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Anarel [89]
3 years ago
14

Write the number below as a fraction in its simplest form 0.˙49˙9 (more clearer picture is attached here)

Mathematics
1 answer:
mars1129 [50]3 years ago
5 0

Answer:

499/999

Step-by-step explanation:

The decimal number written is:

0.499...

Such that these 3 decimals are repeated as:

0.499499499...

Let's define this number as k

k = 0.499...

Let's multiply this number by 1000 (the same number of zeros as important decimals after the decimal point)

we get:

1000*k = (1000)*(0.499...) = 499.499...

Now we can subtract the original number k, so we get:

1000*k - k = 499.499... - 0.499...

In this way, we remove the part after the decimal point:

1000*k - k = 499.499... - 0.499...

(1000 - 1)*k = 499

999*k = 499

Now we can divide both sides by 999

(999*k)/999 = 499/999

k = 499/999

The fraction notation of our number is 499/999 (and this is the simplest form)

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A worker has job offers from two companies. The information below summarizes the job offer from each company.Company A:Starting
Zanzabum

Using linear functions, we have that:

A.

For Company A: S_A(n) = 31000 + 3000n

For Company B: S_B(n) = 38000 + 2000n

B. The salaries will be the same after 7 years.

A linear function is given by:

y = mx + b

In which:

  • m is the slope, which is the rate of change.
  • b is the y-intercept, which is the initial value.

Item a:

  • For Company A, the salary starts at $31,000, with a raise of $3,000 each year. Thus, b = 31000, m = 3000, and the salary after n years is given by:

S_A(n) = 31000 + 3000n

  • For Company B, the salary starts at $38,000, with a raise of $2,000 each year. Thus, b = 38000, m = 2000, and the salary after n years is given by:

S_B(n) = 38000 + 2000n

Item b:

  • They will be the same after n years, for which:

S_A(n) = S_B(n)

Then

31000 + 3000n = 38000 + 2000n

1000n = 7000

n = \frac{7000}{1000}

n = 7

The salaries will be the same after 7 years.

A similar problem is given at brainly.com/question/24282972

7 0
2 years ago
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