<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>
Answer:
375,400
Step-by-step explanation:
- 3.754*10^5
- 10^5=100,000
- 3.754*100,000
- 375,400
YaYYYY u got it! =)
Answer:
19 pens, 7 pencils, 3 erasers
Step-by-step explanation:
Huxian needs to pack 171 pens
63 pencils
27 erasers
Hence the items can be divided in 9 bags
171/9
= 19
63/9
= 7
27/9
= 3
They can be packed in each bags as follows
19 pens
7 pencils
3 erasers
Using the combination formula, it is found that there are 84 ways to choose the three tiles.
The order in which the tiles are chosen is not important, hence the <em>combination formula</em> is used to solve this question.
<h3>What is the combination formula?</h3>
is the number of different combinations of x objects from a set of n elements, given by:
In this problem, three tiles are chosen from a set of nine, hence:
There are 84 ways to choose the three tiles.
More can be learned about the combination formula at brainly.com/question/25821700
Answer:
cups
Step-by-step explanation:
- 1 pound = 1 3/4 cups
- 1/2 pound = 7/8 cups
- 1 3/4 + 7/8 = 21/8
- 21/8 = 2 5/8
I hope this helps!
