Find the missing side.

Mathematics

1 answer:

Hitman42 [59]2 years ago

3 0

Answer:

24.8

Step-by-step explanation:

sin75 = 24/x

x = 24/sin75 = 24.8466 = 24.8 (nearest tenth)

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Calculate the distance between the two given point T(6,-2),U(-2,-12)

slava [35]

Use the distance formula: $\sqrt{(x2 - x1)^2 + (y2 - y1)^2}$

(6, -2), (-2, -12)
$\sqrt{(-2 - 6)^2 + (-12 - -2)^2}$ ⇒ $\sqrt{(-8)^2 + (-10)^2}$
$\sqrt{64 + 100}$ ⇒ $\sqrt{164}$
$\sqrt{164}$ = 12.8

The distance between points T and U is 12.8 units.

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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

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