Ariana starts with 100 milligrams of a radioactive substance. the amount of the substance decreases by 20% each week for a number of weeks, w. the expression 100(1−0.2)w finds the amount of radioactive substance remaining after w weeks. which statement about this expression is true? a) it is the difference between the initial amount and the percent decrease. b) it is the difference between the initial amount and the decay factor after w weeks. c) it is the initial amount raised to the decay factor after w weeks. d) it is the product of the initial amount and the decay factor after w weeks.

D

Step-by-step explanation:

Option D - It is the product of the initial amount and the decay factor after w weeks.

Step-by-step explanation:

Given : Ariana starts with 100 milligrams of a radioactive substance. The amount of the substance decreases by 20% each week for a number of weeks, w. The expression finds the amount of radioactive substance remaining after w weeks.

To find : Which statement about this expression is true?

Solution :

In Ariana's expression,  

100 represents the amount of substance he begins with.

and (1-0.2) i.e, 0.8 is the amount of substance left after each time period or the decay factor after w weeks.  

The given expression represents the product of initial amount and the decay factor after w weeks.

Therefore, Option D is correct.

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .

c. side angle side. u shares the same sides