Determine the product of all values of k for which the polynomial equation $2 x^{3}-9 x^{2}+12 x-k=0$ has a double root.

Which of the following sequences are the first four terms of an arithmetic sequence? For those that are, write down the value of the common difference. (a) 7 10 13 16 ... (b) 3 5 9 15 ... (c) 1 0.1 0.01 0.001 .. . (d) 4 2 0 -2 ... (e) 2 -3 4 -5 ... (f) p - 2q p - q p p + q ... (g) $\frac{1}{2} a \quad \frac{1}{3} a \quad \frac{1}{4} a \quad \frac{1}{5} a \quad \ldots$ (h) x 2x 3x 4x ...

The Gap has some of its jeans stone-washed under a contract with Vietnam Garment Corporation (VGC). If VGC’s estimated operating cost per machine is $26,000 for year 1 and it increases by$1500 per year through year 5, the equivalent uniform annual cost per machine over years 1 to 5, at an interest rate of 8% per year, is closest to: (a) $30,850 (b)$28,770 (c) $26,930 (d)$23,670

Give the maximum number of turning points of the graph of each function. $f(x)=x^{5}-9 x^{2}$

Two large flat metal sheets are located at z = 0 and z = d and are maintained at 0 and $V_{0}$, respectively. The charge density between the sheets is $\rho_{v}(z)=\rho_{o} z / d$, where $\boldsymbol{\rho}_{\boldsymbol{o}}$ is a constant. Determine the potential at all points between the plates.

The campus recruiter for an international conglomerate classifies the large number of students she interviews into three categories-the lower quarter, the middle half, and the upper quarter. If she meets six students on a given morning, what is the probability that they will be evenly divided among the three categories? What is the marginal probability that exactly two will belong to the middle half?

The problem is based on the following cash flows and an interest rate of 10% per year.

$$\begin{array}{lcc} \text { Alternative } & \mathrm{X} & \mathrm{Y} \\ \hline \text { First cost, } \$ & -200,000 & -800,000 \\ \text { Annual cost, } \$ \text {/year } & -60,000 & -10,000 \\ \text { Salvage value, } \$ & 20,000 & 150,000 \\ \text { Life, years } & 5 & \infty \\ \hline \end{array}$$

The annual worth of perpetual service for alternative X is represented by the following equation: (a) −200,000(0.10) − 60,000 + 20,000(0.10) (b) −200,000(A/P,10%,5) − 60,000 + 20,000(A/F,10%,5) (c) −200,000(A/P,10%,5) − 60,000 − 20,000(A/F,10%,5) (d) −200,000(0.10) − 60,000 + 20,000(A/F,10%,5)

Decide whether each statement is true or false. If false, tell why. The graph of a nonzero function cannot be symmetric with respect to the x-axis.

Spectra Scientific of Santa Clara, CA manufactures Q-switched solid state industrial lasers for LED substrate scribing and silicon wafer dicing. The company got a $60 million loan to be repaid over a 5-year period at 8% per year interest. Determine the amount of the unrecovered balance of the principal (a) immediately before the payment is made at the end of year 1, and (b) immediately after the first payment.

Two distinct integers are chosen at random from the first five positive integers. Compute the expected value of the absolute value of the difference of the two numbers.

The function f is defined by $f(x)=x^{2}-3 x+5$. Find the two values of x for which f(x) = f(4).

Two roadway designs are under consideration for access to a permanent suspension bridge. Design 1A will cost $3 million to build and$100,000 per year to maintain. Design 1B will cost $3.5 million to build and$40,000 per year to maintain. Both designs are assumed to be permanent. Use an AW-based rate of return equation to determine (a) the breakeven ROR, and (b) which design is preferred at a MARR of 10% per year.

The population of the United Kingdom in 1971 was $5.5615 \times 10^{7}$; by 1992 it was estimated to be $5.7384 \times 10^{7}$. Assuming a steady exponential growth estimate the population in (a) 2003, (b) 1981.

Two circles of radii 5 cm and 12 cm are drawn, partly overlapping. Their centres are 13 cm apart. Find the area common to the two circles.