Answer:
72.7 is the weighted average score
Step-by-step explanation:
The weighted average score
= score of lab * % share of total grade + score of first major test * % share of total grade + score of second major test * % share of total grade + Score of the final exam * % share of total grade
Substituting the given values, we get -
0.23 * 74 + 0.25 * 69 + 0.25 * 62 + 0.27 * 85
= 72.7
Answer:
Step-by-step explanation:
The 90th percentile of a normally distributed curve occurs at 1.282 standard deviations. Similarly, the 10th percentile of a normally distributed curve occurs at -1.282 standard deviations.
To find the percentile for the television weights, use the formula:
, where is the average of the set, is some constant relevant to the percentile you're finding, and is one standard deviation.
As I mentioned previously, 90th percentile occurs at 1.282 standard deviations. The average of the set and one standard deviation is already given. Substitute , , and :
Therefore, the 90th percentile weight is 5.1282 pounds.
Repeat the process for calculating the 10th percentile weight:
The difference between these two weights is .
Answer:
Peyton: 6 years old
Matt: 24 years old
Justin: 9 years old
Step-by-step explanation:
P= Peyton M= Matt J= Justin
P=J-3
M=4P
J+P+M=39
4J-12=M 4J-12=39-J-P
5J-51=-P P=J-3
5J-51=-J+3 J=9
P=9-3 P=6
M=4(6) M=24
Answer:
Possible derivation:
d/dx(a x + a y(x) + x a + y(x) a)
Rewrite the expression: a x + a y(x) + x a + y(x) a = 2 a x + 2 a y(x):
= d/dx(2 a x + 2 a y(x))
Differentiate the sum term by term and factor out constants:
= 2 a (d/dx(x)) + 2 a (d/dx(y(x)))
The derivative of x is 1:
= 2 a (d/dx(y(x))) + 1 2 a
Using the chain rule, d/dx(y(x)) = (dy(u))/(du) (du)/(dx), where u = x and d/(du)(y(u)) = y'(u):
= 2 a + d/dx(x) y'(x) 2 a
The derivative of x is 1:
= 2 a + 1 2 a y'(x)
Simplify the expression:
= 2 a + 2 a y'(x)
Simplify the expression:
Answer: = 2 a
Step-by-step explanation: