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EST Test 1 (Calculator)

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1. Which of the following is a system of inequalities whose solution is the set of points that belong to the shaded area in the figure above?

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2. In the xy-plane, the line determined by the points (3, m) and (m, 12) passes through the origin. Which of the following could be the value of m?

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3. y ≤ -10x + 2000

y ≤ 5x

In the xy -plane, if a point with coordinates (a, b) lies in the solution set of the system of inequalities above, what is the maximum possible value of b?

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4.  What is the solution of the above system?

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5. When a system of two linear equations has no solution, how do the graphs of the equations appear?

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6. The total revenue of a magic show is 16,360 EGP. If each adult ticket to attend the show cost 12 EGP and each children ticket cost 2 EGP, then what is the number of tickets of each type sold if 3,480 tickets in all were sold?

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7. Questions 7 and 8 refer to the following information.

The expression 1.6 y + 10.8 models the number of eligible voters in millions in a certain country from 1990 to 2015 where y=1 represents the number of years since 1990.

Find the approximate number of eligible voters in millions in 1999.

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8. Questions 7 and 8 refer to the following information.

The expression 1.6 y + 10.8 models the number of eligible voters in millions in a certain country from 1990 to 2015 where y=1 represents the number of years since 1990.

Assume that the model continues to hold for future years, what is the difference between the eligible voters in millions in 2020 and 2017?

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9. The dot plots above show the scores on a common quiz for the three sections A, B, and C. Knowing that the average score is the same for the three sections, which of the following correctly compares the standard deviation (x) of the scores in each of the three sections?

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10. Questions 10, 11, and 12 refer to the following information. The above bar chart shows the scores of a philosophy test over 100.

What is the median score?

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11. Questions 10, 11, and 12 refer to the following information. The above bar chart shows the scores of a philosophy test over 100.

What is the range of the scores?

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12. Questions 10, 11, and 12 refer to the following information. The above bar chart shows the scores of a philosophy test over 100.

If 5 is subtracted from each score, what do the new mean x′ and standard deviation α′ become with respect to the original mean x and standard deviation α?

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13.

Which of the following variables are discrete?
I. Number of players in a playground
II. The speed in miles per hour of cars passing a certain point on a highway
IV. Height in inches
V. Weight in kilograms

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14. At 8:00 a.m., a patient is given a drip feed containing a particular chemical and its concentration in his blood is measured, in suitable units, at one interval as shown above in the scatterplot. A line of best fit and its
equation y = 1.84x + 1.99 are also given.

Which of the following is the best interpretation of the y-intercept in the equation of the line?

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15. If 35% of a number is equal to two-thirds of another number, what is the ratio of the first number to the second number?

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16. Questions 16, 17, and 18 refer to the following information. A kiosk sells slices of pizza and sets the price per slice each week. The scatterplot above shows the price and the number of slices sold over 25 weeks, along with the line of best fit and its equation.

How many slices does the kiosk expect to sell in a week when the price of a slice is 4 EGP?

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17. Questions 16, 17, and 18 refer to the following information. A kiosk sells slices of pizza and sets the price per slice each week. The scatterplot above shows the price and the number of slices sold over 25 weeks, along with the line of best fit and its equation.

What is the best interpretation of the meaning of the slope of the line of best fit?

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18. Questions 16, 17, and 18 refer to the following information. A kiosk sells slices of pizza and sets the price per slice each week. The scatterplot above shows the price and the number of slices sold over 25 weeks, along with the line of best fit and its equation.

For how many weeks was the number of slices sold smaller than the amount predicted by the line of best fit?

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19. Questions 19 and 20 refer to information below.
In a farm, there are 30 rabbits of two sizes “small and big” and three colors “white, brown, and gray” as shown in the table below. One rabbit is selected at random from this farm.

What is the probability that the selected rabbit is white?

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20. Questions 19 and 20 refer to information below.
In a farm, there are 30 rabbits of two sizes “small and big” and three colors “white, brown, and gray” as shown in the table below. One rabbit is selected at random from this farm.

Suppose that the selected rabbit is not of white color, what is the probability for this rabbit to be from the big size?

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21. In a bag, there are 12 identical tokens numbered from 1 to 12. A token is drawn  at random. What is the probability to obtain an even multiple of 3?

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22. A bank has opened a new branch and, as part of a promotion, the bank branch is offering 2,000\$ certificates of deposit at an interest rate of 6% per year, compounded semi-annually. The bank is selling certificates with terms of 1, 2, 3 or 4 years. Which of the following functions gives the total amount, A, in dollars, a customer will receive when a certificate with a term of k years is finally paid?

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23. Which of the expressions is equivalent to the above expression?

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24. Which of the following is a solution for the equation ?

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25. From the set of equations below, which has a real solution?

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26. The curve P above represents function f defined by f(x)=-x²+ax+b. What are the values of the real numbers a and b?

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27. Consider the function f defined by f(x) = 2(x – 3)(x + 2) . What is the ordinate of the vertex of function f?

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28. The solution of the equation is

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29. Which of the following statements is true?

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30. Which of the following is equal to ?

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31. Two numbers are in ratio 3:5. If 9 is subtracted from each, the new numbers are in the ratio 12:23. What is the biggest number?

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32. A musical band agrees to play for 350\$ plus 20% of the ticket sales. What is the total sale price of the tickets needed for the band to receive at least 700\$?

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33. Ahmad runs half the distance to school and walks for the remaining part of the journey. He runs at 3m/s but slows to 2m/s for the second half of the journey. He takes 55 minutes to complete the trip. Find the distance (in meters) Ahmad has to travel to reach school.

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34. A sum of 7,200 \$ is to be divided equally among many people. If five people were excluded, each part would increase by 20\$. What is the number of people?

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35. The original price of an article is 30,000 EGP and its discount price is 27,600 EGP. What is the discount percent?

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36. Bob is paid an hourly rate. One week he earned 165 \$ by working 30 hours. If he works 40 hours the next week, how much will he earn?

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37. In the polynomial function P(x)=3x³ (a – 1) x+7 what is the value of the constant number a if -1 is a root of P?

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38. In the xy–plane, let x²+y²-2kx+4y-3k²=0 be the equation of a circle of center A (½,-2) and radius r = √5. What is the value of the real number k?