Answer: 114°
Step-by-step explanation:
<h2>Concept: </h2>
Here, we need to know the idea of the "Exterior Angle theorem".
<u>The exterior angle theorem</u> states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles of the triangle.
If you are still confused, then refer to the attachment below for a graphical explanation.
<h2>Solve:</h2>
Given
24 + (2x + 18) = 3x + 6
Put like terms together
24 + 18 + 2x = 3x + 6
Combine like terms
42 + 2x = 3x + 6
Subtract 6 on both sides
42 + 2x - 6 = 3x + 6 - 6
36 + 2x = 3x
Subtract 2x on both sides
36 + 2x - 2x = 3x - 2x
x = 36
Exterior angle = 3x + 6 = 3(36) + 6 = 114°
Hope this helps!! :)
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The probability of a randomly selected hard drive from the company lasting between 2 years 3 months and 3 years 3 months is 32.22%
Given here,
Mean (μ) = 3 years 6 months
= (3×12)+6 = 42 months
Standard deviation (σ) = 9 months
We will find the z-score using the formula: z = (X - μ)/σ
Here X₁ = 2 years 3 months
= (2×12)+3 = 27 months
and X₂ = 3 years 3 months
= (3×12)+3 = 39 months
So, z (X₁ =27) = 
and z (X₂ =39) = 
According to the standard normal table,
P(z> -1.666...) = 0.0485 and P(z< -0.333...) = 0.3707
So, P(27 < X < 39)
= 0.3707 - 0.0485
= 0.3222
= 32.22 % [Multiplying by 100 for getting percentage]
So, the probability of a randomly selected hard drive from the company lasting between 2 years 3 months and 3 years 3 months is 32.22%
We are interested in selecting 2 people from the 7-person task force.
n = 7
r = 2
nPr = n! / (n-r)!
7!
------
(7-2)!
=
7!
----
5!
7×6×5×4×3×2×1
------------------------
5×4×3×2×1
= 7×6
= 42
Answer:
difference in the proportion = 0.0452
Step-by-step explanation:
x1 = 27, n1 = 193,
p1 = 27/193
p1 = 0.1399
x2 = 16, n2 = 169,
p2 = 16/169
p2 = 0.0947
a) The best estimate for the difference in the proportion of smokers, using male proportion minus female proportion is 0.0452. Male smokes more than females in given sample.
p1 - p2 = 0.1399 - 0.0947
p1 - p2 = 0.0452
