Write a function that models each variation.

x = 1/3, y = 1/5, and r = 3 when z = 1/2, and z varies directly with x and inversely with the product of r² and y.

Two cards are drawn from a standard 52-card playing deck. what is the probability that the draw will yield an ace and a face card?

A worm is at the bottom of a 10-foot wall. Every day the worm crawls up 3 feet, but at night it slips down 2 feet. How many days does it take the worm to get to the top of the wall?

Put in order from large to small: 0,2,-1.5,-2,0.5,-5

John had 2/3 of his homework complete, Sarah had 5/10, Alex 7/8, and Michelle 1/2. Who competed the most of the homework assignment A) Michelle B) Sarah C) John D) Alex

There are 28 total students in Mr. Flynn's class. The ratio of his students who are in the play to those who are not in the play is 2.5. How many of Mr. Flynn's students are in the play?

How do you multiply a mixed fraction by a regular fraction

Roger has 4 gallons of juice. He puts the same amount of juice into each of 5 pitchers. How many gallons of juice are in 1 pitcher?

400 students were randomly sampled from a large university, and 289 said they did not get enough sleep. Conduct a hypothesis test to check whether this represents a statistically significant difference from 50%, and use a significance level of 0.01.

Round off the number of seconds in an hour to 1 significant figure number of seconds = 3600

The sum of two numbers is 50. Two times the smaller number exceeds the larger number by 31. Find the numbers.