If a= 5^99 x 2^98 and b= 5^72 x 4^38 show ab has 172 digits when written as a ordinary number
This is a proof question. Please show step by step.

Answers

Answer 1

Step-by-step explanation:

ab

= (5⁹⁹ * 2⁹⁸) * (5⁷² * 4³⁸)

= 2⁹⁸ * 2⁷⁶ * 5⁹⁹ * 5⁷²

= 2¹⁷⁴ * 5¹⁷¹

= 2³ * (2¹⁷¹ * 5¹⁷¹).

The 2¹⁷¹ * 5¹⁷¹ will give 171 ending zeroes as 2 * 5 = 10.

And there is a 8 infront as 2³ = 8.

Hence altogether there are 171 + 1 = 172 digits.


Related Questions

Gwen scans a photo that is 4 in. wide by 6 in. tall into her computer. If she scales the
height down to 3 in., how wide should the similar photo be?

Answers

Answer: 2 inches in width

Step-by-step explanation:

4 - 6

divide both by 2

2 - 3

The width of a similar photo comes to be 2 inches.

Width of original photo = 4 inches

Height of the original photo = 6 inches

Height of the scaled photo = 3 inches

What is the scale factor?

A scale factor is a number that multiplies (“scales”) a quantity.

Scale factor = height of scaled photo/ height of the original photo

Scale factor= 3/6 = 1/2

So, the width of the scaled photo = scale factor * width of the original photo

The width of the scaled photo = (1/2)*4

The width of the scaled photo =2 inches.

Therefore, the width of a similar photo comes to be 2 inches.

To get more about scaling visit:

https://brainly.com/question/25722260

Select all diagrams that show 4 x 1/3

Answers

Answer:

b

d

Step-by-step explanation:

chess club with 30 members is electing a new president. Yolanda received 27 votes. What percentage of the club members voted for Yolanda?

Answers

the answer is 90%, because 27/30 in percentage form is 90%.

Answer:

Step-by-step explanation:

90% of the chess club!

✨Hope it helps✨

✨Brainliest?

Is 14x+16x-4=5(4x+9)x=49 a solutionn or problem?

Answers

Answer:

its a problem there is still work to be done with it

Step-by-step explanation:

can someone help me with this?

Answers

R: -4,-3
S: -3,1
T: 1,-2
U: stays the same
((:

Jaxon is deciding between two landscaping companies for his place of business. Company A charges $45 per hour and a $150 equipment fee. Company B charges $35 per hour and a $200 equipment fee. Let AA represent the amount Company A would charge for tt hours of landscaping, and let BB represent the amount Company B would charge for tt hours of landscaping. Write an equation for each situation, in terms of t,t, and determine the interval of hours, t,t, for which Company A is cheaper than Company B.

Answers

Answer:

When the number of hours t is less than 5 hours, Company A is cheaper than Company B

Step-by-step explanation:

Let the number of hours be represented by t

For Company A

Company A charges $45 per hour and a $150 equipment fee.

150 + 45t

For Company B

Company B charges $35 per hour and a $200 equipment fee.

200 + 35t

Write an equation for each situation, in terms of t,t, and determine

The interval of hours,t, for which Company A is cheaper than Company B is given as:

Company A < Company B

Hence:

150 + 45t < 200 + 35t

Collecting like terms

45t - 35t < 200 - 150

10t < 50

t< 50/10

t < 5

When the number of hours t is less than 5 hours, Company A is cheaper than Company B

Answer:

This is the correct answer on Delta Math

Step-by-step explanation:

Can someone help me with this

Answers

Answer:

C

Step-by-step explanation:

I checked it and it’s right hope this helps!!

Follow the directions to solve the system of equations by elimination. 8x + 7y = 39 4x – 14y = –68 Multiply the first equation to enable the elimination of the y-term. Add the equations to eliminate the y-terms. Solve the new equation for the x-value. Substitute the x-value back into either original equation to find the y-value. Check the solution. The solution to the system of equations is (, ).

Answers

Answer:

1/2,5

Step-by-step explanation:

Answer:

1/2     5

Step-by-step explanation:

just got it right on edge

What is the equation of the line shown in the graph?​

Answers

Answer:

y=4x-3

Step-by-step explanation:

We're given that the equation is linear (a line), so it must be in the form y=mx+b. We're also given that it contains the points (0,-3) and (1,1).

Plugging the values of the x and y coordinates in that first point, we get the equation -3=m*0+b, simplifying to -3=b. Therefore, the b-value is -3.

Next, we can plug in the values from the second point to get the equation 1=m*1-3, which simplifies to 1=m-3. Adding 3 to both sides, we get m=4. Therefore, the equation of the line is y=4x-3.

Note that -3 is the value where the line intercepts the y-axis, which means -3 is known as the y-intercept. The value of b is always the y-intercept.

Question 1
factor x^2 +8x +15
A. (x+5)(x+3)
B. (x+5)(x-3)
C. (X-5)(x-3)

Answers

The answer is A (x+5)(x+3)

explanation:
the GCF of 15 is 3 and 5
3 and 5 also add up to 8 making each of the number the zeros

(x+5)(x+3)

there are between 24 and 40 students in a class. The ratio is 4:7, how many students are there

Answers

Answer:

28:35 = 4:7

Step-by-step explanation:

Hope that helped!

Answer:

33 students

Step-by-step explanation:

4 + 7 = 11

8 + 14 = 22

12 + 21 = 33

hope this helps!

The sample space below shows the results the final eight matches played by the English soccer team
Manchester United during their championship 2012 - 2013 season. They won matches where they
scored more goals than their opponent, lost matches where they scored less, and tied matches where they
scored the same amount.
If we take matches 1, 3, 5, 6, and 8 as a subset of the sample space, which of the statements below
describe this subset?

Answers

b. the subset consists of all the matches where there were no ties

and

d. The subset consists of all the matches where manchester united won or lost

I would post the picture of me getting it right if I could, if you want to trust me go ahead. success awaits ig lol

The correct statements are:

The subset consists of all the matches where there was a tie.The subset consists of all the matches where Manchester United's opponent did not lose.

What is Data?

In mathematics, data is a collection of facts and figures that can take any shape, whether it be numerical or not. You can calculate numerical data, which is always gathered in number form and includes things like student test results, employee salaries, football team member heights, etc.

Given:

From the table we can see that

As,  the subset consists of all the matches where there was tie in matches 3, 5 and 8.

and, The subset consists of all the matches where Manchester United's opponent did not  lose.

Learn more about Data here:

https://brainly.com/question/10980404

#SPJ2

1) Arnold has $200 in his bank account. His bank
account earns interest at a rate of 2% each year.
After 15 years, how much money will Arnold have
in his bank account (assuming no withdrawals or
deposits)?

Answers

Answer:

P is the principal amount, $200.00.

r is the interest rate, 2% per year, or in decimal form, 2/100=0.02.

t is the time involved, 15....year(s) time periods.

So, t is 15....year time periods.

To find the simple interest, we multiply 200 × 0.02 × 15 to get that:

The interest is: $60.00

Sherly's Plumbing and Howard's Plumbing have different
ways of charging their customers.
Sherly's Plumbing charges $43 per hour plus a $30 initial
fee.
Howard's Plumbing charges $28 per hour plus a $24
initial fee.
Make a function that represents each person, then find
the cost, f(7), for each person.
Your answer: Not there yet, keep working
Question
Answer
Linear Function for Sherly:
s =
Linear Function for Howard:
Sherly $(7) =
Howard $(7) =

Answers

Answer:

Sherly's Plumbing is : f(x) = 43x + 30 and Howard's Plumbing is f(x) = 28x + 24

sherly's f(7) = 331 and Howard's f(7) = 220

Given f(x) = 17(3+x) what is the value of f(-2)

Answers

Answer:

Step-by-step explanation:

f ( x ) = 17 ( 3 + x )

f ( -2 ) = 17 ( 3 + -2 )

f ( -2 ) = 51 + -34

f ( -2 ) = 17

= 17

A city Carnival has an entry fee of $15. Each Carnival ride cost $7.50. Write a Linear Equation that can be used to solve for total spend at the Carnival. In the form y = mx + b

Answers

The answer would be Y=7.50x+15

11 Karl takes a ride in a taxi and is charged $2.75 for the first of a mile. He is charged $0.25 for each
additional to
of a mile traveled and gives the driver a $3.50 tip. Explain how to determine the number of
miles that Karl can ride in the taxicab for a total of $28.50 including the tip. Show your work.


I WILL GIVE HIGH POINTS JUST PLEASE HELP SOON.

Answers

Answer: 89 miles


Explanation: We can make a linear equation given the problem, where 2.75 is the constant and 0.25 is the slope. M can represent miles 28.5 is what we want the equation to equal, so it will be on one side of the equation.

We can simply add the $3.50 tip to the constant to account for it

Thus we have 28.50=0.25m+6.25.

Solving for m gives us 89 miles.



15 is 60% of what number?

Answers

Answer:

25

Step-by-step explanation:

Answer: 25

Step-by-step explanation:

60 percent (calculated percentage %) of what number equals 15? Answer: 25.

PLEASE HELP, THANK YOU (-:

Answers

Answer:

1 mile per hour

Step-by-step explanation:

What is f(5) for the function f(x)= 2x+4?

f(5)=?

Answers

Answer:

5=2x+4

5-4=2x

1=2x

x=1/2

Answer:

if f(x)=2x+4

Then f(5)=2•5+4=14

The answer is 14

i need help with this please mathematics

Answers

i dont see anything

Liliana is renting a beach house for a family vacation. The house charges a $75 cleaning fee plus $95 per night. If Liliana wants to spend a maximum of $645 on the rental, which inequality represents “n,” the number of nights can she afford to rent the beach house?
A.n ≤ 6
B. n ≥ 6
C. n 5

Answers

Answer:

A.n ≤ 6

Step-by-step explanation:

A. n ≤ 6

May I have brainliest please? :)

Find the slope of: A(-2,-4), B(2, 4) *

Answers

M=y2-y1/x2-x1
4-(-4)/2-(2)
8/4
M=2

Answer:

2/1

Step-by-step explanation:

Follow the formula: (y2 - y1) / (x2 - x1). So 4-(-4) and 2-(-2). A negative and a negative equal a positive so 8/4. Then simplify. Which gives you 2/1. Hope this helps.

PLEASE ANSWER FAST ITS FOR A BIG TEST!!! Find an expression which represents the difference when (−6x+5) is subtracted from (−x−8) in simplest terms. ILL GIVE BRAINLIEST

Answers

Answer:

5x-13

Step-by-step explanation:

What is the prime factorazation of 50

Answers

Answer:

Prime factorization of 50 is 2 x 5 x 5 or 2 x 5^2

Step-by-step explanation:

The diagram below shows a map of the routes taken by Georgia Air-Taxi airline. On this diagram lengths and directions are irrelevant, all that matters is the connections between airports. Choose the adjacency matrix, name it A, that matches the scenario.

Answers

Answer: B

Step-by-step explanation: Adjacency Matrix is a square matrix representing a simple graph with 0 or 1 according to the condition given.

In this diagram, 0 corresponds to no connection between airports and 1 corresponds to connections between airports.

In other words, analysing the image, we see that:

1) Albany just have connection with Atlanta, so in the position of line Albany with column At, it must be a 1. The other columns, there are 0.

The Line for Albany in the matrix will be: [0 1 0 0 0 0]

2) Atlanta has connections with Albany, Dalton, Macon and Augusta. So corresponding position (line and column) must be 1. The only two airports Atlanta doesn't have connection with its own and Waycross, so at the corresponding column and line, it is written 0.

The line for Atlanta in the matrix is [1 0 1 1 1 0]

3) Augusta: connections with Atlanta, Macon, Waycross. At those positions, it will be written 1. At positions related to itself, Albany and Dalton is 0.

The line in the matrix will be [0 1 0 0 1 1]

4) Dalton: connection with Atlanta only. That position will be 1 while the others will be 0.

The line is [0 1 0 0 0 0]

5) Macon: connections with Atlanta, Augusta and Waycon: those positions will have 1 and the other 0.

The line is [0 1 1 0 0 1]

6) Waycross: connections with Macon and Augusta. Those positions will be 1 and the others 0.

The line is [0 0 1 0 1 0]

In conclusion, the adjacency matrix matching the scenario is

[tex]A=\left[\begin{array}{cccccc}0&1&0&0&0&0\\1&0&1&1&1&0\\0&1&0&0&1&1\\0&1&0&0&0&0\\0&1&1&0&0&1\\0&0&1&0&1&0\end{array}\right][/tex]

Simplify the expression.
- 7 + 3 - 14 + 2

Answers

Answer:

-4 - 16

Step-by-step explanation:

Answer:

-16

Step-by-step explanation:

you just use a calculator lol :)

please show work
A car travels 110 miles in 2 hours (with a constant speed. How much time will it take traveling 484 miles?

Answers

Answer:

8.8 hours or 528 minutes

Step-by-step explanation:

110 miles in 2 hours

divide both by 2

55 miles in 1 hour

484/55 = 8.8 hours

If you need it in minutes there are 60 minutes in an hour so multiply 8.8 by 60

8.8*60=528 minutes

Kennedy had the expression 3(2x-3x+8). She simplified and rewrote the
expression 3(8+x). If any, what was her error?

Answers

Answer:

It is -3x+24

Step-by-step explanation:

2x-3x is -x or -1x

It can also be simplified further using multiplication.

3(2x-3x+8)

3(-x+8)

-3x+24

{(2,0), (4, -3), (6, 9), (-2,7), (4,9)}
What is the range?
um...? idk

Answers

Answer:

(8,9)

Step-by-step explanation:

The biggest number minus the smallest number.

The answer is (8,9) ok
Other Questions
HELP!! Unscramble the word gelo est. Hey yall. Im so embarrassed and I want to hit my head so BAD:( Im literally crying. So I had a test in math and Ive always been cheating and I was the best math student but when the class was gonna end I told the teacher I only have two questions and she told me to still stay and when I finished the submit button didnt work and the teacher told me to present my screen and I did but when I did the teacher face wasnt happy because when I showed her my screen in the tabs I had tabs that help me cheat the test. But the teacher didnt tell me anything and she told me that if I have the notes for all my questions answers and I didnt know what to say so I said yes! But I told her if I should take pictures of the answers and she said no. And I started panicking so she told me to reload the WHOLE THING so I did and all my 18 questions answers deleted and I told the teacher I had to go to my other class and she said bye. Im literally crying. Im hitting my head so hard. Karma is real:( F Make a list of different weather patterns Thanks to who ever helped me with this question! why must ports along the Irrawaddy have two areas for docking? Paco buys a total of 15 pencils and markers for $ 11.15. Each pencil costs $ 0.30. Each marker costs $ 1.25 In a few sentences, describe how sedimentary rock forms. You get a student loan from the New Mexico Educational Assistance Foundation to pay for your educational expenses this year. Find the interest on the loan if you borrowed $5000 at 5% interest for 1 year What is the answer to 0.30p+1.25m=11.15 What was Mary Wollstonecraft idea Explain what this excerpt of the Code of Hammurabi suggests about the economy in Babylonia. How was the Boston Tea Party different from an actual tea party? a Many considered the Boston Tea Party an act of vandalismdumping someone elses tea in a harbor. An actual tea party is an event to sip and drink tea.b The Boston Tea Party was an event to sip and drink tea. An actual tea party occurs on a British cricket field.c The tax on tea was celebrated during the Boston Tea Party. An actual tea par ty is an event that serves small sandwiches.d Many considered the Boston Tea Party Britains first tea-drinking party in the colonies. An actual tea party was one that started during the first Continental Congress. The picture shows a 3-D model of a virus called a bacteriophage. Bacteriophages can infect In what way are the bactenophage and E. coli alike? F. They contain antibodies. che produce by tutosis. H They have idenbekl genomes, The lack membrane-bound organelles. Students, dawanywhere on this slide! Will mark you as BRAINLIEST Someone help me please Which point on the number line shown would represent the fraction 3/20? Point APoint BPoint CPoint D If the food is not particularly fresh, it is OK to use additives (for color /appearance) that will misrepresent the appearance of the food to thecustomer.TRUEFALSE What is the volume of a 13.4 g silver coin? explain the energy transformation that takes place in torch light using dry cell What type of sentence is listed below? "The system worked, but the books were heavy and slow to read." A simple B compound C complex D compound-complex I'll give you a brainliest if is right or at least shows some effort(thanks & i hope your having a good day)In your own words, explain how background noise detected in space provides evidence for the Big Bang Theory.