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4 years ago

Let f(x) = 4x3 + 3x2 − 20x − 15 and g(x) = 4x + 3. Find f of x over g of x.

Mathematics

1 answer:

serg [7]4 years ago

8 0

Answer:

$4x^2+15x+15+\frac{35}{x-3}$

Step-by-step explanation:

Let f(x) = 4x3 + 3x2 − 20x − 15 and g(x) = 4x + 3. Find f of x over g of x.

$\frac{f(x)}{g(x)} \\\frac{4x^3 + 3x^2 - 20x - 15}{4x+3}$

$4x^2+15x+15+\frac{35}{x-3}$

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Find the differentiation y=root x

siniylev [52]

Answer:

$\frac{dy}{dx}$ = $\frac{1}{2\sqrt{x} }$

Step-by-step explanation:

Differentiate using the power rule

$\frac{d}{dx}$ (a $x^{n}$ ) = na $x^{n-1}$

Given

y = $\sqrt{x}$ = $x^{\frac{1}{2} }$ , then

$\frac{dy}{dx}$ = $\frac{1}{2}$ $x^{-\frac{1}{2} }$ = $\frac{1}{2\sqrt{x} }$

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4 years ago

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g red bell pepper seeds germinates 85% of the time. planted 25 seeds. What is the probability that 20 or more germinate

bixtya [17]

Answer:

$P(X\geq 20)= P(X=20)+P(X=21)+P(X=22)+P(X=23)+P(X=24)+P(X=25)$

And replacing using the mass function we got:

$P(X=20)=(25C20)(0.85)^{20} (1-0.85)^{25-20}=0.156$

$P(X=21)=(25C21)(0.85)^{21} (1-0.85)^{25-21}=0.211$

$P(X=22)=(25C22)(0.85)^{22} (1-0.85)^{25-22}=0.217$

$P(X=23)=(25C23)(0.85)^{23} (1-0.85)^{25-23}=0.161$

$P(X=24)=(25C24)(0.85)^{24} (1-0.85)^{25-24}=0.0759$

$P(X=25)=(25C25)(0.85)^{25} (1-0.85)^{25-25}=0.0172$

And adding the values we got:

$P(X\geq 20) = 0.8381$

Step-by-step explanation:

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=25, p=0.85)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

We want to find the following probability:

$P(X\geq 20)= P(X=20)+P(X=21)+P(X=22)+P(X=23)+P(X=24)+P(X=25)$

And replacing using the mass function we got:

$P(X=20)=(25C20)(0.85)^{20} (1-0.85)^{25-20}=0.156$

$P(X=21)=(25C21)(0.85)^{21} (1-0.85)^{25-21}=0.211$

$P(X=22)=(25C22)(0.85)^{22} (1-0.85)^{25-22}=0.217$

$P(X=23)=(25C23)(0.85)^{23} (1-0.85)^{25-23}=0.161$

$P(X=24)=(25C24)(0.85)^{24} (1-0.85)^{25-24}=0.0759$

$P(X=25)=(25C25)(0.85)^{25} (1-0.85)^{25-25}=0.0172$

And adding the values we got:

$P(X\geq 20) = 0.8381$

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3 years ago

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VikaD [51]

Answer:

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Step-by-step explanation:

Evaluate f(1) and f(- 1) by substituting x = 1 and x = - 1 into f(x)

Given

f(x) = x² - 4x + 6, then

f(1) = 1² - 4(1) + 6 = 1 - 4 + 6 = 3

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Thus

f(1) - f(- 1) = 3 - 11 = - 8

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