An object falls 9 meters during the first second, another 27 meters during the second second, and then 81 meters more during the third second. If this pattern continues, how far does the object fall during the first 4 seconds?
A. 117
B. 360
C.426
D.980
A mother is convinced by her son that he should have a weekly allowance that is doubled every 2 weeks. In weeks 1 and 2 he receives 1¢ per week; in weeks 3 and 4 he receives 2¢ per week. If his allowance continues to double every 2 weeks, what is the amount of his allowance in week 30 (rounded to the nearest cent) and what is the total amount he receives in allowance for the 30 weeks (rounded to the nearest cent)?
A. The son receives $163.84 in week 30 and he accumulates $655.34 in total for the 30 weeks.
B. The son receives $32,768.00 in week 30 and he accumulates $65,534.00 in total for the 30 weeks.
C. The son receives $157.24 in week 30 and he accumulates $555.24 in total for the 30 weeks.
D. The son receives $60.00 in week 30 and he accumulates $1,800.00 in total for the 30 weeks.
A worker was paid a salary of $29,100 in 1988. Each year, a salary increase of 4% of the previous year's salary was awarded. How much did the worker earn from the beginning of 1988 through the end of 2014? (Round your answer to the nearest cent.)
A. $1,370,150.64
B. $256,527.63
C. $80,678.87
D. $1,289,471.77
What is the equation of a line that passes through point R(−4, −3) and has a slope of 7?
A. y = 7x + 25
B. y = 7x − 25
C. y = 7x + 3
D. y = −7x − 3
The coordinates of the endpoints of line segments are given in the options below. Which line segments are parallel?
A. A(1, 6), B(4, −3) and C(6, 4), D(9, −5)
B. E(1, −2), F(−5, 1) and G(−2, 3), H(−7, 6)
C. R(−2, −3), S(2, 0) and T(1, 4), U(5, 9)
D. W(−4, 4), X(3, 7) and Y(−3, 1), Z(5, 4)
I really do appreciate any and all who answer. Thank you.
I can help you with the first 3 questions, but I'm not competent enough to answer the last 2.
1) At the rule you are given, the object falls at a rate of 3 times the previous second.
So, in the 4th second only, the object will fall 3 x 81 =243 meters. And the total distance covered in all 4 seconds is: 9 + 27 +81 + 243 =360 meters, or "B"
2) In question 2, you have 2 geometric series going in parallel. The first is from week 1 to 29 inclusive, skipping every 2nd week, for a total of 15 weeks. The 2nd is from week 2 to 30 inclusive, skipping every 2nd week, for a total of 15 weeks. If you use the geometric series formula, you will see that the answer is "A"
3) In question 3, it is also a geometric series, with the first term being $29,100, number of terms 27(2014 -1988 +1), and the ratio is 1.04. If you do the Math, you will see that the answer is "A"
+23247 Question 4: Use the slope-intercept form: y - y1 = m(x - x1)
m = 7 and x1= -4 and y1 = -3 ---> y - -3 = 7(x - -4) ---> y + 3 = 7x + 28 ---> y = 7x + 25
Question 5: Lines are parallel when their slopes are parallel.
Slope formula: m = (y2 - y1) / (x2 - x1)
A: (1,6) & (4,-3) ---> m = (-3 - 6) / (4 - 1) ---> m = -9/3 = -3
(6,4) & (9,-5) ---> m = (-5 - 4) / (9 - 6) ---> m = -9/3 = -3 <--- These lines are parallel.
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