Math problem: Of the total # of days in a week, what fraction occur only 52x in a leap year?

Question

Of the total number of days in a week, what fraction of them occur only 52 times in a leap year?
Please explain.

Another math problem:
If x^2 + y^2 = 15, xy=5, then x+y=...
Show work

Answer 1

In a leap year, 2 of the 7 days occur 53 times.
So the answer is 5/7 occur only 52 times.

If x^2 + y^2 = 15, xy=5, then x+y=...
x^2 +y^2 = 15
xy = 5

x^2 +2xy + y^2 = 15 +2*5
(x+y)^2 = 25
x+y = +/- 5

Answer 2

part 1

52 x 7 = 364
in a leap year there are 366 days
therefore 5 of the days will occur 52 times,
while 2 of the days occur 53 times

therefore 5/7 of them occur 52 times in a leap year.

part 2

x²+ y² = 15
xy = 5
xy =5
add all three equation together and we get
x² + 2xy + y² = 15 + 5 + 5
(x+Y)² = 25
x+y = +5 or -5

Answer 3

First multiply 52 times 7 to get the number of days in 52 weeks. This number is 364. In a leap year there are 366 days. The extra days are the only days that will occur 53 times during the year. So 5/7 of the days in a week occur 52 times in a leap year.

Answer 4

(x+y)² = x² + y² + 2xy = 15 + 10 = 25
x+y = 5 or -5.

52*7 = 364


d:

Answer 5

First problem: 1/7th

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