A rectangular pool is 30 1/3 feet long and 12 1/2 feet wide. What is the area of the pool?

DIA [1.3K]

You can do this by first finding the y intercept which is the point where x = 0

-3(0) + y = 2
so y intercept is the point (0,2)

Now find the x intercept by putting y = 0

-3x = 2

x = -2/3

So we have 2 points (-2/3, 0) and (0,2) Draw a line through these 2 points and you have the required graph.

6 0

3 years ago

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Let f(x)= lxl-3 Write a function g whose graph is a translation 5 units down of the graph of f.

soldier1979 [14.2K]

If the function "f(x) = lxl-3" were translated five units down the graph, g(x) would be lxl-8.

We must be familiar with function transformation and different forms of transformation in order to properly understand the question. When a function is transformed, the graph's curve either "moves to the left/right/up/down," "expands or compresses," or "reflects" to create a new function. For instance, by simply pushing the graph of the function g(x) = x2 up by 7 units, the graph of the function f(x) = x2 + 7 is generated. It is advantageous to convert a function since it saves us from having to create a new function from begin. Function transformations typically fall into one of three categories: 1. 2nd translation 3. dilation Reflection

The given query is about Translation of Function. To create a new function, translation moves the curve up or down and modifies its position. Translation comes in two flavours. Vertical and horizontal translation.

When the curve changes, "the function" shifts upward or downward. By doing this, a function of the form y = f(x) is transformed into f(x) ± k, where k stands for the vertical translation. In this case, the function moves up by k units if k > 0.

The function goes down by 'k' units if k < 0.

The curve in the given problem goes down by 5 units, so k = 5. Which is a vertical translation scenario. Consequently, y = f(x) becomes f(x) - k = g(x) and g(x) = f(x) - k = lxl-3 -5 = lxl - 8.

Therefore the new function after translation is g(x) = lxl - 8.

Learn more about function and types of transformation such as translation, dilation etc here

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4 0

1 year ago

How does geography influence your neighborhood?

Snezhnost [94]

Human characteristics of your neighborhood come from humans ideas and actions. They include bridges houses, and parks. Human characteristics of places also include land use, density of population, language patterns, religious, architecture, and political systems. The theme of place helps flesh out information about location

7 0

3 years ago

Find the circumference of the circle shown below if the diameter equals 20 inches. Use 3.14 for π

Tanzania [10]

Answer:

62.8 inches

Step-by-step explanation:

c = πd

c = 3.14 * 20

c = 62.8 inches

4 0

3 years ago

Define z_alpha to be a z-score with an area of alpha to the right. For Example: z_0.10 means P(Z > z_0.10) = 0.10. We would a

Reptile [31]

Answer:

a) P(-z_0.025 < Z < z_0.025)

For this case we want a quantile that accumulates 0.025 of the area on the tails of the normal standard distribution, and for this case we can calculate the z value with the following excel codes:

"=NORM.INV(0.025,0,1)"

And for this case the two values are : $z_{crit}= \pm 1.96$

b) P(-z_{\alpha/2} < Z < z_{\alpha/2})

For this case we want a quantile that accumulates $\alpha/2$ of the area on the tails of the normal standard distribution, and for this case we can calculate the z value with the following excel codes:

"=NORM.INV(alpha/2,0,1)"

c) For this case we want to find a value of z that satisfy:

P(Z > z_alpha) = 0.05.

And we can use the following excel code:

"=NORM.INV(0.95,0,1)"

And we got $z_{\alpha/2}=1.64$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Part a

P(-z_0.025 < Z < z_0.025)

For this case we want a quantile that accumulates 0.025 of the area on the tails of the normal standard distribution, and for this case we can calculate the z value with the following excel codes:

"=NORM.INV(0.025,0,1)"

And for this case the two values are : $z_{crit}= \pm 1.96$

Part b

P(-z_{\alpha/2} < Z < z_{\alpha/2})

For this case we want a quantile that accumulates $\alpha/2$ of the area on the tails of the normal standard distribution, and for this case we can calculate the z value with the following excel codes:

"=NORM.INV(alpha/2,0,1)"

Part c

For this case we want to find a value of z that satisfy:

P(Z > z_alpha) = 0.05.

And we can use the following excel code:

"=NORM.INV(0.95,0,1)"

And we got $z_{\alpha/2}=1.64$

6 0

3 years ago