Answer:
Answers are in bold type
Step-by-step explanation:
f(x) = 
The parabola opens up, so has a minimum at the vertex.
Let (h, k) be the vertex
h = -b/2a = - (-144)/2(1) = 57
k = 57^2 - 144(57) = 3249 - 6498 = -3249
Therefore, the vertex is (57, -3249)
The minimum value is -3249
The domain is the set of real numbers.
The range = {y | y ≥ -3249}
The function decreases when -∞ < x < 57 and increases when 57 > x > ∞
The x - intercepts: = 0
x(x - 114x) = 0
x = 0 or x = 114
x-intercepts are (0, 0) and (0, 114)
When x = 0, then we get the y-intercept. So, 0^2 - 114(0) = 0
y-intercept is (0, 0)
Answer:
a = 
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
a² + 9² = 12²
a² + 81 = 144 ( subtract 81 from both sides )
a² = 63 ( take square root of both sides )
a =
Answer:
1/5, 2/15
Step-by-step explanation:
All the probabilities are the Observed Frequencies/Total Rolls = Observed Frequencies/60
That means A is 12/60 = 1/5
That also means B is 8/60 = 2/15
Step-by-step explanation:
the answer is 25%
hope it helps!
Answer:
p value = 0.039
t = - 2.169
Step-by-step explanation:
Applying the null and alternate hypothesis
using excel worksheet to calculate for ( t and p )
t = -2.169
p = 0.039
from the results obtained
The conclusion is affected by the significance level because : 0.1 < p > 0.01
so when the significance level is = 0.1 the Null hypothesis is rejected and we can say the mean time interval will change while
if the significance level = 0.01 the Null hypothesis is accepted and we can not say the mean time interval has changed because the p -value is greater than 0.01
attached is the excel solution
