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A computer is asked to randomly generate a four-digit number. What is the probability the number is less than 7000 and an odd number

How many distinguishable permutations can be formed from the letters of the given word? lotto

(6.5) Evaluate arcsin \(\left[\sin \left(\frac{5 \pi}{6}\right)\right]\).

Use a calculator to verify that each pair of combinations is equal. $$_{7} C_{2},_{7} C_{5}$$

A number is called a "perfect number" if the sum of its proper factors is equal to the number itself. Six is the first perfect number since the sum of its proper factors is six: \(1+2+3=6 .\) Twenty-eight is the second since: \(1+2+4+7+14=28 .\) A young child is given a box containing eight wooden blocks with the following numbers (one per block) printed on them: four 3 's, two 5 's, one \(0,\) and one \(6 .\) What is the probability she draws the eight blocks in order and forms the fifth perfect number: \(33,550,336 ?\)

Temperature fluctuation: At 5 P.M. in Coldwater, the temperature was a chilly \(36^{\circ} \mathrm{F}\). If the temperature decreased by \(3^{\circ} \mathrm{F}\) every half-hour for the next \(7 \mathrm{hr}\) at what time did the temperature hit \(0^{\circ} \mathrm{F} ?\)

Arc of a baby swing: When Mackenzie's baby swing is started, the first swing (one way) is a 30 -in. arc. As the swing slows down, each successive arc is \(\frac{3}{2}\) in. less than the previous one. Find (a) the length of the tenth swing and (b) how far Mackenzie has traveled during the 10 swings.

Computer animations: The animation on a new computer game initially allows the hero of the game to jump a (screen) distance of 10 in. over booby traps and obstacles. Each successive jump is limited to \(\frac{3}{4}\) in. less than the previous one. Find (a) the length of the seventh jump and (b) the total distance covered after seven jumps.

The Fox Theater creates a "theater in the round" when it shows any of Shakespeare's plays. The first row has 80 seats, the second row has \(88,\) the third row has \(96,\) and so on. How many seats are in the 10 th row? If there is room for 25 rows, how many chairs will be needed to set up the theater? PICTURE CANT COPY

Sales goals: At the time that I was newly hired, 100 sales per month was what I required. Each following month- the last plus 20 more, as I work for the goal of top sales award. When 2500 sales are thusly made, it's Tahiti, Hawaii, and pina coladas in the shade. How many sales were made by this person in the seventh month? What were the total sales after the 12 th month? Was the goal of 2500 total sales met after the 12 th month?