A good-quality measuring tape can be off by 0.50 cm over a distance of 20 m. What is its percent uncertainty?

A good-quality measuring tape can be off by $0.50 \mathrm{~cm}$ over a distance of $20 \mathrm{~m}$. What is its percent uncertainty?

Mount Everest, at 29,028 ft, is the tallest mountain on Earth. What is its height in kilometers? (Assume that 1 m = 3.281 ft.)

An infant's pulse rate is measured to be 130 ± 5 beats/min. What is the percent uncertainty in this measurement?

(a) A car speedometer has a 5% uncertainty. What is the range of possible speeds when it reads 90 km/h? (b) Convert this range to miles per hour. Note 1 km = 0.6214 mi.

In a study conducted by a certain country's Economic Development Board regarding the income distribution of certain segments of the country's workforce, it was found that the Lorenz curve for the distribution of income of college professors is described by the function

$$g(x) = \dfrac{1}{3}x\sqrt{1+8x}$$

Compute the coefficient of inequality of the Lorenz curve.

Tectonic plates are large segments of Earth's crust that move slowly. Suppose one such plate has an average speed of 4.0 cm/yr.

(a) What distance does it move in 1.0 s at this speed?

(b) What is its speed in kilometers per million years?

Use a metric measuring tape (or meterstick) to measure your height, in centimeters. ____ centimeters (cm)

American football is played on a 100-yd-long field, excluding the end zones. How long is the field in meters? (Assume that 1 m = 3.281 ft.)

A generation is about one-third of a lifetime. Approximately how many generations have passed since the year 0 AD?

State how many significant figures are proper in the results of the following calculations: (a) (106.7)(98.2) / (46.210)(1.01); (b) (18.7)²;

$$(c) (1.60 × 10^{-19})(3712)$$

Consider the physical quantities m, s, v, a, and t with dimensions [m] = M, [s] = L,

$$[v] = LT^{-1}, [a] = LT^{-2},$$

and [t] = T. Assuming each of the following equations is dimensionally consistent, find the dimension of the quantity on the left-hand side of the equation: (a) F = ma; (b) K = 0.5mv²; (c) p = mv; (d) W = mas; (e) L = mvr.

A student is trying to remember some formulas from geometry. In what follows, assume A is area, V is volume, and all other variables are lengths. Determine which formulas are dimensionally consistent. (a) V = πr²h; (b) A = 2πr² + 2πrh; (c) V = 0.5bh; (d) V = πd²; (e) V = πd³/6.

A car is traveling at a speed of 33 m/s. (a) What is its speed in kilometers per hour? (b) Is it exceeding the 90 km/h speed limit?