- Vertex Form: y = a(x - h)^2 + k, with (h,k) as the vertex.
To convert it into vertex form, we are going to be completing the square. Firstly, subtract 56 on both sides: 
Next, factor out the GCF, or greatest common factor, of the right side. To find the GCF, list the factors of both terms and the greatest one they share is their GCF. In this case, the GCF is 2: 
Next, we want to make what's inside the parentheses a perfect square. To find the constant of the perfect square, divide the x term by 2 and square the quotient. In this case:
-16 ÷ 2 = -8, (-8)² = 64
So you're gonna have to add 64 to the inside of the parentheses. To cancel this out, you will need to add to the other side the product of 64 and 2 (since 64 is inside the parentheses), which is 128: 
Next, factor the polynomial inside the parentheses: 
Next, subtract 72 on both sides and your vertex form is 
Now looking at this vertex form, the vertex is (8,-72), which means that <u>the x-coordinate of the vertex is 8.</u>
The volume of the cone is 84.9 km³
<h3>How to find the volume of a cone?</h3>
Volume of a cone = 1 / 3 πr²h
where
Therefore,
radius = 3 km
height = √9.5² - 3²
height = √81.25
height = 9.01387818866
height = 9.014 km
Volume of a cone = 1 / 3 × 3.14 × 3² × 9.014
volume of the cone = 254.732197612 / 3
volume of the cone = 84.9107325372
volume of the cone = 84.9 km³
learn more on volume here: brainly.com/question/17075150
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Answer:
The leading coefficient is 1 and the linear term coefficient is an even number
Step-by-step explanation:
Leading coefficient must be one for the application of completing square method. If the completing square is not one than we must apply other methods like Ac method, quadratic formula to solve the equation. To solve the equation with completing square the numerical value must be on other side of the equation. In this method we multiply linear term’s coefficient with one-half and square it therefore, completing square is suitable method for the equation having leading coefficient is 1 and linear coefficient is even.
Answer:
Q1: 2nd row 2nd tile
Q2: 1st row 1st tile
Q3: 1st row 3rd tile
Q4: 2nd row 3rd tile
Step-by-step explanation:
When
Vertex is (-p, q)
Binomial distribution formula: P(x) = (n k) p^k * (1 - p)^n - k
a) Probability that four parts are defective = 0.01374
P(4 defective) = (25 4) (0.04)^4 * (0.96)^21
P(4 defective) = 0.01374
b) Probability that at least one part is defective = 0.6396
Find the probability that 0 parts are defective and subtract that probability from 1.
P(0 defective) = (25 0) (0.04)^0 * (0.96)^25
P(0 defective) = 0.3604
1 - 0.3604 = 0.6396
c) Probability that 25 parts are defective = approximately 0
P(25 defective) = (25 25) (0.04)^25 * (0.96)^0
P(25 defective) = approximately 0
d) Probability that at most 1 part is defective = 0.7358
Find the probability that 0 and 1 parts are defective and add them together.
P(0 defective) = 0.3604 (from above)
P(1 defective) = (25 1) (0.04)^1 * (0.96)^24
P(1 defective) = 0.3754
P(at most 1 defective) = 0.3604 + 0.3754 = 0.7358
e) Mean = 1 | Standard Deviation = 0.9798
mean = n * p
mean = 25 * 0.04 = 1
stdev = 
stdev = 
= 0.9798
Hope this helps!! :)
