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Ksju
8 days ago
14

A maple tree loses 384 leaves during the first week of fall, and 3/2 as many each successive week. At the end of 7 weeks, all th

e leaves have fallen. How many leaves fell from the tree?
Mathematics
1 answer:
babunello [8.4K]8 days ago
4 0

Answer:

12,354 leaves

Step-by-step explanation:

Leaves lost from the maple tree = \sum_{n=0}^{6}  = 384(\frac{3}{2} )^{n}

After a period of 7 weeks

= 384 + 384(1.5) + 384(1.5)² + 384(1.5)³ + 384(1.5)⁴ + 384(1.5)⁵ + 384(1.5)⁶

= 12,354 leaves

A total of 12,354 leaves have fallen from the tree.

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The following data set is provided: (in thousands)

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\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}

where x_i denotes data points, \bar{x} represents the mean, and n indicates the number of samples.

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Initially, we formulate the null hypothesis and the alternative hypothesis.

H_{0}: \mu = 30000\text{ dollars}\\H_A: \mu < 30000\text{ dollars} A one-tailed t-test will be conducted for this analysis.

Formula:

t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }

<pinserting the="" values="" we="" derive="">

t_{stat} = \displaystyle\frac{29512.5 - 30000}{\frac{697.82}{\sqrt{8}} } = -1.975

<pnow>

t_{critical} \text{ at 0.05 level of significance, 7 degree of freedom } = -1.894

<pgiven the="" situation="">

t_{stat} < t_{critical}

<pwe do="" not="" accept="" the="" null="" hypothesis="" and="" reject="" it.="">

Thus, we conclude that the average wedding cost is indeed less than the advertised $30,000.

</pwe></pgiven></pnow></pinserting>
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