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Lina20 [59]
3 years ago
10

A piecewise function is shown below

Mathematics
1 answer:
Greeley [361]3 years ago
8 0

Answer:

p = 5/7

Step-by-step explanation:

The given function is:

g(x) = -3x^{2} - 2x + 8 for -4 ≦ x < 1

g(x) = -2x + 7p for 1 ≦ x ≦ 5

Part a)

A continuous function has no breaks, jumps or holes in it. So, in order for g(x) to be continuous, the point where g(x) stops during the first interval -4 ≦ x < 1 must be equal to the point where g(x) starts in the second interval 1 ≦ x ≦ 5

The point where, g(x) stops during the first interval is at x = 1, which will be:

-3(1)^{2}-2(1)+8=3

The point where g(x) starts during the second interval is:

-2(1)+7(p) = 7p - 2

For the function to be continuous, these two points must be equal. Setting them equal, we get:

3 = 7p - 2

3 + 2 = 7p

p = \frac{5}{7}

Thus the value of p for which g(x) will be continuous is \frac{5}{7}.

Part b)

We have to find p by setting the two pieces equal to each other. So, we get the equation as:

-3x^{2}-2x+8=-2x+7p\\\\ -3x^{2}+8=7p

Substituting the point identified in part (a) i.e. x=1, we get:

-3(1)^{2}+8=7p\\\\ 5=7p\\\\ p=\frac{5}{7}

This value agrees with the answer found in previous part.

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In the data set below, which of these points is most likely and outlier?
shusha [124]
<h2>Answer:</h2>

Option: D is the correct answer.

                 D.  (2,54)

<h2>Step-by-step explanation:</h2>

We know that an outlier of a data set is the value that stands out of the rest of the data point i.e. either it is a too high value or a too low value as compared to other data points.

Here  we are given a set of data points as:

         (2,54)

          (4,7)

         (6, 9)

         (8,12)

         (10,15)

Hence, we see that the output values i.e. 7 in (4,7) ; 9 in (6,9) ; 12 in (8,12) and 15 in (10,15) are closely related.

Hence, the data point that is an outlier is:

                  (2,54)

(As 54 is a much high value as compared to other)

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3 years ago
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Answer:

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Step-by-step explanation:

The length of a side of a triangle is between the sum and the difference of the lengths of the other two sides.

First, we need both sides in the same units. Let's convert feet to inches.

2 ft * (12 in.)/(ft) = 24 in.

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Now we add and subtract the two lengths.

40 in. + 24 in. = 64 in.

40 in. - 24 in. = 16 in.

The length of the third side is between 16 inches and 64 inches.

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