Y > 3x

(3x + 20) (5x) find x

HACTEHA [7]

15x^2+100x

hope this helps

7 0

3 years ago

I don’t know how to use the triangle area to calculate the area of the inscribed polygons

Trava [24]

First of all, let's recall the area of a triangle, knowing its base (b) and height (h):

$A = \cfrac{bh}{2}$

The exercise is showing you that, if you inscribe a polynomial with more and more side, the area of the polynomial will approximate the area of the circle better and better (you can see youself that the polygon is "filling" the circle more and more as the number of sides increase).

Now, the second column tells you the area of each of the triangles the polygon is split into. So, we can see that the first polygon is split into 3 triangles, each of them having base 1.73 and height 0.5.

So, the area of each triangle is

$A = \cfrac{1.73 \cdot 0.5}{2} = 0.4325$

There are three of these triangles, so the area of the whole polygon is

$A = 0.4325 \cdot 3 = 1.2975$

In the second case, you have six triangles, each with base 1 and height 0.87. So, the whole area is

$A = 6 \cdot \cfrac{1\cdot 0.87}{2} = 0.87 \cdot 3 = 2.61$

Finally, in the last case you have 8 triangles, each with base 0.77 and height 0.92. So, the whole area is

$A = 8 \cdot \cfrac{0.77\cdot 0.92}{2} = 0.77\cdot 0.92 \cdot 4 = 2.8336$

3 0

3 years ago

suppose X and Y are independent random variables, both with normal distributions. If X has a mean of 45 with a standard deviatio

djyliett [7]

Answer:

0.9772 = 97.72% probability that a randomly generated value of X is greater than a randomly generated value of Y

Step-by-step explanation:

When the distribution is normal, we use 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 question:

$\mu_X = 45, \sigma_X = 4, \mu_Y = 35, \sigma_Y = 3$

What is the probability that a randomly generated value of X is greater than a randomly generated value of Y

This means that the subtraction of X by Y has to be positive.

When we subtract two normal variables, the mean is the subtraction of their means, and the standard deviation is the square root of the sum of their variances. So

$\mu = \mu_X - \mu_Y = 45 - 35 = 0$