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1 year ago

A direct variation includes the points (3, 12) and (n, 8). Find n.

Mathematics

1 answer:

vampirchik [111]1 year ago

5 0

For a direct variation between each point (x, y),

$\begin{gathered} x\propto y \\ x=ky \\ k=\frac{x}{y} \end{gathered}$

For (x₁, y₁) = (3, 12),

$\begin{gathered} k=\frac{3}{12} \\ k=0.25 \end{gathered}$

To find n, consider (n, 8) = (x, y)

$\begin{gathered} x=ky \\ \end{gathered}$

Substituting,

$\begin{gathered} n=0.25\times8 \\ n=2 \end{gathered}$

Therefore, the value of n is 2

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Answer:

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Step-by-step explanation:

to find the tangent line we need to find the derivative of the function g(x).

$g(x) =e^{x^3}$

we know that $\frac{d}{dx}(e^{f(x)})=e^{f(x)}f'(x)$

$g'(x) =e^{x^{3}}(3 x^{2})$

$g'(x) =3 x^{2} e^{x^{3}}$

this the equation of the slope of the curve at any point x and it also the slope of the tangent at any point x. hence, g'(x) can be denoted as 'm'

to find the slope at (-1,1/e) we'll use the x-coordinate of the point i.e. x = -1

$m =3 (-1)^{2} e^{(-1)^{3}}\\m =3e^{-1}\\m=\dfrac{3}{e}$

using the equation of line:

$(y-y_1)=m(x-x_1)$

we'll find the equation of the tangent line.

here (x1,y1) =(-1,1/e), and m = 3/e

$(y-\dfrac{1}{e})=\dfrac{3}{e}(x+1)\\y=\dfrac{3x}{e}+\dfrac{3}{e}+\dfrac{1}{e}\\$

$y=\dfrac{3x}{e}+\dfrac{4}{e}$

this is the equation of the tangent at point (-1,1/e)

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3 years ago

An event has a 35% chance of occurring. What is the probability that the event will NOT occur?

sashaice [31]

65% is what it would be

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zheka24 [161]

Answer:

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95.44% of the batteries failed between 16.6 and 21.4 hours.

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Step-by-step explanation:

The 68-95-99.7 states that, for a normally distributed sample:

68.26% of the measures are within 1 standard deviation of the sample.

95.44% of the measures are within 2 standard deviations of the sample.

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In this problem, we have that:

Mean of 19 hours, standard deviation of 1.2 hours.

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This is within 1 standard deviation of the mean. So 68.2% of the batteries failed between 17.8 and 20.2 hours.

About 95.44% of the batteries failed between what two values?

This is within 2 standard deviations of the mean. So 95.44% of the batteries failed between 16.6 and 21.4 hours.

About 99.97% of the batteries failed between what two values?

This is within 3 standard deviations of the mean. So 99.97% of the batteries failed between 15.4 and 22.6 hours.

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3 years ago

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expeople1 [14]

Answer:

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Do this by dividing the numerator and the denominator by five.

Then, simplify the fraction twelve-twentieths by dividing the numerator and the denominator by four.

So, Lenora hit three-fifths of the pitches.

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Answer:

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