The vertex of the function is (-6,-36).
<u>Step-by-step explanation:</u>
f(x) = x²+ 12x
From the above function, we can find the x- coordinate of the vertex as,
x = -b/2a
Here a = 1, b = 12
Plugin the values as,
x = -12 /(2×1) = -6
Now plug in the x value in the above function, we will get y as,
f(x) = y = x² + 12x = (-6)² + 12(-6)
= 36-72 = -36
So the vertex is (-6, -36).
Answer: 3.5308
Step-by-step explanation:
Claim : The firm's professionals volunteer an average of more than 15 hours per month.
i.e. 
Null hypothesis : 
Alternative hypothesis : 
Sample size : 
The sample mean : 
Sample standard deviation : 
The test-statistics for the population mean is given by :-

i.e. 
Hence, the correct value of the test statistic for the appropriate hypothesis test is 3.5308.
Step-by-step explanation:

Answer:
54
Step-by-step explanation:
First, subtract the kids in the cars. These kids aren't on buses.
228 - 12 = 216 kids on buses
Next, divide the 216 kids into 4 buses.
216 / 4 = 54
There were 54 kids on each bus.
The first five terms of the recursively defined sequence are 6, 12, 48, 768, 196608
For given question,
We have been given the recursive formula of a sequence.

Also, the first term of the sequence is,
a1 = 6
Substitute k = 1 in given recursive formula.
⇒ 
⇒ a2 = 1/3 (6)²
⇒ a2 = (1/3) × 36
⇒ a2 = 12
Substitute k = 2 in given recursive formula.
⇒ 
⇒ a3 = (1/3) × (12)²
⇒ a3 = (1/3) × 144
⇒ a3 = 48
Substitute k = 3 in given recursive formula.
⇒ 
⇒ a4 = (1/3) × (48)²
⇒ a4 = (1/3) × 2304
⇒ a4 = 768
Substitute k = 4 in given recursive formula.
⇒ 
⇒ a5 = (1/3) × (768)²
⇒ a5 = (1/3) × 589824
⇒ a5 = 196608
Therefore, the first five terms of the recursively defined sequence are 6, 12, 48, 768, 196608
Learn more about the recursive formula of sequence here:
brainly.com/question/14457800
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