Composition of relations $R_2\circ R_1:\{(x,z)|(x,y)\in R_1\text{ and }(y,z)\in R_2\}$

A student wrote the following conjecture. Find a counterexample and explain the error. If x is a positive even number and y is any integer, then the product xy will be positive.

Eliminate the parameter to find a Cartesian equation of the curve. y=(t+1)^1/2, y=(t-1)^1/2

A portfolio’s expected return is 12%, its standard deviation is 20%, and the risk-free rate is 4%. Which of the following would make for the greatest increase in the portfolio’s Sharpe ratio? a. An increase of 1% in expected return. b. A decrease of 1% in the risk-free rate. c. A decrease of 1% in its standard deviation.

A sequence is defined recursively.Write down the first five terms. $a_{1}=1 ;\ a_{n}=n-a_{n-1}$

Evaluate the integrals. $\int x \ln x d x$

The Isosceles Triangle Angle Bisector to Congruent Sides Theorem states: "In an isosceles triangle, the angle bisectors to the congruent sides are congruent." Draw and label a diagram you can use to help you prove this theorem. State the "Given" and "Prove" statements.

a. What are some examples of cognitive activities? b. How do psychologists help their patients control feelings of anxiety? c. Do you think it is worth while for psychologist to conduct their research using animal subjects? Why or why not?

How is it that nonrenewable resources can be extended indefinitely, while renewable resources are exhaustible?

What words are missing? El mesero le sirve una copa de vino a la señorita. El mesero __ __ _____.

What is the physical significance of the Reynolds number? How is it defined for (a) flow in a circular pipe of inner diameter D and (b) flow in a rectangular duct of cross section $a imes b?$

Fill in each blank so that the resulting statement is true. The circumference, C, of a circle with radius r is given by the formula ____.

Draw and label a diagram of the eastern horizon from northeast to southeast and label the rising point of the sun at the solstices and equinoxes.

Briefly explain the importance of each of the following. command economy