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bogdanovich [222]
2 years ago
6

I have 3 1/2 bottles of maple syrup. I filled nine one quart bottles with syrup. How much syrup do I have left?

Mathematics
1 answer:
svetlana [45]2 years ago
3 0

Answer:

\frac{25}{4} bottle of syrup is left

Step-by-step explanation:

Total amount of syrup = \frac{31}{2}

Bottles filled with syrup = 9\frac{1}{4}

Syrup left

= \frac{31}{2} - 9\frac{1}{4}\\= \frac{31}{2} - \frac{37}{4}\\= \frac{62-37}{4}\\= \frac{25}{4}

\frac{25}{4} bottle of syrup is left

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2. Given f(x) = 4x -2 and g(x) = x2 + 1, evaluate:
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The distribution of SAT II Math scores is approximately normal with mean 660 and standard deviation 90. The probability that 100
gayaneshka [121]

Using the <em>normal distribution and the central limit theorem</em>, it is found that there is a 0.1335 = 13.35% probability that 100 randomly selected students will have a mean SAT II Math score greater than 670.

<h3>Normal Probability Distribution</h3>

In a normal distribution with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

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

  • It 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, which is the percentile of X.
  • By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation s = \frac{\sigma}{\sqrt{n}}.

In this problem:

  • The mean is of 660, hence \mu = 660.
  • The standard deviation is of 90, hence \sigma = 90.
  • A sample of 100 is taken, hence n = 100, s = \frac{90}{\sqrt{100}} = 9.

The probability that 100 randomly selected students will have a mean SAT II Math score greater than 670 is <u>1 subtracted by the p-value of Z when X = 670</u>, hence:

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

By the Central Limit Theorem

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

Z = \frac{670 - 660}{9}

Z = 1.11

Z = 1.11 has a p-value of 0.8665.

1 - 0.8665 = 0.1335.

0.1335 = 13.35% probability that 100 randomly selected students will have a mean SAT II Math score greater than 670.

To learn more about the <em>normal distribution and the central limit theorem</em>, you can take a look at brainly.com/question/24663213

7 0
2 years ago
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