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Solve the word problem using this 4-step model. (1) Tell what the variable represents, (that is, x = ??); (2) write a rational equation that models the problem; (3) solve the equation for the exact solution ; (4) write your answer in words, labeling units as necessary. Hank bicycles 5 km/hour slower than Kelly. In the time that it takes Hank to bicycle 42 km, Kelly can bicycle 57 km. How fast does each bicyclist travel?
Find the equation of a parabola whose vertex is (0,0) and directrix is the line y=3. Find the vertex, focus, and directrix of (x-2)^2=12(y+1). Find the latus rectum and graph the parabola, making sure that all points and axis are labeled.
During the first part of a trip, a canoeist travels 42 miles at a certain speed. The canoeist travels 21 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 2 hours. What was the speed on each part of the t..
I wish to find the general nontrivial solution to the fourth order ODE with boundary conditions
On average 12 people every half hour check in at Counter A at the Qantas domestic terminal at Terminal 2 at Sydney airport. The people arrive at the counter randomly and independently.
Derive an identity for nCk via inclusion-exclusion by counting the k-multisets of [n] in which each element of [n] appears at most once. use p_i = "element i appears more than once in the multiset" as the i-th property, for 1
How do you make a decision in this situation? Also, how can one come up with the probability of success (or failure)?
What are the four categories of financial ratios? Choose one category (excluding liquidity ratios) and list and describe the various ratios in that category. What do the calculated numbers mean for these ratios?
Show that if R is a ring with identity element and x is an element in R, then Rx = {rx: r in R} is the principal left ideal generated by x. Similarly,
Total number of ways a customer can place the order, A bagel shop offers 14 varieties of bagels, 11 flavors of cream cheese, and 15 flavors of coffee. How many different orders for a bagel
Suppose that a tank initially contains 2000 gal of water and the rate of change of its volume after the tank drains for t min is '(t)=(0.5)t)-30 (in gallons per minute).
A company manufactures CD players. The quality control department checks 600 CD players and discovers that 12 of them are defective. What is the probability that a CD player is not defective?
One of the most famous unsolved problems in mathematics is a conjecture made by Christian Goldbach in a letter to Leonhard Euler in 1742. The conjecture made in this letter is now known as Goldbach's Conjecture. The conjecture is as follows:
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