Answer: according to spark notes: There can be 0, 1, or 2 solutions to a quadratic equation, depending on whether the expression inside the square root sign, (b2 - 4ac), is positive, negative, or zero. This expression has a special name: the discriminant.
In this case it is 0, not 2, which was my first and wrong answer
Answer:
Yes, we can conclude that the population standard deviation of TV watching times for teenagers is less than 2.66
Step-by-step explanation:
H0 : σ² = 2.66²
H1 : σ² < 2.66²
X²c = (n - 1)*s² ÷ σ²
sample size, n = 40
Sample standard deviation, s = 1.9
X²c = ((40 - 1) * 1.9²) ÷ 2.66²
X²c = 140.79 ÷ 7.0756
X²c = 19.897
Using a confidence level of 95%
Degree of freedom, df = n - 1 ; df = 40 - 1 = 39
The critical value using the chi distribution table is 25.6954
Comparing the test statistic with the critical value :
19.897 < 25.6954
Test statistic < Critical value ; Reject the Null
Hence, we can conclude that the population standard deviation of TV watching times for teenagers is less than 2.66
Answer:
31.5 litres
Step-by-step explanation:
If Mel uses all 30 litres of yellow paint, then:
5 / 2 = 30 / x
5x = 60
x = 12
Mel would need 12 litres of blue paint, but she only has 9 litres. So the amount of yellow paint she needs is:
5 / 2 = x / 9
2x = 45
x = 22.5
Mel will use 22.5 litres of yellow paint with 9 litres of blue paint to make a total of 31.5 litres of green paint.
26×4=104
292-104=188
26÷2=13
188-13=175cm
the tree was 175cm when he moved in
Answer:
vertex = (- 2, 6)
Step-by-step explanation:
Given f(x) then f(x + a) represents a horizontal translation of f(x)
• If a > 0 then a shift to the left of a units
• If a < 0 then a shift to the right of a units
Here a = 5 , thus a horizontal translation left by 5 units.
Thus
vertex of g(x) = (3 - 5, 6 ) = (- 2, 6 )
