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3 years ago

Express the solution of, x^3 + 2x^2 < x + 2, using interval notation.

Mathematics

1 answer:

Rudiy273 years ago

6 0

x³ + 2x² - x - 2 < 0

x³ - x + 2x² - 2 < 0

x(x² - 1) - 2(x² - 1) < 0

(x - 2)(x² - 1) < 0

(x - 2)(x - 1)(x + 1) < 0

by chacking we get the solution

x ∈ (-∞,-1) ∪ (-1,1)

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Answer: The probability that both televisions work is 0.5625 .

The probability at least one of the two televisions does not work is 0.4375.

Step-by-step explanation:

Given : Number of televisions received in shipment= 12

Number of defective televisions received in shipment= 3

Then proportion of defective televisions = $\dfrac{3}{12}=0.25$

Using binomial probability formula, the probability of getting success in x trials is given by :-

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If two televisions are randomly selected, then the probability that both televisions work will be :-

$P(0)=^2C_0(0.25)^0(0.75)^2=(0.75)^2=0.5625$

The probability at least one of the two televisions does not work will be :-

$P(x\geq1)=1-P(0)=1-0.5625=0.4375$

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Step-by-step explanation:

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What is −13+2z=−56 Thanks

Zinaida [17]

<h3>Original Equation:</h3>

$-\frac{1}{3}+2z=-\frac{5}{6}$

<h3>Steps:</h3>

<em>*To solve for a variable, isolate the desired variable onto one side.</em>

Firstly, we want to add 1/3 to each side however -5/6 and 1/3 do not share the same denominator, and we want them to have that and we can do that by finding the LCD, or lowest common denominator. To find the LCD, list the multiples of 6 and 3 and the lowest multiple that they share is their LCD. In this case, their LCD is 6. Multiply -1/3 by 2/2:

$-\frac{1}{3}\times \frac{2}{2}=-\frac{2}{6}\\\\-\frac{2}{6}+2z=-\frac{5}{6}$

Now that we have common denominators, add both sides by 2/6:

$2z=-\frac{3}{6}\\\\2z=-\frac{1}{2}$

Next, you want to cancel out 2 to isolate z. Usually, one would divide both sides by 2, however remember that <u>dividing by a number is the same as multiplying by it's reciprocal.</u> To find a number's reciprocal, flip the numerator and denominator around. In this case, since 2 is a <em>whole number</em> this means that the denominator is 1. In this case: 2/1 would become 1/2. Multiply both sides by 1/2:

$\frac{1}{2}\times 2z= -\frac{1}{2}\times \frac{1}{2}\\\\z=-\frac{1}{4}$

<h3>Final Answer:</h3>

<u>Your final answer is z = -1/4.</u>

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3 years ago