Answer:
$5.82
Step-by-step explanation:
Answer:
Given that is a 45-45 triangle, the hypotenuse should be <em>x</em>
, so in this case. The hypotenuse should be 3, and the other side lengths 3. I see no other way of it going other than that one; I hope I helped at least a bit!
Step-by-step explanation:
Answer:
D) 5/12
Step-by-step explanation:
Suppose there are 30 girls at the school. Then the proportions tell you that 12 of them study music, and 5 of them study both music and dance.
Then 5 of the 12 girls who study music also study dance. That fraction is 5/12.
_____
We chose 30 because it is the least common multiple of the denominators of the fractions (2/5, 3/5, 1/6) in the problem statement.
Of course, you know that 2/5·30 = 12, and 1/6·30 = 5.
A) The empirical rule tells you the probability of being within 1 standard deviation of the mean is 68%.
b) The probability that the sample mean falls within 3 standard deviations* of the mean is 99.7%.
___
* The standard deviation of the sample mean is 1/√9 = 1/3 of the standard deviation of an individual sample. Hence the same limits (90-110) now cover 3 standard deviations of the sample mean.
There is a formula which employs the use of determinants and which helps us calculate the area of a triangle if the vertices are given as 
. The formula is as shown below:
Area=
Now, in our case, we have: 
, and
Thus, the area in this case will become:
Area=
Therefore, Area=![\frac{1}{2}\times [[3(-1\times 1-(-5)\times 1]-3[3\times 1-(-2)\times 1]+1[3\times -5-2]]= \frac{1}{2}\times -20=-10](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%5Ctimes%20%5B%5B3%28-1%5Ctimes%201-%28-5%29%5Ctimes%201%5D-3%5B3%5Ctimes%201-%28-2%29%5Ctimes%201%5D%2B1%5B3%5Ctimes%20-5-2%5D%5D%3D%20%5Cfrac%7B1%7D%7B2%7D%5Ctimes%20-20%3D-10)
We know that area cannot be negative, so the area of the given triangle is <u>10 squared units</u>.
