An isosceles triangle has

Mathematics

1 answer:

Nadya [2.5K]3 years ago

5 0

Answer:

Step-by-step explanation:

The area of an isoceles triangle is:

A = base x height / 2

The base is the unequal side in the isosceles triangle. You have to calculate the height using the Pythagorean Theorem.

Since two side are equal in length, if you draw a vertical lined from where these two sides meet and bisect the base, you will create two right triangles.

So a² + b² = c² where c is the hypotenuse of the right triangle. This hypotenuse is also the two equal sides of the isosceles triangle. They told you the length of the base but you need to divide that in half since your line bisected the base.

So now you know one side of the right triangle is 8cm which is half of 16cm. You also know the hypotenuse is 17cm. Solve the Pythagorean Theorem for the other side and that will give you the height of your bisecting line.

8² + b² = 17² OR 64 + b² = 289

Solve for b

b² = 289 - 64 OR b² = 225 and finally b = $\sqrt{ 225$ which is 15

So now you can calculate the area of the triangle:

A = 16 x 15 / 2 or 240 / 2 which is 120

So the area is 120 cm²

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Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2500 grams and a standard deviation of 500

kolezko [41]

Answer:

The 35-week gestation period baby has a z-score of 0.7.

The 41-week gestation period baby has a z-score of 0.89

Since the 41-week gestation period baby has a higher z-score, he weighs more relatively to his gestation period.

Step-by-step explanation:

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.

Which baby weighs more relative to the gestation period?

The baby with the higher z-score.

35-week gestation period baby weighs 2850 grams

Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2500 grams and a standard deviation of 500 grams

This means that Z is found when $X = 2850, \mu = 2500, \sigma = 500$