In the parallelogram ABCD, M angle A =2x +50 and m angle C= 3x + 40. The measure of ZA is

Mathematics

1 answer:

ipn [44]2 years ago

5 0

Answer:

∠A = 70°

Step-by-step explanation:

I'm... guessing this is what you mean? It would've been helpful if you'd provided pictures.

Since all parallelograms consist of two pairs of vertically opposite angles, ∠A and ∠C are equivalent.

Which means that 2x + 50 = 3x + 40.

In which you solve the equation.

2x + 50 = 3x + 40

-2x -2x

50 = x + 40

-40 -40

x = 10

Now, to find ∠A, substitute x into the equation:

∠A = 2x + 50

x = 10

∠A = 20 + 50

∠A = 70

Hence, ∠A = 70°

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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 normally distributed samples are solved using 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 $s = \frac{\sigma}{\sqrt{n}}$ .