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Jet001 [13]
3 years ago
8

The environmental protection agency is attempting to revive 3 acres of contaminated soil by replacing the top 24 inches of the s

oil.trucks with a hauling capacity of 28 cubic yards of soil are hired to remove the contaminated soil. how many full truckloads of contaminated soil will be hauled away?​
Mathematics
1 answer:
ludmilkaskok [199]3 years ago
5 0

Answer:

346\ trucks

Step-by-step explanation:

1 acre equals to 4840 yard²

So

3\ acres *\frac{4840\ yard^2}{1\ acre}= 14520\ yard^2

Also

1\ in = 0.02778\ yard

So

24\ in *\frac{0.02778\ yard}{1\ in}= 0.667\ yard

So volume V of the contaminated area is:

V = 14520*0.667\ yard^3\\\\V=9680.48\ yard^3

If each truck has a capacity of 28 cubic yards then it is necessary

9680.48\ yard^3 * \frac{1\ truck}{28\ yard^3}=346\ trucks

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A substance with a half life is decaying exponentially. If there are initially 12grams of the substance and after 70 minutes the
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4 0
3 years ago
The number of major earthquakes in a year is approximately normally distributed with a mean of 20.8 and a standard deviation of
SCORPION-xisa [38]

Answer:

a) 51.60% probability that in a given year there will be less than 21 earthquakes.

b) 49.35% probability that in a given year there will be between 18 and 23 earthquakes.

Step-by-step explanation:

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.

In this problem, we have that:

\mu = 20.8, \sigma = 4.5

a) Find the probability that in a given year there will be less than 21 earthquakes.

This is the pvalue of Z when X = 21. So

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

Z = \frac{21 - 20.8}{4.5}

Z = 0.04

Z = 0.04 has a pvalue of 0.5160.

So there is a 51.60% probability that in a given year there will be less than 21 earthquakes.

b) Find the probability that in a given year there will be between 18 and 23 earthquakes.

This is the pvalue of Z when X = 23 subtracted by the pvalue of Z when X = 18. So:

X = 23

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

Z = \frac{23 - 20.8}{4.5}

Z = 0.71

Z = 0.71 has a pvalue of 0.7611

X = 18

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

Z = \frac{18 - 20.8}{4.5}

Z = -0.62

Z = -0.62 has a pvalue of 0.2676

So there is a 0.7611 - 0.2676 = 0.4935 = 49.35% probability that in a given year there will be between 18 and 23 earthquakes.

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