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Lina20 [59]
3 years ago
12

For positive integers $n$, let $f(n)$ return the smallest positive integer $k$ such that $\frac{1}{k}$ has exactly $n$ digits af

ter the decimal point. How many positive integer divisors does $f(2010)$ have?
Mathematics
1 answer:
disa [49]3 years ago
3 0

Answer:

There are a total of 2011 integer divisors.

Step-by-step explanation:

The only primes p such that 1/p has finite spaces after the coma are 2 and 5. If we divide a number with last digit odd we will obtain 1 extra digit after the decimal point and if we divide a number by 5 we will obtain 1 more digit if that number has a last digit in the decimal which is not a multiple of 5.

If we take powers of those primes we will obtian one more digit each time. In order to obtain more digits it is convinient to divide by a power of 2 instead of a power of 5, because the resulting number will be smaller.

If we want 2010 digits after the decimal point, we need to divide 1 by 2 a total of 2010 times, hence f(2010) = 2²⁰¹⁰, which has as positive integer divisors every power of 2 between 0 and 2010, hence there are a total of 2011 integer divisors of f(2010).

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Rabies is a viral disease of mammals transmitted through the bite of a rabid animal. The virus infects the central nervous syste
lisabon 2012 [21]

Answer:

(a) The value of <em>x</em> is 0.30.

(b) The probability that a reported case of rabies is not a raccoon is 0.45.

(c) The probability that a reported case of rabies is either a bat or a fox is 0.15.

Step-by-step explanation:

Denote the events as follows:

<em>R</em> = reported case of rabies is a raccoon

<em>F</em> = reported case of rabies is a fox

<em>B</em> = reported case of rabies is a bat

<em>O</em> = reported case of rabies is a some other animal.

The data provided is:

P (R) = 0.55

P (F) = 0.11

P (B) = 0.04

P (O) = <em>x</em>.

(a)

A property of a probability distribution is that the sum of all individual properties is 1.

That is, \sum P(X)=1

Compute the value of <em>x</em> as follows:

\sum P(X)=1\\P(R)+P(F)+P(B)+P(O)=1\\0.55+0.11+0.04+x=1\\0.70+x=1\\x=1-0.70\\x=0.30

Thus, the value of <em>x</em> is 0.30.

(b)

The probability of the complement of an event is the probability of its not happening.

P(A^{c})=1-P(A)

Compute the probability that a reported case of rabies is not a raccoon as follows:

P(R^{c})=1-P(R)\\=1-0.55\\=0.45

Thus, the probability that a reported case of rabies is not a raccoon is 0.45.

(c)

Compute the probability that a reported case of rabies is either a bat or a fox as follows:

P(B\cup F)=P(B)+P(F)\\=0.11+0.04\\=0.15

Thus, the probability that a reported case of rabies is either a bat or a fox is 0.15.

4 0
3 years ago
Numbers with a sum of 1
riadik2000 [5.3K]

Answer:

0.5 + 0.5, 0 + 1, 0.6 + 0.4, etc etc

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
I am thinking of a number. i will add four and then multiply it by five. the answer will be thirty five. whats the number?
kodGreya [7K]

Answer:

B. 3

Step-by-step explanation:

Let's make an equation for this. Our unknown number is x.

x

We are adding 4.

x + 4

Then multiplying by 5.

(x + 4) • 5

It will equal 35.

(x + 4) • 5 = 35

To solve this, divide both sides by 5.

(x + 4) = 7

Now subtract 4 from both sides.

x = 3

This is your answer.

Check this by plugging it back into our original equation.

(x + 4) • 5 = 35

(3 + 4) • 5 = 35

7 • 5 = 35

35 = 35

Your answer is correct.

Hope this helps!

3 0
2 years ago
Find the value of x.<br><br> help pls
AlexFokin [52]

Answer:

10

Step-by-step explanation:

5 0
2 years ago
1
horsena [70]

Answer:

t=5 dollars per t-shirt

Step-by-step explanation:

<em>Read the problem and write your equation while following along with it</em>

We have 8 t-shirts

Lets 8 t-shirts be represented by 8t

So for our equation we will place and 8

<h3>Our equation: 8t</h3><h3 />

Now it says we have a coupon that subtracts 4 dollars from our total

<h3>Our equation: 8t-4</h3><h3 />

The final part to add to our equation says that our total before tax was 36 dollars

<h3>So here is our equation: 8t-4=36</h3><h3 />

<em>add </em>$4<em> to both sides</em>

8t=40

<em>Divide both sides by</em> 8

t=5 dollars per t-shirt

-Side note, make sure to spell your question right. It was a tad bit confusing to read at the start.

-Brainliest please :)

4 0
2 years ago
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