Answer:
Circumcenter of a triangle is formed by joining the perpendicular bisectors of three sides of triangle.
As we draw perpendicular bisectors of three sides, they will intersect at one point(say O) which lies inside the circle.
From that point of intersection, draw a circle touching each of the vertex of a triangle and we get a circumcircle. And O becomes centre of the circle.
Hence, circumcenter lies inside the triangle.
Answer:
The width of member is as follows:
b = 3 ft
b = 3 × 12 in.
b= 36 in.
The depth of member is as follows:
d = 8 ft
d = 8 × 12 in.
d=96 in.
Since the structure used is Douglas fir-Larch lumber of size 3 × 8 size. Hence, tensile strength, f =1000 psi
Calculate the net area of the member as follows:
A = (b - ∅) × d
A= (36 - 7/8) × 96

Calculate the maximum axial tensile load by ASD method as follows:
P = f × A
P = 1000 x 3372
P = 3372000 lbs
P = 3372 kips
Answer: The running time should at least 119.32 seconds to be in the top 5% of runners.
Step-by-step explanation:
Let X= random variable that represents the running time of men between 18 and 30 years of age.
As per given, X is normally distrusted with mean
and standard deviation
.
To find: x in top 5% i.e. we need to find x such that P(X<x)=95% or 0.95.
i.e. 

Since, z-value for 0.95 p-value ( one-tailed) =1.645
So,
Hence, the running time should at least 119.32 seconds to be in the top 5% of runners.
Answer:
Step-by-step explanation:
We know that normal distribution as special characteristics such as symmetry, unimodal, no skewness, mean =median=mode, etc
A standardized variable for normal variable X is
will be normal with mean =0 and sigma =1
The probability will be divided equally on either side of the mean =0 i.e. y axis
Hence the answers would be
A standardized variable always has a mean of __0_____ and a standard deviation of ___1____. b. The z-score corresponding to an observed value of a variable tells you ____the std normal score.___. c. A positive z-score indicates that the observation is __to the right ____ the mean, whereas a negative z-score indicates that the observation is __to the left_____ the mean
Answer:
see explanation
Step-by-step explanation:
Since the pentagon has one line of symmetry. This will be a vertical line through C, thus
CD = BC = x + 1 and ED = AB = 2x + 3
Perimeter = AE + ED + DC + CB + BA
= 4x + 2x + 3 + x + 1 + x + 1 + 2x + 3 = 10x + 8
Perimeter is given as 21, thus
(b)
10x + 8 = 21 (subtract 8 from both sides )
10x = 13 ( divide both sides by 10 )
x =
= 1.3