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a) Find a recurrence relation for the number of bit strings of length n that contain three consecutive 0s.
b) What are the initial conditions?
c) How many bit strings of length seven contain three consecutive 0s?
Explain Probability of birthdays. Are your best friends' birthdays dependent or independent events?
How many ways are there to deal hands of seven cards to each of five players from a standard deck of 52 cards? A bagel show has onion, poppy seed, egg, salty, pumpernickel, sesame seed, raisin, and plain bagels. How many ways are there to choose:
Factorize the given expression - Evaluate the perfect square
Suppose you throw a baseball straight up at a velocity of 64 feet per second. A function can be created by expressing distance above the ground, s, as a function of time, t. This function is s = -16t2 + v0t + s0
The sides of a triangle are in the ratio of 3:4:5. If the perimeter is 90 centimeters, find the length of each side. Use the Pythagorean Theorem to find the length of the missing side in right triangle. Triangle ABC with right triangle C.
Two angles are complementary of each other. Twice one angle is equal to the other angle plus the product of three and five. Set up a system of linear equations to represent the two angles.
If the minute hand and the hour hand on the clock both start at 12:00 when will the two hands first coincide? How many times will they coincide in 12 hours?
Prepare an equation for the number of cups you sell as a function of the price you charge - Write an equation for the number of cups you sell as a function of the price you charge. Denote "C" for number of cups, and "P" for the price you charge.
Use taylor series expansion to find the given variables.
Let n be a natural number, and let f: R-->R be the function f(x) :=x^n. Show that f is differentiable on R and f '(x)=nx^n-1 for all x belonging to R
Draw a tree diagram that illustrates the following. Three-fifths of kindergarten children are bussed to school, while two-fifths of the first to fifth graders are bussed.
A is the amount of material remaining from an initial amount I at a given time t and k is negative constant determined by the nature of the material.
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