Answer: 30 feet

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Work Shown:

x = height of tree in feet

The larger triangle, and the smaller triangle that fits inside the larger, are similr triangles.

So we can form the proportion
x/5 = 48/8
Note how x/5 is the result of dividing the larger vertical side (x) over the smaller vertical side (5)
The same applies with 48/8. The larger triangle's horizontal side is 8+40 = 48. The corresponding horizontal side for the smaller triangle is 8

Cross multiply to solve for x
x/5 = 48/8
8*x = 5*48
8*x = 240
8*x/8 = 240/8
x = 30

The tree is 30 feet tall

6 0

3 years ago

Solve the system of equations<br> 14x+y=−4<br> y=3x2−11x−4

wel

Answer:

(x,y)= (-2,24)

Step-by-step explanation:

4 0

3 years ago

The width of a casing for a door is normally distributed with a mean of 24 in and a standard deviation of 0.14 in. The width of

Galina-37 [17]

Answer:

0.2296 = 22.96% probability that the width of the casing exceeds the width of the door by more than 0.25 in.

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.

Subtraction of normal variables:

When we subtract normal variables, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.

The width of a casing for a door is normally distributed with a mean of 24 in and a standard deviation of 0.14 in.

This means that $\mu_{C} = 24, \sigma_{C} = 0.14$