Assume that you have 5 different types of vegetables and 10 different types of fruit. a vegetable salad consists of a mixture of any 3 types of vegetables, and a fruit salad consists of a mixture of 2 kinds of fruit. (1) in how many different ways can you prepare a vegetable salad and a fruit salad?

10 different vegetable salads 45 different fruit salads. The formula for picking m of n items is n!/(m! (n-m)!). To show how this formula works, let's deal with the vegetable salad problem. This problem involves using factorials. N factorial is simply 1 times 2 times 3 times ... N. This represents the number of ways you can arrange N objects and is written as N!. So imagine for the vegetable salad, you place on the table all 5 different vegetables and select the 1st 3 of the arrangement. For 5 vegetables, you can arrange them in 5! ways which is 1 * 2 * 3 * 4 * 5 = 120 different arrangements. You pick the 1st 3 vegetables and you're left with 2 vegetables you haven't selected. There are 2! ways for those leftover vegetables to ordered which is 2! = 1 * 2 = 2 and you really don't care what their order is, so divide the 120 by 2 giving you 60 different ways that you could have picked up the 3 vegetables you are going to use. But does it really matter about the order you picked up those 3 vegetables? No it doesn't. So divide once again by 3! giving you 60 / 6 = 10 different possible vegetable salads. If we had plugged in the numbers we get 5!/(3!(5-3)!) = 120/(6(2)!) = 120/(6*2) = 120/12 = 10. Now for the fruit salad, we can plug in the numbers getting 10!/(2!(10-2)!) = 3628800 / (2(8)!) = 3628800/(2*40320) = 3628800/80640 = 45 different fruit salads

Okay so for every triangle has three angles that always add up to 180 degrees. and to tell the difference between whether they are secure, right or obtuse is that acute: has one angle that is less than 90 degrees. right triangle means there is at least one angle that is exactly 90 degrees. and an obtuse angle has an angle that is bigger than 180 degrees. i’ll do #13 as an example: 13. 40 and 50 so if every triangle has 180 degrees 40+50= 90 degrees then180-90= 90 degrees so the third angle is 90 degrees and because this triangle has a 90 degree angle it means it is a right triangle