A restaurant offers three courses, appetizers, main dishes and deserts. It has 6 choices of appetizers, 10 choices of main dishes and 8 choices of desserts. How many different meals are there if a customer can order only one dish from each course and can have a meal consisting of one course only, two different courses or a meal with all three courses.

The distance of a chord from the centre of a circle is 12cm and the lenght of the chord is 10cm. find the radius of the circle

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.

If sr is 4.5cm and tr is 3cm, what is the measure in degrees of angle s? a. 56.3 b. 33.7 c. 41.8 d. 48.2