Carl takes a 4-inch by 3-inch rectangle of fabric and cuts from one corner of the piece of fabric to the diagonally opposite corner. now carl has two equally sized triangles of fabric. what is the perimeter of each triangle?

Find the pattern and use it to list the nth term in the sequence. 6, 12, 20, 30, 42, 56, the nth term of the sequence is

Acompany manufactures three types of cabinets. it makes 110 cabinets each week. in the first week, the sum of the number of type-1 cabinets and twice the number of type-2 cabinets produced was 10 more than the number of type-3 cabinets produced. the next week, the number of type-1 cabinets produced was three times more than in the first week, no type-2 cabinets were produced, and the number of type-3 cabinets produced was the same as in the previous week.

Aclassroom is made up of 11 boys and 14 girls. the teacher has four main classroom responsibilities that she wants to hand out to four different students (one for each of the four students). if the teacher chooses 4 of the students at random, then what is the probability that the four students chosen to complete the responsibilities will be all boys?