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3 years ago

How many consecutive zeros are there at the end of the expansion of 1,000 factorial?

2 answers:

6 0

Finding the number of trailing zeroes in the factorial of a number has a sequence of 3-4 steps which applies for all number. I will list it down for reference

step 1: Divide the given number by 5, the answer will give you the number of multiples. If it gives you a decimal answer, you can just take the whole number

Step 2: Divide the given number with the next power of 5, that is 25( 5 times 5) , find the number of multiples

Step 3: Divide the given number with the next power of 5, that is 125 (5 times 5 times 5) , find the number of multiples

Step 4:Keep doing this with increasing powers of 5 till the given number becomes lesser than the power of 5

Step 5: Now add all the number of multiples you got at each step

This will give you the number of trailing zeroes for the given number

Let's do this process for the given number 1000

Divide by 5

1000÷5 = 200 multiples

1000 ÷25 = 40 multiples (5² = 25)

1000÷125 = 8 multiples (5³=125)

1000÷ 625 = 1.69.... we take only the whole number so 1 multiple

now the next power is 3125 which cannot divide 1000 so we can stop this process

now add all the multiples

200+40+8+1 = 249

So the factorial of 1000 has 249 trailing zeroes

Masja [62]3 years ago

3 0

249 Zeros in the expansion of 1,000

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Colt1911 [192]

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Answer: 8 Students

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3 years ago

Use the given information to find the p-value. Also, use a 0.05 significance level and state the conclusion about the null hyp

Hatshy [7]

Answer:

We can assume that the statistic is $z_{calc}=0.78$

$p_v = 2* P(z>0.78) = 0.435$

So the p value obtained was a very high value and using the significance level given $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the true proportion of interest is not different from 3/5

Step-by-step explanation:

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion is equal to 3/5 or not.:

Null hypothesis: $p=3/5$

Alternative hypothesis: $p \neq 3/5$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Calculate the statistic

We can assume that the statistic is $z_{calc}=0.78$

Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.05$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v = 2* P(z>0.78) = 0.435$

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3 years ago

Hello, i need help with this question please!<br><br> solve x/2 +3 > 4

jeka57 [31]

Answer:

x >2

Step-by-step explanation:

x/2 +3 > 4

Subtract 3 from each side

x/2 +3-3 > 4-3

x/2 >1

Multiply each side by 2

x/2*2 >1*2

x >2

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2 years ago

Read 2 more answers

A right triangle is formed in the first quadrant by the x- and y-axes and a line through the point (5, 3), as shown in the figur

Whitepunk [10]

The area of the triangle as a function of x is A = 3x^2/[2(x -5)] and the domain is x > 5

<h3>Write the area A of the triangle as a function of x</h3>

From the figure, we have the following points:

(0,y), (5,3), and (x,0)

Next, we calculate the slopes between the points.

This is calculated as follows:

Slope between (0,y) and (5,3) = [y - 3]/[0 - 5] = [3 - y]/5
Slope between (5,3) and (x,0) = [3 - 0]/[5 - x] = 3/[5 - x]

The slopes are equal.

So, we have:

[3 - y]/5 = 3/[5 - x]

Cross multiply

(3 - y)(5 -x) = 15

Divide by 5 - x

(3 - y) = 15/(5 -x)

This gives

y = 3 - 15/(5 -x)

This gives

y = [15- 3x - 15]/[5 - x]

Evaluate

y = 3x/(x - 5)

The area is calculated as:

Area = 1/2 * xy

So, we have:

Area = 1/2 * x * 3x/(x - 5)

Evaluate

Area = 3x^2/[2(x -5)]

Hence, the area of the triangle as a function of x is A = 3x^2/[2(x -5)]

<h3>The domain of the function</h3>

We have:

A = 3x^2/[2(x -5)]

Set the denominator > 0

2(x - 5) > 0

Divide by 2

x - 5 > 0

Add 5 to the sides

x > 5

Hence, the domain is x > 5