Answer:
heights are:
66, 74, 76, 77, 78, 79, 80, 80, 82, 84
The mean is: 77.6 inches
Step-by-step explanation:
removing 66 will make the mean increase to 78.9
The set has 66 as an outlier and removing it increases the mean by about 1.3 inches.
He currently has an test score sum of 206. He needs 280 to pass (the average score, 70, multiplied by four different test scores).
280-206=74.
He needs to get a score of 74 to pass.
Answer:
larger number is -5 and smaller one is -1
Step-by-step explanation:
x+y = -6
x = -6-y ....eqn i
x-y = -4...eqn ii
substituting eqn i in ii
x - y = -4
or, - 6 - y - y = -4
or, -6 - 2y = -4
or, - 2y = 2
so, y = -1
x + y = -6
x + (-1) = -6
so, x = -5
1. x/(x - 5) = 4/(x - 4)
x (x - 4) / ((x - 5) (x - 4)) = 4 (x - 5) / ((x - 5) (x - 4))
x (x - 4) = 4 (x - 5)
x² - 4x = 4x - 20
x² - 8x = -20
Solving for x by completing the square gives
x² - 8x + 16 = -4
(x - 4)² = -4
x - 4 = ± 2i
x = 4 + 2i or x = 4 - 2i
2. Since -7 + 2i and -7 - 2i are roots of the given quadratic, we have
z² + bz + c = (z - (-7 + 2i)) (z - (-7 - 2i))
z² + bz + c = (z + (7 - 2i)) (z + (7 + 2i))
z² + bz + c = z² + ((7 - 2i) + (7 + 2i)) z + (7 - 2i) (7 + 2i)
z² + bz + c = z² + 14z + 53
so that b = 14 and c = 53, which makes b + c = 67.
3. If x + y = 4, then
x³ + y³ = 100
x³ + (4 - x)³ = 100
x³ + (64 - 48x + 12x² - x³) = 100
12x² - 48x + 64 = 100
12x² - 48x = 36
x² - 4x = 3
and by completing the square,
x² - 4x + 4 = 7
(x - 2)² = 7
x - 2 = ± 7
x = 2 + 7 or x = 2 - 7
x = 9 or x = -5
If x = 9, then y = -5, so one pair of solutions would be (x, y) = (9, -5).
Answer:
The domain (-∞,∞) and the range (-∞,∞)
Step-by-step explanation:
