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Gelneren [198K]
3 years ago
9

Find (f/g) (x) and state the domain restriction. f (x) = 6x - 3 and g(x) = 12x^2 - 6x

Mathematics
1 answer:
Rufina [12.5K]3 years ago
8 0

9514 1404 393

Answer:

  (f/g)(x) = 1/(2x)

  x ≠ 1/2

Step-by-step explanation:

  (f/g)(x)=\dfrac{f(x)}{g(x)}=\dfrac{6x-3}{12x^2-6x}=\dfrac{6x-3}{2x(6x-3)}\\\\\boxed{(f/g)(x)=\dfrac{1}{2x}}\quad x\ne\dfrac{1}{2}

The domain restriction x ≠ 1/2 comes from the requirement to prevent the denominator factor 6x-3 from being zero.

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7x+6>or equal to -(x-6)
WINSTONCH [101]

Answer:

x≥ 0

Step-by-step explanation:

7x+6 ≥ -(x-6)

Distribute the minus sign

7x+6 ≥ -x+6

Add x to each side

7x+x+6 ≥ -x+x+6

8x+6 ≥ 6

Subtract 6 from each side

8x+6-6 ≥ 6

8x≥ 0

Divide by 8

8x/8≥ 0/8

x≥ 0

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3 years ago
If BC=2x-3 and AC=2x+10, find the length of AB
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Answer:

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Step-by-step explanation:

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5 0
2 years ago
BRAINLEST
Debora [2.8K]
I believe it's cones, cylinders, and spheres, hope this really help, and good luck 
7 0
3 years ago
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An article contained the following observations on degree of polymerization for paper specimens for which viscosity times concen
devlian [24]

Answer:

(a) A 95% confidence interval for the population mean is [433.36 , 448.64].

(b) A 95% upper confidence bound for the population mean is 448.64.

Step-by-step explanation:

We are given that article contained the following observations on degrees of polymerization for paper specimens for which viscosity times concentration fell in a certain middle range:

420, 425, 427, 427, 432, 433, 434, 437, 439, 446, 447, 448, 453, 454, 465, 469.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

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

where, \bar X = sample mean = \frac{\sum X}{n} = 441

            s = sample standard deviation = \sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }  = 14.34

            n = sample size = 16

            \mu = population mean

<em>Here for constructing a 95% confidence interval we have used One-sample t-test statistics as we don't know about population standard deviation.</em>

<em />

<u>So, 95% confidence interval for the population mean, </u>\mu<u> is ;</u>

P(-2.131 < t_1_5 < 2.131) = 0.95  {As the critical value of t at 15 degrees of

                                             freedom are -2.131 & 2.131 with P = 2.5%}  

P(-2.131 < \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } } < 2.131) = 0.95

P( -2.131 \times {\frac{s}{\sqrt{n} } } < {\bar X-\mu} < 2.131 \times {\frac{s}{\sqrt{n} } } ) = 0.95

P( \bar X-2.131 \times {\frac{s}{\sqrt{n} } } < \mu < \bar X+2.131 \times {\frac{s}{\sqrt{n} } } ) = 0.95

<u>95% confidence interval for</u> \mu = [ \bar X -2.131 \times {\frac{s}{\sqrt{n} } } , \bar X +2.131 \times {\frac{s}{\sqrt{n} } } ]

                                      = [ 441-2.131 \times {\frac{14.34}{\sqrt{16} } } , 441+2.131 \times {\frac{14.34}{\sqrt{16} } } ]

                                      = [433.36 , 448.64]

(a) Therefore, a 95% confidence interval for the population mean is [433.36 , 448.64].

The interpretation of the above interval is that we are 95% confident that the population mean will lie between 433.36 and 448.64.

(b) A 95% upper confidence bound for the population mean is 448.64 which means that we are 95% confident that the population mean will not be more than 448.64.

6 0
3 years ago
Angelo charges $30 to mow 1 yard. Which equation could be used to determine the total cost, y, for mowing x yards? A. y = x + 30
alexira [117]

Answer:

D. y=30x

Step-by-step explanation:

So x represents like say if he mowed 3 yards.

y=30(3)

Then y would equal 90

8 0
3 years ago
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