Answer:
93,675
Step-by-step explanation:
We see that the given sequence is an arithmetic sequence with first term 997, common difference -5, and last term 252.
The number of terms in the sequence (n) can be found from the formula for the n-th term:
an = a1 +d(n -1)
(an -an)/d +1 = n
(252 -997)/(-5) +1 = n = 150
The sum of these terms is the average of the first and last terms, multiplied by the number of terms:
S150 = (997 +252)/2·150 = 93,675
The sequence sum is 93,675.
Answer: 12 practice sessions
Step-by-step explanation:
You can represent the word problem in this equation: 200+50x<775 OR 200+50x=775
If you subtract 200 from 775, you’ll be left with: 50x=575
Count by fifties until you get to 575. You’ll notice that 50 doesn’t go into 575 evenly! However, this won’t matter, because Helga wants to make AT LEAST 775. So you can round up to 12 practices instead of 11, which will equal 800 dollars instead of 750.
Answer:
Step-by-step explanation:
4
Answer:
14.52% are unicyclists
Step-by-step explanation:
First, we can use proportions to find the number of unicyclists at the convention. Since we know that the ratio of unicyclists to aerial artists is 9:11, and there are 88 aerial artists, we can set up the following equation:

If we cross multiply, we get that 11x = (88)(9). After we divide through by 11 to isolate x, we get that x = (8)(9) = 72
Second, we have to figure out the number of mimes at the convention to figure out the total number of people there. We know that the ratio of unicyclists to mimes is 3:14, and the number of unicyclists is 72. So, we can set up the following proportion:

If we cross multiply, we get that 3y = 1008, or y = 336 mimes
The total number of people at the convention is 336 mimes + 72 unicyclists + 88 unicyclists = 496. Now we have to figure out what percent of 496 is 72 (the number of unicyclists). If we let z = the percentage, we can simply set up an equation that says that 72 is z% of 496:

This means that approximately 14.52% of the performers are unicyclists.
Answer:
25
Step-by-step explanation:
10 times 5 equals 50
50 divided by 2 equals 25