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zavuch27 [327]
3 years ago
14

Express the function graphed on the axes below as a piecewise function.

Mathematics
1 answer:
dangina [55]3 years ago
8 0

Answer:

y = 2/3x +6  for x< -3

y = 2/3x +1     for x> 3

Step-by-step explanation:

The graph is a line for  x < -3

( - 6,2) and ( -3,4)

The slope is m= ( y2-y1)/(x2-x1)

m = ( 4-2)/(-3 - -6) = 2/ ( -3+6) = 2/3

The slope is 2/3

Using point slope form

y-y1 = m(x-x1)  and the point ( -6,2)

y -2 = 2/3(x - -6)

y -2 = 2/3(x +6)

y-2 = 2/3 x +4

y = 2/3x +6 x< -3

The graph is a line for  x > 3

(3,3) and ( 6,5)

The slope is m= ( y2-y1)/(x2-x1)

m = ( 5-3)/(6-3) = 2/ (3) = 2/3

The slope is 2/3

Using point slope form

y-y1 = m(x-x1)  and the point (6,5)

y -5 = 2/3(x - 6)

y-5 = 2/3 x -4

y = 2/3x +1   x> 3

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A study of peach trees found that the average number of peaches per tree was 725. The standard deviation of the population is 70
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Answer:

She needs to sample 189 trees.

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 - 0.95}{2} = 0.025

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 - 0.025 = 0.975, so Z = 1.96.

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.

The standard deviation of the population is 70 peaches per tree.

This means that \sigma = 70

How many trees does she need to sample to obtain an average accurate to within 10 peaches per tree?

She needs to sample n trees.

n is found when M = 10. So

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

10 = 1.96\frac{70}{\sqrt{n}}

10\sqrt{n} = 1.96*70

Dividing both sides by 10:

\sqrt{n} = 1.96*7

(\sqrt{n})^2 = (1.96*7)^2

n = 188.2

Rounding up:

She needs to sample 189 trees.

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True [87]

3.114

Step-by-step explanation:

Given slope of the line is 1.581,

Mean of the x-coordinate is 5.923,

Mean of the y-coordinate is 12.478

Equation of the line formula is  

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12.478 = 1.581 × 5.923 + c

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⇒ c = 12.478 – 9.364263  

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