Let $G$ be an Abelian group and $H = \{ x \in G | | x |$ is 1 or even $\} .$ Give an example to show that $H$ need not be a subgroup of $G .$

Find (a) the complement and (b) the supplement of an angle with the given measure. $50^{\circ} 40^{\prime} 50^{\prime \prime}$

Consider $f(x)=2 x^{2}$. Give a geometric interpretation of your result from previous sub-question.

Can the perimeter of a rectangle be any integer value?

Round the value of each annuity to the nearest dollar. Suppose that you would like to have $25,000 to use as a down payment for a home in five years by making regular deposits at the end of every three months in an annuity that pays 7.25% compounded quarterly. a. Determine the amount of each deposit. Round up to the nearest dollar. b. How much of the$25,000 comes from deposits and how much comes from interest?

Graph the figure and its image after a reflection in the line $y = x$. $\overline { S T }$ with endpoints $S ( - 2,5 ) \text { and } T ( - 4 , - 1 )$

Simplify the rational expression, if possible.

$$\frac { 3 m ^ { 2 } - 10 m + 8 } { 6 - m - m ^ { 2 } }$$

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 vector (x, y) in

$$\mathbb { R } ^ { 2 }$$

is the same as the vector (x, y, 0) in

$$\mathbb { R } ^ { 3 }.$$

Consider the following cases. $\textbf{(a)}$ A small 0.6 -in.-long fish swims with a speed of 0.8 in/s . Would a boundary layer type flow be developed along the sides of the fish? Explain. $\textbf{(b)}$ A 12 -ft-long kayak moves with a speed of 5 ft/s. Would a boundary layer type flow be developed along the sides of the boat? Explain.

a) Graph the circle defined by $x ^ { 2 } + y ^ { 2 } = 100$ b) Verify algebraically that the points P(-8, 6) and Q(6, 8) are both on the circle. c) Find an equation for the right bisector of the chord PQ. d) Verify that the right bisector in part c) passes through the centre of the circle. e) Do you think that the right bisector of any chord of the circle passes through the centre of the circle? Explain your reasoning.

What is the statement "I'll never be able to do this" an example of? a. aiming for perfection b. negative thinking c. optimism d. resilience

In which phylum do organs and organ systems first appear?

Write a computer program (or develop an algorithm) to determine whether a given nonnegative integer is a Fibonacci number.

You are trying out for the basketball team in a few months. Your friend is trying out for the volleyball team. He asked you to train with him. What types of activities would be beneficial to both of you? What types of activities would be more beneficial to you?