University:
University of Michigan
Course:
MATH 115 | Calculus I
Academic year:

2024
Views:

394

Pages:

2
Author:

Luciano Kirby

Question 1 Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the range and interquartile range. Answer The range is the difference between the largest and the smallest value: RANGE = 20 - 10 = 10 The first quartile is the median of the data values below the median (or at 25% of the data): Q1 = (10 + 12) / 2 = 11 The third quartline is the median of the data values above the median (or at 75% of the data): Q3 = (17 + 20) / 2 = 18.5 The interquartile range IQR is the difference of the third and first quartile: IQR = Q3 - Q1 = 18.5 - 11 = 7.5 Results: RANGE = 10 IQR = 7.5 Question 2 Range Rule of Thumb for Interpreting s The 20 brain volumes (cm³) from Data Set 8 "IQ and Brain Size" in Appendix B have a mean of 1126.0 cm³ and a standard deviation of 124.9 cm³ . Use the range rule of thumb to identify the limits separating values that are significantly low or significantly high. For such data, would a brain volume of 1440 cm³ be significantly high? Answer Step 1 Using the following range as a guide, find the values that are noticeably low or high: Values that are noticeably low are indicated by μ – 2σ. The values lower than or equal to this μ – 2σ values are regarded as being extremely low. Values that are unusually high are indicated by μ + 2σ. The values higher than or equal to this μ + 2σ value are considered to be significantly high. Step 2 Here, the values that are noticeably low and high are determined as follows: Significantly low = 1125 - 2(124.9) = 875.2 Significantly high = 1125 + 2(124.9) = 1374.8 Step 3 Consequently, the indicated brain volume value with 1, 440cm³ is significantly high because it is greater than 1,374.8cm³. Question 3 A racquetball strikes a wall with a speed of 30 m/s and rebounds with a speed of 26 m/s. The collision takes 20ms. What is the average acceleration of the ball during collision? a) 62 b) 50 c) 66 d) 54 e) 58 Answer 1 v₀ = 30m/s v = -26m/s (-ve because it is moving in opposite direction) Δt = 20 x 10⁻³ s a = Δv/Δt = (v - v₀) / Δt = (-26 m/s - 30 m/s) / 20 * 10⁻³ s = -56 / (20 * 10⁻³) = -2800 m/s² The negative acceleration implies the force acting was opposite to the direction of motion None of the choices seem correct Answer 2 2800 m/s² is the answers for this question Question 4 Show that if a|b and b|c, a|c follows. Answer Because a|b and b|c. In order to make b = na and c = mb, respectively, there are integers m & n that exist. Then, because b=na, c = mb = mna. Given that mn is an integer, it follows that a|c Question 5 For Questions I&5, use dimensional analysis with need unit equivalences from this section and for 1. How many miles is a 10-kilometer race? Answer Recall that 1 mile = 1.61 km so we can write: 10km × 1 mile/1.61 km ≈ 6.21 miles