.
Base = 2r = 2*10 = 20 cm
Height = r= 10 cm
Area = 1/2 * base * height
= 1/2 * 20 * 10
= 100 square centimeters
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From the choices below, select all the numbers that could be solutions
to:
A
2x + 5 - 3x < 10
Answer choice:
-10
5
-5
0
-4
Answers
Answer:
0, -4 and 5
Step-by-step explanation:
Given the inequality
2x + 5 - 3x < 10
Collect the like terms
2x-3x < 10 - 5
-x < 5
multiply both sides by -1
-1(-x) > -1(5)
x > -5
Hence the values that are greater than -5 are 0, -4 and 5
(50 points) Compare the two functions represented on the right.
Which of the functions has the greatest rate of change?
Which of the functions has the greatest y-intercept?
Answers
Answer:
The graph has a greater rate of change and y-intercept.
Slope is 3/4 and y-intercept is about -1 which is greater than the one in the equation.
Step-by-step explanation:
Hope this helps. Pls give brainliest.
Which ordered pairs match the mapping diagram? O (1, 0), (7, 2), (3, 1), (-1, 1), (-7, -6) (0, 1), (2, 7), (3, 4), 4, 1), -6, 7) O(0, 1), (0, 4), (0, 7), (2, 7), (6, 7) (0 1), (2, 7), 3, 4), (4, 1), (6, 7)
Answers
Answer:
I've done this b4
(0, 1), (2, 7), (3, 4), (-4, 1) , (-6, 7)
.Solve 3 ( x - 4 ) = -6 for x
Answers
Answer:
2
Step-by-step explanation:
3(x-4)=-6
3x - 12 =-6
3x=- 6 +12
3x =6
x =6 :3
x=2
your favorite restaurant has a promotion where you can win free food. you will roll 2 dice. the sum of the 2 dice will determine which prize you receive. 2-column table with 11 rows. column 1, outcome, entries 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. column 2, probability, entries startfraction 1 over 36 endfraction, startfraction 2 over 36 endfraction, startfraction 3 over 36 endfraction, startfraction 4 over 36 endfraction, startfraction 5 over 36 endfraction, startfraction 6 over 36 endfraction, startfraction 5 over 36 endfraction, startfraction 4 over 36 endfraction, startfraction 3 over 36 endfraction, startfraction 2 over 36 endfraction, startfraction 1 over 36 endfraction. which scenario uses the addition rule for mutually exclusive events? p(rolling a sum of 4) p(rolling a sum of 4 or rolling a sum of 5) p(rolling a sum of 12 or rolling a double 6) p(rolling a sum of 11 and rolling a sum of 12)
Answers
Answer: P(rolling a sum of 4 or rolling a sum of 5)
Step-by-step explanation: edge2023
The scenario that uses the addition rule for mutually exclusive events is:
p(rolling a sum of 4 or rolling a sum of 5) = p(rolling a sum of 4) + p(rolling a sum of 5)
This is because the events "rolling a sum of 4" and "rolling a sum of 5" are mutually exclusive, meaning that they cannot occur at the same time. Therefore, the probability of either event occurring is the sum of their individual probabilities.
The probability of rolling a sum of 4 is 3/36, and the probability of rolling a sum of 5 is 4/36. The addition rule states that the probability of rolling a sum of 4 or 5 is the sum of their individual probabilities: 3/36 + 4/36 = 7/36
The other scenarios do not use the addition rule for mutually exclusive events:
p(rolling a sum of 4) is a single event and does not involve a second event.
p(rolling a sum of 12 or rolling a double 6) although the two events are mutually exclusive, it's not the sum of their individual probabilities.
p(rolling a sum of 11 and rolling a sum of 12) these events are not mutually exclusive, they can happen at the same time, so it's not the sum of their individual probabilities.
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The number of days between May 20 and November 22 is: Multiple Choice O None of these O 186 O 183 O 197 O 206
Answers
The number of days between May 20 and November 22 is 182 days. Option C, 183 is the closest answer to the correct answer.
To determine the number of days between May 20 and November 22, we first need to determine the number of days in each month. Here are the days in each month of the year: January: 31 days, February: 28 days (or 29 in a leap year)March: 31 days, April: 30 days, May: 31 days, June: 30 days, July: 31 days, August: 31 days, September: 30 days, October: 31 days, November: 30 days, December: 31 days. Using the formula D = (M2 - M1) × 30 + (D2 - D1) where D is the number of days, M is the month, and D is the date, we can calculate the number of days between May 20 and November 22:D = (11 - 5) × 30 + (22 - 20)D = 6 × 30 + 2D = 180 + 2D = 182.
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Find the union and the intersection of the given intervals I₁=(-2,2]; I₂=[1,5) Find the union of the given intervals. Select the correct choice below and, if necessary, fill in any answer boxes within your choice A. I₁ UI₂=(-2,5) (Type your answer in interval notation.) B. I₁ UI₂ = ø Find the intersection of the given intervals Select the correct choice below and, if necessary, fill in any answer boxes within your choice. A. I₁ ∩I₂ (Type your answer in interval notation) B. I₁ ∩I₂ = ø
Answers
To find the union and intersection of the intervals I₁ = (-2, 2] and I₂ = [1, 5), let’s consider the overlapping values and the combined range.
The union of two intervals includes all the values that belong to either interval. Taking the union of I₁ and I₂, we have:
I₁ U I₂ = (-2, 2] U [1, 5)
To find the union, we combine the intervals while considering their overlapping points:
I₁ U I₂ = (-2, 2] U [1, 5)
= (-2, 2] U [1, 5)
So the union of the intervals I₁ and I₂ is (-2, 2] U [1, 5).
Now let’s find the intersection of the intervals I₁ and I₂, which includes the values that are common to both intervals:
I₁ ∩ I₂ = (-2, 2] ∩ [1, 5)
To find the intersection, we consider the overlapping range between the two intervals:
I₁ ∩ I₂ = [1, 2]
Therefore, the intersection of the intervals I₁ and I₂ is [1, 2].
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jen smith has decided to become her own boss after spending 5 years as an assistant manager for a restaurant. the owner of a local sandwich store wants to sell the store to jen for $65,000 to be paid in installments of $13,000 in each of the next 5 years. according to the current owner, the store brings in revenue of about $110,000 per year and incurs operating costs of about 63% of sales. thus, once the store is paid for, jen should make about $35,000 -$40,000 per year before taxes. until the store is paid for, she will make substantially less-but she will be her own boss. realizing that some uncertainty is involved in this decision, jen wants to simulate what level of net income she can expect to earn during the next 5 years as she operates and pays for the store. in particular, she wants to see what could happen if sales are allowed to vary based on a normal distribution with mean of $100,000 and standard deviation of $10,000, and if operating costs are allowed to vary uniformly between 60% and 65% of sales. assume that jen's payments for the store are not deductible for tax purposes and that she is in the 28% tax bracket. a. create a spreadsheet model to simulate the annual net income jen will receive during each of the next five years if she decides to buy the store. (3 points) b. given the money she has in savings; jen thinks she can get by for the next five years if she can make at least $12,000 from the store each year. run 100 simulation (replication) and find the probability that jen will make at least $12,000 in each of the next five years? (1 point) c. what is the probability (based on 100 simulation) that jen will make at least $60,000 total over the next five years? (1 point)
Answers
Jen simulated her net income over 5 years assuming sales vary based on a normal distribution $100,000 and operating costs 60% and 65% of sales. keeping the loan payment be fixed at $13,000. The probability of making at least $12,000 each year is the number of successful simulations divided by 100. and at least $60,000 total over 5 years based as the number of successful simulations divided by 100.
To simulate Jen's annual net income over the next 5 years, a spreadsheet model can be created with columns for year, sales, operating costs, loan payment, and net income.
For each year, the sales can be generated from a normal distribution with mean $100,000 and standard deviation $10,000, and the operating costs can be generated from a uniform distribution between 60% and 65% of sales.
The loan payment can be fixed at $13,000, and the net income can be calculated as the difference between the sales, operating costs, loan payment, and taxes (28% of net income).
To find the probability that Jen will make at least $12,000 in each of the next five years, 100 simulations can be run using the model created in part a. For each simulation, the net income for each of the next five years can be calculated, and if the minimum net income is at least $12,000 for each year, then the simulation is counted as a success.
The probability of success can be calculated as the number of successful simulations divided by 100.
To find the probability that Jen will make at least $60,000 total over the next five years, 100 simulations can be run using the model created in part a. For each simulation, the total net income over the next five years can be calculated, and if it is at least $60,000, then the simulation is counted as a success.
The probability of success can be calculated as the number of successful simulations divided by 100.
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