Answer:
x = 2√13.
Step-by-step explanation:
Using the Pythagoras theorem:
14^2 = x^2 + 12^2
x^2 = 14^2 - 12^2
x^2 = (14 + 12)(14 - 12) = 52
x = √52
x = √4*√13
x = 2√13.
Answer:
a= -2 and b=3
Step-by-step explanation:
Step 1) Solve the first equation for a:
a + 3b = 7
a + 3b - 3b = 7 - 3b
a + 0 = 7 - 3b
a = 7 - 3b
Step 2) Substitute(7 - 3b) for a in a second equation and solve for b:
2a = b - 7 becomes:
2(7 - 3b) = b-7
(2 multi.7) - (2 multi.3b)= b-7
14 - 6b = b - 7
14 + 7 - 6b + 6b = b + 6b = b + 6b - 7 +7
21 - 0 = 1b + 6b - 0
21=(1 + 6)b
21 = 7b
21
/7 = 7b/7
3 = 7b/7
3 = b
b = 3
Step 3) Substitute 3 for b in the solution to the first equation at the end of Step 1 and calculate a
:
a = 7 - 3b becomes:
a = 7 − (
3 ⋅ 3)
a = 7 −
9
a = −
2
Answer:
x = 54
Step-by-step explanation:
2x+2 = 3x-52
2x+54 = 3x
54 = x
A) For both sets A and B, calculating the mean, range, and quartiles are a good way of measuring the center and spread. Using standard deviation may not be the best because we do not know whether the distributions are normal or not.
b) For set A, the lowest value is 63, while the highest is 86. An estimate for the mean, based on the average of these, is 74.5. Most of the 70+ values are below 74.5, so we may guess that the mean will be above the median.
For set B, the lowest is 63, while the maximum is 95. The estimated mean would be 79. But since there are more values on the 80+ and 90+ side, the median is likely to be higher than 79.
c) For set A, the mean is 74.79, while the median is 73, therefore the mean is above the median, and the prediction in part b is correct.
2. always
Percents tell us how many parts a certain thing has out of a total of 100 parts; thus, the denominator is always 100.
