What is the value of x?

Mathematics

1 answer:

Studentka2010 [4]3 years ago

6 0

The top smaller sub-triangle and the whole big triangle are similar. This means that the correspondant sides are in proportion. So, we have

$6\div 5 = 54\div 3x+12$

Which implies

$6(3x+12)=5\cdot 54 \iff 3x+12=\dfrac{5\cdot 54}{6}=45$

So, we have

$3x+12 = 45 \iff 3x = 33 \iff x=11$

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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 $s = \frac{\sigma}{\sqrt{n}}$ .