Data were collected on two variables, x and y, to create a model to predict y from x. A scatterplot of the collected data revealed a curved pattern with a possible cubic relationship (y=ax^3, where a is a constant) between the variables. Which of the following transformations would be most appropriate for creating linearity between the variables? A - Taking the cube of y
B - Taking the cube root of y
C - Taking the cube root of both y and x
D - Taking the log of y
E - Taking the log of both y and x

Linearity is the concept used to describe linear relationships between variables.

The appropriate method for creating linearity between the variables is: (e) Taking the log of both y and x

The function is given as:

The function is a power function (i.e. cube of x)

To create linearity between power function, we simply take the logarithms of both variables

So, we have:

Apply law of logarithm

Hence, the appropriate method for creating linearity between the variables is: (e) Taking the log of both y and x

Read more about linearity between variables at:

link

B - Taking the cube root of y

Step-by-step explanation:

Data provided in the question

y = ax^3

Based on the above information

Now we take the cube root of y

So, it would be calculated below:

y1/3 = a1/3 × x

So

As it can seen by the above equation there is a linear relationship between the cube root of y and x

Therefore, the correct option is B.

Hence, all the other options are wrong

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

equation image indicator

x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

equation image indicator

x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

equation image indicator

x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!

see below

step-by-step explanation:

7.   there are 10 data points in the set.   the middle point is between 5 and 6.   the middle point in the top half is 8   and the middle point in the bottom half is 3. to find the iqr , take point 8 and subtract point 3

mid term   point 8 = 100   point 3 = 88

iqr = 100-88 = 12

final   point 8 = 93   point 3 = 78

iqr = 93 - 78 = 15

the final has the greatest iqr

6.   b - there is a high data value that causes the data set to be asymmetrical for the males: the data for males are high and asymmetrical .   there is an outlier for the males that skews the data

5.   the   iqr is a better measure of spread for the movies and basketball games.   since the basketball game has an outlier, we do not want to use standard deviation for measurement.  

3.   the exam median is much higher than the class median.   the median line is farther to the right on the exams

2.   there is no way to tell what the means are from the box and whisker plots.