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jarptica [38.1K]
3 years ago
11

(b) What is 0.36 (six repeating) expressed as a fraction in simplest form?

Mathematics
1 answer:
zubka84 [21]3 years ago
3 0
 0.3666.....

If a number is repeating singly, just know it has to do with dividing by 9.

Let the number be x = 0.36....  (i)

Multiply both sides by 10.

10x = 3.66...         (ii)

Equation (ii) - (i)

10x - x = 3.66 - 0.36

9x = 3.3

x = 3.3/9

x = (33/10)*(1/9)

x = 33/90

x = 11/30

The simplest fraction is 11/30

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3x^2 (x^2 - 4x - 2) + (5x^3 + 7x^2+2x+11) plz show work
matrenka [14]

Let's simplify step-by-step.

3x2(x2−4x−4)+5x3+7x2+2x+11

Distribute:

=(3x2)(x2)+(3x2)(−4x)+(3x2)(−4)+5x3+7x2+2x+11

=3x4+−12x3+−12x2+5x3+7x2+2x+11

Combine Like Terms:

=3x4+−12x3+−12x2+5x3+7x2+2x+11

=(3x4)+(−12x3+5x3)+(−12x2+7x2)+(2x)+(11)

=3x4+−7x3+−5x2+2x+11

Answer:

=3x4−7x3−5x2+2x+11

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5 0
3 years ago
Which of the following numbers could be the sides of a right triangle. A)8,15,17. B)6,8,12 C)9,11,21 D)4,13,16
ArbitrLikvidat [17]

Answer:

A) 8, 15, 17.

Step-by-step explanation:

Right triangle obey the Pythagorean theorem. Thus, we choose the two smaller numbers (being the cathetus) and if after applying the P. Theorem we get the biggest of each option  (the hypotenuse) that means that those numbers could be the sides of a right triangle.

The Pythagorean theorem states that: a^2+b^2=c^2

Thus:

\sqrt{a^2+b^2}=c

Option A:

\sqrt{8^2+15^2}=17 → 17 = 17 OK!

Option B:

\sqrt{6^2+8^2}  = 10 → 10 ≠ 12 NO

Option C:

\sqrt{9^2+11^2} = [tex]\sqrt{202}[/tex] → \sqrt{202} ≠ 21 NO

Option D:

\sqrt{4^2+13^2} = \sqrt{185} → \sqrt{185} ≠ 16 NO

3 0
3 years ago
Which of the following statements best describe tge positive solution of the equation x2=2
777dan777 [17]
X is obviously 1
1x2=2
Entao...(So...)
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4 0
2 years ago
The mean points obtained in an aptitude examination is 159 points with a standard deviation of 13 points. What is the probabilit
Korolek [52]

Answer:

0.4514 = 45.14% probability that the mean of the sample would differ from the population mean by less than 1 point if 60 exams are sampled

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 159, \sigma = 13, n = 60, s = \frac{13}{\sqrt{60}} = 1.68

What is the probability that the mean of the sample would differ from the population mean by less than 1 point if 60 exams are sampled?

This is the pvalue of Z when X = 159+1 = 160 subtracted by the pvalue of Z when X = 159-1 = 158. So

X = 160

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{160 - 159}{1.68}

Z = 0.6

Z = 0.6 has a pvalue of 0.7257

X = 150

Z = \frac{X - \mu}{s}

Z = \frac{158 - 159}{1.68}

Z = -0.6

Z = -0.6 has a pvalue of 0.2743

0.7257 - 0.2743 = 0.4514

0.4514 = 45.14% probability that the mean of the sample would differ from the population mean by less than 1 point if 60 exams are sampled

7 0
3 years ago
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Answer:

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The coordinates of N' are (1/5, 1)

B.) The scale factor of the dialation is 3

7 0
3 years ago
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