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Rudiy27
3 years ago
15

The function C (t) = StartFraction 4 t Over t squared + 2 EndFraction models the cost per student of a field trip when x student

s go on the trip. How is the parent function On a coordinate plane, 3 curves are shown. One curve opens up and to the right in quadrant 1 and goes through (2, 4) and (4, 1). Another curve approaches x = negative 2 in quadrant 2, changes direction at (0, 0), and then decreases in quadrant 4 and approaches y = 2. The third curve opens down and to the left in quadrant 3 and goes through (negative 4, negative 1) and (negative 2, negative 4). transformed to create the function On a coordinate plane, 2 curves are shown. One curve opens up and to the left in quadrant 2 and goes through (negative 4, 8) and (negative 6, 6). Another curve opens down and to the right and goes through (negative 1, negative 3), (0, 0), and (6, 3).?
It is vertically stretched by a factor of 200.
It is vertically stretched by a factor of 200 and shifted 10 units leftt.
It is vertically stretched by a factor of 200 and shifted 10 units up.
It is vertically stretched by a factor of 200 and shifted 10 units right.
Mathematics
1 answer:
choli [55]3 years ago
7 0

Answer:

C. It is vertically stretched by a factor of 200 and shifted 10 units up.

Step-by-step explanation:

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Hello,

p = -6 * 7 / 3 = -14


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The function f(t) = t2 + 6t − 20 represents a parabola.
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Answer:

Step-by-step explanation:

Part A:

To complete the square, we will do the first few steps all at once, since they are necessary but not complicated to follow all at once.  Set the function equal to 0 first, then move the constant over to the other side:

t^2+6t=20

The most important rule for completing the square is that the leading coefficient (the number on the t-squared term) is a positive 1.  Ours is, but if it wasn't it would need to be factored out.

Next, take half the linear term, square it, and add it to both sides.  Our linear term is 6.  Half of 6 is 3, and 3 squared is 9, so we add 9 to both sides:

t^2+6t+9=20+9

On the right is simple addition, but on the left side, during this process we created a perfect square binomial that will reflect the h coordinate of the vertex.  We will state that binomial and do the addition on the right both at the same time:

(t+3)^2=38

If you FOIL out the (t + 3)(t + 3) you will get back the polynomial t^2+6t+9

Now we can move the constant back over and set the polynomial back to equal f(t):

(t+3)^2-38=f(t)

From this we determine the vertex to sit at (-3, -38)

Part B:

Because this is a positive parabola that opens upwards, the function will have a minimum value (if it was negative and opened upside down, it would have a minimum value).  In other words, you know the vertex is a minimum because this is a positive parabola that opens upwards.

Part C:

The axis of symmetry is the line that cuts the parabola in half, creating 2 identical, mirror images.  Because this parabola opens upwards, a vertical line is required to cut it into 2 identical halves.  The vertical line has an equation " x = ".  In the case of a positive parabola that opens upwards, the line of symmetry, what x = , will ALWAYS be the number that is inside the parenthesis with the x.  Since the standard vertex form is

f(t)=(t-h)^2+k

our vertex can be rewritten as (t - (-3)).  Therefore, our axis of symmetry is

x = -3

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2.98x4 
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Researchers studying starfish collected two independent random samples of 40 starfish. One sample came from an ocean area in the
krek1111 [17]

Answer:

The test statistic for the appropriate test is \frac{0.15-0.275}{\sqrt{0.2125(1-0.2125)[\frac{1}{40}+\frac{1}{40}]}}.

Step-by-step explanation:

The experiment conducted here is to determine whether there is a difference in proportion of starfish over 8 inches in length in the two ocean areas, i.e. north and south.

The hypothesis to test this can be defined as follows:

<em>H₀</em>: There is no difference in proportion of starfish over 8 inches in length in the two ocean areas, i.e. <em>p</em>₁ = <em>p</em>₂.

<em>Hₐ</em>: There is a difference in proportion of starfish over 8 inches in length in the two ocean areas, i.e. <em>p</em>₁ ≠ <em>p</em>₂.

The two-proportion <em>z</em>-test would be used to perform the test.

A sample of <em>n</em> = 40 starfishes are selected from both the ocean areas.

It provided that of the 40 starfish from the north, 6 were found to be over 8 inches in length and of  the 40 starfish from the south, 11 were found to be over 8 inches in length.

Compute the sample proportion of starfish from north that were over 8 inches in length as follows:

\hat p_{n}=\frac{6}{40}=0.15

Compute the sample proportion of starfish from south that were over 8 inches in length as follows:

\hat p_{s}=\frac{11}{40}=0.275

The test statistic is:

z=\frac{\hat p_{n}-\hat p_{s}}{\sqrt{P(1-P)[\frac{1}{n_{n}}+\frac{1}{n_{s}}]}}

Compute the combined proportion <em>P</em> as follows:

P=\frac{X_{n}+X_{s}}{n_{n}+n_{s}}=\frac{6+11}{40+40}=0.2125

Compute the test statistic value as follows:

z=\frac{\hat p_{n}-\hat p_{s}}{\sqrt{P(1-P)[\frac{1}{n_{n}}+\frac{1}{n_{s}}]}}

  =\frac{0.15-0.275}{\sqrt{0.2125(1-0.2125)[\frac{1}{40}+\frac{1}{40}]}}

Thus, the test statistic for the appropriate test is \frac{0.15-0.275}{\sqrt{0.2125(1-0.2125)[\frac{1}{40}+\frac{1}{40}]}}.

8 0
3 years ago
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