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Stella [2.4K]
3 years ago
5

Find the equation of plane that contains P(1,-1,2) and has the normal n=2i+3j+5k (please answer quickly )

Mathematics
1 answer:
mixas84 [53]3 years ago
8 0

Answer:

2x + 3y + 5z = 9

Step-by-step explanation:

The normal defines all the planes perpendicular to that vector. To isolate to a single plane, just apply the known point.

ax + by + cz = d

2x + 3y + 5z = d

2(1) + 3(-1) + 5(2) = 9

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The water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day.
valina [46]

Answer:

A sample of 179 is needed.

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1 - 0.85}{2} = 0.075

Now, we have to find z in the Ztable as such z has a pvalue of 1 - \alpha.

That is z with a pvalue of 1 - 0.075 = 0.925, so Z = 1.44.

Now, find the margin of error M as such

M = z\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

A previous study found that for an average family the variance is 1.69 gallon?

This means that \sigma = \sqrt{1.69} = 1.3

If they are using a 85% level of confidence, how large of a sample is required to estimate the mean usage of water?

A sample of n is needed, and n is found for M = 0.14. So

M = z\frac{\sigma}{\sqrt{n}}

0.14 = 1.44\frac{1.3}{\sqrt{n}}

0.14\sqrt{n} = 1.44*1.3

\sqrt{n} = \frac{1.44*1.3}{0.14}

(\sqrt{n})^2 = (\frac{1.44*1.3}{0.14})^2

n = 178.8

Rounding up

A sample of 179 is needed.

7 0
3 years ago
Can someone please explain how to solve this? And give me the answer?! THANK U !
Lyrx [107]

we know the segment QP is an angle bisector, namely it divides ∡SQR into two equal angles, thus ∡1 = ∡2, and ∡SQR = ∡1 + ∡2.

\bf \begin{cases} \measuredangle SQR = \measuredangle 1 + \measuredangle 2\\\\ \measuredangle 2 = \measuredangle 1 = 5x-7 \end{cases}\qquad \qquad \stackrel{\measuredangle SQR}{7x+13} = (\stackrel{\measuredangle 1}{5x-7})+(\stackrel{\measuredangle 2}{5x-7}) \\\\\\ 7x+13 = 10x-14\implies 13=3x-14\implies 27=3x \\\\\\ \cfrac{27}{3}=x\implies 9=x \\\\[-0.35em] ~\dotfill\\\\ \measuredangle SQR = 7(9)+13\implies \measuredangle SQR = 76

4 0
3 years ago
Please help asap I will give you brainliest Find the area of the shaded region
kondaur [170]

Answer:

36

Step-by-step explanation:

Area of total region = 12 ×5

=60

Area of the small region = 8×3

=24

Area of shaded region = Area of Total region - area of small region

= 60 - 24

= 36

4 0
3 years ago
What's the answer????
Svetllana [295]
I would try b the rise\run is 2\2 so give it a go
8 0
3 years ago
Simplify 2[(9 - 5)^5 / 8]
Alenkinab [10]
2[(9 - 5)^5/8] = 2[4^5/8] = 2[1024/8] = 2[128] = 256
5 0
3 years ago
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