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3 years ago

Select the interval where f(x)>0 A: -2 B: 1< x<2 C: 4 HELP

Mathematics

1 answer:

Viefleur [7K]3 years ago

7 0

Answer: 1 < x < 2

Step-by-step explanation:

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9. On a game show, there are 16 questions: 8 easy, 5 medium-hard, and 3 hard. If contestants are given questions

just olya [345]

Answer:

$\frac{7}{30}\approx0.23$

Step-by-step explanation:

Given:

Number of questions (N) = 16

Number of easy questions (E) = 8

Number of medium-hard questions (M) = 5

Number of hard questions (H) = 3

Now, the probability of getting the first question as easy question is given as:

$P(E1)=\frac{\textrm{Number of easy questions}}{\textrm{Total questions}}\\\\P(E1)=\frac{E}{N}=\frac{8}{16}=0.5$

Now, probability of getting the second question as easy question is given as:

$P(E2)=\frac{\textrm{Number of easy questions left}}{\textrm{Total questions left}}\\\\P(E2)=\frac{E-1}{N-1}=\frac{7}{15}$

Now, probability that the first two contestants will get easy questions is given by the product of $P(E1)\ and\ P(E2)$ . So,

$P(2\ easy\ questions)=P(E1)\times P(E2)\\\\P(2\ easy\ questions)=\frac{1}{2}\times \frac{7}{15}\\\\P(2\ easy\ questions)=\frac{7}{30}\approx 0.23$

Therefore, the probability that the first two contestants will get easy questions is $\frac{7}{30}\approx0.23$

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3 years ago

Which relation is displayed on the graph?

solong [7]

D Bc I think is it??

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3 years ago

Mama mia restaurant used 1/2

melamori03 [73]

Answer:

okay

Step-by-step explanation:

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3 years ago

Which of the values shown are potential roots of f(x) = 3x3 â€"" 13x2 â€"" 3x 45? Select all that apply.

Verdich [7]

The potential roots of the function are, $\pm1, \ \pm3, \ \pm5, \ \pm9,\ \pm15, \ \pm45,\ \pm \dfrac{1}{3},\ \pm \dfrac{5}{3}$

And the accurate root is 3 it can be determined by using rules of the rational root equation.

<h2>Given that,</h2>

Function; $\rm f(x) = 3x^3 - 13x^2 -3x + 45$

<h3>We have to determine,</h3>

Which of the values shown are potential roots of the given equation?

<h3>According to the question,</h3>

Potential roots of the polynomial are all possible roots of f(x).

$\rm f(x) = 3x^3 - 13x^2 -3x + 45$

Using rational root theorem test. We will find all the possible or potential roots of the polynomial.

$\rm p=\dfrac{All\ the \ positive}{Negative\ factors \ of\ 45}$

$\rm q=\dfrac{All\ the \ positive}{Negative\ factors \ of\ 3}$

The factor of the term 45 are,

$\pm1, \ \pm3, \ \pm5, \ \pm9,\ \pm15, \ \pm45$

And The factor of 3 are,

$\pm1, \ \pm3$

All the possible roots are,

$\dfrac{p}{q} = \pm1, \ \pm3, \ \pm5, \ \pm9,\ \pm15, \ \pm45,\ \pm \dfrac{1}{3},\ \pm \dfrac{5}{3}$

Now check for all the rational roots which are possible for the given function,

$\rm f(x) = 3x^3 - 13x^2 -3x + 45\\\\ f(1) = 3(1)^3 - 13(1)^2 -3(1) + 45 = 3-13-3+45 = 32\neq 0\\\\ f(-1) = 3(-1)^3 - 13(-1)^2 -3(-1) + 45 =- 3-13+3+45 = 32\neq 0\\\\ f(3) = 3(3)^3 - 13(3)^2 -3(3) + 45 = 81-117-9+45 =0\\\\ f(-3) = 3(-3)^3 - 13(-3)^2 -3(-3) + 45 = -81+117+9+45 =-144\neq 0$