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Kipish [7]
3 years ago
11

To put up several tents for a camping trip, you need several pieces of rope each 6 2/3 feet long. If you have a rope that is 43

feet, how many pieces can you cut for the tents?
Mathematics
1 answer:
Otrada [13]3 years ago
3 0
\bf 43\div 6\frac{2}{3}\implies \cfrac{46}{6\frac{2}{3}}\implies \cfrac{\frac{46}{1}}{\frac{6\cdot 3+2}{3}}\implies \cfrac{\frac{46}{1}}{\frac{20}{3}} \implies \cfrac{46}{1}\cdot \cfrac{3}{20}\implies \cfrac{69}{10}
\\\\\\
\boxed{6\frac{9}{10}}\qquad \qquad 
\cfrac{6\cdot 10+9}{10}\implies \cfrac{69}{10}
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Answer:

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Given

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g(x) = 3x - 2

Solving (a): Compare the slopes

The slope (m) of f(x) is calculated as;

m = \frac{f(x_2) - f(x_1)}{x_2 - x_1}

This gives:

m = \frac{f(0) - f(1)}{0 - 1}

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m = \frac{-1 - 7}{- 1}

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The slope of g(x) can be gotten using the following comparison

g(x) = mx + b

m \to slope

So:

g(x) = 3x -2

m = 3

m_{f(x)} > m_{g(x)}

Solving (b): Compare the y intercept

y intercept is when x = 0

From the table of f(x)

f(0) = -1

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g(x) = 3x -2

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Step-by-step explanation:

To solve this question, we need 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 normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

\mu = 1467, \sigma = 93, n = 49, s = \frac{93}{\sqrt{49}} = 13.2857

What is the probability that the mean weight of the sample of horses would differ from the population mean by less than 9lbs if 49 horses are sampled at random from the stable?

This is the pvalue of Z when X = 1467 + 9 = 1476 subtracted by the pvalue of Z when X = 1467 - 9 = 1458.

X = 1476

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By the Central Limit Theorem

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

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0.7517 - 0.2483 = 0.5034

0.5034 = 50.34% probability that the mean weight of the sample of horses would differ from the population mean by less than 9lbs if 49 horses are sampled at random from the stable

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