# Study Questions for Exam

Anonymous
timer Asked: Dec 22nd, 2017
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Question description

1. You randomly survey people in the mall about whether or not they regularly use text messaging. The results are shown in the tally sheets below based on the people’s ages. a.Make a two-­way table that includes the marginal frequencies. b.Make a two­-way table that shows both the joint and marginal relative frequencies. Round to the nearest hundredth, if necessary. c.What is the probability that someone who is between the ages of 20-29 also texts regularly? d.What is the probability that someone who is between the ages of 40-49 also texts regularly? e.Does the data show a relationship between age and texting? Explain. 2. The data below represents the number of hits on your web site over 10 months. a.Make a scatter plot of ln ​y​ versus ​x​. Use the scatter plot to find the equation for the line of best fit. b.Make a scatter plot of ln ​y​ versus ln ​x​. Use the scatter plot to find the equation for the line of best fit. c.Based on your answers in part a and b, would an exponential model or a power model be better to represent this data? Explain. d.Use your answers from parts a and b to find an exponential model and a power model to represent this data by hand. e.Use the regression feature on your calculator to find an exponential model and a power model to represent this data. f.Use your answer from parts c and d to make the ​best​ estimate for the number of hits your web site will have in 12 months.

Study Questions For Upcoming Exam 1. Solve the system of equations below both algebraically and by graphing. Be sure to show all of your work and state your solution as an ordered pair. 2. The population of a country is initially 2.5 million people and is increasing by 0.8 million people every year. The country’s annual food supply is initially adequate for 4 million people and is increasing at a constant rate for an additional 0.4 million people per year. a. Based on these assumptions, in approximately how many years will the country first experience shortages of food? b. If the country doubled its initial food supply and maintained a constant rate of increase in the supply adequate for an additional 0.5 million people per year, would shortages still occur? If so, how many years would it take for shortages to occur? If not, explain. c. If the country doubled the rate at which its food supply increases, in addition to doubling its initial food supply, would shortages still occur? If so, how many years would it take for shortages to occur? If not, explain. 3. Springfield will be opening a new high school in the fall. The number of underclassmen (9th and 10th graders) must fall between 500 and 600 (inclusive), the number of upperclassmen (11th and 12th graders) must fall between 400 and 500 (inclusive), and the number of students cannot exceed 1000. a. Let x represent the number of underclassmen and y represent the number of upperclassmen. Write a system of inequalities that models the situation. b. Graph the solution to the system of inequalities in part a. 4. A projectile is fired upward from the ground with an initial velocity of 300 feet per second. Neglecting air resistance, the height of the projectile at any time t can be described by the polynomial function P(t) = 16t2 + 300t a. Find the height of the projectile when t = 1 second. b. Find the height of the projectile when t = 5 seconds. c. How long will it be until the object hits the ground? 5. A board has length (3x4 + 6x2 18) meters and width of 2x + 1 meters. The board is cut into three pieces of the same length. a. Find the length of each piece. b. Find the area of each piece. c. Find the area of the board before it is cut. d. How is the area of each piece of the board related to the area of the board before it is cut? 6. A cubic equation has zeros at 2, 1, and 3. a. Write an equation for a polynomial function that meets the given conditions. b. Draw the graph of a polynomial function that meets the given conditions. 7. Alice was having a conversation with her friend Trina, who had a discovery to share: Pick any two integers. Look at the sum of their squares, the difference of their squares, and twice the product of the two integers you chose. Those three numbers are the sides of a right triangle. a. Write an equation that models this conjecture using the variables x and y. b. Investigate this conjecture for at least three pairs of integers. Does her trick appear to work in all cases, or only in some cases? Explain. c. Use Trina’s trick to find an example of a right triangle in which all of the sides have integer length, all three sides are longer than 100 units, and the three side lengths do not have common factors. If Trina’s conjecture is true, use the equation found in part a to prove the conjecture. If it is not true, modify it so it is a true statement, and prove the new statement.

Barbartos
School: UT Austin

All right, parts 1 and 2 complete. Let me know if you need any explanations!

Study Questions for Upcoming Exam
December 23, 2017

1

Problem 1

Graphically, we plot each equation as the equation of a line and find the intersection.

The lines intersect at the solution (x, y) = (−2, 1).
Algebraically, we solve using elimination. Multiplying through by 2 in our
first equation, we obtain

2y = x + 5
3x + 2y = 1
Then subtracting the first equation from the second, we obtain

1

3x = −x − 4 =⇒ x = −1
Then substituting in for x we have y = 21 (−1) + 52 = 2 so our solution is
(x, y) = (−1, 2) which agrees with the graphical solution.

Problem 2
a)
Let t be the number of years from the initial starting time. Then the country’s
population in millions is modeled by p(t) = 2.5 + .8t while the annual food
supply is modeled by f (t) = 4 + .4t. Then there will first be food shortages
when f (t) = p(t). Solving, we have
2.5 + .8t = 4 + .4t
t = 3.75 years

b)
The changes to the food supply can be represented as f2 (t) = 8 + .5t. Shortages
will still occur as the rate of increase in the population each year is greater than
the rate of increase in the food supply (so we know at some point the population
must overtake the food supply). We can find this point by setting p(t) = f2 (t)
and solving for t:
2.5 + .8t = 8 + .5t
1
t = 18 years
3
Therefore, a food shortage will still occur, but in 18 31 years, a much longer
time period.

c)
We can represent our new food supply as f3 (t) = 8 + .8t. Then food shortages
would not occur because the food supply increases at the same rate as the
population and the food supply is initially greater than the population. That
is p(0) < f3 (0) and p(t) = f3 (t) has no solution:
2.5 + .8t = 8 + .8t
2.5 = 8
This equation clearly has no solution, so there will be no food shortages.
2

Problem 3
a)
We have

 500
400

x+y

≤ x ≤ 600
≤ y ≤ 500
≤ 1000

b)
We graph only the intersecti...

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Anonymous
Wow this is really good.... didn't expect it. Sweet!!!!

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