What is the volume of a sphere with a radius of 12 units?
1 answer:
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Answer:
interval = [17.3948 , 20.6052]
Step-by-step explanation:
given,
random sample (n) = 45
average product lifespan = 19 years
standard deviation = 4 years
confidence interval of 99 % = ?
we know,
t* = qt(1.99/2 + 44 ) = qt(0.995,44)
t* = 2.692
so,
interval
interval = [19 - 1.6052 , 19 + 1.6052]
interval = [17.3948 , 20.6052]
Answer:
" Vertical angles are congruent " ⇒ 2nd answer
Step-by-step explanation:
* <em>Look to the attached figure </em>
- There are three lines intersected at point D
- We need to find the missing in step 3
∵ Line FA intersects line EC at point D
- The angles formed when two lines cross each other are called
vertical angles
- Vertical angles are congruent (vertical angles theorem)
∴ ∠ADC and ∠FDE are vertical angles
∵ Vertical angles are congruent
∴ ∠EDF ≅ ∠ADC
∴ m∠EDF ≅ m∠ADC
∵ m∠EDF = 120° ⇒ given
∵ m∠ADC = m∠ADB + m∠BDC
∴ m∠ADB + m∠BDC = 120°
∵ m∠ADB = (3x)° ⇒ given
∵ m∠BDC = (2x)° ⇒ given
∴ 3x + 2x = 120 ⇒ add like terms
∴ 5x = 120 ⇒ divide both sides by 5
∴ x = 24
Column (1) Column (2)
m∠EDF = 120° given
m∠ADB = 3 x given
m∠BDC = 2 x given
∠EDF and ∠ADC are vertical angles defin. of vert. ∠s
∠EDF is congruent to ∠ADC vertical angles are
congruent
m∠ADC = m∠ADB + m∠BDC angle add. post.
m∠EDF = m∠ADC defin. of cong.
m∠EDF = m∠ADB + m∠BDC substitution
120° = 3 x + 2 x substitution
120 = 5 x addition
x = 24 division
∴ The missing reason is " vertical angles are congruent "
- From the explanation above ∠ADC and ∠FDE are vertical
angles then they are congruent according to vertical angle
theorem
