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3 years ago

Which simplified fraction is equal to 0.53 (the 3 is repeating)

Mathematics

2 answers:

Anni [7]3 years ago

8 0

Answer: B
explanation: just divide 8/15

Cerrena [4.2K]3 years ago

6 0

<h3>Answer: Choice B. 8/15</h3>

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Explanation:

x = 0.53333333... the 3's go on forever

10x = 5.3333333..... we have infinitely many 3's here as well

100x = 53.333333..... same story

Each time we multiply both sides by 10, we move the decimal point over 1 spot to the right.

Focus on this system of equations

$\begin{cases}100x = 53.33333\ldots\\\ \ \ 10x = 5.333333\ldots\end{cases}$

Note how the decimal points line up so we can see both right sides have the same 33333... pattern

If we subtract those equations straight down, the left hand side turns into 90x because 100x-10x = 90x

The right hand side terms subtract to 48. The infinite number of 3's after the decimal will cancel out when we subtract. So we basically have 53-5 = 48.

After those subtractions, we now have the new equation 90x = 48

Divide both sides by 90 and reduce

90x = 48

90x/90 = 48/90

x = 48/90

x = (6*8)/(6*15)

x = 8/15

8/15 = 0.53333333....

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The Highway Safety Department wants to study the driving habits of individuals. A sample of 40 cars traveling on a particular st

Ipatiy [6.2K]

Answer:

We need a sample size of at least 101

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.99}{2} = 0.005$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.005 = 0.995$ , so $z = 2.575$

Now, find the margin of error M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

What sample size is needed to estimate the true average speed to within 2 mph at 99% confidence?

We need a sample of at least n.

n is found when M = 2. So

$M = z*\frac{\sigma}{\sqrt{n}}$

$2 = 2.575*\frac{7.8}{\sqrt{n}}$

$2\sqrt{n} = 2.575*7.8$

$\sqrt{n} = \frac{2.575*7.8}{2}$

$(\sqrt{n})^{2} = (\frac{2.575*7.8}{2})^{2}$

$n = 100.85$

Rounding up

We need a sample size of at least 101

8 0

3 years ago

Read 2 more answers

Round 2.51 to 1 decimal place

Leni [432]

Answer:

2.5

Step-by-step explanation:

It's because 1is less than 5

8 0

2 years ago

Read 2 more answers

Is it possible to have a triangle with 150 20 20 degrees angle and why ?

OLga [1]

No, it is not possible. The total measure of all angles in a triangle must be 180. If you add these three together, you get 190.

4 0

3 years ago

Solve for the indicated variable.<br><br> y = mx + b for x<br><br> x=

kogti [31]

Answer:

y-b/m = x

Step-by-step explanation:

y = mx + b

~Subtract b to both sides

y - b = mx

~Divide m to both sides

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Best of Luck!

3 0

4 years ago

How can you represent all of the solutions to systems of inequalities?

Dimas [21]

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Step-by-step explanation:

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6 0

3 years ago