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3 years ago

The graph below shows the solution set of which inequality?

Mathematics

2 answers:

ozzi3 years ago

8 0

Answer:

Step-by-step explanation:

AlekseyPX3 years ago

3 0

For this case, we observe in the graph that the solution is given by:

$x 2$

Inequality does not contain equality because the boundaries of the solution are open.

Thus, we can discard options A and B.

From option C we have:

$x ^ 2> 4$

Applying root to both sides:

$x> \pm \sqrt {4}$

Thus, the solutions are:

$x> 2\\x$

Answer:

Option C

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Find the indicated probability. Round to three decimal places. The participants in a television quiz show are picked from a larg

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Use binomial probability:

P = nCr pʳ (1−p)ⁿ⁻ʳ

where n is the number of trials,

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p is the probability of success,

and q is the probability of failure (1-p).

Here, p = 0.5, q = 0.5, and n = 11.

We need to find P when r is 0, 1, and 2, then add up the results to get the total probability.

r = 0:

P = ₁₁C₀ (0.5)⁰ (0.5)¹¹⁻⁰

P ≈ 0.0005

r = 1:

P = ₁₁C₁ (0.5)¹ (0.5)¹¹⁻¹

P ≈ 0.0054

r = 2:

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Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .