Write two different proportions using each set of numbers. Use cross products to justify your answer. A. $1.80,$1.20, 14, 21 B. 1, 3.5, 31.50, 9.0 C. 11.7, 8424, 0.02, 14.4

Find the mass and center of mass of the object corresponding to the given surface and mass density. The portion of the plane x+2y+z=4 above the region bounded by $y=x^{2}$ and $y=1, \rho(x, y, z)=y$

Let A = {1, 2, 3, 4} and B = {1, 2, 3, 4, 5, 6}. (a) How many functions are there from A to B? How many of these are one-to-one? How many are onto? (b) How many functions are there from B to A? How many of these are onto? How many are one-to-one?

Many senior statesmen, including Henry Clay and John C. Calhoun, worked on the ____ .

If a quadratic equation has imaginary solutions, how is this shown on the graph of

$$y = a x ^ { 2 } + b x + c ?$$

An unfinished concrete duct, of diameter 1.5 m, is flowing half-full at

$$8.0 m^3/s$$

. (a) Is this a critical flow? If not, what is (b) the critical flow rate, (c) the critical slope, and (d) the Froude number? (e) If the flow is uniform, what is the slope of the duct?

True or False. The value of the opportunity cost of a particular choice is the same for all people.

Use properties of exponents to simplify each expression. Express answers in exponential form with positive exponents only. Assume that any variables in denominators are not equal to zero. $\frac{2 x^{5} \cdot 3 x}{15 x^{6}}$

Decide if the given statement is true or false, and give a brief justification for your answer. If true, you can quote a relevant definition or theorem. If false, provide an example, illustration, or brief explanation of why the statement is false. The charge on a capacitor in an RL circuit with no driving force varies periodically with time.

A tennis court is surrounded by a fence so that the distance from each boundary of the tennis court to the fence is the same. If the tennis court is 78 feet long and 36 feet wide, what is the area of the entire surface inside the fence?

True/False. If a child class defines a method with the same signature as a method in its parent class, an error will occur.

Yolanda's sunflower plant was 64.34 centimeters tall in July. During August, the plant grew 18.2 centimeters. Part A Estimate the height of Yolanda's plant at the end of August by rounding each value to the nearest whole number. Will your estimate be less than or greater than the actual height? Explain your reasoning. Part B What was the exact height of the plant at the end of August? Was the estimate less than or greater than the exact value?

use the Law of Sines to solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places. A = 76°, a = 34, b = 21

Solve the equation, using the quadratic formula. If the equation has no real solution, so state. 3x²=9x-5