We will set a variable, d, to represent the day of the week that January starts on. For instance, if it started on Monday, d + 1 would be Tuesday, d + 2 would be Wednesday, etc. up to d + 6 to represent the last day of the week (in our example, Sunday). The next week would start over at d, and the month would continue. For non-leap years:
If January starts on <u>d</u>, February will start 31 days later. Following our pattern above, this will put it at <u>d</u><u> + 3</u> (28 days would be back at d; 29 would be d+1, 30 would be d+2, and 31 is at d+3). In a non-leap year, February has 28 days, so March will start at <u>d</u><u>+3</u> also. April will start 31 days after that, so that puts us at d+3+3=<u>d</u><u>+6</u>. May starts 30 days after that, so d+6+2=d+8. However, since we only have 7 days in the week, this is actually back to <u>d</u><u>+1</u>. June starts 31 days after that, so d+1+3=<u>d</u><u>+4</u>. July starts 30 days after that, so d+4+2=<u>d</u><u>+6</u>. August starts 31 days after that, so d+6+3=d+9, but again, we only have 7 days in our week, so this is <u>d</u><u>+2</u>. September starts 31 days after that, so d+2+3=<u>d</u><u>+5</u>. October starts 30 days after that, so d+5+2=d+7, which is just <u>d</u><u />. November starts 31 days after that, so <u>d</u><u>+3</u>. December starts 30 days after that, so <u>d</u><u>+5</u>. Remember that each one of these expressions represents a day of the week. Going back through the list (in numerical order, and listing duplicates), we have <u>d</u><u>,</u> <u>d,</u><u /> <u>d</u><u>+1</u>, <u>d</u><u>+2</u>, <u>d+3</u><u>,</u> <u>d</u><u>+3</u>, <u>d</u><u>+3</u>, <u>d</u><u>+4</u>, <u>d</u><u>+5</u>, <u>d</u><u>+5</u>, <u /><u /><u>d</u><u>+6</u><u /><u /> and <u>d</u><u>+6</u>. This means we have every day of the week covered, therefore there is a Friday the 13th at least once a year (if every day of the week can begin a month, then every day of the week can happy for any number in the month).
For leap years, every month after February would change, so we have (in the order of the months) <u></u><u>d</u>, <u>d</u><u>+3</u>, <u>d</u><u>+4</u>, <u>d</u><u />, <u>d</u><u>+2</u>, <u>d</u><u /><u>+5</u>, <u>d</u><u />, <u>d</u><u>+3</u>, <u>d</u><u /><u>+6</u>, <u>d</u><u>+1</u>, <u>d</u><u>+4</u>, a<u />nd <u>d</u><u>+</u><u /><u /><u>6</u>. We still have every day of the week represented, so there is a Friday the 13th at least once. Additionally, none of the days of the week appear more than 3 times, so there is never a year with more than 3 Friday the 13ths.<u />
I think B I'm not sure but if I think it's B, if it is not, let me know.
Answer:
True.
Step-by-step explanation:
Since they are all on the number line and some are negative, you would go back and go up instead. If you were to check again, it would be all on the number line.
Answer:3^x
9, 15, 33, 87, 249
(4, 87) for example
Step-by-step explanation:
a) First differences of the f(x) values in the table are ...
19 -13 = 6, 37 -19 = 18, 91 -37 = 54, 253 -91 = 162
The second differences are not constant:
18 -6 = 12, 54 -18 = 36, 162 -54 = 108
But, we notice that both the first and second differences have a common ratio. This is characteristic of an exponential function. The common ratio is 18/6 = 3, so the parent function is 3^x.
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b) Translating a function down 4 units subtracts 4 from each y-value. The values of f(x) in the table would be ...
9, 15, 33, 87, 249
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c) The x-values of the function stay the same for a vertical translation, so the points in the table of the transformed function are ...
(x, f(x)) = (1, 9), (2, 15), (3, 33), (4, 87), (5, 249)
i hope this helps
I think the answer is 18.
Equation/ steps:
12+v=30
30-12= 18
V=18
Hope this helps!
