All Answers 358087 Answers

 it seems to be common pracice to accept that the first line is the 0 line, so it is easiest just to ignore that one

the sequence is    2,4,8,16,32

I can just see that this is   2^n    but if that is not immediately obvious to you, you can inspect it as a sequence.

since  4/2 = 8/4 = 16/8 = 32/16 = 2

this is a GP   

the first term is 2 and the common difference is 2

\(T_n=ar^{(n-1)}\\~\\ T_n=2*2^{(n-1)}\\~\\ T_n=2^{(n-1+1)}\\~\\ T_n=2^n\)

i think you mean 2 instead of 22

What is the total patient revenue for a physician practice that recorded $1.2 million in cash deposits and the gross collection rate for the same consecutive 12-month period is 60%?

15566 , 15656 , 15665 , 16556 , 16565 , 16655 , 23556 , 23565 , 23655 , 25356 , 25365 , 25536 , 25563 , 25635 , 25653 , 26355 , 26535 , 26553 , 32556 , 32565 , 32655 , 33455 , 33545 , 33554 , 34355 , 34535 , 34553 , 35256 , 35265 , 35345 , 35354 , 35435 , 35453 , 35526 , 35534 , 35543 , 35562 , 35625 , 35652 , 36255 , 36525 , 36552 , 43355 , 43535 , 43553 , 45335 , 45353 , 45533 , 51566 , 51656 , 51665 , 52356 , 52365 , 52536 , 52563 , 52635 , 52653 , 53256 , 53265 , 53345 , 53354 , 53435 , 53453 , 53526 , 53534 , 53543 , 53562 , 53625 , 53652 , 54335 , 54353 , 54533 , 55166 , 55236 , 55263 , 55326 , 55334 , 55343 , 55362 , 55433 , 55616 , 55623 , 55632 , 55661 , 56156 , 56165 , 56235 , 56253 , 56325 , 56352 , 56516 , 56523 , 56532 , 56561 , 56615 , 56651 , 61556 , 61565 , 61655 , 62355 , 62535 , 62553 , 63255 , 63525 , 63552 , 65156 , 65165 , 65235 , 65253 , 65325 , 65352 , 65516 , 65523 , 65532 , 65561 , 65615 , 65651 , 66155 , 66515 , 66551 , Total =  120 five-digit such integers.

To get a product of 900, we need to find the prime factorization of 900: $900=2^2 \cdot 3^2 \cdot 5^2$.

Since we're rolling a standard 6-sided die, the only possible prime factors of each roll are 2, 3, and 5 (which are the prime factors of 6).

We need to distribute the prime factors of 900 among the five rolls in such a way that we get 2, 3, or 5 as the outcome of each roll. Note that each factor can appear zero or more times in each roll.

To do this, we can use the following technique: we represent each roll as a string of three digits, where each digit is either 0, 1, or 2, representing the number of times the factor 2, 3, or 5 appears in that roll. For example, the roll (2, 2, 5) would be represented as the string "220".

Now, we need to count how many such strings of length 15 (5 rolls, each represented by a string of length 3) we can form, where each digit is 0, 1, or 2, and the product of the five rolls is 900.

We can solve this problem using a technique called stars and bars. Imagine we have 15 stars, representing the 15 digits in the 5 rolls. We want to divide these stars into 3 bins, representing the factors 2, 3, and 5. We can do this by placing 2 bars among the stars, which will divide the stars into 3 groups. The number of stars in the first group represents the total number of 2's rolled, the number of stars in the second group represents the total number of 3's rolled, and the number of stars in the third group represents the total number of 5's rolled.

For example, if we roll 2 2 3 3 5, we would represent this as the string "220330550", which corresponds to the stars-and-bars representation "||||*****", where the first two stars are in the first bin (representing the 2's), the next two stars are in the second bin (representing the 3's), and so on.

The number of ways to place 2 bars among 15 stars is ${15+2\choose 2}={17\choose 2}=136$. Therefore, there are 136 different sequences of rolls that could have led to a product of 900.

The probability is 7/96.

thankyou

Did you look under your first post?

n=(1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989)=1,000 decimal digits of Pi.

0=93 , 1=116 , 2=103 , 3=102 , 4=93 , 5=97 , 6=94 , 7=95 , 8=101 , 9=106 Total of all digits = 1000 

skill difficulty

So Melody,

How do we go about finding what type of sequence is generated here?

Ok, so we can start off by expanding each side:

6c+3=84c-9

Add 9 to both sides:

6c+12=84c

Subtract 6c on both sides:

12=72c

Finally, you can divide 72 on both sides to isolate c:

1/6=c

So the answer I think is just 1/6

No,because using the triangle inequality, 12+30 is less than 43, so there is no way it could make a triangle

The sum of the 0 row is 2^0 = 1

the sume of the nth row is  2^n

the sum of the 10th row is 2^10  = 1024

the sum of the 20th row is  2^20

etc

Could you perhaps indicate what the sum of the 10th row would be?

Thank you guest,

still no idea what all thatmeans, but thank you...do appreciate your time.