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3 years ago

Finding the inverse function for f(x)=1/x^2

Mathematics

1 answer:

Anna [14]3 years ago

4 0

to get the inverse of any expression, we start off by doing a quick switcheroo on the variables and then solve for "y".

$\stackrel{f(x)}{y}=\cfrac{1}{x^2}\implies \stackrel{\textit{quick switcheroo}}{x=\cfrac{1}{y^2}}\implies y^2=\cfrac{1}{x}\implies y=\sqrt{\cfrac{1}{x}}\implies \stackrel{f^{-1}(x)}{y}=\cfrac{1}{\sqrt{x}}$

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A researcher examines 27 water samples for iron concentration. The mean iron concentration for the sample data is 0.802 cc/cubic

Delvig [45]

Answer:

90% confidence interval for the population mean iron concentration is [0.771 , 0.832].

Step-by-step explanation:

We are given that a researcher examines 27 water samples for iron concentration. The mean iron concentration for the sample data is 0.802 cc/cubic meter with a standard deviation of 0.093.

Firstly, the pivotal quantity for 90% confidence interval for the population mean iron concentration is given by;

P.Q. = $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean iron concentration = 0.802 cc/cubic meter

s = sample standard deviation = 0.093

n = number of water samples = 27

$\mu$ = population mean

<em>Here for constructing 90% confidence interval we have used t statistics because we don't know about population standard deviation.</em>

So, 90% confidence interval for the population mean, $\mu$ is ;

P(-1.706 < $t_2_6$ < 1.706) = 0.90 {As the critical value of t at 26 degree of

freedom are -1.706 & 1.706 with P = 5%}

P(-1.706 < $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ < 1.706) = 0.90

P( $-1.706 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X - \mu}$ < $1.706 \times {\frac{s}{\sqrt{n} } }$ ) = 0.90

P( $\bar X -1.706 \times {\frac{s}{\sqrt{n} }$ < $\mu$ < $\bar X +1.706 \times {\frac{s}{\sqrt{n} }$ ) = 0.90

<u>90% confidence interval for</u> $\mu$ = [ $\bar X -1.706 \times {\frac{s}{\sqrt{n} }$ , $\bar X +1.706 \times {\frac{s}{\sqrt{n} }$ ]

= [ $0.802 -1.706 \times {\frac{0.093}{\sqrt{27} }$ , $0.802 +1.706 \times {\frac{0.093}{\sqrt{27} }$ ]

= [0.771 , 0.832]

Therefore, 90% confidence interval for the population mean iron concentration is [0.771 , 0.832].

4 0

3 years ago

Ava has $400 on her credit card. She bought a laptop for $315, and decided to spend the rest on shirts. The unit price of shirts

Montano1993 [528]

Answer:

A is 805i tink and B is for sure 17

Step-by-step explanation:

5 0

3 years ago

Find the solutions to the system; y=x^2-3x-1 and y=8x-1

PSYCHO15rus [73]

${x}^{2} - 3x - 1 = 8x - 1 \\ {x}^{2} - 11x = 0 \\ x(x - 11) \\ x = 0 \: or \: x = 11$

When x = 0,
$y = 8x - 1 \\ y = 0 - 1 \\ y = - 1$

When x = 11
$y = 8(11) - 1 \\ y = 87$
x = 0, y = - 1
x = 11, y = 87

Answer is B.

Hope this helps. - M

8 0

3 years ago

Can anybody explain to me what this question mean so it says "8 more than a number n is written ___________ in algebraic form"

Umnica [9.8K]

Answer:

They want you to put it into an expression so that it could be expressed. So, 8 more than n would be 8+n.

Hope This Helps!!! :D

3 0

3 years ago

Read 2 more answers

The points A, B, and C lie on a line so that AB = 12 cm and BC = 13.5 cm. Find the length of segment AC. Give all possible answe

natita [175]

Answer:

25.5 and 1.5

Step-by-step explanation:

AC = 12 cm

BC = 13.5 cm

12 + 13.5 = 25.5 cm

13.5 - 12 = 1.5 cm

4 0

3 years ago