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docker41 [41]
3 years ago
14

Suppose the total benefit of watching 1 baseball game is 100, the total benefit of watching 2 games is 120, and the total benefi

t of watching 3 games is 125. In this case, the marginal benefit of watching the 3rd game is:A 5B 125C 41.67D 375
Mathematics
1 answer:
77julia77 [94]3 years ago
4 0

Answer:

A. 5

Step-by-step explanation:

The marginal benefit of an article, B_m is calculated as:

B_m=\frac{DB_t}{DQ}

Where DB_t is the change in the total benefit of the article, and DQ is the change in the units of the article.

If we want to know the marginal benefit of watching the 3rd game, we need to use the information of total benefit of watching 2 games and 3 games.

In this case, the total benefit of watching 2 games is 120 and the total benefit of watching 3 games is 125, so DB_t and DQ are equal to:

DB_t=125-120=5

DQ = 3 - 2 = 1

Then, the marginal benefit of watching the third game is:

B_m=\frac{5}{1}=5

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A popular soft drink is sold in 2-liter (2000 milliliter) bottles. Because of variation in the filling process, bottles have a m
andrezito [222]

Answer:

a) 0.27% probability that the mean is less than 1995 milliliters.

b) 2002.3 milliliters or more will occur only 10% of the time for the sample of 100 bottles.

Step-by-step explanation:

To solve this problem, it is important 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 random variable X, with mean \mu and standard deviation \sigma, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 2000, \sigma = 18

A) If the manufacturer samples 100 bottles, what is the probability that the mean is less than 1995 milliliters?

So n = 100, s = \frac{18}{\sqrt{100}} = 1.8

This probability is the pvalue of Z when X = 1995. So

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

By the Central Limit Theorem

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

Z = \frac{1995 - 2000}{1.8}

Z = -2.78

Z = -2.78 has a pvalue of 0.0027

So 0.27% probability that the mean is less than 1995 milliliters.

B) What mean overfill or more will occur only 10% of the time for the sample of 100 bottles?

This is the value of X when Z has a pvalue of 1-0.1 = 0.9.

So it is X when Z = 1.28

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

1.28 = \frac{X - 2000}{1.8}

X - 2000 = 1.8*1.28

X = 2002.3

2002.3 milliliters or more will occur only 10% of the time for the sample of 100 bottles.

3 0
2 years ago
(15.34) The level of nitrogen oxides (NOX) in the exhaust of cars of a particular model varies Normally with mean 0.21 g/mi and
MrMuchimi

Answer:

a level of significance of 0.01 = 1%

Step-by-step explanation:

given

Z = 0.0001

mean μ=0.21 g/mi

variate x= 0.21 + 0.03

standard deviation σ= 0.05 g/mi.

N = sample population  20 cars

z = (x −μ )/[σ /√N  ]

Z =\frac{x −μ}{\frac{σ}{√N} }

Z = 0.03/ (0.05/√20) = 0.03/0.0111

Z = 2.63 +- 0.0001

Z=  2.6301  or 2.6299

checking the level of significance table from a statistical book gives

a level of significance of 0.01 = 1%

therefore the null hypothesis is accepted.

7 0
3 years ago
What is the growth (or slope) of the simplified equation??
DIA [1.3K]

Answer:i think its y+3x+8x-7

Step-by-step explanation:i dont have to explain

4 0
2 years ago
Find the value of x.
nikklg [1K]

Answer:

x = 13

Step-by-step explanation:

Sum or interior angles of a triangle is 180,

6x + 19 + 5x - 15 + 3x - 6 = 180

6x + 5x + 3x + 19 - 15 - 6 = 180

14x + 19 - 21 = 180

14x - 2 = 180

14x = 180 + 2

14x = 182

x = 182 / 14

x = 13

5 0
2 years ago
ILL GIVE BRAINLIST ON WHOEVER GETS RIGHT!!!!
tiny-mole [99]

Answer:

The first and third answer I believe.

Step-by-step explanation:

The side with 3 can go over 1.5, since they are both at the same side. It will be equivalent to 4 over 2 because they are also the same side. (1st option)

Multiplying each side by 1/2, does result you to the final image.

3 multiplied by 1/2 is 1.5

4 multiplied by 2 is 2

7 0
2 years ago
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