1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ioda
2 years ago
13

Find the remainder when 1 + 2 + 2^2 + 2^3 + ... + 2^100 is divided by 7. Thanks in advance!

Mathematics
1 answer:
Firlakuza [10]2 years ago
4 0

Answer:

3.

Step-by-step explanation:

This is a geometric series so the sum is:

a1 * r^n - 1 / (r - 1)

= 1 * (2^101 -1) / (2-1)

= 2^101 - 1.

Find the remainder when 2^101 is divided by 7:

Note that 101 = 14*7 + 3 so

2^101 = 2^(7*14 + 3) =  2^3  * (2^14)^7 = 8 * (2^14)^7.

By Fermat's Little Theorem  (2^14) ^ 7 = 2^14 mod 7 = 4^7 mod 7.

So 2^101 mod 7 = (8 * 4^7) mod 7

                           = (8 * 4) mod 7

                            = 32 mod 7

                            = 4 = the remainder when 2^101 is divided by 7.

So the remainder when 2^101- 1 is divided by 7 is 4 - 1 = 3..

You might be interested in
Please answer quick! I've been stuck on this one a bit, I keep getting the wrong answer. (I'm not the best at math so maybe ya'l
g100num [7]

Answer:

x= 5.6

Step-by-step explanation:

Basically, if you do 7÷5 it would equal 1.4 so you would have to multiply 4x1.4 which would equal 5.6.

In conclusion 4/7 = 5.6/5

8 0
3 years ago
Read 2 more answers
I rlly need this now, show work pls :((
Sunny_sXe [5.5K]

Answer:

1. y=-x-3 2.y=1/3x-4

Step-by-step explanation:

1. 3x+3y=-9

3y=-3x-9

y=-x-3

2. x-3y=12

-3y=-x+12

y=1/3x-4

3 0
3 years ago
Eunice buys dog bed with a listed price of $31. Eunice uses a sale that provides 30% off. What is the total
Pachacha [2.7K]

Answer:

21.70

Step-by-step explanation:

First find the discount

31 * 30%

31 *.30

9.3

Subtract from the original amount

31 - 9.3

21.70

3 0
3 years ago
Determine the measure of each indicated angle. Show all necessary steps!
Rasek [7]

a)

We know that a 4-sided polygon's angles add up to 360 degrees

so to find x:

360-(69+118+84)=89 degrees

b)

For a 4-sided polygon we also know that the outside angles add up to 360 degree.

so to find p:

360-(100+62+106)=92 degrees

Hope it helps!

3 0
2 years ago
A scuba diver was at a depth of 125 feet below sea level. He descends 205 more feet below sea level. What is the new depth of th
EleoNora [17]

Answer:

The new depth of the scuba diver is 330 feet below sea level.

Step-by-step explanation:

125 + 205 more below sea level = 330 below sea level

4 0
3 years ago
Other questions:
  • Sammy has 20 cookies what is 20 rounded to the nearest ten
    15·2 answers
  • Help plz answer this
    7·2 answers
  • What is life? so yeah other than 42 of course
    10·2 answers
  • A flower arrangement has 8 carnations for every 4 roses. There are 14 carnations. How many roses are in the arrangement?
    11·1 answer
  • Simplify the expression <br>Plz help
    10·2 answers
  • What is 35÷7(2) equal in PEMDAS method
    6·2 answers
  • What is the domain of g(x)?
    7·1 answer
  • The points (2,4), (3,9), (7,8), and (6,3) form a quadrilateral. Graph the quadrilateral,
    10·2 answers
  • The bottom of a cylinder has a circumference of about 60 in. What is the approximate diameter of the cylinder? Round to the near
    6·1 answer
  • A card is picked from a standard deck of 52 cards. Determine the odds against and the odds in favor of selecting a jack .
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!