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kykrilka [37]
3 years ago
14

Eight is less than 4 times another number can be shown by the inequality 8 < 4n. Choose the answer that make this inequality

a true statement.
Mathematics
1 answer:
gladu [14]3 years ago
7 0

Answer:

n < 2

Step-by-step explanation:

Let

The unknown number = n

8 < 4n

n < 8 / 4

n < 2

therefore, n must be less than 2

If n = 2

Then, 8 Will be equal to 4 times the number

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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
Sammy's Sandwich Shop has a mean delivery time of 25 minutes with a standard deviation of 2 minutes. Determine the z-score for t
fiasKO [112]

Answer:

 -1

Step-by-step explanation:

Given: Mean= 25 minutes.

           Standard deviation= 2 minutes

           x= 23 minutes.

Lets find the z-score for the number of sandwiches delivered in less than 23 mins.

Formula: Z-score= \frac{x-mean}{standard\ deviation}

Z-score= \frac{23-25}{2}

⇒ Z-score= \frac{-2}{2}

∴ Z-score will be -1

Hence, -1 is the z-score for the number of sandwiches delivered in less than 23 minutes.

6 0
3 years ago
Which of the following options represents the graph of the function shown below?
grigory [225]
I think the answer is B but not sure about "11" in A
4 0
3 years ago
Read 2 more answers
Mike has a collection of 16 antique tin toys, including 2 airplanes. If Mike randomly selects a toy, what is the probability it
myrzilka [38]

Answer:

C. 1/8

Step-by-step explanation:

This is because the number two goes into sixteen eight times. This is the simplest form of the fraction.

6 0
3 years ago
Write the equation of the line that contains the points (4, −7) and (1, 5). The slope of the line that contains the points (4, −
deff fn [24]
Slope = (5+7)/(1-4) = 12/-3 = -4

slope = -4

y = mx + b
-7 = -4(4) + b
-7 = -16 + b
b = 9

equation
y = -4x + 9
4 0
3 years ago
Read 2 more answers
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