Answer:
The 95% confidence interval is 
Step-by-step explanation:
From the question we are told that
The sample mean difference is 
The standard error is SE = 0.03
Given that the confidence interval is 95% then the level of significance is mathematically evaluated as
Next we obtain the critical value of 
from the normal distribution table, the value is 
Generally the margin of error is mathematically represented as
substituting values
The 95% confidence interval is mathematically represented as
substituting values
Answer:
3/8
Step-by-step explanation:
8/8 - 5/8 = 3/8
Answer:
Option (2). x = 20°
Step-by-step explanation:
In the figure attached,
ΔABC is an equilateral triangle.
By the property of equilateral triangle, all sides of the triangle are equal and measure of all angles of the triangle is 60°.
By this property,
m∠B = 60°
and y = 46 - 16 = 30
By applying Sine rule in ΔBCD,
sin(∠CBD) = 
= 0.6423
m∠CBD = 39.96
≈ 40°
m∠ABD = 60° - 40°
= 20°
Therefore, Option (2). 20° will be the answer.
Answer:
volume of xy-plane outside the cone = 16π/3
Step-by-step explanation:
using cylindrical coordinates
z² = x² +y² =====>z²=r²=====>z=r
x² + y² =4 ====>r = 2
So, the volume ∫∫∫dV equal
∫(θ = 0 to 2π) ∫(r = 0 to 2) ∫z=0 to r) 1 x (r dz dr dθ) via cylindrical coordinates
= ∫(θ = 0 to 2π) ∫(r = 0 to 2) r² dr dθ
= ∫(θ = 0 to 2π) (1/3)r³ {for r = 0 to 2} dθ
= 2π x 8/3
= 16π/3
Okay, so you see that linear pair formed of angle 1,2,3
Now <1 = <5 and <3 = <6
So if 1 = 5, and 3 = 6
We also know that linear pair has 180 degrees and Hence proved angle 6,5 and 2 is equal to 180 degrees
