Answer:
x =5.1
Step-by-step explanation:
For the angle 82, we know the adjacent side and the opposite side
tan 82 = opposite/ adjacent
tan 82 = 36/x
Multiply by x on each side
x tan 82 = 36/x*x
x tan 82 =36
Divide by tan 82
x tan 82/ tan 82 = 36 / tan 82
x = 36/ tan 82
x=5.059470049
To the nearest tenth
x =5.1
IQR = 40
1) Put the numbers in order: 40, 45, 50, 60, 60, 75, 90, 90, 120
2) Find the median: Median is 60 (the 2nd one)
3) Place parentheses around the numbers above and below the median. For easy identification of Q1 and Q3. (40, 45, 50, 60,) 60, (75, 90, 90, 120)
4) Find the Q1 and Q3. Q1 = median of the lower half of the data; Q3 = median of the higher half of the data. Q1 and Q3 have even sets so its median cannot be defined.
5) Had both sets contain odd sets, the median of Q1 is subtracted from the median of Q3 to get the IQR.
We can then use the Alternative definition of IQR.
IQR is the difference between the largest and smallest values in the middle 50% of a set data.
40, 45, 50, 60, 60, 75, 90, 90, 120
Middle 50% is 50, 60, 60, 75, 90; IQR = Largest value - smallest value;
IQR = 90 - 50 = 40
Remark
The equation is job1/ time + job2/time = job3/time
Discussion
job one is the time it takes one of the workers to complete the job.
job two is the time it takes the other workers to complete the job
job three is the time it takes to do the job together.
Givens.
Let Marcus's time = m
Let Tony's time be =t
Let their together time = t1
Equation Substitution and solution.
1/m + 1/t = 1/t1
1/6 + 1/4 = 1/t1 The common denominator on the left is 12.
2/12 + 3/12 = 1 / t1
5/12 = 1/t1 Cross multiply.
5*t1 = 12 Divide by 5
t1 = 12/5
t1 = 2 2/5
t1 = 2.4 hours
Cost
1 hour = 43 dollars for labor.
2.4 hours = x dollars for labor.
1*x = 43 * 2.4
x = 103.2 dollars. <<<<< Answer
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