A grocery store has available n watermelons to sell and makes $1.00 on each sale. Say the number of consumers of these watermelons is a random variable that has a distribution that can be approximated by

f(x) = 1/200, 0 < x < 200,

a p. d.f. of the continuous type. If the grocer does not have enoughwatermelons to sell to all consumers, she figures that she loses$5.00 in "good-will" from each unhappy customer. But if she has surplus watermelons, she loses 50 cents on each extra watermelon. What should n be to maximize "profit"? Hint : if X? n, then her profit is (1.00)X +(-0.50)(n-X); but if X > n, her profit is (1.00)n+(-5.00)(X-n). Find the expected value of profit asa function of n and then select n to maximize this.

In tossing one coin 10 times, what are your chances for tossing a head? a tail? 2. in tossing one coin 100 times, what are your chances for tossing a head? a tail? 3. in tossing one coin 200 times, what are your chances for tossing a head? a tail? deviation = ((absolute value of the difference between expected heads and observed heads) + (absolute value of the difference between expected tails and observed tails)) divided by total number of tosses. this value should always be positive. 4. what is the deviation for 10 tosses? 5. what is the deviation for the 100 tosses? 6. what is the deviation for 200 tosses? 7. how does increasing the total number of coin tosses from 10 to 100 affect the deviation? 8. how does increasing the total number of tosses from 100 to 200 affect the deviation? 9. what two important probability principles were established in this exercise? 10. the percent of occurrence is the obtained results divided by the total tosses and multiplied by 100%. toss the coins 100 times and record your results. calculate the percent occurrence for each combination. percent head-head occurrence: percent tail-tail occurrence: percent head-tail occurrence:

Acabinmaker buys 3.5 liters of oat varnish the varnish cost $4.95 per liter what is the total cost of 3.5 liters

In one day there are too high tides into low tides and equally spaced intervals the high tide is observed to be 6 feet above the average sea level after six hours passed a low tide occurs at 6 feet below the average sea level in this task you will model this occurrence using a trigonometric function by using x as a measurement of time assume the first high tide occurs at x=0. a. what are the independent and dependent variables? b. determine these key features of the function that models the tide: 1.amplitude 2.period 3.frequency 4.midline 5.vertical shift 6.phase shift c. create a trigonometric function that models the ocean tide for a period of 12 hours. d.what is the height of the tide after 93 hours?