Answer:
Step-by-step explanation:
Answer:
The answer is D. 1/5
Step-by-step explanation:
Let´s write equation for each of the senteneces in the question:
- Alice saved the same fraction for her take-home pay (THP) each month => Savings_month = X*THP, where "X" is the fraction of the THP she saves.
- She saved 3 times the amount of money she didn´t save by the end of 12 months => Savings_12months = 12*X*THP = 3*Y*THP, where "Y" is the fraction of the money she did not save
- We can also conclude that the THP is the sum of her savings and what she did not save => THP = X*THP + Y*THP
We have 2 equations:
THP is on both sides on both equations, that means we can divide the equation on both sides by THP to get rid of it and have easier to read equations:
- 12X = 3Y
- 1 = X + Y
From equation 1, solve for Y and we get the following:
Substitute Y in equation 2:
Solve for X:
We know that X is the fraction of THP Alice is saving, therefore the answer is D.
Answer:
13,260.22 mm²
Step-by-step explanation:
the area of the shaded region is the area of the larger circle minus the area of the smaller one
to find the area of the larger we will use half of 62 plus 41 as the radius:
Area (larger) = 3.14(72)²
= 16,277.76
Area (smaller) = 3.14(31)²
= 3,017.54
Area (shaded region) is 16277.76 - 3017.54 = 13,260.22 mm²
The reference angle is the angle made with the x-axis. For two points to have the same reference angle, they would need to have the same absolute value of their tangents = y/x.
For the first pair of points: the first point has a tangent value of 1/sqrt(3), while the second has a tangent value of sqrt(3), so these are not identical.
For the second pair of points: the first point has a tangent value of -sqrt(3), while the second has a tangent value of -1/sqrt(3), so these are
not identical.
For the third pair of points: the first point has a tangent value of sqrt(3), while the second also has a tangent value of sqrt(3), so these have the same reference angle.
For the fourth pair of points: the first point has a tangent value of
1/sqrt(3), while the second has a tangent value of sqrt(3), so these are
not identical.
So the only correct answer is the third choice.