August 2023 Algebra 1 Regents Part III

This exam was adminstered in August 2023.

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August 2023

Part III: Each correct answer will receive 4 credits. Partial credit can be earned.


33. The senior class at Hills High School is purchasing sports drinks and bottled water to sell at the school field day. At the local discount store, a case of sports drinks costs $15.79, and a case of bottled water costs $5.69. The senior class has $125 to spend on the drinks.
If x represents the number of cases of sports drinks and y represents the number of cases of bottled water purchased, write an inequality that models this situation.

Nine cases of bottled water are purchased for this year’s field day. Use your inequality to determine algebraically the maximum number of full cases of sports drinks that can be purchased.
Explain your answer.

Answer:

They have to spend less than or equal to $125.

15.79x + 5.69y < 125

For the second part, substitute y = 9 and solve the inequality for x.

15.79x + 5.69(9) < 125
15.79x + 51.21 < 125
15.79x < 73.79
x < 4.67...

The maximum is four full cases of sports drink.

34. The path of a rocket is modeled by the function h(t) = -4.9t² + 49t, where h is the height, in meters, above the ground and t is the time, in seconds, after the rocket is launched. Sketch the graph on the set of axes below.
Her data are modeled on the graph below.

State the vertex of this function.
Explain what the vertex means in the context of this situation.

Answer:

Use your graphing calculator to find the table of values for the function. The vertex is the highest point and the time at the vertex will be halfway to the time that it lands.

Plot the following points (0,0), (1,44.1), (2,78.4), (3.102.9), (4,117.6), (5,122.5), (6,117.6), etc.

The "et cetera" is because we found the axis of symmetry at x = 5, so for 6 < x < 11, the values will repeat. "What goes up must come down."

The vertex is (5,122.5) and in this context it is the maximum height that the rocket will reach will be 122.5 meters which it will reach in 5 seconds.

35.A software company kept a record of their annual budget for advertising and their profit for each of the last eight years. These data are shown in the table below.

Write the linear regression equation for this set of data.

State, to the nearest hundredth, the correlation coefficient of these linear data.

State what this correlation coefficient indicates about the linear fit of the data.

Answer:

Place all the information into a list on your graphing calculator. Then perform a linear regression. DIAGNOSTICS ON needs to be specified on the calculator, or you will not see the correlation coefficient.

You should get the results a = 0.41, b = -2.31, and r = 0.99, when rounded to two decimal places.

The regression would be y = 0.41x - 2.31.

The correlation coefficient is 0.99, which indicates that there is a very strong, positive correlation between the annual advertising budget and profit.

36. Graph the following system of inequalities on the set of axes below: -2y < 3x + 12
x > -3
Label the solution set S.

Allison thinks that (2,-9) is a solution to this system. Determine if Allison is correct.
Justify your answer.

Answer:

Rewrite the flip equation. Flip the inequality sign when dividing by a negative number.

Greater than means it will be a broken line and the shading will be above the line.

x > -3 is a solid, vertical line above and below the x-axis where x is equal to 3. You will shade to the RIGHT of the line, where the x values are greater than -3.

Look at the graph:

Allison is INCORRECT that (2,-9) is a solution to the system. (2,-9) is a point on the broken line, and points on the broken line are not part of the solution.

End of Part III

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