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3 years ago

Select the correct answer. If f(x) = |x| - 4, which translation is applied fo f(x) to get g(x)?

Mathematics

1 answer:

solmaris [256]3 years ago

8 0

Answer:

It is a vertical translation of f(x) four units downward.

Step-by-step explanation:

We are given the original equation f(x) = |x| and the transformed function is g(x) = |x| - 4.

It is clear that the transformed function that g(x) = f(x) - 4.

So, the y-value in g(x) is reduced by 4 units from the y-value of f(x) i.e. the transformation is by 4 units down of function f(x).

Therefore, it is a vertical translation of f(x) four units downward. (Answer)

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The Wall Street Journal reported that Walmart Stores Inc. is planning to lay off employees at its Sam's Club warehouse unit. App

tatyana61 [14]

Answer:

a) $\bar X = 52$

$Median = 55$

b) $Q_1= \frac{44+44}{2}=44$

$Q_3= \frac{57+60}{2}=58.5$

c) $Range = Max -Min = 69-36=33$

d) $s^2 =100.1429$

$s= \sqrt{100.143}=10.0071$

e) $Lower = Q_1 -1.5 IQR = 44-1.5(58.5-44) = 22.25$

$Upper = Q_1 +1.5 IQR = 44+1.5(58.5-44) = 65.75$

A possible outlier would be the value of 69 since its above the upper limti for the boxplot.

Step-by-step explanation:

For this case we have the following dataset:

55 56 44 43 44 56 60 62 57 45 36 38 50 69 65

A total of 15 observations

Part a

We calculate the mean with the following formula:

$\bar X = \frac{\sum_{i=1}^{15} X_i}{15}$

And for this case we got $\bar X = 52$

For the median we ust need to order the data on increasing way like this:

36, 38,43,44,44,45,50,55,56,56,57,60,62,65,69

Since the number of observations is an odd number the median would be on the 8 position from the dataset ordered on this case:

$Median = 55$

Part b

In order to calculate the Q1 we need to select the following data:

36, 38,43,44,44,45,50,55

And the Q1 would be the average between the 4 and 5 positions like this:

$Q_1= \frac{44+44}{2}=44$

And for the Q3 we select these values:

55,56,56,57,60,62,65,69

And the Q3 would be the average between the 4 and 5 positions like this:

$Q_3= \frac{57+60}{2}=58.5$

Part c

The Range is defined as:

$Range = Max -Min = 69-36=33$

Part d

In order to calculate the sample variance we can use the following formula:

$s^2 = \frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}$

And if we replace we got:

$s^2 =100.1429$

And the deviation is just the square root of the variance:

$s= \sqrt{100.143}=10.0071$

Part e

For this case we need to find the lower and upper limits for the boxplot given by:

$Lower = Q_1 -1.5 IQR = 44-1.5(58.5-44) = 22.25$

$Upper = Q_1 +1.5 IQR = 44+1.5(58.5-44) = 65.75$

A possible outlier would be the value of 69 since its above the upper limti for the boxplot.

4 0

4 years ago

30% of the students in sixth grade have a pet. There are 130 students in the sixth grade how many of them have a dog as a pet?

Zigmanuir [339]

39 students have a pet because 130 times .30 which represents thirty percent gives you the answer

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4 years ago

How would i solve this? Thank you

WITCHER [35]

6 because 2 divided by 12 is 6

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3 years ago

A line goes through points (0, 2) and (1, 1). What is the x-coordinate of the intersection of this line with the line y = 3x + 3

dybincka [34]

Answer:

The x-coordinate of the intersection of the lines is $x=-\frac{1}{4}$

Step-by-step explanation:

First you need to know the equation of the line that passes through the points (0,2) and (1,1).

The equation of the line in slope intercept form is y=m*x + b

By having two points, you can use them to find the slope m using the expression:

$m=\frac{y2-y1}{x2-x1}$

In this case (x1,y1)= (0,2) and (x2,y2)= (1,1). Replacing:

$m=\frac{1-2}{1-0}=\frac{-1}{1}=-1$

Now you can replace in the values of m, and the values of a point x and y into the equation y = mx + b to find the value of b.

1=(-1)*1 +b

So: 1=-1 +b

b=1+1

b=2

Then you have: y=-1*x +2

So you have the following system of equations:

$\left \{ {{y=-1*x+2} \atop {y=3*x+3}} \right.$

Equating both equations you have:

-1*x+2= 3*x+3

Solving:

-1*x-3*x= 3-2

-4*x= 1

$x=-\frac{1}{4}$

The x-coordinate of the intersection of the lines is $x=-\frac{1}{4}$

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Alecsey [184]

Answer:

Step-by-step explanation:

Just add 19 and 11 and you will get your answer!

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3 years ago

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