<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>
<h3>
Answer: 4900 (choice D)</h3>
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Work Shown:
1 km = 1000 m
3.5 km = 3500 m ............. multiplying both sides by 3.5
(70 paces)/(50 m) = (x paces)/(3500 m)
70/50 = x/3500
7/5 = x/3500
7*3500 = 5x .............. cross multiply
5x = 7*3500
x = (7*3500)/5
x = (7*5*700)/5
x = 7*700
x = 4900
Ann takes 4900 paces to walk 3.5 km
Answer:
Problem 4: y = -8x+b
Problem 5: C: 3x-2
Step-by-step explanation:
<u>Problem 4:</u>
The given line is in slope intercept form.
The slope-intercept form is:
Here the co-efficient of x is the slope of the line. Comparing the given equation with general form
m = -8
Two parallel lines have same slope so the slope of line will be -8.
b can be any positive or negative integer as we don't know any point on the line parallel to given line.
<u>Problem 5:</u>
Slope = 3
y-intercept = -2
Slope intercept of line is given by:
here m is slope and b is y-intercept
Putting the values
Option C: y=3x-2 is the correct answer
Hence,
Problem 4: y = -8x+b
Problem 5: C: 3x-2
Answer: yes, the equation 
is a slope-intercept form.
Step-by-step explanation:
-The equation of a slope-intercept form:
(where 
represents the slope, and 
represents the y-intercept).
Step-by-step explanation:
The answer is
If naya is 4 years old then 3 times Adam age is 12
After 4 years naya is 8 years old and Adam is 16
We can check it because twice of 8 is 16
So now Adam is 12 years and Naya is 4 years old
