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timofeeve [1]
2 years ago
5

If x=1 -√2 find the value of ( x-1/x) ⁴​

Mathematics
1 answer:
soldier1979 [14.2K]2 years ago
6 0

Answer:

Step-by-step explanation:

<em>side note i love ur pfp</em>

ok so basically u want to plug in ur value of x into the expression right away and combine everything in the parentheses so it's one fraction which is -

((1 -√2-1)/(1 -√2))⁴ = (-√2/(1 -√2))⁴ and then u get 4/(1 -√2)⁴ as ur final answer

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At a sporting event, the price for 3 cheeseburgers and 2 cups of lemonade is $14 and the price for 2 cheeseburgers and 4 cups of
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C= the price of a cheeseburger and l = the price of a lemonade:

3c + 2l=14\\2c+4l=12

Divide the second equation by -2 to begin the process of solving by elimination:

3c + 2l=14\\-1/2\ (2c+4l=12)\\\\3c+2l=14\\-c-2l=-6\\\\2c=8\\c=4

Now that we have c, 4, we can plug it in to one of the equations to find l:

3c + 2l=14\\3(4)+2l=14\\12+2l=14\\2l=2\\l=1

So, each cheeseburger is $4 and each lemonade is $1.  The final answer is:

1 cheeseburger and 2 cups of lemonade would cost $6.
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3 years ago
The average amount of water in randomly selected 16-ounce bottles of water is 16.15 ounces with a standard deviation of 0.45 oun
vekshin1

Answer:

0.0179 = 1.79% probability that the mean of this sample is less than 15.99 ounces of water.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use 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 normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

\mu = 16.15, \sigma = 0.45, n = 35, s = \frac{0.45}{\sqrt{35}} = 0.0761

What is the probability that the mean of this sample is less than 15.99 ounces of water?

This is the pvalue of Z when X = 15.99. So

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

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

Z = \frac{15.99 - 16.15}{0.0761}

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Z = -2.1 has a pvalue of 0.0179

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