7 teams compete in a track competition. if there are 20 events in the competition, no event ends in a tie, and no team wins more than 3 events, what is the minimum possible number of teams that won at least one event?
Answers
7 teams compete in a track competition. If there are 20 events in the competition, no event ends in a tie, and no team wins more than 3 events, the minimum possible number of teams that won at least one event is 7.
The answer is 7.
The ' no event in a tie' implies there is only two possible outcomes for an event either they win or they lose. This is a limiting problem as they have given no team wins more than 3 events.
Now let us assume only 6 teams win at least once. So we know that out of the twenty events, 6 events are team 1 to 6 winning. There are 14 events remaining and 7th team would not win as it will contradict our assumption.
So now let us consider team 1 wins not just once, but thrice. They cannot win more than 3 as it is given no team wins more than 3 events. This makes 12 events remaining (20-5×1-1×3).
So let us now consider all the 6 teams win at least thrice, then 2 events are remaining (20 - 6×3). But no team can win more than 3 and there is no case of tie. So our assumption is false and 7th team has to win at least twice. So in the given case 7 teams has to win at least once.
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Related Questions
Alex has 70% of her weekly paycheck automatically deposited in her savings account. This week, $35 is deposited. Alex wants to know the total amount of her paycheck this week.
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What is the expected value?
Answers
Answer:
2.1
Step-by-step explanation:
The expected value of a probability is given by the formula:
E(x) = Σxp(x)
Therefore from the table showing the winnings of a game, the expected value of the probability distribution is:
E(x) = Σxp(x) = (0 * 0.5) + (2 * 0.2) + (4 * 0.15) + (6 * 0.1) + (10 * 0.05)
E(x) = 0 + 0.4 + 0.6 + 0.6 + 0.5 = 2.1
Hence we can conclude that the expected value of the winnings of the game is 2.1.
6. why is profitability alone not an adequate measure of a project's value to an organization
Answers
Probability Distributions for Discrete Random Variables
Which of the following are discrete random variables?
Select all that apply
1-The number of CDs that a college student owns
2- The number of dogs you own
3- The amount of gas in your car
4- Number of 6s you get when you throw 5 number cubes
5- The number of dog sleds that a competitor uses in an annual sled dog race
Answers
The discrete random variables from the given options are: 1, 2, 4, and 5.
The number of CDs that a college student owns: This is a discrete random variable because the number of CDs can only be a whole number. You cannot have a fractional or continuous value for the number of CDs.
The number of dogs you own: This is a discrete random variable because you can only own a whole number of dogs. You cannot own a fractional or continuous number of dogs.
Number of 6s you get when you throw 5 number cubes: This is a discrete random variable because the number of 6s can only be a whole number from 0 to 5. You cannot have a fractional or continuous value for the number of 6s obtained.
The number of dog sleds that a competitor uses in an annual sled dog race: This is a discrete random variable because the number of dog sleds can only be a whole number. You cannot have a fractional or continuous value for the number of dog sleds used.
On the other hand, the following option is not a discrete random variable:
The amount of gas in your car: This is a continuous random variable because the amount of gas can be any non-negative real number. It can have fractional or continuous values, such as 10.5 liters or 20.25 gallons. Option 1,2,3,4 and 5
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Use curve sketching guidelines to sketch y = x + 3 a) Give the domain in interval notation. b) Identify the Intercepts if any. c) Determine whether there's symmetry. d) Determine any horizontal, vertical or slant asymptotes if they exist. e) Find f 'to determine Intervals of Increase/Decrease. f) Find f" to determine the concavity and any Inflection Point(s). g) Use your answers above to generate the graph of y.
Answers
a) Domain: (-∞, +∞)
b) Intercepts: x-intercept at (-3, 0)
c) Symmetry: No symmetry
d) Asymptotes: No horizontal, vertical, or slant asymptotes
e) Intervals of Increase/Decrease: Increasing for all x
f) Concavity/Inflection Points: Constant concavity, no inflection points
g) Graph: A straight line with a positive slope intersecting the y-axis at (0, 3) and the x-axis at (-3, 0)
a) The domain of the function y = x + 3 is (-∞, +∞) since there are no restrictions on the input x. The graph y=x+3 is sketched below.
b) To find the intercepts, we set y = 0 and solve for x:
0 = x + 3
x = -3
Therefore, the function intersects the x-axis at (-3, 0).
c) There is no symmetry in the function y = x + 3 because it is a linear function.
d) Since y = x + 3 is a linear function, there are no horizontal or vertical asymptotes. Similarly, there are no slant asymptotes.
e) To find the intervals of increase and decrease, we need to find the derivative f'(x):
f'(x) = 1
The derivative f'(x) = 1 is positive for all values of x. This means that the function is always increasing.
f) To find the concavity and any inflection points, we need to find the second derivative f''(x):
f''(x) = 0
The second derivative f''(x) = 0 is always zero for the function y = x + 3, indicating a constant concavity of the function. There are no inflection points.
g) Based on the information above, we can generate the graph of y = x + 3. Since it is a linear function with a positive slope and no inflection points, the graph will be a straight line slanting upwards. It will intersect the y-axis at (0, 3) and the x-axis at (-3, 0).
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HELP! FAST! I'LL GIVE BRAILYEST!!!!
Answers
Answer:
Last one
Option D is correct
2x^3 - 7x^2 + 4x - 3
Step-by-step explanation:
= x(2x^2 - x + 1) -3 (2x^2 - x + 1)
= 2x^3 - x^2 + x - 6x^2 + 3x - 3
= 2x^3 - x^2 - 6x^2 + x + 3x - 3
= 2x^3 -7x^2 + 4x -3 (Ans)
polydactyly is a fairly common congenital abnormality in which a baby is born with one or more extra fingers or toes. it is reported in about one child in every 500 . a young obstetrician celebrates her first 100 deliveries. assuming that these 100 births are unrelated and independent, what is the probability that the obstetrician has delivered no child with polydactyly? (enter your answer rounded to four decimal places, for example, 0.1111.)
Answers
The probability that the obstetrician has delivered no child with polydactyly is 0.8187.
To find the probability that the obstetrician has delivered no child with polydactyly, we can use the formula:
P(no polydactyly) = \((1 - P(polydactyly))^{number of births}\)
First, we need to find the probability of a child having polydactyly. This is given as 1 in every 500, which can be expressed as a decimal: 1/500 = 0.002.
Next, we find the probability of a child not having polydactyly: 1 - 0.002 = 0.998.
Now, we can find the probability of the obstetrician delivering no child with polydactyly in 100 unrelated and independent births by raising the probability of no polydactyly to the power of the number of births (100):
P(no polydactyly in 100 births) = (0.998)¹⁰⁰ ≈ 0.8187
So, the probability that the obstetrician has delivered no child with polydactyly is approximately 0.8187.
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A group of students and teachers are going on a field trip. One-ninth of the group will fit on 1/3 of a school bus. How many buses are
needed to transport the entire group?
Answers
Answer: 3 buses
Step-by-step explanation:
a group of students and teachers are going on a field trip. one ninth of the group will fit on 1/3 of a school bus how many buses are needed to transport the entire group
1/9g = 1/3b
We want to find g, so we multiply each side through by 9
g = 9/3b
Simplify:
g = 3b, so we need 3 buses
5/7 = a/35 what is the answer ?
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.........
.............
Answer:
hello! I am pretty sure the missing number is 25!
Step-by-step explanation:
Here is why I think so, I believe that because it seems to me that you are multiplying 7 by 5 so I think that you should multiply 5 by 5 and if you do that it is 25. Hope this helps!
very unsure of this answer so pls help asap if you can!!
Answers
The following can be shown about the diagonals of parallelogram PQRS to compare the proof that diagonals of a parallelogram bisect each other: B. PR and SQ have the same midpoint.
What is a parallelogram?In Mathematics and Geometry, a parallelogram is a geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that has two (2) equal and parallel opposite sides.
In order for any quadrilateral to be considered as a parallelogram, two pairs of its parallel opposite sides must be equal (congruent). This ultimately implies that, the diagonals of a parallelogram would bisect one another only when their midpoints are the same:
(Line segment PR)/2 = (Line segment SQ)/2
Line segment PR = Line segment SQ
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What is an equation of the line that passes through the points (6, -6) and (-6, -8)
Answers
Answer:
An equation of the line that passes through the points (6, -6) and (-6, -8) is \(\mathbf{y+6= \frac{1}{6}(x-6)}\)
Step-by-step explanation:
We need to write an equation of the line that passes through the points (6, -6) and (-6, -8)
We would use point slope formula: \(y-y_1=m(x-x_1)\)
where \(x_1=6, y_1=-6 \ and \ m \ is \ slope\)
Finding slope using formula: \(Slope=\frac{y_2-y_1}{x_2-x_1}\\\)
We have \(x_1=6, y_1=-6, x_2=-6, y_2=-8\)
Putting values and finding slope
\(Slope=\frac{y_2-y_1}{x_2-x_1}\\\\Slope=\frac{-8-(-6)}{-6-6}\\Slope=\frac{-8+6}{-12}\\Slope=\frac{-2}{-12}\\Slope=\frac{1}{6}\)
So, slope = 1/6
The required equation having \(x_1=6, y_1=-6 \ and \ m =\frac{1}{6}\)
\(y-(-6)=\frac{1}{6}(x-6)\\y+6= \frac{1}{6}(x-6)\)
An equation of the line that passes through the points (6, -6) and (-6, -8) is \(\mathbf{y+6= \frac{1}{6}(x-6)}\)
Water vapor constitutes about this much of the atmosphere by volume.
-0-4 percent
-4-12 percent
-0-12 percent
-0-100 percent
-4-25 percent
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Water vapor is an important component of the Earth's atmosphere, and it plays a crucial role in regulating the climate. water vapor makes up about 0-4% of the Earth's atmosphere by volume . So the correct option is A.
It is a greenhouse gas, which means that it can trap heat in the atmosphere and contribute to global warming. The amount of water vapor in the atmosphere can vary depending on location, temperature, and weather conditions. On average, water vapor makes up about 0-4% of the Earth's atmosphere by volume. This may seem like a small amount, but it has a significant impact on weather patterns and climate. As temperatures rise due to climate change, the amount of water vapor in the atmosphere is expected to increase, which could have further impacts on global climate.
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what geometric shape forms the hole that fits an allen wrench
Answers
Answer:
A hexagon
Step-by-step explanation:
A hexagon - - - the allen wrench has 2 hexagonal heads. See attached pic.
The geometric shape that forms the hole that fits an allen wrench is a hexagon, which is a six-sided polygon with straight sides and angles.
The geometric shape hexagon-shaped hole in an allen wrench, also known as a hex key, is designed to fit tightly over the hexagonal socket of a screw or bolt head. A hexagon is a six-sided polygon, meaning it has six straight sides and angles. In the case of an allen wrench, the hexagon has internal angles of 120 degrees and opposite sides that are parallel.
The hexagonal shape of the hole in the wrench allows for a tight and secure fit onto the corresponding hexagonal socket of the screw or bolt head. This design ensures that the wrench can apply a significant amount of torque to the fastener without slipping, which is essential for many applications in construction, mechanics, and other industries.
The use of a hexagonal shape also allows for greater precision and control when turning the screw or bolt, making it easier to achieve the desired level of tightness. Overall, the hexagon is an ideal shape for the hole in an allen wrench due to its strength, stability, and precision.
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Tekan-Tekan Sdn. Bhd. has order for 200 Model AS-120 calculator for delivery on day 200. The calculator consists of three parts. Components 2 and 3 form subassembly 1 . Sub-assembly 1 and component 4 form the final assembly. Following are the work centers and times of each operation. Table Q3(a) shows routine file of the operation. Assuming: - Only one machine is assigned to each operation - The factory works on 8-hour shift, 5 days a week - All parts move in one lot of 200. (a) Illustrate the backward schedule based on the information given above. (12 marks) (b) Identify when component 3 must be started to meet the delivery date. (2 marks)
Answers
Component 3 must be started on day 197 to meet the delivery date of day 200.
To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.
(a) Backward schedule:
Operation | Work Center | Time (hours) | Start Day
--------------------------------------------------------
Final Assembly | Work Center 1 | 1 | 200
Sub-assembly 1 | Work Center 2 | 2 | 199
Component 4 | Work Center 3 | 3 | 197
Component 2 | Work Center 4 | 4 | 196
Component 3 | Work Center 5 | 3 | ????
(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.
From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.
Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.
Hence, component 3 must be started on day 197 to meet the delivery date of day 200.
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To be considered 18-karat (18K) gold, a piece of jewelry must be made of 75% pure gold. The higher the karats, the more valuable a piece of jewelry. A jewelry designer is purchasing a large quantity of 18K gold from a new supplier. To see if the new supplier is being dishonest about the karat rating in the shipment, the designer melts a random sample of the gold and conducts a hypothesis test with H0: The proportion of metal that is gold is 75%, and Ha: The proportion of metal that is gold is less than 75%. What is a Type I error and its consequence in this context
Answers
Answer:
The gold shipment truly is made of 75% gold, but the designer concludes that it is made of less than 75% gold. The designer will reject the shipment of gold and miss out on an honest business relationship with the supplier.
Step-by-step explanation:
Type I error is defined as the rejection of the true null hypothesis. It is also called as the 'false positive' conclusion or 'false positive' findings. The value of alpha or the significance level determines the probability of making the error type I.
In the context, it is given that for a gold piece to be of 18 karat , the piece of jewelry must be made of 75% of pure gold.
The null hypothesis is, H0: The proportion of metal that is gold is 75%
The alternative hypothesis is Ha: The proportion of metal that is gold is less than 75%.
Thus the type I error is when the gold shipment is made of 75% gold but the jewelry designer rejects the shipment thinking that the shipment is made of less than 75% gold.
Thus it shows the error of type I rejecting the null hypothesis.
Write the equation of a line through (1,2), parallel to y=4x+1O y=-4x-2O y=-2x+5O y=4x-2O y=5x-2
Answers
The slope of the line y = 4x + 1 is 4 because is the number beside the x.
Then, the equation of a line through (1,2) needs to have the same slope.
So, we can calculate the equation using the following equation:
\(y-y_1=m(x-x_1)\)Where m is the slope and (x1, y1) is a point in the line.
Replacing m by 4 and (x1, y1) by (1, 2), we get:
\(\begin{gathered} y-2=4(x-1) \\ y-2=4x-4 \\ y-2+2=4x-4+2 \\ y=4x-2 \end{gathered}\)Answer: y = 4x - 2
What is |3|? I need help
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on a 50-question multiple choice math contest, students receive 4 points for a correct answer, 0 points for an answer left blank, and $-1$ point for an incorrect answer. jesse's total score on the contest was 99. what is the maximum number of questions that jesse could have answered correctly?
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The maximum number of questions Jesse could have answered correctly is 36.
Let's assume Jesse answered x questions correctly. Since there are 50 questions in total, Jesse must have attempted 50 - x questions incorrectly or left blank.
For each correct answer, Jesse receives 4 points, so the total points for correct answers would be 4x. For incorrect answers, Jesse loses 1 point for each, resulting in a deduction of (50 - x) points. The total score is given as 99.
We can now set up an equation to represent this situation:
4x - (50 - x) = 99
Simplifying the equation, we get:
5x - 50 = 99
5x = 149
x = 29.8
Since x represents the number of questions answered correctly, it must be a whole number. Therefore, the maximum number of questions Jesse could have answered correctly is 36 (as 35 would result in a score of 140, which is greater than 99
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Please help due in 10 minutes!!!!!!!
Answers
Answer:
23.42 ft is the perimeter of the hole that should be cut in the wall.
WILL GIVE BRAINLIEST IMMEDIATELY. CORRECT ANSWER + EXPLANATION REQUIRED FOR BRAINLIEST. NO LINKS OR FAKE ANSWERS! IF YOU PUT A LINK OR FAKE ANSWER I WILL REPORT YOU!!!
look at the photos for question, diagram, and answer choices :)
Answers
Answer: A. alternate interior angles
Step-by-step explanation:
Line 2 (l₂) and Line 3 (l₃) will be the focus of this question. Since both angle 3 and angle 5 are inside of the lines, they are interior angles. Since they are on alternate sides of the central line (t₁), they are alternate angles. Since they are both alternate and interior angles, they are alternate interior angles.
A water tank can be filled by an inlet pipe in 8 hours. It takes 3 times as long for the outlet pipe to empty the tank. How long will it take to fill the tank if both pipes are open
Answers
If both pipes are open, the outlet pipe will empty the tank faster than the inlet pipe can fill it, and the tank will never be filled.
Let us consider the work done by the inlet pipe as positive (+) and the work done by the outlet pipe as negative (-). Suppose the work done by the inlet pipe is represented as x, and the work done by the outlet pipe is -3x.
We know that the time taken by the inlet pipe to fill the tank is 8 hours. Therefore, we can determine the rate of work of the inlet pipe as:
Rate of work = Work done / Time taken = x / 8
Since the outlet pipe is emptying the tank, its rate of work is negative. We are given that it takes 3 times as long for the outlet pipe to empty the tank compared to the inlet pipe to fill it. Thus, the outlet pipe takes 8 x 3 = 24 hours to empty the tank, and its rate of work is:
-3x / 24 = -x / 8
The question asks how long it will take to fill the tank if both pipes are open. When both pipes are open, their rates of work add up. Hence, we can state that:
Rate of work of both pipes = x / 8 - x / 8 = 0
We know that work done is given by the equation: Work done = Rate of work x Time taken
Therefore, the work done by both pipes is: 0 x t = 0, where t represents the time taken to fill the tank with both pipes open. This implies that the work done by the inlet pipe must equal the work done by the outlet pipe. In other words:
x = -3x / 24
Multiplying both sides by 24 gives us:
24x = -3x
Simplifying this equation yields:
27x = 0
x = 0
Thus, the inlet pipe and outlet pipe cancel each other out when they are open together. This means that the tank will never get filled. However, this scenario is impossible given the fact that the tank can be filled by the inlet pipe alone in 8 hours.
Therefore, it is not possible to fill the tank if both pipes are open. The reason is that the outlet pipe takes 24 hours to empty the tank, which is three times as long as it takes the inlet pipe to fill it. Consequently, if both pipes are open, the outlet pipe will empty the tank faster than the inlet pipe can fill it, and the tank will never be filled.
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Determine if the expression 9y^5+ y − 3y^3is a polynomial or not. If it is a
polynomial, state the type and degree of the polynomial.
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PLEASE HELP SUPER EASY MATH PROBLEM WILL MARK BRAINLIEST
Answers
Answer:
m∠5 = 67
m∠7 = 67
Step-by-step explanation:
m∠4 and m∠5 add up to 180 because they are same side interior angles.
180 - 113 = m∠5
m∠5 = 67
m∠5 = m∠7 because they are vertically opposite angles
hence, m∠7 = 67 degrees
Answer:
angle 5: 67 degrees. Angle 7: 67 degrees. (make sure to add the degrees logo)
Step-by-step explanation:
basically, angle 4 is 113 degrees. 180 degrees minus 113 is 67, which is how much angles 1 and 3 are. angles one and three are also equivalent to 5 and 7, which means they are also 67 degrees
What is the y-intercept of the function f(x)= -4(6)^x +1
a) (0, 1)
b) (0, -3)
c) (-4, 0)
d) (-0.774, 0)
Answers
Answer plz and do y’all wanan start a chat
Answers
Answer:
Sorry, no thanks
Step-by-step explanation:
The answer for the equation is A and B... I think
Answer:
A B that is what I think the answer is
prove that: tan[(π/4)+(x/2)] + tan[(π/4)-(x/2)]= 2secx
Answers
we will use the formula of tan(A+B)= (tanA+tanB)/(1-tanAtanB)
and tan(A-B)= (tanA-tanB)/(1+tanAtanB)
tan[(pie/4)+(x/2)]= [1+tan(x/2)]/[1-tan(x/2)] ......(1)
tan[(pie/4)-(x/2)]= [1-tan(x/2)]/[1+tan(x/2)]......(2)
now add the equation (1) and (2) which is LHS of question. So we get:
{[1+tan(x/2)]^2 + [1- tan(x/2)]^2}/1-tan^2(x/2)=2[1+tan^2(x/2)]/1-tan^2(x/2)= 2/cosx = 2secx =RHS
Hence proved.
What are the first 3 consecutive odd numbers?
Answers
The first 3 consecutive odd numbers are 1,3,5. x and x + 2 are consecutive odd numbers if x is an odd number.
Consecutive numbers are those that always appear in the same order, from smallest to largest.
For instance:
The numbers 1, 2, 3, 4, 5, 6, and so on are consecutive.
consecutive odd numbers:
Let's call the odd number "x." The subsequent term becomes "x + 4" and the next consecutive odd number becomes "x + 2."
Numbers that begin with 1, 3, 5, 7, or 9 are considered odd. 1, 3, 5, 7, 9, 11, 13, 15, and so on are examples of consecutive odd numbers.
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Please help asap calculate the slope of the line through the points (6,-8) and (3,-4).
a. Write the equation of the line
b. Is the point (-3,4) on the line you found in part a?
Answers
Answer: y = -4/3x + 0. Yes, that point lies on the line
Step-by-step explanation:
Use this equation, Δy/Δx and this one, y = mx + b. Or, change in the y value divided by the change in the x value.
-4 + 8 = 4
3 - 6 = -3
The slope, m, is -4/3. Now solve for b by plugging in the slope.
\(-4 = \frac{-4}3 (3) + b\). B is equal to 0
To see if that point lies on the function, plug it in the equation and see if it is true. Multiply -4 x -3 to get 12, divide by 3 to get 4, then add 0. The equation says that 4 = 4, which is infact true
Answer:
y=-4x/3
the point (-3,4) is on the line y= -4x/3
Step-by-step explanation:
the points (6,-8) and (3,-4)
a) (y- y1)/(y2- y1)=(x- x1)/(x2- x1)
(y+8)/(-4+8)=(x-6)/(3-6)
(y+8)/4=(x-6)/(-3)
-3y-24=4x-24
So, y=-4x/3
b) (-3; 4)
4= -4*(-3)/3
4=4 it is true,
the point (-3,4) is on the line y= -4x/3
I need help with this problem please
Answers
Answer:
see picture... In simpler terms, take each point and count Ys down to the line (P=1) (don't count the line) then count that many down from the line.
Works the same with vertical lines except do Xs not Ys.
Step-by-step explanation: given P=1... orange line is the origin, don't forget to count it
coordinates of old shape
red (-2,7)
green (-6,8)
Blue (-6,6)
Black (-4,4)
NEW SHAPE
red (-2,-4)
green (-6,-5)
blue (-6,-3)
black (-4,-1)
Suppose that t years from now, one investment plan will be generating profit at the rate of P₁ (t) = 60e0.0⁹t thousand dollars per year, while a second investment will be generating P₂(t) = 130e0.05t thousand dollars per year. a. For how many years does the rate of profitability of the second investment exceed that of the first? Answer: b. Compute the net excess profit, in thousands of dollars, assuming that you invest in the second plan for the time period determined in part a. Answer: c. Sketch the rate of profitability curves y = P₁ (t) and y = P₂ (t) and shade the region whose area represents the net excess profit computed in part b. There is nothing to submit here unless your instructor asks for your sketch.
Answers
Given, P1 (t) = 60e0.09t thousand dollars per yearP2(t) = 130e0.05t thousand dollars per year For how many years does the rate of profitability of the second investment exceed that of the first? To find the time period in which P2(t) exceeds P1(t), we need to equate both.130e0.05t = 60e0.09t
Let us take the natural log of both sides: ln(130) + 0.05t = ln(60) + 0.09t0.04t = ln(130) - ln(60)t = (ln(130) - ln(60)) / 0.04 = 15.63Thus, it takes approximately 15.63 years for the rate of profitability of the second investment to exceed that of the first. Therefore, the answer is 15.63 years. Let us compute the net excess profit, in thousands of dollars, assuming that we invest in the second plan for the time period determined in part a. Net excess profit = ∫[P2(t) - P1(t)] dt where t goes from 0 to 15.63.Substituting the given functions, we get Net excess profit = ∫[130e0.05t - 60e0.09t] dt where t goes from 0 to 15.63= [2.6e0.05t - 0.6667e0.09t] from 0 to 15.63= [2.6e0.05(15.63) - 0.6667e0.09(15.63)] - [2.6e0.05(0) - 0.6667e0.09(0)]= [2.6e0.7815 - 0.6667] - [2.6 - 0.6667e0]= $81.39 thousands Therefore, the net excess profit is $81.39 thousands. Hence the answer is 81.39 thousands of dollars.
The rate of profitability of the second investment exceeds that of the first after 15.63 years. If we invest in the second plan for the time period of 15.63 years, we will make an excess profit of $81.39 thousand.
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