The rule (x, y)→(−x,−y)(x, y)→(−x,−y) maps △rst△rst to △r′s′t′△r′s′t′.

which statement correctly describes the relationship between △rst△rst and △r′s′t′△r′s′t′ ?

the triangles are congruent because △r′s′t′△r′s′t′ is a translation of △rst△rst , and a translation is a rigid motion.

the triangles are congruent because △r′s′t′△r′s′t′ is a rotation of △rst△rst , and a rotation is a rigid motion.

the triangles are not congruent because △r′s′t′△r′s′t′ is a rotation of △rst△rst , and a rotation is not a rigid motion.

the triangles are not congruent because △r′s′t′△r′s′t′ is a translation of △rst△rst , and a translation is not a rigid motion.

The correct option is 2. The triangles are congruent because △R′S′T′ is a rotation of △RST, and a rotation is a rigid motion.

Step-by-step explanation:

It is given that △RST maps to △R′S′T′ by using the rule

Since the absolute values of x and y-coordinates are same but the sign of both coordinates are changed. It is possible, if the figure is rotated 180 degree about the origin.

When a figure rotated 180 degree about the origin, then

Rotation is a rigid motion and image and preimage are congruent to each other.

Therefore option 2 is correct.

amount of oatypop that contains the prize = 40%

amount   of oatypop which doesn't contain the prize = (100-40)=60%

probability that hannah will win a prize

    = s +f s +f f s+ff   f s+ff f f s+ infinity.where f= failure,s= success

=   or 60%

probability that hannah only has to buy 3 or less boxes before getting a prize= (s) and ( f s) and (ff s) and (f f f s)

        = = 87.04 %  

step-by-step explanation: