Daniel is multiplying consecutive counting numbers together, beginning with 1. He finds that 1 x 2 x 3 x 4 x 5 = 120 and that1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 = 3628800. He continues to multiply consecutive counting numbers together until the resulting product has a string of 20 zeroes at the end of the number, at which point he stops. How many counting numbers does Daniel multiply together to find his final product?

Answers

Answer 1

9514 1404 393

Answer:

  85

Step-by-step explanation:

A number will end in 0 if it has a factor of 10. For a number to end in 20 zeros, it must have 20 factors of 10. That means 2^20 and 5^20 must both be factors of the number.

In any group of sequential numbers, the number of them divisible by 2 will exceed the number divisible by 5, so we only need to have 20 factors of 5 in the group.

Every 5th multiple of 5 will have an additional multiple of 5, so 3 groups of 5 multiples of 5 will have 18 factors of 5. That is, the sequential numbers 1 .. 75 will have a total of 18 factors of 5. For two more factors of 5, we need to have two more multiples of 5: 80 and 85.

The sequential numbers 1 .. 85 will have 20 factors of 5 and at least 20 factors of 2. Hence 85! will end in 20 zeros.

Daniel must multiply together 85 sequential counting numbers to have a product ending in 20 zeros. (It will have a total of 129 digits.)


Related Questions

Complete the following equation using <,>, or = 7___24/4

Answers

Answer:

<

Step-by-step explanation:

Have a Great Day!!!

Find the amount of tax and the tax rate. Round to nearest hundredth of a percent . Cost of item: $118 Selling price: $132.37 Tax Amount: $ Tax Rate percentage%​

Answers

Answer:

The amount of tax is $14.37 and the tax rate percentage is 12.18%

Step-by-step explanation:

Find the amount of tax by finding the difference between the cost and selling price:

132.37 - 118

= 14.37

Find the tax rate percentage by dividing the tax by the original cost, and multiplying it by 100:

(14.37/118) x 100

= 12.18

The amount of tax is $14.37 and the tax rate percentage is 12.18%

I NEED HELP NOW PLEASE

Answers

Answer: B : Stretches vertically by factor 3

Step-by-step explanation: Can you mark this brainliest if this is right?

graph a line with slope 1/3 and y-intercept -2

Answers

I graphed it for you.

Yolanda is planning out her square vegetable garden. One side 4 feet. How
can I represent the area with exponents? *

HELPP MEEE ASAP PLSS

Answers

A stands for area. So here we know that a squares area is side to the power of 2 and thats the only way to show area with exponent. So here we get A=4^2 feet squared. Hope it helped :)!

A spinner has three equal sections labeled 1, 2, and 3
Which organized list shows the possible outcomes for spinning the spinner twice?
Ο Α
o 1,1; 1,2; 1,3
o 2,1,2,2,2,3
o 3,1; 3,2; 3,3
ОВ
o 1,2; 1,3
o 2,1,2,3
o 3,1,3,2
Ос.
o 1,1; 1,2; 1,3
o 2.2; 2,3
o 3,3
OD
1,1; 1,2; 1,3

Answers

the answer is hi Step-by-step explanation:

Answer:

answer: A

Hope that helps!

The function f(x) = -2x2 + 10x models the height above the ground, in
cm, of a jumping frog where x is the horizontal distance, in cm, the frog
traveled during the jump. What was the horizontal distance, in cm, that
the frog traveled during its jump?pls explain how u got the answer

Answers

Answer: I think its 1

Step-by-step explanation:

What’s the answer??
15 points

Answers

Answe

5

Step-by-step explanation:

Raul has a garden shaped like the trapezoid below. All the
measurements are in feet.
6
7
4
5
8
What is the area of the garden in square feet?

Answers

The answer is zhdhdbshsbdbdhdjdhdvfodjsksvsjskdbfndlssvsvvdsorry

Complete the statement.
63 mi
mi
h
sec

Please answer ASAP worth 25 points

Answers

0.0175 mi/sec, that is the answer

Answer:

63miles/hour=63miles/[60×60]sec=

0.0175miles/sec

Find the value of c that makes each trinomial a perfect square. Then write the trinomial as a perfect square.
6. x2 – 20x + c
a. c = 64; (x – 8)2 b. c = 20; (x – 10)2 c. c = 100; (x + 10)2 d. c = 100; (x – 10)2

Answers

Answer:

d. c = 100; (x – 10)²

Step-by-step explanation:

Note that (x+a)²=x²+2ax+a².

In our case, 2a=-20, so 'a' must be -10.

Since c=a², and a=-10, c=(-10²)=100.

Since a=-10, the perfect square is (x – 10)²

On a certain hot summer day, 606 people used the public swimming pool the daily prices are 1.50 for children and 2.00 for adults the receipts for admission totaled 1042.50 how many children and how many adults swam at the public pool that day

Answers

Answer:

rsgsadfg

Step-by-step explanation:

d dhrtyeyerte

i have 25 coins,x of them ard R5 coins and the rest are R2 coins.What is an expression in terms of x for number of R2 coins?​

Answers

9514 1404 393

Answer:

  25 - x

Step-by-step explanation:

Subtracting the number of R5 coins from the total number of coins will give the number of R2 coins:

  25 - x . . . . . . number of R2 coins

Directions: Write your answer in the box. Do not use spaces.
Find the volume of the microwave popcorn box when the length is doubled.
XOTIR
FOPCOXE
h = 6.25 in.
Nota
TN
show
side.
w - 2.5 in.
26 in.
I
Volume doubled =
in3
a
b

Answers

Answer:

New volume will become 187.5 inch²

Step-by-step explanation:

Initial volume,

V = lbh

Put all the values,

V = 6.25 × 2.5 × 6

V = 93.75 inch³

When the length is doubled, l' = 2(6) = 12 inch

New volume,

V' = 12 × 6.25 × 2.5

= 187.5 inch²

So, when the length is doubled, the new volume will become 187.5 inch².

Pls help I need a good grade

Answers

A

Step-by-step explanation:

m+n

2..................

What is the equation for this word problem?:
Ravi needs to read 3 novels each month.
Let N be the number of novels Ravi reads in M months
Help!

Answers

Answer:

N = 3M

Step-by-step explanation:

pls answer this about mathh



Note :: no links no explain no ​

Answers

Step-by-step explanation:

B.

AC =BC

2x-6=x+8

2x-x=8+6

x=14

5) AC = 2x-6=2(14)-6=28-6= 22

6) BC = x+8= 14+8= 22

7) AB = AC+BC = 22+22= 44

C.

AC =BC

4x+10=7x-5

4x-7x= -5-10

-3x= -15

x= -15/-3 = 5

8) AC = 4x+10=4(5) +10=20+10= 30

9) BC = 7x-5= 7(5) -5=35-5= 30

10) AB = AC+BC = 30+30= 60

B) Solution

AC = BC

→ 2x-6 = x+8

→ 2x-x = 8+6

→ x = 14

5:- AC = 2x-6 = 2(14)-6 = 28-6 = 22

6:- BC = x+8 = 14+8 = 22

7:- AB = AC+BC = 22+22 = 44

C) Solution

AC = BC

→ 4x+10 = 7x-5

→ 4x-7x = -5-10

→ -3x = -15

→ x = -15/-3

→ x = 5

8:- AC = 4x+10 = 4(5) +10 = 20+10 = 30

9:- BC = 7x-5 = 7(5)-5 = 35-5 = 30

10:- AB = AC+BC = 30+30 = 60

Find the slope (m) and y-intercept (b) of each line.

Answers

Answer:

y-int:(0,-2)

slope: 5/2

Step-by-step explanation:

slope is rise over run, so you just need to find 2 points (0,-2) and (2,3) and calculate (3-(-2))/(2-0) and get 5/2. y intercept is just the point located at X=0

Answer:

The y-intercept is (0, -2) and the slope is 5/2

Step-by-step explanation:

Write an algebraic expression for the situation.

3.2 less than a number m

An algebraic expression for the situation is _

Answers

Answer:

m - 3.2

Step-by-step explanation:

Match each of the parts of the following polynomial with the vocabulary.
7x 2 + 9y3 + 2y - 8

Answers

Answer:

1. {c} (Coefficients)

2. {a} (Terms)

3. {b} (Variables)

4. {d} (Constants)

If the spinner to the right is spun once, what is the probability

that it lands on a star or a shaded region?

Answers

Answer: i think its star because it sounds right and well i tryed it before and you should to.

Find the greatest power of 3 that is divisible of 100!

Answers

Answer:

There is no greatest power of 3 that is divisible of 100.

Step-by-step explanation:

Since any number can always be divisible of 100, there would be no greatest power of 3 that is divisible of 100 since the powers can go on and on forever without stopping, and all powers of 3 is able to be divided by 100.

i am too lazy can someone solve this for me.
A bakery sold a total of 500 cupcakes in a day, and 190 of them were vanilla flavored. What percentage of cupcakes sold that day were vanilla flavored?

Answers

Answer:

20% of them we flavored vanilla that day

Step-by-step explanation:

What is the slope of the line that passes through the points (26, 7) and (-39, 12)?​

Answers

I think it’s A. m = -1 over 13

A 11/13

Step-by-step explanation:

1

1. Which expression represents the
factored form of x2 - 13x + 36?
A (x - 4)(x - 9)
B (x - 3)(x - 12)
C (x + 9)x - 4)
D (x + 12)(x - 3)

Answers

Answer: Hello, There! your Answer is Below

A (x - 4)(x - 9)

Step-by-step explanation:

Find p, and q, knowing sum = b = 13 and product c = 36. Compose factor pairs of 36-> (2, 18)(2, 12)(4, 9). this last sum is 9 = b. Then p = 4 and q = 9

Hope this Helps you!!

Have a great day!!

The answer is choice A. The middle number, the one with the x, in this case 13, is what the factors should add up to. so, -4 plus -9 equals -13, which is our middle number. the last number, without the x, is what the numbers must multiply to, in this case 36. so, -4 times -9 equals positive 36. So, choice A is the answer.

Answer this simple quick question!! Pls :)

Answers

Answer:

D

pls mark me as Brainiest  :}

Step-by-step explanation:

The long side of a rectangle is 2b + 3 units, and its area is 2b ^ 2 - 5b - 12 Find the width .

Answers

Answer:

b - 4

Step-by-step explanation:

This can be done by factoring.

Area = length x width

2b^2 - 5b - 12 = (2b + 3)( ???)

Factor the area into (2b + 3)(b - 4).  The width is b - 4.

Answer:

The answer is b - 4

Step-by-step explanation:

ANSWER ASAP DONT SEND A FILE. IS THIS SHAPE A ROTATION, REFLECTION,TRANSLATION, DILATION OR NONE????ONLY ANSWER IF YOU ACTUALLY KNOW THE ANSWER

Answers

Answer:

its a reflection

Step-by-step explanation:

its a reflection across the y axis

Answer:

REFLECTION

Step-by-step explanation:

same shape, same size just flipped

Barak asked 50 students which type of flower they liked best. The results are displayed in the pie chart. If Barak asked 200 students which flower they liked best, how many students would you predict would choose tulips?
A. 15
B. 30
C. 60
D. 67​

Answers

Answer:

C. 60 among 200 students would like Tulip (Assuming pie chart - 15 among 50 students like Tulip)

Step-by-step explanation:

Percent students liking tulip = (Tulip liking students / Total students) x 100

= (15 / 50) x 100 = 30%

Expected students to like Tulip among 200 students =  30% of 200

( 30 / 100 ) x 200

= 60 students

Dara has to solve 35 math problems for homework. She has completed 14 of them. What fraction of the problems does she have left to do?

Answers

Answer:

The answer is 21/35 or 3/5

Step-by-step explanation:

35-14=21

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