Simplify the following expressions without using a calculator

How do you rewrite 3x-9y=18 as a slop-intercept form?

Norma-Jean [14]

I believe it would be y=-1/3x-2

5 0

3 years ago

How do you simplify 50 1/2+ -12.3

levacccp [35]

50 1/2 = 50.5

50.5 + -12.3

When adding a negative number to a positive number, it basically becomes just subtraction so 50.5 + -12.3 means 50.5 - 12.3

50.5 - 12.3 = 38.2

3 0

3 years ago

A bench is 35 inches long and 19 inches wide. how many square inches does it cover?

vfiekz [6]

Do 35 times 19 and that is the whole square inches or so 35 squared times 19 squared

4 0

3 years ago

Sample annual salaries (in thousands of dollars) for employees at a company are listed. 42 36 48 51 39 39 42 36 48 33 39 42 45 (

Sonja [21]

Answer:

a) Data given: 42 36 48 51 39 39 42 36 48 33 39 42 45

$\bar X = 41.538$

$s = 5.317$

b) 44.1, 37.8, 50.4, 53.55, 40.95, 44.1, 37.8, 50.4 ,34.65, 40.95, 44.1, 47.25

$\bar X = 43.615$

$s= 5.583$

c) 3.5, 3, 4, 4.25, 3.25, 3.25, 3.5, 3, 4, 2.75, 3.25, 3.5, 3.75

$\bar X= 3.462$

$s = 0.443$

d) As we can see, the average of part b is 1.05 times the average of part a (1.05 * 41.538 = 43.615) and the average of part c is equal to the average obtained in part a divided by 12 (41.538 / 12 = 3.462).

And that happens because we create linear transformations for the parts b and c and the linear transformation affects the mean.

And you have the same interpretation for the deviation, it is affected by the linear transformation as the mean.

Step-by-step explanation:

For this case we can use the following formulas for the mean and standard deviation:

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

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

Part a

Data given: 42 36 48 51 39 39 42 36 48 33 39 42 45

And if we calculate the mean we got:

$\bar X = 41.538$

$s = 5.317$

Part b

For this case we know that each value present a 5% of rise so we just need to multiply each value bu 1.05 and we have this new dataset:

44.1, 37.8, 50.4, 53.55, 40.95, 44.1, 37.8, 50.4 ,34.65, 40.95, 44.1, 47.25

And if we calculate the new mean and deviation we got:

$\bar X = 43.615$

$s= 5.583$

Part c

The new dataset would be each value divided by 12 so we have:

3.5, 3, 4, 4.25, 3.25, 3.25, 3.5, 3, 4, 2.75, 3.25, 3.5, 3.75

And the new mean and deviation would be:

$\bar X= 3.462$

$s = 0.443$

Part d

As we can see, the average of part b is 1.05 times the average of part a (1.05 * 41.538 = 43.615) and the average of part c is equal to the average obtained in part a divided by 12 (41.538 / 12 = 3,462).

And that happens because we create linear transformations for the parts b and c and the linear transformation affects the mean.

And you have the same interpretation for the deviation, it is affected by the linear transformation as the mean.

5 0

3 years ago

What is the equation of the line containing the points (3,1), (9,3) and (27,9)

aleksley [76]

Answer:

y = (1/3)x

Step-by-step explanation:

If this is truly a line, then we can find its equation using any two of the three given points. If we go from (3, 1) to (27, 9), x increases by 24 and y increases by 8. Thus, the slope of this line is m = rise / run = 8 / 24, or m = 1/3.

Using the point (3, 1) and the slope m = 1/3, the slope-intercept form y = mx + b becomes 1 = (1/3)(3) + b. Thus, b = 0, and the line is y = (1/3)x.

5 0

3 years ago

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