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2 answers:
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Answer:
P(N = n) =
Step-by-step explanation:
to find out
Find the PMF PN (n)
solution
PN (n)
here N is random variable
and n is the number of times
so here N random variable is denote by the same package that is N (P)
so here
probability of N is
P(N ) = Ф ( N = n) .................. 1
here n is = 1, 2,3, 4,...................... and so on
so that here P(N = n) will be
P(N = n) =
m∠1 = 30° (by Vertical angle theorem)
m∠A = 80° (by Triangle sum theorem)
m∠D = 80° (by Triangle sum theorem)
The value of x is 7.5 and y is 9.
Solution:
∠ACB and ∠DCE are vertically opposite angles.
Vertical angle theorem:
<em>If two lines are intersecting, then vertically opposite angles are congruent.</em>
⇒ m∠DCE = m∠ACB
⇒ m∠1 = 30° (by Vertical angle theorem)
In triangle ACD,
Triangle sum property:
<em>Sum of the interior angles of the triangle = 180°</em>
⇒ m∠A + m∠C + m∠B = 180°
⇒ m∠A + 30° + 70° = 180°
⇒ m∠A + 100° = 180°
⇒ m∠A = 100° – 180°
⇒ m∠A = 80° (by Triangle sum theorem)
Similarly, m∠D = 80° (by Triangle sum theorem)
In ΔACD and ΔDCE,
All the angles are congruent, so ΔACD and ΔDCE are similar triangles.
<em>In similar triangle corresponding sides are in the same ratio.</em>
Do cross multiplication.
90 = 12x
7.5 = x
Now, to find y:
Do cross multiplication.
9y = 72
Divide by 9, we get
y = 8
Hence the value of x is 7.5 and y is 9.
See the attached drawing for a visual.
Since we know that AC = CB is half the length of AB, we can write that in equation form. The goal is to determine the length of
Now that we know the value of , we can find the value of
: