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1 answer:
Hi there!
53)
The altitude of a triangle is always perpendicular to the base, therefore:
5x° must equal 90°.
Solve for x:
5x = 90
5x / 5 = 90 / 5 ----> x = 18
KL is equal to 2x - 5, so plug the value of x into the equation:
KL = 2(18) - 5
KL = 36 - 5 ---> KL = 31
54)
A median bisects the base, therefore:
AD ≅ DC
Set both equations equal to each other:
3x = 2x + 1
Subtract 2x from both sides:
x = 1
Plug in the value of x into the equation for DC:
2(1) + 1 = 3.
DC = 3.
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Answer:
(a) 0.00605
(b) 0.0403
(c) 0.9536
(d) 0.98809
Step-by-step explanation:
We are given that 40% of first-round appeals were successful (The Wall Street Journal, October 22, 2012) and suppose ten first-round appeals have just been received by a Medicare appeals office.
This situation can be represented through Binomial distribution as;
where, n = number of trials (samples) taken = 10
r = number of success
p = probability of success which in our question is % of first-round
appeals that were successful, i.e.; 40%
So, here X ~
(a) Probability that none of the appeals will be successful = P(X = 0)
P(X = 0) =
= = 0.00605
(b) Probability that exactly one of the appeals will be successful = P(X = 1)
P(X = 1) =
= = 0.0403
(c) Probability that at least two of the appeals will be successful = P(X>=2)
P(X >= 2) = 1 - P(X = 0) - P(X = 1)
= 1 -
= 1 - 0.00605 - 0.0403 = 0.9536
(d) Probability that more than half of the appeals will be successful = P(X > 0.5)
For this probability we will convert our distribution into normal such that;
X ~ N()
and standard normal z has distribution as;
Z = ~ N(0,1)
P(X > 0.5) = P( >
) = P(Z > -2.26) = P(Z < 2.26) = 0.98809
3=x
-4=y
sin0= 4/5
cos0=3/5
tan0=4/3
Answer:
Radius of the sphere =
Step-by-step explanation:
Volume of a sphere is :
For, Volume =
As,
The radius of the sphere is :