Find the values of x and y in the diagram.

Mathematics

1 answer:

brilliants [131]3 years ago

7 0

Answer:

x = 2, y = 6

Step-by-step explanation:

Δ WXY is equilateral ( 3 congruent angles ), then the sides are equal

WY = WX , that is

y - 1 = 5 ( add 1 to both sides )

y = 6

Δ WYZ is isosceles ( 2 congruent base angles ) then the legs are congruent

YZ = WY , that is

x + 3 = 5 ( subtract 3 from both sides )

x = 2

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Final numeric grades in a certain course are normally distributed with a mean of 72.3 and a standard deviation of 6.4. The profe

Dimas [21]

Answer:

The minumum numeric grade you have to earn to obtain an A is 81.29.

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:

$\mu = 72.3, \sigma = 6.4$

The professor curves the grades so that the top 8% of students will receive an A. What is the minumum numeric grade you have to earn to obtain an A?

The minimum numeric value is the value of X when Z has a pvalue of 1-0.08 = 0.92. So it is X when Z = 1.405.

$Z = \frac{X - \mu}{\sigma}$

$1.405 = \frac{X - 72.3}{6.4}$