Mr. Scott likes to pose interesting problems to his Mathematics classes. Today,
he started with the expression 6^2020 + 7^2020. He stated that the expression was
not equivalent to 13^2020 and that he was not interested in the actual sum. His
question to his class and to you is, “What are the final two digits of the sum?

Answers

Answer 1

Answer:

The last two digits of 6²⁰²⁰ + 7²⁰²⁰ is 7, 7

Step-by-step explanation:

The given question is to find the value of the sum of two numbers 6²⁰²⁰ + 7²⁰²⁰, where,  6²⁰²⁰ + 7²⁰²⁰ ≠ 13²⁰²⁰

We have;

The last two digits of the powers of 6 are;

6¹ = 6, last two digits = 06

6² = 36, last two digits = 36

6³ = 216, last two digits = 16

6⁴ = 1,296, last two digits = 96

6⁵ = 7,776, last two digits = 76

6⁶ = 46,456, last two digits = 56

6⁷ = 279,936, last two digits = 36

6⁸ = 1,679,616, last two digits = 16

6⁹ = 10,077,696, last two digits = 96

6¹⁰ = 60,466,176, last two digits = 76

6¹¹ = 362,767,056, last two digits = 56

Therefore, the last two digits repeat itself every 5 times

For 6²⁰²⁰, the last two digits will be for the 2020/5 = 404 complete times, which will be 76

The last two digits of the powers of 7 are;

7¹ = 7, last two digits = 07

7² = 49, last two digits = 49

7³ = 343, last two digits = 43

7⁴ = 2,401, last two digits = 01

7⁵ = 16,807, last two digits = 07

7⁶ = 117,649, last two digits = 49

7⁷ = 823,543, last two digits = 43

7⁸ = 5,764,801, last two digits = 01

Therefore, the last two digits repeat itself every 4 times

For 7²⁰²⁰, the last two digits will be for the 2020/4 = 505 complete times, which will be 01

Therefore, the last two digits of 6²⁰²⁰ + 7²⁰²⁰ is 76 + 01 = 77, which is 7, 7


Related Questions

I have 10 minutes left someone help

Answers

Answer: there is no question. Its empty

Step-by-step explanation:

Answer:

with what

Step-by-step explanation:

There are two types of cellular phones, handheld phones (H)that you carry and monile phones (M) that are mounted invehicles. Phone calls can be classified by the travelingspeed of the user as fast (F) or slow (W). The probabilitymodel for this experiment has the following information: P[F] =0.5, P[HF] = 0.2, P[MW] = 0.1. What is the sample space ofthe experiment? Calculate the followng probabilites:a) P[W]b) P[MF]c) P[H]

Answers

Answer:

Explained below.

Step-by-step explanation:

(1)

Sample space is a set of all possible outcomes of an experiment.

The sample space in this case is:

S = {HF, HW, MF, MW}

(a)

Compute the value of P (W) as follows:

P (F) + P (W) = 1

P (W) = 1 - P (F)

P (W) = 1 - 0.50

P (W) = 0.50

(b)

Compute the value of P (MF) as follows:

P (HF) + P (MF) = P (F)

P (MF) = P (F) - P (HF)

P (MF) = 0.50 - 0.20

P (MF) = 0.30

(c)

Compute the value of P (M) as follows:

P (M) = P (MF) + P (MW)

P (M) = 0.30 + 0.10

P (M) = 0.40

Compute the value of P (H) as follows:

P (H) + P (M) = 1

P (H) = 1 - P (M)

P (H) = 1 - 0.40

P (H) = 0.60

Which is the graph of x - y = 1?

Answers

i’m pretty sure this is what x-y=1 would look like graphed

Blow this question up with random stuff

Answers

Answer:

yay

Step-by-step explanation:

hi my unicorn ate the dog

9. 1.3(c – 4) ≤ 2.6 + 0.7c

Answers

Answer:

c ≤ 13

I think what was the question tho

Step-by-step explanation:

Can someone help me please

Answers

Answer:

D

Step-by-step explanation:

the domain is all x values. so:

0, 4, 5, 10

I think that's answer d

Answer:

Step-by-step explanation:

The domain is the x so 0,4,5,10 or D

The x and y intercepts are:

x=(1,0)

y=(0,3)

California, the most populous state, has approximately 4 x 107​ ​ people living in it. The population of the entire United States is approximately 3 x 108​ ​. About how many times greater is the population of States than the population of California

Answers

Answer:

3 x 108 =324 United States

4 x 107 =428 california

Step-by-step explanation:

United States is 3 times greater while california is 4 time greater

How does the graph of g(x)=⌈x⌉+7 differ from the graph of f(x)=⌈x⌉?




The graph of g(x)=⌈x⌉+7 is the graph of f(x)=⌈x⌉ shifted up 7 units.

The graph of g(x)=⌈x⌉+7 is the graph of f(x)=⌈x⌉ shifted right 7 units.

The graph of g(x)=⌈x⌉+7 is the graph of f(x)=⌈x⌉ shifted down 7 units.

The graph of g(x)=⌈x⌉+7 is the graph of f(x)=⌈x⌉ shifted left 7 units.

Answers

Answer: A) shift up 7 units

The +7 at the end effectively adds 7 to each y coordinate output, which is why the entire graph shifts up 7 units. For instance, a point like (1,2) moves to (1,9) after shifting up 7 units.

Side note: The function f(x)=⌈x⌉ is the ceiling function. It takes any decimal value and rounds it up to the nearest whole number. If you had an input like x = 2.01 then the output would be y = 3 even though 2.01 is closer to 2 than it is to 3.

Answer: A) shift up 7 units

Step-by-step explanation:

The +7 at the end effectively adds 7 to each y coordinate output, which is why the entire graph shifts up 7 units. For instance, a point like (1,2) moves to (1,9) after shifting up 7 units.

Side note: The function f(x)=⌈x⌉ is the ceiling function. It takes any decimal value and rounds it up to the nearest whole number. If you had an input like x = 2.01 then the output would be y = 3 even though 2.01 is closer to 2 than it is to 3.

please, i need to answer this for tomorrow and i dont get it!

Answers

Answer:

1.72r²

Step-by-step explanation:

total Rectangle area = 4r*2r = 8r²

total circles area = 2(π r²) = 2*3.14*r² = 6.28r²

then:

the area of the shaded region:

= 8r² - 6.28r²

= (8-6.28)r²

= 1.72r²

Answer:

2r²(4 - π)

Step-by-step explanation:

The shaded area (A) is calculated as

A = area of rectangle - area of 2 circles

The rectangle has a length of 4r and a width of 2r , then

A = (4r × 2r) - (2πr²)

   = 8r² - 2πr² ← factor out 2r² from each term

    = 2r²(4 - π)

PLEASE HELP!!

Which is the simplified form of the expression

1 - StartFraction 1 Over q Superscript 30 Baseline EndFraction

2 - q Superscript 30

3 - StartFraction p Superscript 12 Baseline Over q Superscript 60 Baseline EndFraction

4 - p Superscript 12 Baseline q Superscript 60

Answers

jjabsbsbabsvAHSBDHAHAHSHSHSHSH

Answer:

1/q^30

Step-by-step explanation:

Simplified

To find the inverse of f(x) = 2x – 1, Patel begins by replacing f(x) with y. He then switches x and y. What is the next step?
A.Solve the equation for x.
B.Subtract 1 from both sides of the equation.
C.Solve the equation for y.
D.Replace y with f–1(x).
it a

Answers

Answer:

Step-by-step explanation:

C. Solve for y

1. Prove that root15 is irrational
-​

Answers

root15 has no square factors, so i cant be simplified which makes it irrational

Step-by-step explanation:

V15 is rational ( contradiction method). V15=a/b (a and b are not common factor). squaring on both sides, we get, 15= a^2/b^2. 15b^2=a^2 (a=15c) b^2=15/a^2 (assume, a^2 =225c^2) 15b^2=225c^2 b^2=225c^2/15 b^2=15c^2 c^2=15/b^2 c =15/b. 15 divided both a and b which is a contradiction. ie, is irrational.

Your friend comes from a large family. This list shows the ages of all of the children in her family. What is the median age of the children?

12, 9, 15, 7, 9, 13, 16
OPTIONS:
A. 11 4/7
B. 7
C. 12
D. 9

Answers

Answer:

It is 11 and 4/7 I am pretty sure hope I helped!

i'll give brainliest!!

solve 3 + 4x > -5 for x

a: x > -2

b: x < -1.75

c: x < -2

d: x > -1.75

Answers

Answer:

x>-2

3+4x>-5

4x>-5-3

4x>-8

x>-2

the answer is x>-2

Answer:

x > -2

Step-by-step explanation:

What's 8.517 in expanded form

Answers

(8x1)+(5/10)+(1/100)+(7/1000)

Answer:

8.517 in expanded form is 8*1) + (5*0.1) + (1*0.01) + (7*0.001). 8.517 in word form is eight and five hundred seventeen thousandths.

An empty shipping box weighs 250 grams. The box is then filled with T-shirts. Each T-shirt weighs 132.5 grams. The equation W = 250 + 132.5T represents the relationship between the quantities in this situation, where W is the weight, in grams, of the filled box and T the number of shirts in the box. Select two possible solutions to the equation W = 250 + 132.5T .

Answers

Answer:

For 20  t shirts  the weight is 2900 grams

and for 25 t- shirts the weight is 3562.5 gms  

Step-by-step explanation:

W = 250 + 132.5T

1) If we know the total weight we can find the number of t- shirts and

2) if the number of shirts are known the total weight can be calculated.

For example if the expression W= 250 + 132.5T is written like is written like

2900 = 250 + 132.5T

2900-250 = 132.5T

T = 2650/132.5= 20 shirts

Similarly if we have 25 t- shirts then the weight would be

W = 250 + 132.5(25)

W= 250+ 3312.5=  3562.5 gms  

During a weekend trip, Selena drove 4 times as far as Jason. Altogether they drove 380 miles. Which equation can be solved for x, the number of miles Jason drove?

Answers

Answer:

4x+x=360 (whole equation)

x=72 (answer)

Step-by-step explanation:

Let the distance driven by Jason be x.

Selena drove four times as far.

Hence, distance Selena drove is 4x.

They drove 380 miles altogether.

Hence, 4x + x = 380

5x = 380

x = 72

Hope this helped!

-59 = m - 11, m = ? i dont know the answer

Answers

Answer:

m = -48

Step-by-step explanation:

m - 11 = -59 (add 11 on both sides)

m = -48

Hope this helps!!

Answer:

m = -48

Step-by-step explanation:

m - 11 = -59

you add the 11 to both sides crossing it out from the left side and then you get an equation that looks like this.

m = -59 + 11

Now you can just solve it like a simple subtraction problem, -59 + 11 = -48

Hope I was able to help :)

Graph the linear equation y = 4x - 8

Answers

Answer:

The image is the graph

Step-by-step explanation:

Answer:

Step-by-step explanation:

-8 is the y int and 4 your slope

need answer quick!
Simplify.

[3 × (3 + 10)] × 7

Answers

Answer:

Hey I think I have the Answer 273

Step-by-step explanation:

[3x(3+10)x7]

First add 3+10

Then multiply 3x13

Then 39x7

Then you get 273 Hope this help mark me BRAINLEST!!!! PLZ

HAVE A NICE DAY!!!

Answer: 273

Step-by-step explanation: 1. PEMDAS P=parenthesis E=exponents M=multiplication D=division A=addition S=subtraction

                              [3 x (3 + 10)] x 7

1. 3 + 10 = 13

2. 3 x 13 = 39

3. 39 x 7 = 273

                            PLZ MAKE ME BRIANLIEST                

                             IF THIS IS THE WRONG ANSWER IM VERY SORRY

                            I DOUBLE CHECKED THOUGH SO ITS NOT :P

write this number in scientific notation 29,400,000

Answers

29,400,000 in scientific notation is 2.94 × 10^7

Can yall plz help me answer this!!!

Answers

Answer:

d=1

Step-by-step explanation:

distribute 0.5 through the parentheses

3.5d+2=7-1.5d

move variable to the left-hand side and change its sign

3.5d+1.5d+2=7

move constant to the right-hand side and change its sign

3.5d+1.5d=7-2

collect all like terms

5d=7-2

subtract the numbers

5d=5

divide both sides

d=1

Please help someone
2/5

Answers

Answer:

B

Step-by-step explanation:

Answer:

B is correct

Step-by-step explanation:

√5 ≈ 2,24

since it is - √5 the answer must be -2,24 so B is correct

For every $890 lawn
mower Kelly sells, she
gets a commission of
$178. What percentage
is Kelly's
commission?

Answers

Answer:

20%

Step-by-step explanation:

178/890= .2 or 20%

Can someone plz help with 7-8 plz ASAP will give 10 points and mark brainliest

Answers

7. c

8. d

those are the answers

114 + 70 + n ≥ 200

184 + n ≥ 200

n ≥ 200 -184

n ≥ 16

Michael and Imani go out to eat for lunch. Part A If their food and beverages cost $25.30 and there is an 8% meals tax, how much is the bill? Enter your answer in the box.

Answers

Answer:

Step-by-step explanation:

25.30*8% tax = 2.02 tax

total 25.30+2.02= $27.32

Answer:

$27.32

Step-by-step explanation:

Multiply $25.30 by 0.08 (8% is equal to 0.08)

2.024

Add 2.024 to $25.30

That would be 27.324

Round to the nearest hundredth

$27.32

Hope this helps :)

Please consider Brainliest :)

What are the intersection points of the function: (x - 9)(x + 1) = (x + 1) *

Answers

Answer:

The intersection points are (-1,0) and (10,0)

Step-by-step explanation:

Brainliest if i am right? uwu

What does F(1) represent ?

Answers

Answer:

F(1) represents the first term of the sequence.

Step-by-step explanation:

Let us suppose the sequence function

[tex]F(n) = 16-3n[/tex]

We can find the first term of the sequence by substituting n=1 in the function sequence

[tex]F(1) = 16-3(1)[/tex]

        [tex]= 16-3[/tex]

        [tex]=13[/tex]

We can find the 2nd term of the sequence by substituting n=2 in the function sequence

[tex]F(2) = 16-3(2)[/tex]

        [tex]= 16-6[/tex]

        [tex]=10[/tex]

We can find the 3rd term of the sequence by substituting n=3 in the function sequence

[tex]F(3) = 16-3(3)[/tex]

        [tex]= 16-9[/tex]

        [tex]=7[/tex]

So the first three terms of the sequence is:

13, 10, 7...

As the common difference is the same.

i.e. d = 10-13 = -3, d = 7-10 = -3

Hence, it is an Arithmetic sequence.

As the first term is 13, which can be obtained by putting n=1 in the function sequence.

Therefore, from the above discussion, we can conclude that F(1) represents the first term of the sequence.

A picture 10 inches tall and 14 inches wide is to be scaled to 1.5 inches tall to be displayed on a webpage. How wide should the picture be on the webpage for the two pictures to be similar?

Answers

Answer:

1.8

Step-by-step explanation:

ILL MARK U BRAINLIEST!!!

Answers

Answer:

20

Step-by-step explanation:

first take out the cost of the cup 31.75-6.75=25

then divide by the cost of the refills 25/1.25=20

hope this helps :)

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