Given rectangle ABCD with vertices A(1, 4), B(3, 6), C(6, 3), and D(4, 1), what is the

Mathematics

1 answer:

Hitman42 [59]3 years ago

6 0

Answer:

10√2

Step-by-step explanation:

A(1, 4), B(3, 6), C(6, 3), D(4, 1)

The distance formula tells you the distance d between two points (x1, y1) and (x2, y2) is given by ...

d = √((x2-x1)² +(y2-y1)²

Then the side lengths are ...

AB = √(2² +2²) = √8 = 2√2

BC = √(3² +(-3)²) = √18 = 3√2

The perimeter is twice the sum of these sides, so is ...

P = 2(2√2 +3√2) = 10√2 . . . the perimeter of the rectangle

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The weight of laboratory grasshoppers follows a Normal distribution, with a mean of 90 grams and a standard deviation of 2 grams

JulsSmile [24]

Answer:

95.44% of the grasshoppers weigh between 86 grams and 94 grams.

Step-by-step explanation:

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.

Mean of 90 grams and a standard deviation of 2 grams.

This means that $\mu = 90, \sigma = 2$