Which graph has the same end behavior as the graph of f(x) = –3x^3 – x^2 + 1?

Mathematics

1 answer:

ololo11 [35]2 years ago

4 0

To find out end behavior, we always look at the largest exponent (3 in this case) and the sign of the term with the largest exponent (negative in this case). We can rule out the first two choices because since it is a cubic graph (exponent of 3) the graph will be pointing in opposite directions. Then, the negative tells us that as the x values approache infinity, the y values will approach negative infinity. So the correct answer is the last choice.

Hope this helps

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QUESTION THREE (30 MARKS) 3.1 The mass of a standard loaf of white bread is, by law meant to be 700g with a population standard

kiruha [24]

Using the normal distribution and the central limit theorem, it is found that there is a 0.0284 = 2.84% probability of finding a sample mean mass of 695g or below.

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Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

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Mean of 700g means that $\mu = 700$
Standard deviation of 21g means that $\sigma = 21$
Sample of 64, thus $n = 64$
<u>For the sampling distribution of the sample mean</u>, the standard deviation is of $s = \frac{21}{\sqrt{64}} = \frac{21}{8} = 2.625$