Hypothesis:
The ratio of ladies giving multiple birth to total number of women for any race will be the same.
Test:
Ratio of white women giving multiple births = 94 / 3132 = 0.0300
Ratio of black women giving multiple births = 20 / 606 = 0.0330
Conclusion:
There is no racial difference in the likelihood of multiple births. Although we do see a difference in the ratios calculated above, the difference is small enough to be due to sample size difference of white and black women. The smaller number of total black women makes the ratio calculated from this sample have a higher probability to deviate from what is expected. This deviation will account for the difference in probability between both races.
We can see the effects of this small sample size by increasing or decreases the numerator by 1 for black women:
21 / 606 = 0.0347
19 / 606 = 0.0313
This change in the data of one woman produces a very large percentage change in our ratio for black women (5%). Thus despite inaccuracy due to small sample size, our hypothesis is correct.
Y = 3x^2 - 3x - 6 {the x^2 (x squared) makes it a quadratic formula, and I'm assuming this is what you meant...}
This is derived from:
y = ax^2 + bx + c
So, by using the 'sum and product' rule:
a × c = 3 × (-6) = -18
b = -3
Now, we find the 'sum' and the 'product' of these two numbers, where b is the 'sum' and a × c is the 'product':
The two numbers are: -6 and 3
Proof:
-6 × 3 = -18 {product}
-6 + 3 = -3 {sum}
Now, since a > 1, we divide a from the results
-6/a = -6/3 = -2
3/a = 3/3 = 1
We then implement these numbers into our equation:
(x - 2) × (x + 1) = 0 {derived from 3x^2 - 3x - 6 = 0}
To find x, we make x the subject of 0:
x - 2 = 0
OR
x + 1 = 0
Therefore:
x = 2
OR
x = -1
So the x-intercepts of the quadratic formula (or solutions to equation 3x^2 - 3x -6 = 0, to put it into your words) are 2 and -1.
We can check this by substituting the values for x:
Let's start with x = 2:
y = 3(2)^2 - 3(2) - 6
= 3(4) - 6 - 6
= 12 - 6 - 6
= 0 {so when x = 2, y = 0, which is correct}
For when x = -1:
y = 3(-1)^2 - 3(-1) - 6
= 3(1) + 3 - 6
= 3 + 3 - 6
= 0 {so when x = -1, y = 0, which is correct}
Every "normal" hour worked by Julio is paid
dollars. He works 29 "normal" hours per week.
Every extra hour worked by Julio is paid
dollars.
If he worked 34 hours last week, he worked the usual 29 hours, plus 5 extra hours. This means that he earned
dollars.
We know that this equals 479.55, so we have
![34.5r = 479.55 \iff r = \dfrac{479.55}{34.5} = 13.9](https://tex.z-dn.net/?f=%2034.5r%20%3D%20479.55%20%5Ciff%20r%20%3D%20%5Cdfrac%7B479.55%7D%7B34.5%7D%20%3D%2013.9%20)