The function is
f(x) = (1/3)x² + 10x + 8
Write the function in standard form for a parabola.
f(x) = (1/3)[x² + 30x] + 8
= (1/3)[ (x+15)²- 225] + 8
= (1/3)(x+15)² -75 + 8
f(x) = (1/3)(x+15)² - 67
This is a parabola with vertex at (-15, -67).
The axis of symmetry is x = -15
The curve opens upward because the coefficient of x² is positive.
As x -> - ∞, f -> +∞.
As x -> +∞, f -> +∞
The domain is all real values of x (see the graph below).
Answer: The domain is (-∞, ∞)
Answer:
Mean: 17
Median: 16
Mode: 10
Step-by-step explanation:
8, 10, 10, 11, 16, 17, 19, 21, 41
Median: (the middle number in the number list/data set) 16
Mode: 10
Mean: 8 + 10 + 10 + 11 + 16 + 17 + 19 + 21 + 41 = 153/9 = 17
Answer:
9.1 minutes.
Step-by-step explanation:
Let t represent time taken to fill the tank.
We have been given that a cold water faucet can fill a sink in 12 min, so the part of sink filed in 1 minute would be
.
The hot-water faucet can fill it in 15 min, so the part of sink filed in 1 minute would be
.
The drain can empty the sink in 25 min, so the part of drain emptied in 1 minute would be
.
The part of 1 full tank filled in t minutes, when both faucets are on and the drain is open would be:

Make a common denominator:









Therefore, it will take 9.1 minutes to fill the sink.
Blocks would he need on the 12th step of the pattern is 34.
The correct option is A
<h3>
</h3><h3>What is series?</h3>
A series is the cumulative sum of a given sequence of terms.
Given:
We can write the series as follows:
1,4,7,10,13,.......
First term =1
common difference= 4-1=3
Using Arithmetic series
= a+11d
= 1 +11*3
= 1+33
= 34.
Hence, 34 blocks need on 12th step.
Learn more about arithmetic series here:
brainly.com/question/2171130
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