If you have a 40% chance of making a free throw, what is the probability of missing a free throw?
2 answers:
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Answer:
1) c ║ d by consecutive interior angles theorem
2) m∠3 + m∠6 = 180° by transitive property
3) ∠2 ≅ ∠5 by definition of congruency
4) t ║ v Corresponding angle theorem
5) ∠14 and ∠11 are supplementary Definition of supplementary angles
6) ∠8 and ∠9 are supplementary Consecutive interior angles theorem
Step-by-step explanation:
1) Statement Reason
m∠4 + m∠7 = 180° Given
m∠4 ≅ m∠6 Vertically opposite angles
m∠4 = m∠6 Definition of congruency
m∠6 + m∠7 = 180° Transitive property
m∠6 and m∠7 are supplementary Definition of supplementary angles
∴ c ║ d Consecutive interior angles theorem
2) Statement Reason
m∠3 = m∠8 Given
m∠8 + m∠6 = 180° Sum of angles on a straight line
∴ m∠3 + m∠6 = 180° Transitive property
3) Statement Reason
p ║ q Given
∠1 ≅ ∠5 Given
∠1 = ∠5 Definition of congruency
∠2 ≅ ∠1 Alternate interior angles theorem
∠2 = ∠1 Definition of congruency
∠2 = ∠5 Transitive property
∠2 ≅ ∠5 Definition of congruency.
4) Statement Reason
∠1 ≅ ∠5 Given
∠3 ≅ ∠4 Given
∠1 = ∠5 Definition of congruency
∠3 = ∠4 Definition of congruency
∠5 ≅ ∠4 Vertically opposite angles
∠5 = ∠4 Definition of congruency
∠5 = ∠3 Transitive property
∠1 = ∠3 Transitive property
∠1 ≅ ∠3 Definition of congruency.
t ║ v Corresponding angle theorem
5) Statement Reason
∠5 ≅ ∠16 Given
∠2 ≅ ∠4 Given
∠5 = ∠16 Definition of congruency
∠2 = ∠4 Definition of congruency
EF ║ GH Corresponding angle theorem
∠14 ≅ ∠16 Corresponding angles
∠14 = ∠16 Definition of congruency
∠5 = ∠14 Transitive property
∠5 + ∠11 = 180° Sum of angles on a straight line
∠14 + ∠11 = 180° Transitive property
∠14 and ∠11 are supplementary Definition of supplementary angles
6) Statement Reason
l ║ m Given
∠4 ≅ ∠7 Given
∠4 = ∠7 Definition of congruency
∠2 ≅ ∠7 Alternate angles
∠2 = ∠7 Definition of congruency
∠2 = ∠4 Transitive property
∠2 ≅ ∠4 Definition of congruency
∠2 and ∠4 are corresponding angles Definition
DA ║ EB Corresponding angle theorem
∠8 and ∠9 are consecutive interior angles Definition
∠8 and ∠9 are supplementary Consecutive interior angles theorem.
This question is Incomplete because it lacks the diagram showing the containers as well as the required options. Find attached to this answer the appropriate diagram.
Complete Question
Aluminium coated dewars are cylindrical flasks used to safely store and transport liquid nitrogen, dry ice etc. A company manufactures such dewars of different sizes. Shown here are two dewars, both of the same height but of different diameters. How much aluminium will be required to cover Dewar A compared to that required for Dewar B? (Note: The base and the lid are NOT made up of aluminium.)
A) 1/3 times
B) 3 times
C) 9 times
D) The same amount of aluminum will be required.
Answer:
B) 3 times
Step-by-step explanation:
From the question, we are told that we are to find the amount of aluminum to cover Dewar A and B , we are also told that the base and the lid are not covered with aluminum.
From this information, we can determine that we are to find the curved or Lateral surface area of the cylinder because the base and lid are not included
The curved surface area of a cylinder is calculated as 2πrh
We told that both cylinders have the same height. Hence,
For Dewar A
We have Diameter of 30 cm, radius = Diameter ÷ 2 = 30cm ÷ 2 = 15cm.
Height = h
The curved surface area = 2πrh
= 2 × π × 15 ×h
= 30πhcm²
For Dewar B
We have Diameter of 10 cm, radius = Diameter ÷ 2 = 10cm ÷ 2 = 5cm.
Height = h
The curved surface area = 2πrh
= 2 × π × 5 ×h
= 10πhcm²
When we compare the curved surface Dewar A to the curved surface area of Dewar B
Dewar A : Dewar B
30πhcm² : 10πhcm²
3(10πhcm²) : 10πhcm²
From the above comparison, we can see that 3 times more aluminum is required to cover Dewar A compared to Dewar B.
