Kris has 24 points and Julio has 12 points. I kept on trying different numbers until I got 12. Next, I multiplied 12 by 2 and it equaled 24. Finally, I added 24+12 which equaled 36. This is how I knew that Julio has 12 points and Kris has 24 points.
<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:
2 = x
Step-by-step explanation:
1: Add 5x to both sides ( to get rid of 5x, we are adding it because it is negative )
3 - 5x + 5x = -9 + x + 5x
3 = 6x -9
2: Add 9 to both sides ( to get rid of the 9, we are adding it because it is negative )
3 + 9 = 6x - 9 + 9
12 = 6x
3: Divide both sides by 6 to get x by itself
12/6 = 6x/6
2 = x
- Note: the reason why we make changes to both sides is to keep the statement true ( equal ) -
If there are any questions, feel free to comment or message me!
Answer:
Length of rear-view mirror = 0.3462 m
Step-by-step explanation:
- As per the attachment first thing we need to calculate is the angle of incidence of light "α" reflected from the rear view mirror to the eyes of the driver.
- As per the diagram the following calculations are:
- α = arctan(half length L of the rear view window / distance between the focus point and the centre of the rear view window).
- half length L of the rear view window = 1.5/2 = 0.75 m
- Distance between the focus point and the center of the rear view window = 0.6+2.0 = 2.6 m
hence,
- α = arctan(0.75/2.6)
- α = 16.091 degrees
Now the we will use α to calculate length of the rear view mirror.
length of the rear view mirror = 2 x 0.6 x tan(α)
length of the rear view mirror = 2 x 0.6 x tan(16.091)
length of the rear view mirror = 0.3462 m