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3 years ago

Write y=2x^2+12x+1 in vertex form.

Mathematics

1 answer:

Amiraneli [1.4K]3 years ago

8 0

Answer:

y = 2(x + 3)^2 - 17.

Step-by-step explanation:

y=2x^2+12x+1

y = 2(x^2 + 6x) + 1

y = 2[( x + 3)^2 - 9] + 1

y = 2(x + 3)^2 - 18 + 1

y = 2(x + 3)^2 - 17.

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3 years ago

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

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

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

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

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

= [3.4125 , 3.4155]

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

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3 years ago

Four artists open a business selling paintings and agree to split the profits equally. They spent $150 on supplies. If their tot

pashok25 [27]

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2 years ago

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kogti [31]

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3 years ago

-7x - 2y = 19 4x + y = -12 Solve the system

nalin [4]

-7x - 2y = 19

4x + y = -12

Set y equal to each other (opposite signs are fine and you could also set x equal instead of y)

-7x - 2y = 19

8x + 2y = -76

Add equations together

x = -52

Plug x value into an equation

4(-52) + y = -12

Solve for y

-208 + y = -12

y = 196

Hope this helps! ;)

4 0

3 years ago