Suppose that a state introduces a state income tax which will be at a flat rate of 3%. the state legislature wishes to estimate how much money they will receive in taxes, and to do this they need to know the average income of residents of the state. which information would be most useful, the mean income, the median income, or the mode of the incomes? why?

The mean income is more useful

Step-by-step explanation:

If you know the mean income, then you can obtain the total income by multiplying for the total population. Once you know the total income, you can deduce the amount of money collected by multiplting the total income by 0.03.

Knowing the median income does only help you so much. The mediam income is only a parameter that says that 50% of the population earn less than that. However, if you dont know how much the richer people earn, you cant deduce how much from taxes will you collect. For a simplified example, the sets A = {1,3,18} and B = {1,3,4} have the same median, 3. however A sums a total of 22, while B only sums 8.

The mode of income alone is also not enough. Again, You can have a lot of salaries ranging from similar values, but if you dont know the exact value of other clusters of salaries, specifically the biggest ones, you will lack a lot of information. As a simplified example, the Sets A = {1,3,3,3,3,3,3, 7, 7,7} and B = {1,3,3,3,3,3,3,3,3,75} have both of them 3 as the most frequent number, however A has a mean of 4, while B has a mean of 10, despite having only 1 mayor cluster of numbers.

Is short, the mean is the bets way to determine the amount of rax collection, because it puts more realistic 'weights' on higher income, and because it lets you obtain exact results for the total amount of income.

I hope this helped you!

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.