In the above figure, m∠p = 105° and m∠q = 5x. if angles p and q are supplementary angles, what is the value of x and the measure of angle q? a. x = 15, m∠q = 20° b. x = 15, m∠q = 75° c. x = 57, m∠q = 75° d. x = 39, m∠q = 195°

B. x = 15, m∠Q = 75°

Step-by-step explanation:

Given:

m∠P = 105°

m∠Q =

Angles P and Q are supplementary angles

To find value of and m∠Q.

Solution:

    [Sum of supplementary angles =180°]

  [Substitution ∵ m∠P = 105° and m∠Q = ]

Subtracting both sides by 105°.

Dividing both sides by 5.

∴

∴

The correct option is option [B].

The probability that both girls Selena and Tracey will a next at bat is .

Step-by-step explanation:

Independent events:

If A and B are event. The occurrence of one of them does not affect the outcomes of other event. Then A and B are independent events.

P(A and B) =P(A)× P(B)

Dependent events:

If A and B are event. The outcomes of one of them affects the outcomes of other event. Then A and B are called dependent events.

P(A and B) =P(A)× P(B|A)= P(B)×P(A|B)

Given that,

Selena has 8 hits out of 20 times at bat.

The number of hits by Tracey out of 16 is 6 at bat.

A= Selena hits a softball.

B= Tracey hits a softball.

The probability that the Selena his a softball is

=P(A)

The probability that the Tracey his a softball is

=P(B)

Both event are independent. Sine the events do not affect the outcomes of other event.

The probability that both girls will a next at bat is

=P(A and B)

=P(A)×P(B)