The table gives the gross world product, G, which measures global output of goods and services. If t is in years since 1950, the regression line for these data is $G=3.543+0.734 t$.

$$\begin{array}{|c|ccccccc|} \hline \text { Year } & {1950} & {1960} & {1970} & {1980} & {1990} & {2000} \\ \hline G & {6.4} & {10.0} & {16.3} & {23.6} & {31.9} & {43.2} \\ \hline \end{array}$$

Plot the data and the regression line on the same axes. Does the line fit the data well?

Researchers studying acid rain measured the acidity of precipitation in a Colorado wilderness area for 150 consecutive weeks. Acidity is measured by pH. Lower pH values show higher acidity. The researchers observed a linear pattern over time. They reported that the regression line

$$\widehat{pH} = 5.43 - 0.0053$$

(weeks) fit the data well. Identify the y intercept of the line and explain what it means in this setting.

The acidity of a solution is measured by its pH, with lower pH values indicating more acidity. A study of acid rain was undertaken in Colorado between 1975 and 1978, in which the acidity of rain was measured for 150 consecutive weeks. The data followed a generally linear pattern. If P is the pH and t is the number of weeks into the study, the regression line was determined to be $P=5.43-0.0053 t$. According to the line , what was the pH at the begin of the study? At the end of the study (t=150)?

Review. A particle moves along the x axis. It is initially at the position 0.270 m, moving with velocity 0.140 m/s and acceleration –0.320 m/s2. Suppose it moves as a particle under constant acceleration for 4.50 s. Find (a) its position and (b) its velocity at the end of this time interval. Next, assume it moves as a particle in simple harmonic motion for 4.50 s and x = 0 is its equilibrium position. Find (c) its position and (d) its velocity at the end of this time interval.

Pat always trips on the third step and she thinks that step may be a different size. The contractor told her that all the treads and risers are perpendicular to each other. Is that enough information to state that the steps are the same size? In other words, if $\overline{WN}\perp\overline{NZ}$ and $\overline{ZH}\perp\overline{HK}$, is $\triangle WNZ\cong\triangle ZHK$?

“The wave” is a particular type of pulse that can propagate through a large crowd gathered at a sports arena. The elements of the medium are the spectators, with zero position corresponding to their being seated and maximum position corresponding to their standing and raising their arms. When a large fraction of the spectators participates in the wave motion, a somewhat stable pulse shape can develop. The wave speed depends on people’s reaction time, which is typically on the order of 0.1 s. Estimate the order of magnitude, in minutes, of the time interval required for such a pulse to make one circuit around a large sports stadium. State the quantities you measure or estimate and their values.

The 20-lb block and the 50-lb block are connected by a rope hung over the fixed curved surface. If the system is on the verge of slipping, calculate the coefficient of friction between the rope and the surface.

An engineer is designing a triangular weir for measuring the flow rate of a stream of water that has a discharge of 6 cfm. The weir has an included angle of 45$^{\circ}$ and a coefficient of discharge of 0.6. Find the head on the weir.

A simple pendulum with a length of 2.23 m and a mass of 6.74 kg is given an initial speed of 2.06 m/s at its equilibrium position. Assume it undergoes simple harmonic motion. Determine (a) its period, (b) its total energy, and (c) its maximum angular displacement.

For each of the following pdfs let X1, …, Xn be iid observations. Find a complete sufficient statistic, or show that one does not exist. (a) $f(x | \theta)=\frac{2 x}{\theta^{2}}$, 0 < x < $\theta$, $\theta$ > 0 (b) $f(x | \theta)=\frac{\theta}{(1+x)^{1+\theta}}$ , 0 < x < $\infty$, $\theta$ > 0 (c) $f(x | \theta)=\frac{(\log \theta) \theta^{x}}{\theta-1}$, 0 < x < 1, $\theta$ > 1, (d)

$$f(x | \theta)=\left(\begin{array}{l}{2} \\ {x}\end{array}\right) \theta^{x}(1-\theta)^{2-x}$$

, f(x|$\theta$) = e−(x − $\theta$) exp(−e−(x − $\theta$)), $-\infty<x<\infty,-\infty<\theta<\infty$(e) , x = 0, 1, 2, $0 \leq \theta \leq 1$

Water (p=1000 kg/m3) is accelerated from rest in a horizontal pipe that is 80 m long and 30 cm in diameter. If the acceleration rate (toward the downstream end) is 5 m/s2, what is the pressure at the upstream end if the pressure at the downstream end is 90 kPa gage?

In a given city it is assumed that the number of automobile accidents in a given year follows a Poisson distribution. In past years the average number of accidents per year was 15, and this year it was 10. Is it justified to claim that the accident rate has dropped?

Review. Photons of wavelength λ are incident on a metal. The most energetic electrons ejected from the metal are bent into a circular arc of radius R by a magnetic field having a magnitude B. What is the work function of the metal?

A 15.0-mW helium–neon laser emits a beam of circular cross section with a diameter of 2.00 mm. (a) Find the maximum electric field in the beam. (b) What total energyis contained in a 1.00-m length of the beam? (c) Find the momentum carried by a 1.00-m length of the beam.