2.5 rounds up to 3. Because the digit after the decimal point is 5 or more.
The easiest way to find the vertex is to convert this standard form equation into vertex form, which is y = a(x - h)^2 + k.
Firstly, put x^2 - 10x into parentheses: y = (x^2 - 10x) + 30
Next, we want to make what's inside the parentheses a perfect square. To do that, we need to divide the x coefficient by 2 and square it. In this case, the result is 25. Add 25 inside the parentheses and subtract 25 outside of the parentheses: y = (x^2 - 10x + 25) + 30 - 25
Next, factor what's inside the parentheses and combine like terms outside of the parentheses, and your vertex form is: y = (x - 5)^2 + 5.
Now going back to the formula of the vertex form, y = a(x - h)^2 + k, the vertex is (h,k). Using our vertex equation, we can see that the vertex is (5,5).
Step-by-step answer:
standard deviation (sigma) = 12 inches
mean (mu) = 90 inches.
For 36 years, the standard error of the mean is
e = sigma / sqrt(n) = 12" / sqrt(36) = 2".
Deviation from the mean
= 92.8 -90 = 2.8
Since the standard error of the mean follows the normal distribution, we have
Z=(92.8-90)/2 = 1.4
Looking up the normal distribution tables, or check R, we find
P(Z>1.4) = 1-P(Z<1.4) = 1-0.9192433 = 0.08075666
Answer: P(snowfall>92.8) = 0.0808 (to four decimal places)
Answer:
You would work 5 hours a day
