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4 years ago

What is the solution to the compound inequality in interval notation?

Mathematics

2 answers:

mars1129 [50]4 years ago

6 0

Answer: The correct option is

(D) (−∞, −5] or (0, ∞).

Step-by-step explanation: We are given to select the solution to the following inequality in interval notation :

$2(x+3)>6~~\textup{or}~~2x+3\leq-7~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

To find the correct solution, we need to solve both the inequalities in (i) separately.

The solution of (i) is as follows :

$2(x+3)>6\\\\\Rightarrow x+3>\dfrac{6}{2}\\\\\Rightarrow x+3>3\\\\\Rightarrow x>3-3\\\\\Rightarrow x>0$

and

$2x+3\leq -7\\\\\Rightarrow 2x\leq-7-3\\\\\Rightarrow 2x\leq-10\\\\\Rightarrow x\leq-\dfrac{10}{2}\\\\\Rightarrow x\leq -5.$

That is, the solution is given by

$x\epsilon (-\infty,-5]~or~(0,\infty).$

Thus, (D) is the correct option.

Eduardwww [97]4 years ago

5 0

First solve the 2 inequalities for x:-

x > 0 or x <= -5

The last choice is the correct one.

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Step-by-step explanation:

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Maksim231197 [3]

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Step-by-step explanation:

In regression analysis there are two kinds of variables: Explanatory and Response variable.

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4 years ago

Hank is throwing a party. The party costs $20 per person. Answer the questions below to describe the relationship between the co

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Step-by-step explanation:

On a graph called the coordinate plane, there are two axis. The horizontal axis is the x-axis and is known as the independent variable. A great example of an independent variable is time. Time is always represented on the x-axis because time passes by. It does not depend on anything.

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In a game called taxation and evasion, a player rolls a pair of dice. if on any turn the sum is 7, 11, or 12, the player gets au

bezimeni [28]

The probability that she gets audited no more than 2 times is 0.896482...

As, a pair of dice are rolling here, so the number of total possible outcome = (6×6) = 36

For Sum = 7 , the favorable outcomes are: (1,6) (2,5) (3,4) (4,3) (5,2) and (6,1)

For Sum = 11 , the favorable outcomes are: (5,6) and (6,5)

For Sum = 12 , the favorable outcome is: (6,6)

Probability = (Number of favorable outcomes)÷(Number of total outcomes)

So, $P(7)= \frac{6}{36} =\frac{1}{6}$

$P(11) = \frac{2}{36} = \frac{1}{18}$

$P(12) = \frac{1}{36}$

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Here the total number of trials = 5 and the probability of getting audited = $\frac{1}{4}$

According the binomial distribution formula:

P(X) = (ⁿCₓ )(P)ˣ (1-P)ⁿ⁻ˣ

where P(X) is the probability of x successes out of n trials

Here, n= 5 and P = 1/4 and we need to find the probability of getting audited no more than 2 times. This means she can gets audited 0, 1 or 2 times.

So,

$P(X=0)+P(X=1) +P(X=2)\\\\= [^5C^0 (\frac{1}{4})^0 (1-\frac{1}{4})^5^-^0 ]+[^5C^1 (\frac{1}{4})^1 (\frac{3}{4})^5^-^1]+[^5C^2 (\frac{1}{4})^2 (\frac{3}{4})^5^-^2]\\\\= (\frac{3}{4})^5+ (5) (\frac{1}{4}) (\frac{3}{4})^4 +(10)(\frac{1}{4})^2 (\frac{3}{4})^3\\\\=0.237304... +0.395507...+0.263671...\\\\ = 0.896482...$

So, the probability that she gets audited no more than 2 times is 0.896482...

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