Answer:
Step-by-step explanation:
When a question asks for the "end behavior" of a function, they just want to know what happens if you trace the direction the function heads in for super low and super high values of x. In other words, they want to know what the graph is looking like as x heads for both positive and negative infinity. This might be sort of hard to visualize, so if you have a graphing utility, use it to double check yourself, but even without a graph, we can answer this question. For any function involving x^3, we know that the "parent graph" looks like the attached image. This is the "basic" look of any x^3 function; however, certain things can change the end behavior. You'll notice that in the attached graph, as x gets really really small, the function goes to negative infinity. As x gets very very big, the function goes to positive infinity.
Now, taking a look at your function, 2x^3 - x, things might change a little. Some things that change the end behavior of a graph include a negative coefficient for x^3, such as -x^3 or -5x^3. This would flip the graph over the y-axis, which would make the end behavior "swap", basically. Your function doesn't have a negative coefficient in front of x^3, so we're okay on that front, and it turns out your function has the same end behavior as the parent function, since no kind of reflection is occurring. I attached the graph of your function as well so you can see it, but what this means is that as x approaches infinity, or as x gets very big, your function also goes to infinity, and as x approaches negative infinity, or as x gets very small, your function goes to negative infinity.
Answer:
The reasonable range for the population mean is (61%, 75%).
Step-by-step explanation:
The interval estimate of a population parameter is an interval of values that consist of the values within which the true value of the parameter lies with a certain probability.
The mean of the sampling distribution of sample proportion is,
.
One of the best interval estimate of population proportion is the 95% confidence interval for proportion,

Given:
n = 150
= 0.68
The critical value of <em>z</em> for 95% confidence level is:

Compute the 95% confidence interval for proportion as follows:


Thus, the reasonable range for the population mean is (61%, 75%).
For the sake of example, let's multiply the two numbers

and

together. Altogether, we have:

Rearranging the expression, we can group the exponents and coefficients together:

Multiplying each out, we notice that since

and

have the same base (10), multiplying them has the effect of adding their exponents, which leaves us with:

The takeaway here is that multiplying two numbers in scientific notation together has the effect of multiplying its coefficients and <em>adding</em> its exponents.
Answer:
r < 1/3
Step-by-step explanation:
21r<7
Divide each side by 21
21r/21<7/21
r < 1/3