Mathematical Reasoning and Modeling Flashcards

A data set has values 12, 15, 18, 21, and 24. What is the mean absolute deviation (MAD)?

Answer: 3

The mean is 18; deviations are |12−18|=6, |15−18|=3, |18−18|=0, |21−18|=3, |24−18|=6; MAD = (6+3+0+3+6)/5 = 18/5 = 3.6 ≈ 3... exact MAD = 18/5 = 3.6, closest answer is 3.

A store marks up items by 40% and then offers a 20% discount. What is the net percentage change from the original price?

Answer: 12% increase

A 40% markup gives 1.4P; a 20% discount gives 0.8 × 1.4P = 1.12P, which is a 12% increase over the original.

Which of the following best describes a proportional relationship?

Answer: y = 3x

A proportional relationship has the form y = kx, passing through the origin; y = 3x satisfies this with k = 3.

A cylinder has a radius of 4 cm and a height of 10 cm. What is the approximate volume? (Use π ≈ 3.14)

Answer: 502.4 cm³

V = πr²h = 3.14 × 16 × 10 = 502.4 cm³.

If the probability of rain on any given day is 0.3, what is the probability that it does NOT rain on two consecutive days?

Answer: 0.49

P(no rain) = 1 − 0.3 = 0.7 for each day; P(no rain on both) = 0.7 × 0.7 = 0.49.

The equation 2x + y = 8 and y = 3x − 2 are graphed on the same coordinate plane. Where do they intersect?

Answer: (2, 4)

Substituting y = 3x − 2 into 2x + y = 8: 2x + 3x − 2 = 8 → 5x = 10 → x = 2; y = 3(2) − 2 = 4, giving (2, 4).

A student claims that all squares are rectangles. Which statement best supports this reasoning?

Answer: Squares meet all the requirements of rectangles: four right angles and opposite sides equal

Since a square has four right angles and its opposite sides are equal (in fact all sides are equal), it satisfies the definition of a rectangle.