What is the probability of having 53 Sunday in the year 2024​

here in ques it is not specifically said that the year is leap year or non leap year . so i am writing the answer for both conditions.

considering a non leap year

see we have 365 days in a non-leap year.

52 weeks and one extra day= 365 days

52 weeks means definitely there are 52 sundays (this is true for all other days also).

that means if the extra day comes out to be sunday then we will have 53 sundays.

so now the ques boils down to what is the prob of this extra day to be a sunday .

this extra one day can be {monday or tuesday or wednesday or thursday or friday or saturday or sunday }= samplespace (s)

i.e n(s) = 7

so prob of this extra one day to be a sunday is 1/7.

[note - this is also the answer for having 53 mondays or 53 tuesdays or 53 wednesdays or 53 thursdays or 53 fridays or 53 saturdays.]

considering a leap year

leap year contains 366 days

52 weeks plus two two extra days

52 weeks means definitely there are 52 sundays (this is true for all other days also).

if either of these two is sunday then we will have 53 sundays

these two days can be {mon, tue} or { tue , wed} or { wed , thurs} or {thurs , fri} or { fri, sat} or { sat , sun} or {sun , mon} i.e total =7

out of these only two outcomes i.e { sat , sun} and {sun , mon} is having sunday with them .

so our desired prob is 2/7.

Step-by-step explanation:

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt