What is the height of the ramp shown? (Measurements are in feet)

Mathematics

1 answer:

SOVA2 [1]3 years ago

7 0

Answer:

8.9 ft. (Option C)

Step-by-step explanation:

Here, we are given a right angled triangle. We are asked to find the value of perpendicular (y).

We'll be using pythagoras property.

According to the pythagoras property, sum of the squares of base and perpendicular is equivalent to the square of hypotenuse.

Here,

Hypotenuse = 12 ft
Base = 8 ft
Perpendicular (y) = ?

→ H² = B² + P²

→ H² - B² = P²

→ (12 ft)² - (8 ft)² = y²

→ 144 ft² - 64 ft² = y²

→ 80 ft² = y²

→ √(80 ft²) = y

→ 8.94427191 ft = y

→ 8.9 ft = y

$\therefore$ Value of y is 8.9. (Option c)

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A 500-page book contains 250 sheets of paper. The thickness of the paper used to manufacture the book has mean 0.08 mm and stand

LenaWriter [7]

Answer:

10.20% probability that a randomly chosen book is more than 20.2 mm thick

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.

In this problem, we have that:

250 sheets, each sheet has mean 0.08 mm and standard deviation 0.01 mm.

So for the book.

$\mu = 250*0.08 = 20, \sigma = \sqrt{250}*0.01 = 0.158$