As a television executive, you have been given 21 shows to choose from to run during your prime time slots each week. If you have to choose 7 shows to run on your network, how many ways can you choose which shows to pick up?

116,280 ways.

Step-by-step explanation:

In choosing the shows, the order in which you pick them does not matter; therefore it is a combination. Thus, the number ways you can choose 7 shows from 21 is

You can choose 7 shows from 21 in 116,280 ways.

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.