If P is the incenter of triangle JKL, find the measure of JKP.
1 answer:
Answer:
m∠JKP = 31.5°
Step-by-step explanation:
Incenter of a triangle is the point where all the bisectors of interior angles intersect each other.
JN is the angle bisector of ∠KJL.
Therefore, m∠KJN = m∠LJN
(7x - 6) = (5x + 4)
7x - 5x = 6 + 4
2x = 10
x = 5
m∠KJN = (7x - 6)
= 7(5) - 6
= 35 - 6
= 29°
In ΔKJN,
m∠JKN + m∠KNJ + m∠NJK = 180°
m∠JKN + 90° + 29° = 180°
m∠JKN = 180°- 119° = 61°
Since KO is the angle bisector of ∠JKN,
m∠JKP =
=
= 30.5°
You might be interested in
Answer:
The probability that at least two stocks will have a return of more than 12% is 0.1810.
Step-by-step explanation:
Let <em>X</em> = rate of return on stocks.
The random variable <em>X</em> follows a Normal distribution, N (9, 3²).
Compute the probability that a stock has rate of return more than 12% as follows:
**Use the <em>z</em> table for the probability.
The probability of a stock having rate of return more than 12% is 0.1587.
Now define a random variable <em>Y</em> as the number of stocks that has rate of return more than 12%.
The sample size of stocks selected is, <em>n</em> = 5.
The random variable <em>Y </em>follows a Binomial distribution.
The probability of a Binomial distribution is:
Compute the value of P (X ≥ 2) as follows:
P (X ≥ 2) = 1 - P (X < 2)
= 1 - P (X = 0) - P (X = 1)
Thus, the probability that at least two stocks will have a return of more than 12% is 0.1810.