Answer:
See the attached figure which represents the problem.
As shown, AA₁ and BB₁ are the altitudes in acute △ABC.
△AA₁C is a right triangle at A₁
So, Cos x = adjacent/hypotenuse = A₁C/AC ⇒(1)
△BB₁C is a right triangle at B₁
So, Cos x = adjacent/hypotenuse = B₁C/BC ⇒(2)
From (1) and (2)
∴ A₁C/AC = B₁C/BC
using scissors method
∴ A₁C · BC = B₁C · AC
Answer:
Part A) Circumference
Part B)
Part C) The distance traveled in one rotation is 628.32 feet
Step-by-step explanation:
Part A) we know that
The distance around the circle is equal to the circumference.
The Ferris Wheel have a circular shape
so
To find out the distance around the Ferris Wheel you should use the circumference
Part B) What is the formula needed to solve this problem?
we know that
The circumference is equal to multiply the number π by the diameter of the circle
so
Part C) What is the distance traveled in one rotation?
we know that
One rotation subtends a central angle of 360 degrees
The distance traveled in one rotation is the same that the circumference of the Ferris wheel
we have
----> diameter of the Ferris wheel
substitute in the formula of circumference
assume
therefore
The distance traveled in one rotation is 628.32 feet
Answer:
a) H0 : P = 0.07
Ha : P ≠ 0.07
b) p -value = 0.1770
Step-by-step explanation:
P = 7% = 0.07
x (result ) = 7 , n = 163
p = x / n = 7 / 163 = 0.043
<u>a) Using a significance level ( ∝ ) of 0.05, estimate the appropriate hypothesis</u>
H0 : P = 0.07
Ha : P ≠ 0.07
conduct a Z- test statistic
Z = ( p - P ) /
= ( 0.043 - 0.07 ) / = - 1.35
Critical value ( Z₀.₀₂₅ ) = ± 1.96
<em>we fail to reject H0 given that | z | < Zcritical because there is not enough evidence to conclude that proportion change</em>
<u>b) Determine the p-value of the test </u>
P-value = P ( | Z | > Z )
= 2 * P ( Z < -1.35 )
= 0.1770
The p-value ( 0.1770 ) > ∝ ( 0.05 ) hence we fail to reject H0 ( i.e. the conclusion agrees with part a above )