Given the event "a die lands with a 6 on top", which of the following is the complement of this event? choose the correct answer below.
a. the number of times the die lands with a 6 on top in n throws of the die
b. the die lands with a 3 on the top
c. the die lands with a 6 on the bottom
d. the die lands with a 1, 2, 3, 4, or 5 on top

The die lands with a 1, 2, 3, 4, or 5 on top ⇒ answer D

Step-by-step explanation:

- Complementary events are two outcomes of an event that are the

 only two possible outcomes

- The Complement Rule states that the sum of the probabilities of

  an event and its complement must equal 1

- P(A) + P(A') = 1

- Lets solve the problem

- The event A is:

  " a die lands with a 6 on top "

∴ P(A) =

∵ P(A) + P(A') = 1

∴ + P(A') = 1

- Subtract from both sides

∴ P(A') =

∵ The die has six numbers from 1 to 6

∴ The other numbers than 6 are 1 , 2 , 3 , 4 and 5

∴ The complement of event A is:

   " A die lands with 1 , 2 , 3 , 4 or 5 "

* The complement of the event is:

 The die lands with a 1, 2, 3, 4, or 5 on top

168

step-by-step explanation:

i am pretty sure that the answer is 168

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.