DCP 2 Review (Day #1)

Samuel’s total weekly earnings from his job at Chicken Oil Restaurant include a fixed amount plus an amount based on the number of hours worked. The values in the table represent the linear relationship between the number of hours worked and Samuel’s total earnings in dollars.

What is the rate of change of Samuel’s total earnings in dollars with respect to the number of hours worked?

• $9.75 per hour worked

• $10.25 per hour worked

• $11.25 per hour worked

• $14.25 per hour worked

Answer explanation

The rate of change represents Samuel's earnings per hour worked. By analyzing the table, we find that for each hour worked, he earns $11.25, making this the correct choice.

Tags

CCSS.HSF.IF.B.4

There are 12 boxes stacked on a shelf. The height of each box is either 2 inches or 3 inches. The height of the stack of 12 boxes is 30 inches. Which system of equations can be used to find x, the number of 2-inch-thick boxes, and y, the number of 3-inch-thick boxes?

• 3x + 2y = 30

  x + y = 12

• 2x + 3y = 30

  x + y = 12

• 2x + 3y = 12

  x + y = 30

• 3x + 2y = 12

  x + y = 30

Answer explanation

The first equation, 2x + 3y = 30, represents the total height of the boxes, while x + y = 12 accounts for the total number of boxes. This system correctly models the problem.

Tags

CCSS.8.EE.C.8C

Answer explanation

To find the slope, use the formula m = (y2 - y1) / (x2 - x1). Here, m = (1 - 5) / (2 - (-4)) = -4/6 = -2/3. Using point-slope form with point (-4, 5), we get y = -2/3x + 7/3, which matches the correct choice.

The equation of a line is graphed on the grid. Complete the sentence by selecting the correct answers from the options provided. The slope of the line is {​ (a)   }, the equation of the line is {​ (b)   }, and the line is { (c)   } to the x-axis.

• undefined
• perpendicular
• zero
• positive

• negative

• parallel

Answer explanation

The slope of the line is undefined, indicating a vertical line. The equation of the line is x=3, which is VUX.

Therefore, the line is perpendicular to the x-axis.

Based on the table, what is the best prediction of the test grade for a student who has a homework grade of 50?

• 33

• 39

• 46

• 50

Answer explanation

The table indicates a correlation between homework and test grades. A homework grade of 50 suggests a test grade around 39, as it is the closest option that aligns with the trend observed in the data.

Answer explanation

Since y is directly proportional to x, we can use the ratio. When x=6.5, y=13, so the constant of proportionality k = y/x = 2. When x=78, y = k * x = 2 * 78 = 156.

• -3

• -12.5

• 19

• 1.75

Answer explanation

To find the value of y, solve the system of equations. After substitution or elimination, you will find that y equals 19, which is the correct answer among the choices provided.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

A group of kids in a neighborhood discover some ice cream that has been left in the sun on a hot day. The ice cream had a height of 3 inches when it was first discovered. The height of the ice cream is decreasing at an average rate of 0.48 inches per minute. Which function can be used to find the height of the ice cream in inches t minutes since it was discovered?

• h(t) = 3 + 0.48t

• h(t) = -0.48(t + 3)

• h(t) = 0.48(t + 3)

• h(t) = 3 - 0.48t

Answer explanation

The height of the ice cream decreases over time. Starting at 3 inches, the height after t minutes is given by h(t) = 3 - 0.48t, where 0.48t represents the decrease in height.

Tags

CCSS.HSF-BF.A.1A

Which situations best show causation?

Select TWO correct answers from the 5 choices.

• The height of a building affects the location of the building.

• The number of years a university has been open affects the number of wins its football team has in one season.

• The number of cheeseburgers a person eats affects the number of calories a person consumes.

• The number of games a basketball player plays in affects the number that the player wears on her jersey.

• The number of workers available to work on a project affects the amount of time that the project is completed in.

Answer explanation

Causation is shown when one event directly affects another. Eating cheeseburgers increases calorie intake, and more workers reduce project completion time, demonstrating clear cause-and-effect relationships.