The area of the square is 9 in^2
The side of a square is the square root of the area.
Side of square = √9 = 3 inches.
The side of the square is the diameter of the inscribed circle.
Circumference of a circle is PI x diameter.
Circumference of inscribed circle = 3.14 x 3 = 9.42 inches
The diameter for the circumscribed circle would be the diagonal of the square which is 3√2 = ( Side length x √2) ≈ 4.2426
The circumference = 3.14 x 3√2 = 13.321
Find the ratio between the two circles:
Circumscribed / inscribed =
13.321 / 9.42 = 1.41
Answer: Angles are supplementary if and only if their sum is 180° is true.
Step-by-step explanation:
Test by making both parts negative: Angles are not supplementary if and only if their sum is not 180° This is also true.
Answer: D) vertical angles theorem, alternate interior angles theorem
Angle 5 = Angle 6 by the alternate interior angles theorem
Angle 5 = angle 4 by the vertical angles theorem
By the transitive property, we can then say angle 4 = angle 6. These angles are also corresponding angles.
We won't use the angle addition theorem or the right angles theorem.
Answer:
the 99% confidence interval for the true mean number of mosquitos caught in all mosquito traps is ( 667.81, 732.19 )
Step-by-step explanation:
Given the data in the question;
sample mean x' = 700
sample size n = 64
the standard deviation σ = 100
99% confidence interval for the true mean number of mosquitos caught in all mosquito traps = ?
significance level ∝ = 1 - 99% = 1 - 0.99 = 0.01
∝/2 = 0.01 / 2 = 0.005
Z-critical = 2.575 { from table }
So, to get the 99% confidence interval;
⇒ x' ± ( σ / √n )
we substitute
⇒ 700 ± 2.575 ( 100 / √64)
⇒ 700 ± 2.575( 12.5 )
⇒ 700 ± 32.1875
⇒ ( 700 - 32.1875 ), ( 700 + 32.1875 )
⇒ ( 667.81, 732.19 )
Therefore, the 99% confidence interval for the true mean number of mosquitos caught in all mosquito traps is ( 667.81, 732.19 )