Determine the largest positive integer N such that 1005! is divisible by 10N.

Answers

Answer 1

9514 1404 393

Answer:

  N = 250

Step-by-step explanation:

The way your question is written, the answer is a number of 2582 digits, much too large to show here. We assume you actually want N such that 10^N is the largest power of 10 that will divide 1005!.

__

That factor is limited by the number of factors of 2 and 5 in 1005!. Of those, there are far more factors of 2, so the actual limit is the number of factors of 5 in 1005!.

Every 5th number is divisible by 5, so there are 1005/5 = 201 numbers divisible by 5 in 1005!.

Every 5th one of those is divisible by another factor of 5, so an additional 201/5 ≈ 40.

Every 5th one of those is divisible by another factor of 5, so an additional 40/5 = 8.

Finally, every 5th one of those has yet another factor of 5, so an additional 8/5 ≈ 1.

Then the total number of factors of 5 in 1005! is 201 +40 +8 + 1 = 250.

That is, the number 1005! will end in 250 zeros. It will be divisible by 10^250.

  N = 250


Related Questions

please help me get the right answer!!

Answers

Answer:

is that distance and bearing . really cool lol

Whoever gets this question right, I will mark brainilest! Thanks!​

Answers

10. 2/10 = 0.2 or 0.20

11.  8/10 = 0.8 or 0.80

12. 5/10 = 0.5 or 0.50

13. 17/100 = 0.17

14. 89/100 = 0.89

15. 68/100 = 0.68

One week, Rachel earned $250. She spent $120 on food, $30 on miscellaneous items, and saved the rest.

If Rachel makes a pie chart showing how she spends her money, the central angle for the food sector would be __________.


187°


173°


90°


144°

Answers

250 is the total
120 is 48% of 250
A pie chart is a complete circle which is 360 degrees and 48% of 360 is 172.8 round that up to 173 degrees

The answer is 173

Jazmine is on a trịp to San Antonio, a distance of 330 km. She only has 3.5 hours to get to a job interview there. She gets stuck in traffic for the first 1.5 hours out of Houston and averages a speed of 60 km/hr. In order to not be late, what speed does she need to travel for the rest of the trip? (Organize your information carefully - total, first part, second part)

Answers

Answer:

Jazmine must travel for the rest of the trip at 120km/hr.

Step-by-step explanation:

To find the speed for the latter half of the trip necessary to arrive on time, we can divide the remaining distance by the remaining time.

The remaining distance, in km, is found by subtracting the distance already covered, which is the product of the speed during the first part of the trip and the elapsed time during this part, from the total distance:

[tex]330-1.5\times60=330-90=240[/tex]

The remaining time, in hr, is found by subtracting the elapsed time during the first part from the total time limit:

[tex]3.5-1.5=2[/tex]

Therefore, the necessary speed in km/hr is:

[tex]\frac{240}2=120[/tex]

Match the line described on the left with the slope of the line on the right. y = 3‐--------------------------------------undefined 9x – 3y = 18.--------------------------,------- - 2 the line through (5, 7) and (5, – 8) -------0 the line through ( – 4, – 1) and (-1,–7)--- 3. ​

Answers

Answer:

y=3, 0; 9x-3y=18, 3; line through (5, 7) and (5, – 8), undefined; the line through ( – 4, – 1) and (-1,–7), -2;

Step-by-step explanation:

y=3 is a horizontal line so the slope is 0

9x-3y=18 can be written as 3y=9x-18 or y=3x-6 so the slope is 3

the line through (5,7) and (5,-8) is a vertical line since the x value didnt change between the two points so the slope is undefined

we have to find the slope of the line through ( – 4, – 1) and (-1,–7). to do this use the formula (y_2-y_1)/(x_2-x_1)=(-7-(-1))/(-1-(-4))=(-7+1)/(-1+4)=-6/3=-2 so the slope is -2

turn 5/9 into a decimal.​

Answers

5/9 to a decimal would be .5 repeated

The answer is .5 repeated

Do not put your answer as .5 because .5 is 5/10

A proper answer can be something like "0.5 repeated, 0.5555..., or .5 with a line over the 5"

497 + 184

A. 581
B. 671
C.681
D.571

Answers

Answer:C. 681Hope this helps!! <3

Answer:c

Step-by-step explanation:

Help please due today

Answers

Answer:

the scale factor is greater than 1

hope this helps!:)

How many gallons of a 70% antifreeze solution must be mixed with 90 gallons of 15% antifreeze to get a mixture that is 60% antifreeze? Use the six-step method.

Answers

Answer:

405 gallons

Step-by-step explanation:

Let it be that the amount of gallons of a 70% antifreeze solution  is x, when a mixture that is 60 percents of antifreeze is placed in y gallons

x+90=y - the equation of dependence between solutions

The amount of antifreeze in the first one is x/100*70= 0.7x (in gallons), in the second solution (15percents) antifreeze is 90/100*15=13.5 (in gallons).

In the mixture we should get there will be y/100*60=0.6y - gallons of antifreeze

0,7x+13.5=0.6y

We have two equations x+90=y and 0,7x+13.5= 0.6y

0.6x+54=0.6y

0.7x+13.5=0.6y

0.7x+13.5-0.6x-54= 0.6y-0.6y

0.1x-40.5=0

x=405- the answer

p.s. sorry, I don't know what the six-step method is. But the answer is right.

help please! will give brainliest

Answers

(f – g)(x) = f (x) – g(x)
(5-x)^2-(5-x)^2 = 0

Help with this please now

Answers

Answer:

ok dude

Step-by-step explanation:

Wʜᴇʀᴇ ɪs ǫᴜᴇsᴛɪᴏɴ?

Answer:

what help l don't understand please sorry I didn't help you explain your problem l will help you

Solve 2/5 x + 1/2 = 5/6

Answers

The answer is x= 5/6

Answer:

5/6

Step-by-step explanation:

I'm assuming the x in your equation is used as a variable.

5/6-1/2= 2/6=1/3

2/5x=1/3

x=5/6

adriana has already taken 11 pictures at home, and she expects to take 1 during every vacation. After 6 days of vacation , how many picures would adriana hve taken

Answers

Answer:

The answer is 17

Step-by-step explanation:

11 + 6 = 17

The area of a rectangular garden 42 square meters. The width is 5 meters longer than one-third of the length. Find the length and the width of the garden Use the formula, area =length x width

Answers

The width is 9 the length is 12

What is the solution to this system of equations?
-a – 3 + 4c = 3
5a - 8b + 5c = 27
5a – 2b + 6c = 1
A. a = -4, b = -2, c = 1
B. a = 4, b = 2, c = -1
C. a = 1, b = -4, c = -2
D. a = -2, b = –1, c = 4

Answers

Step-by-step explanation:

hope it can work for you mark me as brain liest

3(4x+1)=15? X=
What is the solution?

Answers

Answer:

x=1

Step-by-step explanation:

3(4x+1)=15

12x+3=15

12x=15-3

12x=12

x=12/12

x=1

Write the number in expanded form 71,621

Answers

Answer:

there are a few types of 'expanded form' but i`ll just do this one

seventy-one thousand, six hundred and twenty-one

The average price of a 0.5- carat round diamond is $3700 and the average price of a 0.75- carat diamond is $4950. If the weight and the price of the diamond is linearly related, how much will a 2.5 -carat round diamond cost?

Answers

Since the problem stated the weight and price are in a linear relationship, we can use y=mx+b.

First, let's calculate our slope.

m = (4950-3700)/(0.75-0.5) = 5000

Now, let's solve for b.

3700 = 5000(0.5) + b

Simplify the right side of the equation.

3700 = 2500 + b

Subtract 2500 from both sides

1200 = b

Now our equation looks like this:

y  = 5000x + 1200

Let's plug 2.5 in for x to solve for the diamond cost.

y = 5000(2.5) + 1200

Simplify the right side.

y = 13700

The average price of a 2.5 carat diamond is $13700

Type the correct answer in the box. Use numerals instead of words.
Consider this expression.
| m^2+n^2 |

When m= -5 and n= 3, the value of the expression is ____.

**I answered 16 and it was wrong**

Answers

The value of the expression | m^2+n^2 | at m = -5 and n = 3 is 34.

Given,

| m^2+n^2 |

We need to find the value of this expression at m = -5 and n = 3.

What is the modulus of x?

The modulus of x is given as |x|.

The modulus of a negative x is also positive.

|-x| = x

How do we find an expression at a given point?

Example:

x + 2  at x = 1

= 1 + 2

= 3

Find the value of | m^2+n^2 | at m = -5 and n = 3.

| m^2+n^2 |

= | (-5)² + (3)² |

= | 25 + 9 |

= | 34 |

= 34

Thus the value of the expression | m^2+n^2 | at m = -5 and n = 3 is 34.

Learn more about finding the value of an expression at a point here:

https://brainly.com/question/17077979

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Which statement compares the two numbers correctly?

0.799 ________ 0.8 I need help thanks if you will ill give you 70 points but you have to help me before 4:00 thanks soo much if you do

Answers

Answer:

the statements are missing can you post them please

Answer:

C. 0.799 < 0.8

Step-by-step explanation:

0.799 ________ 0.8

Choices:

0.799 > 0.8 0.799 = 0.8 0.799 < 0.8 0.8 < 0.799

Comparing this two, compare 0.799 and 0.800 and if you ignore the decimals, it will be same as comparing 799 and 800.

We know 799 < 800, so apply the same here to get:

0.799 < 0.8

Correct choice is C

given that 3x+2=4 and 2y+6=5 what is x+y?

Really need help on this one!

Answers

Answer: 1/6

x = (4-2)/3 = 2/3
y = (5-6)/2 = -1/2
x + y = 2/3 + (-1/2)
2/3 - 1/2
LCM (least common multiple) is 6 so just cross multiply
4/6 - 3/6 = 1/6

I hope this helps :)

The value of x+y using given equations is 3x+2y=1.

The given equation are 3x+2=4 and 2y+6=5.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

To find x+y:

3x+2+2y+6=4+5

⇒ 3x+2y+8=9

⇒ 3x+2y=1

Hence, the value of x+y using given equations is 3x+2y=1.

To learn more about an equation visit:

https://brainly.com/question/14686792.

#SPJ2

I need help finding x

Answers

Answer:

x = 40.3

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp / hyp

sin x = 11/17

Taking the inverse sin of each side

sin ^-1 ( sin x) = sin ^-1( 11/17)

x = 40.32

Rounding to the nearest tenth

x = 40.3

Answer:

45°

Step-by-step explanation:

You can tell the distance from the right angle from each leg is the same and the angle measurements are the same.

Find the slope that is PARALLEL and PERPENDICULAR to the equation of the line y = -1/2x+6.

Answers

Step-by-step explanation:

For parallel line:

slope of given line:

m=-1/2

Parallel lines have equall slopes:

required slope=-1/2

For perpendicular line:

m1×m2=-1

-1/2×m2=-1

m2=2

slope of perpendicular line=2

Note:if you need to ask any question please let me know.

When analyzing an argument, the first task is to identify its premise or premises and its conclusion. Conclusion indicators are words or phrases that can help you identify which statement in an argument is the conclusion.Each argument shown next uses a conclusion indicator. Identify the conclusion indicator and the argument's conclusion. Type the indicator word or phrase into the space provided, and then select which statement best represents the argument's overall conclusion.Argument ASilver cars are more likely to be pulled over than any other kind of car. This is because there are more silver-colored cars on the road than any other kind of car. Kari drives an average-looking silver car to and from work everyday. We may infer that Kari is more likely to be pulled over.From this argument, type the conclusion indicator word or phrase here:Which statement best represents the conclusion of the argument?Kari is more likely to be pulled over.Kari drives an average-looking silver car to and from work everyday.Silver cars are more likely to be pulled over than any other kind of car.There are more silver-colored cars on the road than any other kind of car.Argument BScissors are not a toy. If you run with scissors, then you could get hurt. You could poke your eye out or cut yourself with the scissors if you fall. For these reasons, you should never run with scissors.From this argument, type the conclusion indicator word or phrase here:Which statement best represents the conclusion of the argument?You could poke your eye out or cut yourself with the scissors if you fall.If you run with scissors, then you could get hurt.Scissors are not a toy.You should never run with scissors.Argument CWe know that the natural world is governed by scientific laws of regularity. Those laws express predictable relationships that do not allow any wiggle room for variant outcomes. So, humans do not have free will. This is because the human body is as much a part of the natural world as any other physical object.From this argument, type the conclusion indicator word or phrase here:Which statement best represents the conclusion of the argument?Humans do not have free will.The natural world is governed by scientific laws of regularity.The human body is as much a part of the natural world as any other physical object.Scientific laws express predictable relationships that do not allow any wiggle room for variant outcomes.

Answers

In Argument A the conclusion indicator  is "we may infer that" and the conclusion  is Kari is more likely to be pulled over.

In Argument B the conclusion indicator  is "For these reasons" and the conclusion  is You should never run with scissors.

In Argument C the conclusion indicator  is "So" and the conclusion  is Humans do not have free will.

To identify the conclusion of each argument, we can either separate the premises (examples of the author's opinion) from the entire argument or we can identify the conclusion indicators.

Some conclusion indicators include:

therefore, thus, hence, so, for these reasons, we may infer, as a result,consequently, etc

Argument A:

conclusion indicator = we may infer that

Conclusion = Kari is more likely to be pulled over.

Argument B:

conclusion indicator = For these reasons,

Conclusion = You should never run with scissors

Argument C:

conclusion indicator = So,

Conclusion = Humans do not have free will

Learn more here: https://brainly.com/question/14583700


Solve for x.
(2x - 5°
(5x + 10)
B

Answers

i think the answer is x=25. if not then it’s x=-5

if a shirt selling for $ 18 is marked up to $20 then the percentage increased is equal to

Answers

Answer:

11.11%

Step-by-step explanation:

the increased price = 20-18 = $2

the percentage increased = 2/18 ×100%

= 11.11%

Answer: Percent increase = 11.11%

Concept:

Here, we need to know how to find the percentage of increase.

Percent increase is a measure of percent change, which is the extent to which something gains value.

Percent increase = [(final value - initial value) / initial value] × 100%

Solve:

Given information

Initial value = $18

Final value = $20

Given expression

Percent increase = [(final value - initial value) / initial value] × 100%

Substitute values into the expression

Percent increase = [(20 - 18) / 18] × 100%

Simplify values in the parentheses

Percent increase = [2 / 18] × 100%

SImplify by multiplication

Percent increase = 11.11 % (Rounded to the hundredth place)

Hope this helps!! :)

Please let me know if you have any questions

Can I please have some help fast

Answers

Answer:

The second one

Step-by-step explanation:

In that table, all the numbers in the column B can be found multiplying the numbers of column A by 4, and that's a property of ratio

700000 is _ times as much as 700 ANSWER FAST!!!!

Answers

1,000

theres 4 more 0's in 700,000 than in 700

Find the midline for f(x)=sinx+1.
a. y=0
B. y=−1
C. y=1
D. y=−2

Answers

Answer:

B Y=1

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

What is the greatest value that sin(x) + 1 can have? It isn't 1.

f(90) = sin(90) + 1

f(90) = 1 + 1 = 2

What is the smallest value that sin(x) + 1 can have? It still isn't one.

f(-90) = sin(-90) + 1

f(-90) = -1 + 1 = 0

So the midline is (2 + 0)/2 = 1

y = 1 is the answer.

In which quadrant , the point (2, -1) lies
1st
2nd
3rd
4th​

Answers

Answer:

4 th quadrant

Step-by-step explanation:

hope it helps you

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