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

Answers

Answer 1
Answer:

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..


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Write 36.14 in expanded form

Answers

The correct answer is:


30 + 6 + 0.1 + 0.04.


Explanation:


We write numbers in expanded form using place value.


3 is in the tens place; this makes its value 30.

6 is in the ones place; this makes its value 6.

1 is in the tenths place; this makes its value 0.1.

4 is in the hundredths place; this makes its value 0.04.


Together we find the sum:

30 + 6 + 0.1 + 0.04.

we can write 36.14 in an expanded form as:
36.14 = (3 x 10) + (6 x 1) + (1/10) + (4/100)
and the expanded form with decimals is:
36.14 = 30+6+0.1+0.04

What is the polygon being rotated to create the blue quilt block patterns??????

Answers

Answer:

D. Triangle is correct

Step-by-step explanation:

We are given that,

A polygon is rotated to form the blue block patterns,

As, from the figure, we see that,

The polygon being rotated has three sides.

So, the polygon is a triangle.

Thus, a triangle is rotated to form the blue block pattern.

Hence, option D is correct.

Answer:

The answer is D) Triangle

Samira ran around a park loop that was 1/3 mile long. She ran around the loop 9 times. Samira says she ran 9/3 miles. Her brother says she ran 3 miles. Who is correct?Use words and drawings to explain

Answers

They both are correct . 
 9/3 = 3 so its 3 miles 

Can someone explain this to me

Answers

My phone almost no battery hope this helps to start you off .

Monique had $15. After paying for 6 pounds of squid, she had $3 left. Find the cost of 1 pound of squid.$
per pound of squid

Answers

Answer:

2 For each pound

Step-by-step explanation:

It is two per pound because 15-12=3 meaning 6 pounds is equal to $12 12 divided by 2 is 6 so 1 pound is $2

Answer:

2

Step-by-step explanation:

15-3=12

12/6=2

A punch recipe calls for orange juice and pop in the ratio of 2:5 the recipe requires 1L of Pop to serve 7 people a) how much orange juice is needed for 7 people?
b)about how much orange juice and pop do you need to serve 15 people? 20 people?
plz say how you answered this

Answers

O : P => 2 : 5

(a)    1 liter of pop to serve 7 people

=>           5 units = 1

               1 unit = 1 / 5

Orange juice => 2 units

Hence, Orange juice needed is 2 * 1 / 5 = 0.4 liters

 

(b)    If 1 liter of pop is needed to serve 7 people, then we will need (1 / 7) * 15 for 15 people

i.e. 2.14 liters

 

As the ratio of O : P = 2 : 5,

               5 units = 2.14

               1 units = 2.14 / 5

 

For Orange juice, we will need 2 * 2.14 / 5 = 0.856 liters for 15 people