See the attached image for the drawings of the 45-45-90 triangle and the 30-60-90 triangle.
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For the 45-45-90 triangle, the two legs are both 3 while the hypotenuse is unknown. Call it x for now.
Using trig we can say
sin(angle) = opposite/hypotenuse
sin(A) = BC/AC
sin(45) = 3/x
sqrt(2)/2 = 3/x
sqrt(2)*x = 2*3
sqrt(2)*x = 6
x = 6/sqrt(2)
x = (6/sqrt(2))*(sqrt(2)/sqrt(2))
x = (6*sqrt(2)/(sqrt(2)*sqrt(2))
x = (6*sqrt(2)/(2)
x = 3*sqrt(2)where "sqrt" is shorthand for "square root"
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For the 30-60-90 triangle, we can say
cos(angle) = adjacent/hypotenuse
cos(D) = DE/FD
cos(60) = 4/y
1/2 = 4/y
1*y = 4*2
y = 8and we can also say
sin(angle) = opposite/hypotenuse
sin(D) = EF/FD
sin(60) = z/y
sin(60) = z/8
8*sin(60) = z
z = 8*sin(60)
z = 8*sqrt(3)/2
z = (8/2)*sqrt(3)
z = 4*sqrt(3)
Answer:
i think 3.5 gallons per week
Step-by-step explanation:
15 gallons every 30 days
x gallons per weeks (7 days)
15×7 = 30x
105 = 30x
105/30 = x
3.5 = x
answer as a mixed number in simplest form = 3 1/2
I love your name it it so great
Answer:
Y does not have a binomial distribution since p, the probability of being a binge drinker, is not the same for all the trials.
Step-by-step explanation:
For a binomial distribution, condition required include :
A fixed number of trials ; Here the number of trials is 20 ; hence, this condition is met.
Each trial must be independent : yes, it is independent as a selected individual could either be a binge drinker or not. The outcome of each trial is either a success or a failure ; being a drinker or not.
However, the probability of being a binge drinker (that is probability of success) could vary for male and female. The probability of male being a binge drinker is 0.21 while that if female isn't specified, this probability, p value should be the same for all trials. Hence, with this value not being the same for all trials, the binomial probability condition is violated.
2-i. Complex roots always come in pairs (complex conjugates)