The number N is the produce of the first 1000 positive integers and can be written as 1000!.We say "1000 factorial."This is, N=1000!=1000x999x998x997x...x3x2x1.N is divisible by 5, 25, 125, 625,...Each of these factors is a power of 5.That is 5=5^1, 25=5^2, 125=5^3,625=5^4, and so on. Determine the largest power of 5 that divides N.

Answers

Answer 1

From 1000 to 1, there are 200 numbers that are divisible by 5, which means that 1000! is divisible by at least 5^200.Then there are 40 numbers that are divisible by 25 (5^2), so this adds another 5^40.Then there are 8 numbers divisible by 125 (5^3), so this adds another 5^8.Finally, 1 number is divisible by 625 (5^4), so this adds 5^1.
Therefore, the total sum is 5^(200+40+8+1) = 5^249. Therefore, the largest N = 249.

Related Questions

Find the missing values given that cos(theta) = 1.
Sin(Theta):
Csc(Theta)
Sec(Theta):
Cot(Theta):

Answers

we know that
cos(theta) = 1---------> the value of cos is positive
then
angle theta------> could be in the first or fourth quadrant

Part 1) find sin theta
sin² theta+cos² theta=1------> sin² theta=1-cos² theta----> 1-1²----> 0
sin theta=0

Part 2) find csc theta
csc theta=1/sin theta
but sin theta =0
therefore
csc theta-------> it does not exist, it is not defined

Part 3) find sec theta
sec theta=1/cos theta
cos theta=1
so sec theta=1/1----> sec theta=1

Part 4) find cot theta
cot theta=cos theta/sin theta
but sin theta=0
therefore
cot theta-------> it does not exist, it is not defined

What is the vertex of the absolute value function defined by f (x) = |x - 7| + 1?

A. (7,1)

B. (-7, -1)

C. (-7, 1)

D. (7, -1)

Answers

The vertex of function y = |x| is (0; 0).
We have: f(x) = |x - 7| + 1
shift the graph of the function y = |x| 7 units right and 1 unit up. Then the vertex of function f is (7; 1).
Your answer is A. (7; 1)
Look at the picture.

The coach attempts to determine an association between shirt size and hat size. Which is most likely true?

Answers

It would be shirt size

Answer:

There is likely an association because 0.8 is not similar to ≈ 0.33.

divide (x^3-20x+16)divide (x-4)

Answers

Your answer is x² + 4x - 4

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Eliminate the parameter to find a cartesian equation of the curve. x = 3sin(t), y = 4cos(t)

Answers

Final answer:

To eliminate the parameter and find the cartesian equation of the curve x=3sin(t), y=4cos(t), we can use trigonometric identities. The cartesian equation of the curve is (x/3)^2 + (y/4)^2 = 1.

Explanation:

To eliminate the parameter and find the cartesian equation of the curve x=3sin(t), y=4cos(t), we can use trigonometric identities. Starting with the given equations:

x = 3sin(t)

y = 4cos(t)

We can rewrite the equation for x as:

x/3 = sin(t)

And the equation for y as:

y/4 = cos(t)

Using the identities sin2(t) + cos2(t) = 1, we can square both equations and add them together:

(x/3)2 + (y/4)2 = (sin2(t) + cos2(t)) = 1

This is the cartesian equation of the curve.

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if a recipe calls for 0.800 kg of flour , about how many ounces of flour does it need? (1lb=16 oz, 1 lb = 0.454 kg )

5.8 oz

11.0oz

28.2oz

227oz

Answers

For this case we must take into account the following conversions of units:
1lb = 16 oz
1 lb = 0.454 kg
Applying the conversion of units we have:
(0.800) * (1 / 0.454) * (16/1) = 28.1938326
Rounding off we have:
28.2 oz
Answer:
it needs 28.2 oz of flour

Answer: The correct option is (C) 28.2 oz.

Step-by-step explanation: Given that a recipe calls for 0.800 kg of flour.

We are to find the number of ounces of flour that the recipe needs.

Given that

1 lb=16 oz and 1 lb = 0.454 kg

We will be using the UNITARY method for solving the given problem.

We have

0.454 kg = 1 lb

So, 1 kg will be equal to [tex]\dfrac{1}{0.454}~\textup{lb}.[/tex]

Therefore, 0.8000 kg is equal to

[tex]\dfrac{1}{0.454}\times 0.800=1.762~\textup{lb}.[/tex]

Now, 1 lb = 16 oz.

So, 1.762 lb = 16 × 1.762 = 28.19 = 28.2 oz.

Thus, the recipe needs 28.2 oz of flour.

Option (C) is CORRECT.

A gas station sells regular gas for $2.20 per gallon and premium gas for $3.00 a gallon. at the end of a business day 300 gallons of gas has been sold, and receipts totaled $700. how many gallons of each type of gas had been sold

Answers

You can use a system of equations to answer this question.

1st: 2.20r + 3p = 700 is showing how to get the total cost.
2nd: r + p = 300 shows how many gallons were sold.

If we solve r + p = 300 for r, we can then solve the first equation in terms of r only.

r + p =300
p = 300 - r Use this in place of p in the first equation.

2.20r + 3p = 700
2.2r + 3(300 - r) = 700
2.2r + 900 - 3r = 700
-900 -900
2.2r - 3r = -200
-0.8r = -200
-0.8 -0.8
r = 250 gallons

There were 250 regular gallons sold and 50 premium gallons sold (300 - 250).

Aaron took three times as many pictures as jennifer.jennifer has 16 fewer pictures than aaron.which system of equations can be used to find the number of oictures each person took?

Answers

A=Aaron
J=Jennifer
a=3j
j=a-16

I NEED HELP ON THIS EQUATION PLEASE (:

Answers

4.5 in. Or 4 1/2 inches just depending how they want you to write it.

Area = Length x Width

45 = Length x 10

Length = 45 ÷ 10 = 4.5 in

Answer: 4.5 in

Solve for m -20+14m=10m+16

Answers

-20+14m=10m+16
-10m. -10m
-20+4m=16
+20. +20
4m=36
/4. /4
m=9

PLEASE HELP ME FIND THE VALUE OF X
25 POINTS

Answers

right triangle so
Pythagorean theorem:
c^2 = a^2 + b^2
a = 6 and c =√117
to find b:
b^2 = c^2 - a^2
b^2 = (√117)^2 - 6^2
b^2 = 117 - 36
b^2 = 81
b = √81
b = 9

answer:
x = 9 cm

Answer:

the answer is x = 9 cm

Step-by-step explanation:

Mrs. rifkin had 84 oranges. 24 of her oranges were rotten; the rest were either ripe or unripe. there were 18 more ripe oranges than unripe oranges. find the ratio of the number of ripe oranges to the number of rotten oranges to the number of unripe oranges.

Answers

84 oranges - 24 rotten = 60 oranges that are either ripe or unripe Let x = number of unripe orangesLet x + 18 = number of ripe oranges You know that the number of ripe oranges plus the number of unripe oranges is equal to 60 (x) + (x + 18) = 60 Subtract 18 from each side x + x = 42 x + x is the same as 2x, so 2x = 42 Divide each side by 2 2x/2 = 42/2 The 2s on the left side cancel out x = 21 So the number of unripe oranges is 21 The number of ripe oranges is x + 18,which is 21 + 18 = 39 So the number of ripe oranges is 39

39:24:21
There were 39 ripe oranges
There were 24 rotten oranges
and there were 21 unripe oranges
for a total of 84 oranges.

A cylinder has a radius of 10m and a 8m. What is the exact volume of the cylinder?

160 TT m3

80 TT m3

800 TT m3

18 TT m3

Answers

The formula for the volume of a cylinder is πr^2*h. If you plug in the numbers of the radius and the height. π10^2*8=800π meters^3.

If you take 5 quizzes and get scores of 95%, 95%, 80%, 85%, and 75%, how would you find your mean quiz score?

Answers

Add all of the numbers together and divide by 5. The average ends up being 86.

The mean of the quiz scores is given by the equation M = 86 %

What is Mean?

The mean value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.

Mean = Sum of Values / Number of Values

Given data ,

Let the mean of the quizzes be represented as M

Now , the equation will be

Let the number of quizzes be n = 5

Let the scores of each quizzes be represented by set A

Set A = { 95% , 95%, 80%, 85%, 75% }

So , the mean of the quizzes M = sum of the quizzes / number of quizzes

Substituting the values in the equation , we get

The mean of the quizzes M = ( 95% + 95% + 80% + 85% + 75% ) / 5

The mean of the quizzes M = ( 430/5 )

The mean of the quizzes M = 86 %

Therefore , the value of M is 86 %

Hence , the mean of the quizzes is 86 %

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Which one is it? Will give brainiest

Answers

180° - [180° - (34° + 103°)]
180° - 180° + 34° + 103°
34° + 103°
137°
~C

Rebecca is planting an orange grove that covers 32 acres she uses the same amount of ground space for each tree Rebecca plants 15 trees in a section of the grove that measures 250 feet by 25 feet what is the population density of this section of the grove use 1 acre= 43,560 square feet

Answers

Area of the garden that 15 trees are planted will be:
Area=250×25=6250 ft²
but 1 acre= 43560 ft²
thus converting our area to acres we get:
6250/(43560)
=0.1435 acres
thus the population density will be:
(Population)/(area)
=15/0.1435
=104.544 trees/acre

9) If the circle x2 - 4x + y2 + 2y = 4 is translated 3 units to the right and 1 unit down, what is the center of the circle?

Answers

(5, -2)
_____________

Please help with geometry

Answers

Use:[tex]A_\Delta=\dfrac{1}{2}ab\sin\alpha[/tex]
[tex]a=503ft=\dfrac{503}{3}yd\approx168yd\\\\b=516ft=\dfrac{516}{3}yd=172yd\\\\\sin38^o\approx0.616[/tex]
Substitute:
[tex]A_\Delta=\dfrac{1}{2}\cdot168\cdot172\cdot0.616\approx8,877yd^2[/tex]

A triangle has sides with lengths: 6, 9, and 5. How do you find the area of the triangle using Heron's formula?

Answers

Area of triangle=Δ=√s(s-a)(s-b)(s-c)
a=6
b=9
c=5
s=(a+b+c)/2
s=(6+9+5)/2
s=10
Δ=√10(10-6)(10-9)(10-5)
Δ=10√2 sq. units
OR
Δ=14.14 sq. units

In the figure above, Angle FEB is a central angle. True or False?

A. True
B. False

Answers

False
A central angle is formed at the center of the circle (C).

We know that the central angle is an angle subtended at the center of the circle by any two points on the circle.

In the given figure of the circle, the center of the circle is C. Hence, the central angle must be subtended at the center C.

Since, angle FEB is not subtended at the center of the circle.

Hence, angle FEB is not a central angle.

Therefore, the given statement is FALSE.

What’s the answer for No.29 & 30 please hurry

Answers

29) replace Y in the 2nd equation with the first equation and solve:

4x -3(2x-3) = 31

distribute the -3(2x-3)

4x-6x+9 = 31

combine 4x-6x

-2x +9 = 31

subtract 9 from each side

-2x = 22

divide both sides by -2 to get x

x = 22 / -2 = -11

x = -11

now replace x in the first equation with -11 to solve for y

y = 2(-11) -3
y = -22 -3
y = -25

x = -11, y = -25 which is (-11,-25) so A is the correct answer

30) the solution is where the 2 lines cross which is at X = 2 and Y = 4 which is (2,4) so B is the correct answer

Solve 5x = 10x - 5(2x-3) for x. Show your work.

Answers

Eliminate parentheses using the distributive property.

... 5x = 10x -10x +15

Collect terms, then divide by the coefficient of x.

... 5x = 15

... x = 3

Determine whether quantities vary directly or inversely and find the constant of variation. It takes four identical water pumps 6 hours to fill a pool. How long would it take three of these same pumps to fill the pool, assuming they all pump at the same rate?

Answers

Let the number of water pumps be n and the time taken to fill the pool is t.

Now, we can see that higher the number of water pumps, lesser the time to fill the pool.

It means quantities vary indirectly.

Thus, [tex]n=\frac{k}{t} , \text{ where k is the constant of variation}[/tex]

Now, we have been given that It takes four identical water pumps 6 hours to fill a pool.

Thus, we have

[tex]4=\frac{k}{6} \\ \\ k=24[/tex]

Hence, constant of variation is 24.

Now, we have to find the time that three pumps will take to fill the same pool.

[tex]3=\frac{24}{t} \\ \\ 3y=24\\ \\ y=\frac{24}{3} \\ \\ y=8[/tex]

Hence, it will take 8 hours to fill the pool by three identical pumps.

The larger square garden at Volterra Hall has sides twice as long as the smaller square garden. Together the gardens cover 18,000 square feet. Find the dimensions of each garden.

Answers

We will call:
[tex] G_{1}[/tex]: The larger square garden.
[tex] G_{2}[/tex]: The smaller square garden.

Given that both of then have square areas, then:
[tex] A_{G1} = L_{G1}^{2} [/tex]
[tex] A_{G2} = L_{G2}^{2} [/tex]

Being [tex] L_{G1} [/tex] the side of the larger garden and [tex] L_{G2} [/tex] the side of the smaller garden as shown in the figure.

The larger square garden at Volterra Hall has sides twice as long as the smaller square garden, thus:

[tex] L_{G1} = 2L_{G2}[/tex]

Together the gardens cover 18,000 square feet, so:
[tex]A_{G1} + A_{G2} = L_{G1}^{2} + L_{G2}^{2} = 18000[/tex]

Then:
[tex](2L_{G2})^{2} + L_{G2}^{2} = 18000[/tex]
[tex]4L_{G2}^{2} + L_{G2}^{2} = 18000[/tex]
[tex]5L_{G2}^{2} = 18000[/tex]
[tex]L_{G2}^{2} = 3600[/tex]
[tex]L_{G2} = \sqrt{3600}[/tex]
[tex]L_{G2} = 60[/tex]
[tex]L_{G1} = 2L_{G2} = 2(60) = 120[/tex]

Therefore:
Each side of the larger square garden is [tex] 120 ft [/tex] and each side of the smaller one is [tex] 60 ft[/tex] each. These are the dimensions.

Can derivatives be used to measure the the slope of the tangent line at x=a

Answers

Yes. In fact, that is basically the definition of a derivative. It is the instantaneous rate of change of a function.

For example, picture the graph of the following function:

[tex]f(x) = x^2[/tex]

The slope is constantly changing at every x-value, so to find the slope at x=a, we find the derivative of the function.

[tex]f'(x)=2x[/tex]

Once we have the derivative, simply plug in a for x to find the slope of the line tangent to f(x) at x=a.

For example, at x=5:

[tex]f'(5)=2(5)[/tex]

The slope of f(x) at x=5 is 10.

Jayden wants to find the dimensions of this parallelogram. He knows that the first step is to find the value of x. Which of these equations will result in the correct value of x?

A. 2x – 1 = x + 8

B. 2x – 1 = x + 1

C. x + 1 + 2x – 1 = 180

D. x + 1 = x + 1

Answers

In a parallelogram opposite sides are equal. So in your picture, you either have x + 1 = x + 1, or x + 8 = 2x - 1. Since the 1st equation will give you 0 = 0, which will not help at all. So you gave to do the other equation x + 8 = 2x - 1 or B

Answer:

2x – 1 = x + 8

Step-by-step explanation:

how do you evaluate 71 - b, if b is 27

Answers

if you subtract 71 and 27, you will get 44

!!!!!!!!!!!!!which answe

Answers

Question: "A coin is tossed 8 times. Find the probability P(of exactly 6 occurrences of tails)"

Answer:
When we toss a coin we have 50% of probability to get a tail and 50% probability to get heads.

If we toss the coin 8 times, in order to find P(T=6), we need to use the binomial distribution:
[tex]P = \frac{n!}{k!(n-k)!} p^{k} (1-p)^{n-k} [/tex]
where:
n = total number of events
k = number of successes we want
p = probability of success

Therefore:
[tex]P(T=6) = \frac{8!}{6!(2)!} 0.5^{6} (1-0.5)^{2} [/tex]
= 28 · 0.015625 · 0.25
= 0.109375

Hence, the probability of getting 6 tails out of 8 tosses is D) 10.94%.

Answer:

I think it's D

Step-by-step explanation:

Write an equation in intercept form of the parabola that passes through the point (1,32) and has x-intercepts −7 and 3?

Answers

Given that the parabola passes through points (1,32) and the x-intercepts are (-7,0) and (3,0)
thus the equation will be as follows:
y=a(x-k)(x-h)
where:
(x-k) and (x-h) are the factors:
thus
y=a(x+7)(x-3)
y=a(x^2+4x-21)
But, when x=1, y=32
plugging this in the equation we get:
32=a(1^2+4(1)-21)
32=a(1+4-21)
32=-16a
hence:
a=-2
thus the eqiation will be:
y=-2(x^2+4x-21)
hence the equation is:
y=-2x^2-8x+42

The correct equation of the parabola in intercept form is [tex]2 (x+2)^2 -50[/tex].

To derive this equation, we will use the fact that the parabola passes through the given point (1,32) and has x-intercepts at -7 and 3.

[tex]y = k*(x+7)(x-3)[/tex]

[tex]y = k *(x^2 + 4x - 21)[/tex]

[tex]32 = k ( 8 * -2)32 = -16* kk = 32/-16 = -2[/tex]

[tex]y = -2(x+7)(x-3)[/tex]

[tex]= -2(x^2 + 4x - 21)[/tex]

[tex]= -2(x^2 +4x ) -42[/tex]

[tex]= 2(x^2 + 4x + 4) - 42 - 8[/tex]

[tex]= 2 (x+2)^2 -50[/tex]

Find the volume of a cube that is 7 cm on each edge.

Answers

WE KNOW THAT THE VOLUME OF THE CUBE IS '
V=a^3
our a=7
V=343 cm^3

Final answer:

The volume of a cube with each edge measuring 7 cm is calculated using the formula V = s^3, which results in a volume of 343 cubic centimeters (cm3).

Explanation:

To find the volume of a cube that is 7 cm on each edge, we use the formula for the volume of a cube, which is V = s3, where s is the length of one side of the cube. In this case, s is 7 cm. Therefore, the volume can be calculated as follows:

V = 7 cm imes 7 cm imes 7 cm = 343 cm3

So the volume of the cube is 343 cubic centimeters (cm3).

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