Suppose you can replace one number cube with a nonstandard number cube, where any of the numbers 1 through 6 can appear on multiple faces. how can you arrange the numbers on the nonstandard cube so that the mean of the rolls is the same as that of two standard number cubes, but the standard deviation is as large as possible? what is this value? explain your thinking

Replace 5 and 4 with 6s. Replace 2 and 3 with 1s. Then there will be 3 faces with 6 and 3 faces with 1.

Step-by-step explanation:

In order for the mean to remain unchanged, the sum of opposite faces must remain the same: 7. In order to have the standard deviation as large as possible, the largest and smallest possible numbers need to be used: 6 and 1.

Replacing 4 and 5 with 6s, and replacing 2 and 3 with 1s will accomplish your goal.

the answer would be 484

step-by-step explanation:

just multiply 0.484 times 1,000 (formula)

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places