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Given the scatterplot graph above, ten students at Welton Academy were polled at random about their usage of the school's new physics-centered social media app, E = MC Shared. The app was developed to encourage students to discuss physics curricula and concepts in ways that mirrored social media trends in 2013. Students were asked how many times they logged into the app each day as well as how many posts they actually made using the app. With the given data, what conclusions can be drawn about this group of students?
Two graphs, f(x) and h(x), are shown above. If f(x) = 3x + 4 and f(x) and h(x) are perpendicular, which of the following could be the equation of h(x) ?
3. The number of eggs that Farmer Jones has in his chicken coop will grow exponentially as Farmer Jones buys more chickens to increase production. The number of eggs Farmer Jones has in the coop can be modeled by the equation y = 3x beginning on Day 1, where x is given by x = 1, and y is the number of eggs currently in the coop. If the coop can support only 4,000 eggs, and Farmer Jones empties the coop every day, on which day will the chickens produce too many eggs for the coop to support?
4. If a = and a is a nonzero integer, which of the following is equivalent to a ?
5. Three different chefs work together to prepare meals for 280 dinner guests. Each works at a different speed, and their combined output throughout the night is modeled by the equation 8x + 4x + 2x = 280. If x is a positive integer, which of the following could 8x represent in the equation?
The graph, y = f(x), shown above models the performance of a certain crop, where x is the nutrients subtracted or added to the soil and y is the gain or loss of pieces of fruit added to the total harvest. A more powerful fertilizer that is used causes the graph y = f(x) to be reflected over the line y = x. Which of the following best describes the behavior of the crop with the new fertilizer?
7. George and Joe both interview the same 20 fellow students regarding their interest in their school's new Model UN Club. George asked the students to respond with Interested, Sort of Interested, and Not Interested. Joe asked the students to rate their interest on a scale of 1 to 5. The results of the polls are below.
After reviewing the data, the Model UN advisors determine that Joe neglected to include whether a 1 or 5 was the best rating in his report. What additional piece of information would most help the advisor determine whether a 1 or 5 was the best rating?
8. Each winter, Captain Dan's Ski Lodge rents both pairs of skis and snowboards to its guests for a flat daily rate per pair of skis and a flat daily rate per snowboard. Five pairs of skis and two snowboards will cost a family $370. Three pairs of skis and four snowboards will cost a family $390. During a particularly slow season, Captain Dan announces a 10% discount on all skis and snowboards. What would be the cost of renting two pairs of skis and two snowboards if they were rented during this discount period?
9. If 8x + 8y = 18 and x2 - y2 = - , what is the value of 2x - 2y ?
10. Shaun is developing a weight loss regimen, which includes both a workout plan and a calorie-restriction plan. Shaun wants to work out for no less than 30 minutes and no more than 60 minutes a day and consume no less than 2,000 and no more than 2,500 calories. If each minute, m, of his workout time burns 50 calories, which of the following inequalities represents the number of minutes, m, that Shaun can work out each day to burn off as many calories as he consumes?
11. A professional baseball team wishes to average 45,500 ticket purchases per game for the entire 162-game season. Through the first 60 games of the season, the team has averaged 43,000 ticket purchases per game. Which of the following most closely approximates how many ticket purchases per game the team must average for the remainder of the season in order to hit its overall goal of an average of 45,500 ticket purchases per game for the season?
12. A certain polynomial, P, has a degree of 2. Polynomial P has zeros of 2 and -3, and a > 0 when the function of polynomial P is written in the form of y = ax2 + bx + c. Given this information, which of the following could be the graph of polynomial P ?
13. Circle O (not shown) is divided into three sectors. Points P, Q, and R are on the circumference of the circle. Sector POR has an area of 8π, and sector ROQ has an area of 6π. If the radius of circle O is 4, what is the measure of the central angle of sector QOP, in degrees?
14. Medical residents at Lakewood Hospital are choosing their individual specialties. Among them, 40% choose cardiology, 16% choose oncology, 34% choose endocrinology, and the remaining x% choose hematology. Once the doctors pick their first specialty, they are then each asked to choose a second specialty from the previous four options in case their original specialty is already filled. They may not pick their original specialty again. 20% of those who originally picked cardiology choose oncology as their second choice. If no other field chooses oncology as their second choice, and the hospital boasts 200 medical residents, then what is the total number of residents who named oncology as either their first or second choice, in terms of x ?
15. Mr. Lastorka's science class is running experiments with an energy-efficient model electric car. As the initial rate of energy delivered to the car, measured in watts, increases, the number of millimeters moved by the car from its starting position increases exponentially. The results of several trial runs are shown on the scatterplot graph below.
Based on the data, the students in Mr. Lastorka's class determine the exact equation involving Watts, x, and total distance from start, y . They call the function y = f(x). Mr. Lastorka then instructs his class to reflect y = f(x) over the x-axis. He challenges each student to determine the new function and what it would mean from a physics perspective. Four student pairs gave their answers below. Who is correct, and for what reasons?
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