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Mila [183]
3 years ago
14

Detections for the last 2/3 : whirred the equation in point-slope form and slope-intercept form for each line

Mathematics
2 answers:
Lilit [14]3 years ago
5 0

slope intercept form

y = mx + b

Find the slope

slope = (y₂ - y₁)/(x₂ - x₁)

let (-2, 5) = (x₁, y₁), and (3, 9) = (x₂, y₂)

Plug in the corresponding numbers to the variables.

slope = (9 - 5)/(3 - (-2))

Simplify

slope = 4/(3 + 2)

slope = 4/5

Plug in 4/5 for m

y = mx + b

y = (4/5)x + b

Solve for b. Plug in a coordinate for x and y: I am using (3,9) in this case

x = 3, y = 9

9 = (4/5)3 + b

Simplify

9 = 12/5 + b

Isolate the b. Note the equal sign. What you do to one side, you do to the other.

9 (-12/5) = 12/5 (-12/5) + b

9 - 12/5 = b

9 - 2 2/5 = b

b = 6 3/5 or 6.6

y = 4/5x + 6.6  is your slope intercept form

--------------------------------------------------------------------------------------------------------------

Point slope form: (y - y₁) = m(x - x₁)

(x, y) = (-2, 5), (x₁, y₁) = (3, 9)

Plug in the corresponding number to the corresponding variable

(5 - 9) = m(-2 - 3)

Simplify

-4 = m(-5)

Note the equal sign. What you do to one side, you do to the other. Isolate the m.

Divide -5 from both sides

(-4)/-5 = (-5m)/-5

-4/-5 = m

m = 4/5

you're slope = 4/5 (as seen in the equation above).

--------------------------------------------------------------------------------------------------------------

hope this helps

Aleks04 [339]3 years ago
3 0
The answer to the question

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A laboratory scale is known to have a standard deviation (sigma) or 0.001 g in repeated weighings. Scale readings in repeated we
weqwewe [10]

Answer:

99% confidence interval for the given specimen is [3.4125 , 3.4155].

Step-by-step explanation:

We are given that a laboratory scale is known to have a standard deviation (sigma) or 0.001 g in repeated weighing. Scale readings in repeated weighing are Normally distributed with mean equal to the true weight of the specimen.

Three weighing of a specimen on this scale give 3.412, 3.416, and 3.414 g.

Firstly, the pivotal quantity for 99% confidence interval for the true mean specimen is given by;

        P.Q. = \frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } } ~ N(0,1)

where, \bar X = sample mean weighing of specimen = \frac{3.412+3.416+3.414}{3} = 3.414 g

            \sigma = population standard deviation = 0.001 g

            n = sample of specimen = 3

            \mu = population mean

<em>Here for constructing 99% confidence interval we have used z statistics because we know about population standard deviation (sigma).</em>

So, 99% confidence interval for the population​ mean, \mu is ;

P(-2.5758 < N(0,1) < 2.5758) = 0.99  {As the critical value of z at 0.5% level

                                                            of significance are -2.5758 & 2.5758}

P(-2.5758 < \frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } } < 2.5758) = 0.99

P( -2.5758 \times {\frac{\sigma}{\sqrt{n} } } < {\bar X - \mu} < 2.5758 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.99

P( \bar X-2.5758 \times {\frac{\sigma}{\sqrt{n} } } < \mu < \bar X+2.5758 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.99

<u>99% confidence interval for</u> \mu = [ \bar X-2.5758 \times {\frac{\sigma}{\sqrt{n} } } , \bar X+2.5758 \times {\frac{\sigma}{\sqrt{n} } } ]

                                             = [ 3.414-2.5758 \times {\frac{0.001}{\sqrt{3} } } , 3.414+2.5758 \times {\frac{0.001}{\sqrt{3} } } ]

                                             = [3.4125 , 3.4155]

Therefore, 99% confidence interval for this specimen is [3.4125 , 3.4155].

6 0
2 years ago
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