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Mathematics

1 answer:

Marina86 [1]3 years ago

8 0

1. Given that we have 4 green marbles, 4 pink marbles and 5 orange marbles, let us first find the probability that we select a pink marble.

We can find this by taking the number of pink marbles and dividing it by the total number of marbles:

Pr(P) = 4/(4 + 4 + 5)

= 4/13

2. Now that we have chosen one pink marble, we must find the probability that we choose an orange marble from the remaining marbles (4 green, 3 pink, 5 orange):

Pr(O) = 5/(4 + 3 + 5)

= 5/12

3. If we want to find the probability of picking a pink marble and then an orange marble, we must multiply the probabilities we have found in the first two steps:

Pr(P)*Pr(O) = (4/13)*(5/12)

= 20/156

= 5/39

Therefor, there is a probability of 5/39 that you pick a pink and then an orange marble.

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konstantin123 [22]

Consider the given parallelogram KLMN.

Prove: $\angle N \cong \angle L, \angle K \cong \angle M$

Statement Reason

1. $KL \parallel NM, KN \parallel LM$ Definition of parallelogram

2. $\angle K+ \angle N = 180^\circ$ Same Side interior angle theorem

$\angle L+ \angle M = 180^\circ$

$\angle K+ \angle L = 180^\circ$

3. $\angle K+ \angle N=\angle K+ \angle L$ Substitution property

$\angle L+ \angle M=\angle K+ \angle L$

4. $\angle N = \angle L$ Subtraction property of equality

$\angle M = \angle K$

Subtraction property of equality tells us that if we subtract some number from one side of an equation, we also must subtract from the other side of the equation to keep the equation the same.

5. $\angle N \cong \angle L$ Angle Congruence Postulate