91Ó°ÊÓ

Explain what is wrong with the statement. If \(p(x)\) is a probability density function with \(p(1)=\) \(0.02,\) then the probability that \(x\) takes the value 1 is 0.02

A business associate who owes you \(\$ 3000\) offers to pay you \(\$ 2800\) now, or else pay you three yearly installments of \(\$ 1000\) each, with the first installment paid now. If you use only financial reasons to make your decision, which option should you choose? Justify your answer, assuming a \(3 \%\) interest rate per year, compounded continuously.

Find the length of the parametric curve. \(x=3+5 t, y=1+4 t\) for \(1 \leq t \leq 2 .\) Explain why your answer is reasonable.

Find the length of the parametric curve. \(x=\cos \left(e^{t}\right), y=\sin \left(e^{t}\right)\) for \(0 \leq t \leq 1 .\) Explain why your answer is reasonable.

Find the continuous interest rate per year that yields a future value of \(\$ 18,000\) in 20 years for each \(\$ 9000\) investment. A single \(\$ 9000\) deposit.

A metal plate, with constant density \(2 \mathrm{gm} / \mathrm{cm}^{2},\) has a shape bounded by the curve \(y=x^{2}\) and the \(x\) -axis, with \(0 \leq x \leq 1\) and \(x, y\) in \(\mathrm{cm}\) (a) Find the total mass of the plate. (b) Sketch the plate, and decide, on the basis of the shape, whether \(\bar{x}\) is less than or greater than \(1 / 2\) (c) Find \(\bar{x}\)

Explain what is wrong with the statement. If \(P(x)\) is a cumulative distribution function with \(P(5)=0.4,\) then the probability that \(x=5\) is 0.4

Find the area inside the spiral \(r=\theta\) for \(0 \leq \theta \leq 2 \pi\)

Find the area between the two spirals \(r=\theta\) and \(r=2 \theta\) for \(0 \leq \theta \leq 2 \pi\)

Construct and evaluate definite integral \((s)\) representing the area of the region described, using: (a) Vertical slices (b) Horizontal slices Enclosed by \(y=x^{2}\) and \(y=3 x\)