An article describes a study in which a new type of ointment was applied to forearms of volunteers to study the rates of absorption into the skin. Eight locations on the forearm were designated for ointment application. The new ointment was applied to four locations, and a control was applied to the other four. How many different choices were there for the four locations to apply the new ointment

There were 70 choices for the four locations to apply the new ointment

Step-by-step explanation:

The order in which the locations are chosen is not important. So we use the combinations formula to solve this question.

Combinations formula:

is the number of different combinations of x objects from a set of n elements, given by the following formula.

How many different choices were there for the four locations to apply the new ointment

Four locations from a set of 8. So

There were 70 choices for the four locations to apply the new ointment

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 .