Answer:
2 containers should be used
As the system improves, neither more or fewer containers be required
Step-by-step explanation:
According to the given data we have the following:
D=83 pieces per hour.
T=80 minutes=1.33 hour
X=0.18
C=53
In order to calculate how many containers should be used we would have to use the following formula:
Number of containers=<u>DT(1+X)</u>
C
Number of containers=<u>(83)(1.33)(1+0.18)</u>
53
Number of containers=2.45=2
2 containers should be used.
As the system improves, neither more or fewer containers be required
Option D. 96 is the correct answer.
Explanation:
Let the higher grade be = x
Let the lower grade be = y
As given, The difference of the two grades is 16
or .... (1)
The sum of one-eighth of the higher grade and one-half of the lower grade is 52.
... (2)
Putting the value of x=16+y in equation (2)
As x=16+y
x=16+80 = 96
Hence, higher grade is 96.
Answer:
10 five-point questions and 40 two-point questions
Step-by-step explanation:
Let x represent the total number of five-point questions and y represent the total number of two-point questions.
Equation 1: 5x+2y=130
Equation 2: x+y=50
Multiplying Equation 2 by 2: 2x+2y=100 (Equation 3)
(Equation 1) - (Equation 3): 3x=30
x=10
Substituting x=10 into x+y=50: 10+y=50
y=40
Therefore, there are 10 five-point questions and 40 two-point questions.
<h2><u>Check</u></h2>
Substituting x=10 and y=40 into Equation 1:
LHS=5x+2y=5(10)+2(40)=50+80=130
RHS=130
LHS=RHS
Substituting x=10 and y=40 into Equation 2:
LHS=x+y=10+40=50
RHS=50
LHS=RHS
Since in both cases the left-hand side is equal to the right-hand side, the answer is correct.
(LHS: left-hand side, RHS: right-hand side)
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Add sides 3x
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Answer: 289 ft.
Explanation:
You can form a right triangle with these features:
1) Base = adjacent-leg = 500 feet
2) angle between the hypotenuse and the base = 30° ( I use 30° instead of 30', because 30' does not make sense, it is a too small angle)
3) Height = opposite-leg = height of the Statue of LIberty = x
Now, use the equation for the trigonometric ratio tangent:
tan(angle) = opposite-leg / adjacent-leg
=> tan (30°) = x / 500ft
=> x = 500ft * tan(30°)
x = 288.67 ft which rounded to the nearest foot is 289 ft.