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

Suppose that your bathroom scale reads your mass as 65 kg with a 3 % uncertainty. What is the uncertainty in your mass (in kilograms)?

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.)

Soccer fields vary in size. A large soccer field is 115 m long and 85.0 m wide. What is its area in square feet? (Assume that 1 m = 3.281 ft.)

Suppose your bathroom scale reads your mass at 65 kg with a 3% uncertainty. What is the uncertainty in your mass (in kilograms)?

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?

Let X be a discrete random variable that takes on values 0, 1, 2 with probabilities $\frac{1}{2}, \frac{3}{8}, \frac{1}{8}$, respectively. Find the moment-generating function of X, M(t), and verify that $E(X)=M^{\prime}(0) \text { and that } E\left(X^{2}\right)=M^{\prime \prime}(0)$.

The speed limit on some interstate highways is roughly 100 km/h. (a) What is this in meters per second? (b) How many miles per hour is this?

For the following exercise, find $\frac{d y}{d x}$ for the given function. $y=\frac{1}{\tan ^{-1}(x)}$

Suppose your bathroom scale reads your mass as 65 $\mathrm{kg}$ with a $3 \%$ uncertainty. What is the uncertainty in your mass (in kilograms)?

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) You stand on a spring-loaded bathroom scale in a bath- room. The scale “reads” your mass. What is the scale actually $\it{measuring?}$ (b) You stand on a spring-loaded bathroom scale in an elevator that is accelerating upward at $2.0$ m/s$^2$. The scale “reads” your mass. What is the scale $\it{measuring?}$
(A) Your mass.
(B) Your weight. (C) The force of the scale pushing up on your feet.
(D) The force of your feet pushing down on the scale.

The following lengths are given using metric prefixes on the base SI unit of length: the meter. Rewrite them in scientific notation without the prefix. For example, 4.2 Pm would be rewritten as

$$4.2 × 10^{15} m.$$

(a) 89 Tm; (b) 89 pm; (c) 711 mm; (d) 0.45 μm.