If you cut a 12-inch loaf of bread into1/2 -inch slices, you would have slices of bread.
2 answers:
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BC is 10 units and AC is units
Step-by-step explanation:
Let us revise the sine rule
In ΔABC:
- AB is opposite to ∠C
- BC is opposite to ∠A
- AC is opposite to ∠B
Let us use this rule to solve the problem
In ΔABC:
∵ m∠A = 45°
∵ m∠C = 30°
- The sum of measures of the interior angles of a triangle is 180°
∵ m∠A + m∠B + m∠C = 180
∴ 45 + m∠B + 30 = 180
- Add the like terms
∴ m∠B + 75 = 180
- Subtract 75 from both sides
∴ m∠B = 105°
∵
∵ AB =
- Substitute AB and the 3 angles in the rule above
∴
- By using cross multiplication
∴ (BC) × sin(30) = × sin(45)
∵ sin(30) = 0.5 and sin(45) =
∴ 0.5 (BC) = 5
- Divide both sides by 0.5
∴ BC = 10 units
∵
- Substitute AB and the 3 angles in the rule above
∴
- By using cross multiplication
∴ (AC) × sin(30) = × sin(105)
∵ sin(105) =
∴ 0.5 (AC) =
- Divide both sides by 0.5
∴ AC = units
BC is 10 units and AC is units
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Answer:
a) 240 ways
b) 12 ways
c) 108 ways
d) 132 ways
e) i) 0.55
ii) 0.4125
Step-by-step explanation:
Given the components:
Receiver, compound disk player, speakers, turntable.
Then a purcahser is offered a choice of manufacturer for each component:
Receiver: Kenwood, Onkyo, Pioneer, Sony, Sherwood => 5 offers
Compact disc player: Onkyo, Pioneer, Sony, Technics => 4 offers
Speakers: Boston, Infinity, Polk => 3 offers
Turntable: Onkyo, Sony, Teac, Technics => 4 offers
a) The number of ways one component of each type can be selected =
b) If both the receiver and compact disk are to be sony.
In the receiver, the purchaser was offered 1 Sony, also in the CD(compact disk) player the purchaser was offered 1 Sony.
Thus, the number of ways components can be selected if both receiver and player are to be Sony is:
c) If none is to be Sony.
Let's exclude Sony from each component.
Receiver has 1 sony = 5 - 1 = 4
CD player has 1 Sony = 4 - 1 = 3
Speakers had 0 sony = 3 - 0 = 3
Turntable has 1 sony = 4 - 1 = 3
Therefore, the number of ways can be selected if none is to be sony:
d) If at least one sony is to be included.
Number of ways can a selection be made if at least one Sony component is to be included =
Total possible selections - possible selections without Sony
= 240 - 108
= 132 ways
e) If someone flips switches on the selection in a completely random fashion.
i) Probability of selecting at least one Sony component=
Possible selections with at least one sony / Total number of possible selections
ii) Probability of selecting exactly one sony component =
Possible selections with exactly one sony / Total number of possible selections.