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Citrus2011 [14]
3 years ago
9

Solve x2 - 4x = 12 by completing the square, show work please!!

Mathematics
1 answer:
Rudik [331]3 years ago
8 0
x^2-4x=12\\\\x^2-2x\cdot2=12\ \ \ |add\ 2^2\ to\ both\ sides\\\\x^2-2x\cdot2+2^2=12+2^2\ \ \ \ \ |use\ a^2-2ab+b^2=(a-b)^2\\\\(x-2)^2=12+4\\\\(x-2)^2=16\iff x-2=\pm\sqrt{16}\\\\x-2=-4\ or\ x-2=4\ \ \ |add\ 2\ to\ both\ sides\\\\\boxed{x=-2\ or\ x=6}
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Assume that blood pressure readings are normally distributed with a mean of 115 and a standard deviation of 8. If 100 people are
Sergeu [11.5K]

Answer:

D. 0.9938.

Step-by-step explanation:

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

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes 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.

Mean of 115 and a standard deviation of 8.

This means that \mu = 115, \sigma = 8

100 people are randomly selected

This means that n = 100, s = \frac{8}{\sqrt{100}} = 0.8

Find the probability that their mean blood pressure will be less than 117.

This is the p-value of Z when X = 117, so:

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

By the Central Limit Theorem

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

Z = \frac{117 - 115}{0.8}

Z = 2.5

Z = 2.5 has a p-value of 0.9938, and thus, the correct answer is given by option D.

8 0
3 years ago
Add or subtract. (3/x-2)+(4/x+5)
Alex787 [66]
The answer is 7x+7/x^2+3x-10
3 0
3 years ago
How can I solve (b)?
dsp73
90/3 parts of silver = 30 times multiplied by
tin = 12 × 30 = 360g
lead = 8 × 30 = 240g

12.5 / 23 = 0.5434 parts per metal

tin = 12 × 0.5434 = 6.5kg
lead = 8 × 0.5434 = 4.5kg
silver = 3 × 0.5434 = 1.5kg
5 0
3 years ago
12w-24=12 solve for 12​
USPshnik [31]

Answer:

3

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Please help in for tomorrow
Sauron [17]
The answer is 271.04 because you have to do 242 times .12 then add your answer to 242.
4 0
3 years ago
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