Answer:
Refer below
Step-by-step explanation:
a) a and b are the lower and higher values of the interval for which uniform distribution is defined.
Here a= 6 and b =10
b) Mean of the uniform distribution= (a+b)/2 = (6+10)/2 =8
Or int x (1/4) dx = x^2/8 = 8
c) Variance of the uniform distribution = (b^2-a^2)/12 = (100-64)/12
= 36/12 =3
Std dev = sq rt of 3 = 1.732
d) To find total area
PDF of the distribution = 1/(b-a) = 1/4, 6<x<10
Area = \int 6 to 10 of 1/4 dx
= x/4
Subtitute limits
= (10-6)/4 =1
So total area = 1
d)P(X>7) = int 7 to 10 of 1/4 dx = 3/4
e) P(7<x<9) = Int 7 to 9 of 1/4 dx = 2/4 = 1/2
Answer: statement 2: a square is always a rhombus.
Step-by-step explanation:
A parallelogram does not have all the interior angle as right angle.
Therefore, it does not satisfy property of rectangle.
A square has all sides equal and its diagonals are perpendicular bisector.
Thus, square satisfies all the properties of rhombus .
A rectangle does not have all the sides are equal.
Therefore, it cannot b e a square.
Answer:
3 inches
Step-by-step explanation:
(14+2x) × (15+2x) = 2(14×15)
210 +30x +28x + 4x² = 420
4x² + 58x - 210 = 0
2x² + 29x - 105 = 0
2x² + 35x - 6x - 105 = 0
x(2x + 35) - 3(2x + 35) = 0
(x - 3)(2x + 35) = 0
x = 3, -35/2(not possible)
Answer:
∠B = 41°
Step-by-step explanation:
∠BCD is an exterior angle of the triangle
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠A and ∠ B are the 2 opposite interior angles, hence
∠A + ∠B = 113, that is
72 + ∠B = 113 ( subtract 72 from both sides )
∠B = 41°
