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2 years ago

Classify the decimal forms of 3/12 and 2/9 as repeating or terminating.

Mathematics

2 answers:

Amiraneli [1.4K]2 years ago

8 0

Answer:

3/12= terminating

2/9= repeating

Step-by-step explanation:

Simplify the fractions

3/12= 1/4

You have to then change it to a decimal,

= 0.25. This number can end (its finite) Therefore if will be terminating.

Which means the number ends.

You cant simplify 2/9 so you go ahead and change it to a decimal.

2/9= 0.2222222........

This decimal does not end so its repeating or recurring.

romanna [79]2 years ago

4 0

3/12 = 0.25 This is a terminating decimal, as the decimal has a finite number of digits.

2/9 = 0.222222... This is a repeating decimal, as there is no end to the number of digits.

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3 years ago

According to a Yale program on climate change communication survey, 71% of Americans think global warming is happening.† (a) For

SpyIntel [72]

Answer:

a) 0.2741 = 27.41% probability that at least 13 believe global warming is occurring

b) 0.7611 = 76.11% probability that at least 110 believe global warming is occurring

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be 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.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$p = 0.71$

(a) For a sample of 16 Americans, what is the probability that at least 13 believe global warming is occurring?

Here $n = 16$ , we want $P(X \geq 13)$ . So

$P(X \geq 13) = P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 13) = C_{16,13}.(0.71)^{13}.(0.29)^{3} = 0.1591$

$P(X = 14) = C_{16,14}.(0.71)^{14}.(0.29)^{2} = 0.0835$

$P(X = 15) = C_{16,15}.(0.71)^{15}.(0.29)^{1} = 0.0273$

$P(X = 16) = C_{16,16}.(0.71)^{16}.(0.29)^{0} = 0.0042$

$P(X \geq 13) = P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16) = 0.1591 + 0.0835 + 0.0273 + 0.0042 = 0.2741$

0.2741 = 27.41% probability that at least 13 believe global warming is occurring

(b) For a sample of 160 Americans, what is the probability that at least 110 believe global warming is occurring?

Now $n = 160$ . So

$\mu = E(X) = np = 160*0.71 = 113.6$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{160*0.71*0.29} = 5.74$

Using continuity correction, this is $P(X \geq 110 - 0.5) = P(X \geq 109.5)$ , which is 1 subtracted by the pvalue of Z when X = 109.5. So

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

$Z = \frac{109.5 - 113.6}{5.74}$

$Z = -0.71$

$Z = -0.71$ has a pvalue of 0.2389

1 - 0.2389 = 0.7611

0.7611 = 76.11% probability that at least 110 believe global warming is occurring

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2 years ago

The linear function graphed below represents the value of a comic book since Lucy purchased it. What was the value of the comic

zhuklara [117]

Answer:

C. $25

Step-by-step explanation:

We will find,

The slope of the function using $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ .

Taking the points (1,40) and (2,55).

Slope = $\frac{55-40}{2-1}$

i.e. Slope = $\frac{15}{1}$

i.e. Slope = 15

Substituting the slope and point (1,40) in the equation $y=mx+b$ ,

We have, $40=15\times 1+b$

i.e. $b=40-15$

i.e. b= 25

Thus, the equation of the linear function is $y=15x+25$ .

<em>This linear function represents the cost of the comic book since Lucy purchased it, where x= years.</em>

So, the initial value of the comic book is when x= 0.

So, $y=15\times 0+25$ i.e. y= 25

Hence, the cost of the book when Lucy purchased it was $25.

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