Answer:
Kelvin miscalculated and wrote 60 incorrectly.
He should have calculated $30.65 minus 60% instead of using 0.60.
The accurate final equation is:
$30.65 - 60% = 12.26
Response:
Detailed explanation:
Probability for an event is calculated as the ratio of the size of the event space compared to that of the sample space.
The sample space encompasses all possible outcomes.
Event space represents the number of favorable outcomes for the event in question.
Thus
Let
x ------> size of event space
y ----- → size of sample space
so
Calculate the probability of the first student being left-handed
we have
substituting values
Simplify
Calculate the probability of the second student being left-handed
we have
substituting values
Calculate the probability that both selected students will be left-handed
Multiply the probabilities together.
Convert to percentage
Multiply by 100
Assuming arcs are measured in degrees, let S represent the following sum:
S = sin 1° + sin 2° + sin 3° +... + sin 359° + sin 360°
By rearranging, S can be reformulated as
S = [sin 1° + sin 359°] + [sin 2° + sin 358°] +... + [sin 179° + sin 181°] + sin 180° +
+ sin 360°
S = [sin 1° + sin(360° – 1°)] + [sin 2° + sin(360° – 2°)] +... + [sin 179° + sin(360° – 179)°]
+ sin 180° + sin 360° (i)
However, for any real k,
sin(360° – k) = – sin k
Thus,
S = [sin 1° – sin 1°] + [sin 2° – sin 2°] +... + [sin 179° – sin 179°] + sin 180° + sin 360°
S results in 0 + 0 +... + 0 + 0 + 0 (... since sine of 180° and 360° are both equal to 0)
Therefore, S equals 0.
Each pair within the brackets negates itself, leading the sum to total zero.
∴ sin 1° + sin 2° + sin 3° +... + sin 359° + sin 360° equals 0. ✔
I hope this clarifies things. =)
Tags: sum summatory trigonometric trig function sine sin trigonometry
Answers:
C - The value of w cannot be negative.
D - The variable l is substituted with the value 20.
E - To isolate the variable w, the subtraction property of equality is applied.
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