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 $\triangle WNZ\cong\triangle ZHK$?

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.

According to a study released by the federal Substance Abuse and Mental Health Services Administration (Knight Ridder Tribune, September 9, 1999), approximately $8\%$ of all adult full-time workers are drug users and approximately $70\%$ of adult drug users are employed full-time. a. Is it possible for both of the reported percentages to be correct? Explain. b. Define the events D and E as D = event that a randomly selected adult is a drug user and E = event that a randomly selected adult is employed full-time. What are the estimated values of P(D\ E) and P(E \D) ? c. Is it possible to determine P(D), the probability that a randomly selected adult is a drug user, from the information given? If not, what additional information would be needed?

Solve $\nabla^{2} u=Q(x, y)$ on a rectangle (0 < x < L, 0 < y < H) subject to

$$\ \begin{aligned} &u(0, y)=0, \quad u(x, 0)=0,\\ &u(L, y)=0, \quad u(x, H)=0. \end{aligned}$$

Use a Fourier sine series in y.

One mediator of the weak interaction is the Z0 boson, with mass 91 GeV/c2. Use this information to find the order of magnitude of the range of the weak interaction.

In a small city, approximately $15\%$ of those eligible are called for jury duty in any one calendar year. People are selected for jury duty at random from those eligible, and the same individual cannot be called more than once in the same year. What is the probability that an eligible person in this city is selected 2 years in a row? 3 years in a row?

Describe the sampling distribution for the sample sum Is it unlikely (improbable) that would be more than 70 units away from 960? Explain. REFERENCE: A random sample of 16 measurements is drawn from a population with a mean of 60 and a standard deviation of 5. Describe the sampling distribution of the sample mean. Within what interval would you expect to lie approximately 95% of the time? $\Sigma y _ { i }$ $\overline { y }$

The reaction turbines at Niagara Falls are of the Francis type. The impeller outside diameter is 4.5 m. Each turbine produces 54 MW at 107 rpm, with 93.8 percent efficiency under 65 m of net head. Calculate the specific speed of these units. Evaluate the volume flow rate to each turbine. Estimate the penstock size if it is 400 m long and the net head is 83 percent of the gross head.