First subtract the constant to the other side to simplify it for now
y-5=-x^2+6x
Then pull out a common factor so the coefficient is x^2
y-5=-1(x^2-6x)
Next you take 1/2 of the b value (-6) and square it to find your c value
[1/2(-6)]^2=9
After that plug 9 into your equation as your c value
y-5=-1(x^2-6x+9)
Adding the C-value (9) causes the equations to become unbalanced so you need to balance them back out by minus 9 to the other side
y-14=-1(x^2-6x+9)
Now you want to simplify the equation on the right side.
y-14=-1(x-3)^2
Finally you want to add the constant back to the right side.
y=-1(x-3)^2+14 <——— vertex form
maximum=(3,14)
Answer:
<u>Equation of a circle:</u>
- (x - h)² + (y - k)² = r², where (h, k) is the center and r- radius
<u>Substitute the given values to get the equation of this circle:</u>
- (x - (-5))² + (y - (-9))² = 7² ⇒
- (x + 5)² + (y + 9)² = 49
Answer:
the 90% confidence interval is ( 48.684 , 51.316 )
Step-by-step explanation:
Given that :
the sample size = 36
Sample Mean = 50
standard deviation = 4.80
The objective is to calculate a 90% confidence interval.
At 90% confidence interval ;
the level of significance = 1 - 0.9 = 0.1
The critical value for
= 1.645
The standard error S.E =
=
= 0.8
The Confidence interval level can be computed as:
For the lower limit :
=50 - 1.316
= 48.684
For the upper limit :
=50 + 1.316
= 51.316
Thus, the 90% confidence interval is ( 48.684 , 51.316 )
Step-by-step explanation:
Simplify the following expression then state the property used:
9^-2
Property:
Given,
9^-2
For any real numbers a and b a, b ≠ 0, and for any two positive integers, n and n
a^-m
=> 1/a^m [By doing reciprocal]
So,
9^-2
=> 1/9^2
=> 1/(3^2)^2
=> 1/(3^4)
=> 1/(3*3*3*3)
=> 1/81. Ans.
Hope this helps.
Answer:
0.5969 = 59.69% probability that it was a flight of airline A
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Left on time.
Event B: From airline A.
Probability of a flight leaving on time:
81% of 48%(airline A).
61% of 26%(airline B)
40% of 26%(airline C). So
Probability of leaving on time and being from airline A:
81% of 48%. So
What is the probability that it was a flight of airline A?
0.5969 = 59.69% probability that it was a flight of airline A