Ok so domain is all allowed numbers
look at deonomenator and don't allow any numbers that will make it zero
none
that means
domain=all real numbers
vertex
in form
y=a(x-h)^2+k
(h,k)=vertex
we have
y=-2(x+3)^2-1
h=-3
k=-1
vertex=(-3,-1)
range
the vertex opens down so max is y=-1
y≤-1
domain is all real
vertex is (-3,-1)
y≤-1
C
(a) Average time to get to school
Average time (minutes) = Summation of the two means = mean time to walk to bus stop + mean time for the bust to get to school = 8+20 = 28 minutes
(b) Standard deviation of the whole trip to school
Standard deviation for the whole trip = Sqrt (Summation of variances)
Variance = Standard deviation ^2
Therefore,
Standard deviation for the whole trip = Sqrt (2^2+4^2) = Sqrt (20) = 4.47 minutes
(c) Probability that it will take more than 30 minutes to get to school
P(x>30) = 1-P(x=30)
Z(x=30) = (mean-30)/SD = (28-30)/4.47 ≈ -0.45
Now, P(x=30) = P(Z=-0.45) = 0.3264
Therefore,
P(X>30) = 1-P(X=30) = 1-0.3264 = 0.6736 = 67.36%
With actual average time to walk to the bus stop being 10 minutes;
(d) Average time to get to school
Actual average time to get to school = 10+20 = 30 minutes
(e) Standard deviation to get to school
Actual standard deviation = Previous standard deviation = 4.47 minutes. This is due to the fact that there are no changes with individual standard deviations.
(f) Probability that it will take more than 30 minutes to get to school
Z(x=30) = (mean - 30)/Sd = (30-30)/4.47 = 0/4.47 = 0
From Z table, P(x=30) = 0.5
And therefore, P(x>30) = 1- P(X=30) = 1- P(Z=0.0) = 1-0.5 = 0.5 = 50%
Answer:
(1 
, 2 )
Step-by-step explanation:
Given the 2 equations
7x - y = 7 → (1)
x + 2y = 6 → (2)
Multiplying (1) by 2 and adding to (2) will eliminate the y- term
14x - 2y = 14 → (3)
Add (2) and (3) term by term to eliminate y
15x = 20 ( divide both sides by 15 )
x = 
= 
= 1
Substitute this value of x into either of the 2 equations and solve for y
Substituting in (2)
+ 2y = 6
2y = 6 - = 
( divide both sides by 2 )
y = 
= 2
Answer:
5.5 minutes
Step-by-step explanation:
Fill in the given information and solve for t.
75 = -15cos(2πt/15) +65
-10/15 = cos(2πt/15)
t = 15/(2π)arccos(-2/3) ≈ 5.492
The volume reaches 75 dB about 5.5 minutes after the truck arrives.
