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3 years ago

What expression represents the value of x?

Mathematics

1 answer:

pogonyaev3 years ago

6 0

Answer:

Answer A

Step-by-step explanation:

The Pythagorean formula in the small triangle gives

x² = w² + y²

x = √( w² + y² )

By this answer alone, answer C √( w * y ) is defenately false, because w*y is not w² + y², and therefore this answer can be discarded.

Answer B is also defenately wrong because the area indicated by the square on side z is much bigger then the area indicated by the square on side x.

Supose answer D is right, then

w*z must be equal to w² + y².

But from the big triangle we know that

v² = y² + z² , so y² = v² - z²

Since w*z is not v² - z², answer D must be wrong also.

The only answer which we can choose from is answer A, which must be the right answer since it is the only possibility left...

EXTRA

We have already deduced that answer A must be the right one, so we have already finished this question.

How ever, if answer A is right, then x = √( w(w + z) )

x = √( w² + wz )

From Pythagoras we know the next line to be true:

x = √( w² + y² )

From this, w*w = w² , no problem there, but then w*z must be equal to y². This is a problem for me at least...

At this moment I am unable to prove that w*z = y² but this seems at least plausible...

I leave it for now.

You might be interested in

The Undergraduate grade point average (UGPA) of students taking the Law School Admissions Test in recent year can be approximate

Ronch [10]

Answer:

$a=3.36 +0.816*0.18=3.507$

The value of height that separates the bottom 90% of data from the top 10% is 3.507.

Step-by-step explanation:

1) Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

2) Solution to the problem

Let X the random variable that represent the grades of a population, and for this case we know the distribution for X is given by:

$X \sim N(3.36,0.18)$

Where $\mu=3.36$ and $\sigma=0.18$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.10$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.90 of the area on the left and 0.10 of the area on the right it's z=0.816. On this case P(Z<0.816)=0.90 and P(Z>0.816)=0.1

If we use condition (b) from previous we have this:

$P(X$