What is the arithmetic mean of the following numbers? 10.6, 4, 4, 6, 4,1

1 answer:

6 0

The mean is 4.93333 (3 is repeating)

Explanation

So mean is just the sum of the numbers divided by the number of terms
So we would solve this by adding up all terms as shown here

10.6 + 4 + 4 + 6 + 4 + 1 = 29.6 = sum

Then we will divide the sum by the number of terms which is 6 in this case to get our mean as shown here

29.6 / 6 = 4.9333

The mean is 4.9333 (3 is repeating)

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A food packet is dropped from a helicopter and is modeled by the function f(x) = −15x2 + 6000. The graph below shows the height

melisa1 [442]

General Idea:

Domain of a function means the values of x which will give a DEFINED output for the function.

Applying the concept:

Given that the x represent the time in seconds, f(x) represent the height of food packet.

Time cannot be a negative value, so

$x\geq 0$

The height of the food packet cannot be a negative value, so

$f(x)\geq 0$

We need to replace $-15x^2+6000$ for f(x) in the above inequality to find the domain.

$-15x^2+6000\geq 0 \; \; [Divide \; by\; -15\; on\; both\; sides]\\ \\ \frac{-15x^2}{-15} +\frac{6000}{-15} \leq \frac{0}{-15} \\ \\ x^2-400\leq 0\;[Factoring\;on\;left\;side]\\ \\ (x+200)(x-200)\leq 0$

The possible solutions of the above inequality are given by the intervals $(-\infty , -2], [-2,2], [2,\infty )$ . We need to pick test point from each possible solution interval and check whether that test point make the inequality $(x+200)(x-200)\leq 0$ true. Only the test point from the solution interval [-200, 200] make the inequality true.