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Grace [21]
3 years ago
5

.) Suppose college students produce 650 pounds of solid waste each year, on average. Assume that the distribution of waste per c

ollege student is normal with a mean of 650 pounds and a standard deviation of 20 pounds. What is the probability that a randomly selected student produces either less than 620 or more than 700 pounds of solid waste
Mathematics
1 answer:
amid [387]3 years ago
4 0

Answer:

0.073 = 7.3% probability that a randomly selected student produces either less than 620 or more than 700 pounds of solid waste

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Mean of 650 pounds and a standard deviation of 20 pounds.

This means that \mu = 650, \sigma = 20

What is the probability that a randomly selected student produces either less than 620 or more than 700 pounds of solid waste?

Less than 620:

pvalue of Z when X = 620. So

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

Z = \frac{620 - 650}{20}

Z = -1.5

Z = -1.5 has a pvalue of 0.0668

More than 700:

1 subtracted by the pvalue of Z when X = 700. So

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

Z = \frac{700 - 650}{20}

Z = 2.5

Z = 2.5 has a pvalue of 0.9938

1 - 0.9938 = 0.0062

Total:

0.0668 + 0.0062 = 0.073

0.073 = 7.3% probability that a randomly selected student produces either less than 620 or more than 700 pounds of solid waste

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Murrr4er [49]

Answer:

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Step-by-step explanation:

Step 1: <u>Define/explain.</u>

To subtract fractions with different denominators, you must first find the least common denominator (LCM).

You can do this by listing the multiples of each denominator.

Step 2: <u>Solve.</u>

11: 11, 22, 33, 44, 55, 66, 77, 88, 99, 110

2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22

22 is the LCM.

Now, we change the fractions to where they both have denominators of 22.

**REMEMBER: WHICHEVER NUMBER YOU MULTIPLY THE DENOMINATOR BY, YOU MULTIPLY IT BY THE NUMERATOR AS WELL!!**

9/11*2/2=18/22

1/2*11/11=11/22

Now, subtract as normal.

18/22-11/22=7/22

7/22 (simplified).

Step 3: <u>Conclude.</u>

Therefore, 9/11 - 1/2 = 7/22.

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3 years ago
12x +10+3+8x ? What do I have to do ?
Annette [7]

Simplifying

12x + 10 + 3 + 8x = 0

Reorder the terms:

10 + 3 + 12x + 8x = 0

Combine like terms: 10 + 3 = 13

13 + 12x + 8x = 0

Combine like terms: 12x + 8x = 20x

13 + 20x = 0

Solving

13 + 20x = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-13' to each side of the equation.

13 + -13 + 20x = 0 + -13

Combine like terms: 13 + -13 = 0

0 + 20x = 0 + -13

20x = 0 + -13

Combine like terms: 0 + -13 = -13

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Divide each side by '20'.

x = -0.65

Simplifying

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3 years ago
Read 2 more answers
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olya-2409 [2.1K]

Answer:

x - 6

Step-by-step explanation:

A = L x W

A / L = W

x^2-11x+30 / x -5  = W (Simplify the numerator)

(x - 6) x ( x - 5) / x - 5  = W     (Cancel the similar ones which is (x - 5) )

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Hope that helps

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3 years ago
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Conner and Jana are multiplying (3⁵6⁸)(3⁹6¹⁰).
ad-work [718]
<h3>Conner work is correct. Jana work is wrong</h3>

<em><u>Solution:</u></em>

<em><u>Given that,</u></em>

<em><u>Conner and Jana are multiplying:</u></em>

(3^56^8)(3^96^{10})

Given Conner's work is:

(3^56^8)(3^96^{10}) = 3^{5+9}6^{8+10} = 3^{14}6^{18}

We have to check if this work is correct

Yes, Conner work is correct

From given,

(3^56^8)(3^96^{10})\\\\3^5 \times 6^8 \times 3^9 \times 6^{10}

Use the following law of exponent

a^m \times a^n = a^{m+n}

Therefore,

3^5 \times 6^8 \times 3^9 \times 6^{10} = 3^5 \times 3^9 \times 6^8 \times 6^{10} = 3^{5+9} \times 6^{8+10} = 3^{14} \times 6^{18}

<em><u>Given Jana's work is:</u></em>

(3^56^8)(3^96^{10}) = 3^{5.9}6^{8.10} = 3^{45}6^{80}

This is incorrect

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