Juanita runs every third day and swims every fifth day. If Juanita runs and swims today, in how many days will she run and swim again on the same day?

Simplify: 8 1/3 · 1 4/5

We now have $5,000 in assets and are given a choice between investment 1 and investment 2. With investment 1, 80% of the time weincrease our asset position by$295,000, and 20% of the time we increase our asset position by $95,000. With investment 2, 50% of the time we increase our asset position by$595,000, and 50% of the time we increase our asset position by $5,000. Our utility function for final asset position x is u(x). We are given the following values for u(x): u(0) = 0, u(640,000) = .80, u(810,000) = .90, u(0) = 0, u(90,000) = .30, u(1,000,000) = 1, u(490,000) = .7. a. Are we risk-averse, risk-seeking, or risk-neutral? Explain. b. Will we prefer investment 1 or investment 2?

The change in diameter of a large steel bolt is carefully measured as the nut is tightened. Knowing that $E=200$ GPa and $y=0.30$. delermine the internal force in the bolt if the diameter is observed to decrease by $13 \mu \mathrm{m}$.

choose the statement that is true about the given quantities.
A. The quantity in column A is greater.
B. The quantity in column B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the given information.

Prove that each of the following exists as a Lebesgue integral. (a) $\int_{0}^{1} \frac{x \log x}{(1+x)^{2}} d x$, (b) $\int_{0}^{1} \frac{x^{p}-1}{\log x} d x \quad(p>-1)$, (c) $\int_{0}^{1} \log x \log (1+x) d x$, (d) $\int_{0}^{1} \frac{\log (1-x)}{(1-x)^{1 / 2}} d x$.

Do you agree with Albert Ellis that it is not the event in a person’s life that causes trouble but rather the way a person thinks about the event? Explain.

Prepare a cost of goods sold budget for MyLife Magnolia Candle Inc. using the information in Practice Exercises 22-3B and 22-4B. Assume the estimated inventories on January 1, 2016, for finished goods and work in process were $9,800 and$3,600, respectively. Also assume the desired inventories on December 31,2016, for finished goods and work in process were $12,900 and$3,500, respectively. Factory overhead was budgeted at $109,600.

A brand of lunchmeat contains $0.10 \%$ by mass of sodium benzoate, $\mathrm{C}_6 \mathrm{H}_5 \mathrm{COONa}$. How many mg of Na does a person ingest by eating $2.52 \mathrm{oz}$ of this meat?

Prepare a cost of goods sold budget for LifeTyme Publishers Inc., using the information in Practice Exercises 22-3A and 22-4A. Assume the estimated inventories on January 1, 2014, for finished goods and work in process were $28,000 and$17,000, respectively. Also assume that the desired inventories on December 31, 2014, for finished goods and work in process were $23,700 and$19,500, respectively. Factory overhead was budgeted at $205,800.

Test for exactness. If exact, solve. If not, use an integrating factor as given or find it by inspection or from the theorems . Also, if an initial condition is given, determine the corresponding particular solution.

$-y d x+x d y=0$

Find general solutions of the equation. First find a small integral root of the characteristic equation by inspection; then factor by division.

$$y ^ { ( 4 ) } + y ^ { ( 3 ) } - 3 y ^ { \prime \prime } - 5 y ^ { \prime } - 2 y = 0$$

Solve the equation.

$$\log _3(x+4) = \log _3(1-x)$$

Fill in the blanks. Given a relation in x and y, if to each value of x in the domain there corresponds exactly one value of in the range, y is said to be a _____ of x. We call x the independent _____ and y the _____ variable.