What is the molality of ethanol (C2H5OH) in an aqueous solution that is 48.2% ethanol by mass? (Report your answer to two decimal places, i.e. xx.xx, and no units are necessary in the answer.)

A volume of 25.0 mL of 0.100 M C6H5CO2H(aq) is titrated with 0.100 M NaOH(aq). What is the pH after the addition of 12.5 mL of NaOH? (Ka of benzoic acid = 6.4 × 10–5) (Report your answer to two decimal places, i.e. x.xx)

Kelly, the clinical documentation improvement (CDI) manager at UC Health, has assessed the attributes of her workgroup, and most of them exhibit high-performance abilities and high motivation to achieve within the job setting. She is going to adjust her leadership style to match the workgroup’s attributes. The type of theory that this addresses is the _______________ and the type of leadership she needs to practice is ________________________.

On paper, show how to find lcm(77, 70) without using a calculator.

Which method of proof would be the best choice for proving the following claim? Claim: For all positive integers m{“version”:”1.1″,”math”:”m”} and n{“version”:”1.1″,”math”:”n”}, if mn≥65{“version”:”1.1″,”math”:”mn≥65″}, then m>8{“version”:”1.1″,”math”:”m>8″} or n>8{“version”:”1.1″,”math”:”n>8″}.

Simplify the proposition ¬∃x(Z(x)∧¬R(x)){“version”:”1.1″,”math”:”¬∃x(Z(x)∧¬R(x))”} by moving the negation symbol as far inside the parentheses as possible.  Show all work on paper.  When you are finished, type “done” in the space below.

Let R(x) = “x is a rational number” and let Z(x) = “x is an integer”.  The domain of x is the real numbers.  Match each proposition below with its English translation.  Not all translations will be used.  

Free point (pick TRUE)

High heat and high pressure without full melting will lead to ________ rocks.

An avulsion fracture, Jones fracture, and stress fracture are the three most common types of fractures sustained by this bone.