<span>There are several ways to do this problem. One of them is to realize that there's only 14 possible calendars for any year (a year may start on any of 7 days, and a year may be either a leap year, or a non-leap year. So 7*2 = 14 possible calendars for any year). And since there's only 14 different possibilities, it's quite easy to perform an exhaustive search to prove that any year has between 1 and 3 Friday the 13ths.
Let's first deal with non-leap years. Initially, I'll determine what day of the week the 13th falls for each month for a year that starts on Sunday.
Jan - Friday
Feb - Monday
Mar - Monday
Apr - Thursday
May - Saturday
Jun - Tuesday
Jul - Thursday
Aug - Sunday
Sep - Wednesday
Oct - Friday
Nov - Monday
Dec - Wednesday
Now let's count how many times for each weekday, the 13th falls there.
Sunday - 1
Monday - 3
Tuesday - 1
Wednesday - 2
Thursday - 2
Friday - 2
Saturday - 1
The key thing to notice is that there is that the number of times the 13th falls upon a weekday is always in the range of 1 to 3 days. And if the non-leap year were to start on any other day of the week, the numbers would simply rotate to the next days. The above list is generated for a year where January 1st falls on a Sunday. If instead it were to fall on a Monday, then the value above for Sunday would be the value for Monday. The value above for Monday would be the value for Tuesday, etc.
So we've handled all possible non-leap years. Let's do that again for a leap year starting on a Sunday. We get:
Jan - Friday
Feb - Monday
Mar - Tuesday
Apr - Friday
May - Sunday
Jun - Wednesday
Jul - Friday
Aug - Monday
Sep - Thursday
Oct - Saturday
Nov - Tuesday
Dec - Thursday
And the weekday totals are:
Sunday - 1
Monday - 2
Tuesday - 2
Wednesday - 1
Thursday - 2
Friday - 3
Saturday - 1
And once again, for every weekday, the total is between 1 and 3. And the same argument applies for every leap year.
And since we've covered both leap and non-leap years. Then we've demonstrated that for every possible year, Friday the 13th will happen at least once, and no more than 3 times.</span>
16 wide
Step-by-step explanation:
because i do 8 x 2
Answer:Jason is 5 years old.
John is 4 years old.
Jackson is 12 years old.
Step-by-step explanation:
Let x represent the age of Jason.
Let y represent the age of John.
Let z represent the age of Jackson.
The ages of three siblings Jason John and Jackson totals 21 years. It means that
x + y + z = 21 - - - - - - - - - - -1
Jason is one year older than John. It means that
x = y + 1
Jackson is three times as old as John. It means that
z = 3y
Substituting x = y + 1 and z = 3y into equation 1, it becomes
y + 1 + y + 3y = 21
5y = 21 - 1 = 20
y = 20/5 = 4
x = y + 1 = 4 + 1
x = 5
z = 3y = 3 × 4
z = 12
The greatest common factor of the three numbers is 15
In order to use the elimination method<span>, you have to create variables that have the same coefficient—then you </span>can eliminate<span> them. Multiply the top </span>equation<span> by 5. Next add the </span>equations<span>, and </span>solve<span> for y. Substitute y = 10 into one of the original </span>equations<span> to find x.</span>
