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EastWind [94]
3 years ago
10

9/11 - 1/2 in it's simplest form​

Mathematics
1 answer:
Murrr4er [49]3 years ago
5 0

Answer:

7/22

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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Step-by-step explanation:

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Subtraction of normal variables:

When we subtract normal variables, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.

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This means that \mu_{C} = 24, \sigma_{C} = 0.14

The width of a door is normally distributed with a mean of 23.87 in and a standard deviation of 0.08 in.

This means that \mu_{D} = 23.87, \sigma_{D} = 0.08.

Find the probability that the width of the casing exceeds the width of the door by more than 0.25 in?

This is P(C - D > 0.25).

Distribution C - D:

The mean is:

\mu = \mu_{C} - \mu_{D} = 24 - 23.87 = 0.13

The standard deviation is:

\sigma = \sqrt{\sigma_{C}^2+\sigma_{D}^2} = \sqrt{0.14^2+0.08^2} = 0.1612

Probability:

This probability is 1 subtracted by the pvalue of Z when X = 0.25. So

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

Z = \frac{0.25 - 0.13}{0.1612}

Z = 0.74

Z = 0.74 has a pvalue of 0.7704

1 - 0.7704 = 0.2296

0.2296 = 22.96% probability that the width of the casing exceeds the width of the door by more than 0.25 in.

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3 years ago
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