The volume, V, of any cube with a side length, s, can be determined using the formula V=s3. What is the volume, in cubic centime
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Answer:
The 99% confidence interval is
Step-by-step explanation:
From the question we are told that
The sample size is n = 100
The sample mean is
The population standard deviation is
From the question we are told the confidence level is 99% , hence the level of significance is
=>
Generally from the normal distribution table the critical value of is
Generally the margin of error is mathematically represented as
=>
Generally 95% confidence interval is mathematically represented as
=>
=>
If we draw the diagonals of the octagonal gazebo, the 4 diagonals divide the octagon into 8 triangles.
Note that each triangle is an isosceles triangle whose equal sides are x, the radius of the circle.
The top angle of each triangle is obtained by dividing the full angle by 8.
So, each top angle =
= 45°
Now, in fig., consider one of the triangles Δ OAB. Draw an altitude OC from O to the opposite side AB.
This altitude OC bisects the top angle 45°.
Therefore, ∠ AOC = 22.5°.
Now, in Δ AOC,
So, AC = x sin 22.5°
Note that, AB = 2 AC.
Therefore, AB = 2x sin 22.5°.
Also,
So, OC = x cos 22.5°.
Area of Δ AOB =
= × (2x sin 22.5°) × (x cos 22.5°)
= (2 sin 22.5° cos 22.5°)
= sin 45°
= /
Area of the octagonal gazebo = 8 × one triangular area
= 8 × ( /
)
Area required for mulch = circular area - area of the gazebo
Now, cost per unit area = $1.50.
Hence, total cost g(m) = area × cost per unit area
Total cost g(m) = × 1.5
Hence, total cost g(m) = .
