This exam was adminstered in June 2021. These answers were not posted until they were unlocked on the NY Regents website or were posted elsewhere on the web.
Part II is located here.
June 2021 (v202)
Part III
Each correct answer will receive 3 credits. Partial credit can be earned. It is usually possible to get 1 point for a correct answer with no correct work shown.
State the linear regression equation that estimates the heart rate per number of jumping jacks
State the correlation coefficient of the linear regression equation, roudned to the nearest hundredth
Explain what the correlation coefficient suggest in the context of this problem.
33. Joey recorded his heartbeats, in beats per minute (bpm), after doing different numbers of jumping jacks. His results are shown in the table below.
(x, y), (0, 68), (10, 84), (15, 104), (20, 100), (30, 120)
Answer:
Put the data into a table in your graphing calculator. Then go to Stats and perform a linear regression.
You will get the a = 1.72 and b = 69.4. Written in the form y = ax + b, that gives you y = 1.72x + 69.4
The correlation coefficient is 0.967..., which is 0.97 to the nearest hundredth.
In the context of this problem, this suggests a very strong positive correlation between the number of jumping jacks and heartbeats per minute.
If x represents the number of pens Hannah bought, write an equation in terms of x than can be used to find how many of each item she bought. Use your equation to determin algebraically how many pens Hannah bought.
34. Hannah went to the school store to buy supplies and spent $16.00. She bought four more penciels than pens and two fewer erasers than pens. Pens cost $1.25 each, pencils cost $0.55 each, and erasers are 0.75 each.
Answer:
x = the number of pens Hannah bought
(x + 4) = the number of pencils Hannah bought
(x - 2) = the number of erasers Hannah bought
The equation to solve would be 1.25x + 0.55(x + 4) + 0.75(x - 2) = 16
1.25x + 0.55x + 4 * 0.55 + 0.75x - 2 * 0.75 = 16.00
1.25x + 0.55x + 2.20 + 0.75x - 1.50 = 16.00
1.25x + 0.55x + 0.75x = 15.30
2.55x = 15.30
x = 6
Note: if you didn't get a Whole Number, you know that you must've made a mistake. You can't buy part of a pen or pencil or eraser.
x = the number of pens Hannah bought = 6
(x + 4) = the number of pencils Hannah bought = 6 + 4 = 10
(x - 2) = the number of erasers Hannah bought = 6 - 2 = 4
You can check your work: 1.25(6) + 0.55(6 + 4) + 0.75(6 - 2) = 1.25(6) + 0.55(10) + 0.75(4) = 16 (check!)
Is (6, 3) a solution to the system of inequalities? Explain your answer.
35. Graph the given set of inequalities on the set of axes below:
3x - 2y > 4
Answer:
Remember: when answering the final question, answer it based on YOUR graph, even if you made a mistake on your graph. The graph is your justification. As long as you are consistent, you will get a point for your answer. If you did not do the graph, you cannot get a point for "Yes" or "No" unless you back it up with some work, such as substitution into both inequalaities.
The first inequality can be graphed as is because you have a slope and a y-intercept. Since it has a "<" sign, it will be a solid line with shading beneath it. All points on the line and below it are solutions to the inequality.
The second inequality needs to be rewritten into a more useful form. (Standard form can be useful, too, but in this case the x-intercept is (4/3, 0), which would be difficult to graph.)
Do the following:
-2y > -3x + 4
y < 3/2x - 2
The "<" symbol means it will be a broken or dashed line with shading beneath it. The line itself is a boundary and none of those points are solutions.
Put a captial "S" in the section of the graph with double-shading (the criss-cross pattern shown below). That is the section that is the solution to the system. Be sure to label the lines.
According to the graph, (6, 3) is not a solution because it is not in the double-shaded section of the graph.
36. A ball is projected up into the air from the surface of a platform to the ground below. The height of the ball above the ground, in feet, is modeled by the function f(t) = -16t2 + 96t + 112, where t is the time, in seconds, after the ball is projected.
State the height of the platform in feet.
State the coordinates of the vertex. Explain what it means in the context of this problem.
State the entire interval over which the ball's height is decreasing.
Answer:
This is a problem of projectile motion that uses gravity (the -16 leading coefficient is a giveaway!). It's a quadratic function and will follow the path of a parabola with the following limitations: the independent variable cannot be negative because that would be negative time, and the dependent variable cannot be negative because that would be below the ground. In reality, the ball will bounce when it strikes the ground, and the function does not model this.
The height of the platform is 112, which is the y-intercept. When t = 0, the ball has not left the platform yet, so the platform is 112 feet.
The cooridinates of the vertex can be found in your calculaor, or you can use the formula for the Axis of Symmetry:
x = -b / (2a)
x = -96 / (2(-16)) = -96 / -32 = 3
h(3) = -16(3)2 + 96(3) + 112 = 256
The vertex is (3, 256) which is the ball will reach its highest point of 256 feet at 3 seconds.
The ball will be decreasing after t = 3 until it hits the ground. The ground has a height = 0. We have to find the zeroes of the equation.
t2 - 6t + 7 = 0
(t - 7)(t + 1) = 0
t = 7 or t = -1
Discard t = -1 because time cannot be negative.
The ball is decreasing over the interval 3 < t < 7.
Part IV
Each correct answer will receive 4 credits. Partial credit can be earned. It is usually possible to get 1 point for a correct answer with no correct work shown.
The cost of 4 large plants and 8 medium plants is $40. The cost of 5 large plants and 2 medium plants is $28.
If L is the cost of a large plant and M is the cost of a medium plant, write a system of equatios that models this situation.
Could the cost of one large plant be $5.50 and the cost of one medium plants be $2.25? Justify your answer.
Determine algebraically both the cost of a lare planst and the cost of a medium plant.
37. At a local shop, the price of plants includes sales tax.
Answer:
Note that the problem actually used l and m (lower case). However, on this blog it would be difficult to distinguish the l from a 1 (one). To avoid confusion, you should either use a capital L or a script l that doesn't look like a 1.
Translate the two sentences into a system of equations.
4L + 8M = 40
5L + 2M = 28
To find if (5.50, 2.25) is a solution, substitute these numbers into BOTH equations. If they do not work for both equations, then it isn't a possible solution.
4(5.50) + 8(2.25) = 40 (check!)
5(5.50) + 2(2.25) = 32, not 28. This is not a solution.
To solve the system, multiply the second equation by 4, then subtract the equations:
4L + 8M = 40
5L + 2M = 28
4L + 8M = 40
20L + 8M = 112
16L = 72
L = 4.50
4L + 8M = 40
4(4.50) + 8M = 40
18 + 8M = 40
8M = 22
M = 2.75
The cost of a Large plant is $4.50 and the cost of a Medium plant is $2.75.
End of Exam
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