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Unless otherwise specified, assume that all matrices in these exercises are n X n. Determine which of the matrices in are invertible. Use as few calculations as possible. Justify your answers.
A standard drinking straw is 23 cm tall. What pressure difference is needed to raise a column of water that high? (When we drink, this pressure difference is supplied by one's mouth.) Assume the density of water is 1.0 g/cm3. You will need to use F =..
You pick cards one at a time without replacement from an ordinary deck of 52 playing cards. What is the minimum number of cards you must pick in order to guarantee that you get (a) a pair
A parcel delivery service will deliver a package only if the length plus girth does not exceed 108 inches.
You're buying a new car that sells for $12006. The state sales tax rate, as a decimal, is .07. How much will the sales tax come to?
A regular triangular pyramid has a base, b, of 3.9m, a height, h, of 3.9m, and a height, H, of 15.8m. Find the volume of the pyramid to the nearest square unit.
Make sure you build or generate at least five more Pythagorean Triples using one of the many formulas available online for doing this. After building your triples, verify each of them in the Pythagorean Theorem equation.
Over the last ?fty years, mortgage rates have ?uctuated from a high of around $18 1/2 % in the early 1980s to a low of around $4 1/2 % last fall. What would the monthly payments be on a thirty-year $100,000 mortgage at each rate? What would the to..
A 180-lb man carries a 5-lb can of paint up a helical staircase that encircles a silo with radius 25 ft. If the silo is 80 ft high and the man makes exactly four complete revolutions, how much work is done by the man against gravity in climbing to..
Kaya has two 750ml cans of juice. She wants to put the juice in a 1.5L pitcher. Will the pitcher hold all of the juice? Explain your answer.
Define the following predicate P(x,y,z) for naturals x and y and positive naturals z. If x = z, then P(x,y,z) is false.
Probability of Lamp Failure, A lamp has two bulbs, each of a type with an average lifetime of 6 hours. The probability density function for the lifetime of a bulb
Calculate the molar mass of the polymer sample from the mark-houwink equation
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