a. Repeat the following procedure with at least five people. Write a conjecture that relates the result of the procedure to each person’s birthday. Take the number of the month of your birthday ( January = 1 , February = 2 , ... , December = 12 ) , multiply by 5, add 6, multiply this sum by 4, add 9, multiply this new sum by 5, and add the number of the day on which you were born. Finally, subtract 165. b. Let M represent the month number and let D represent the day number of any person’s birthday. Use deductive reasoning to prove your conjecture in part (a).
a. Repeat the following procedure with at least five people. Write a conjecture that relates the result of the procedure to each person’s birthday. Take the number of the month of your birthday ( January = 1 , February = 2 , ... , December = 12 ) , multiply by 5, add 6, multiply this sum by 4, add 9, multiply this new sum by 5, and add the number of the day on which you were born. Finally, subtract 165. b. Let M represent the month number and let D represent the day number of any person’s birthday. Use deductive reasoning to prove your conjecture in part (a).
Solution Summary: The author explains how to calculate a conjecture that relates to the process described in the question below.
a. Repeat the following procedure with at least five people. Write a conjecture that relates the result of the procedure to each person’s birthday.
Take the number of the month of your birthday
(
January
=
1
,
February
=
2
,
...
,
December
=
12
)
, multiply by 5, add 6, multiply this sum by 4, add 9, multiply this new sum by 5, and add the number of the day on which you were born. Finally, subtract 165.
b. Let M represent the month number and let D represent the day number of any person’s birthday. Use deductive reasoning to prove your conjecture in part (a).
2. Suppose the graph below left is the function f(x). In the space below, describe what
transformations are occuring in the transformed function 3ƒ(-2x) + 1. The graph it on the
coordinate plane below right. (4 points)
1
1. Suppose we have the function f(x) = = and then we transform it by moving it four units to the
right and six units down, reflecting it horizontally, and stretching vertically by 5 units. What will
the formula of our new function g(x) be? (2 points)
g(x) =
Suppose an oil spill covers a circular area and the radius, r, increases according to the graph shown below where t
represents the number of minutes since the spill was first observed.
Radius (feet)
80
70
60
50
40
30
20
10
0
r
0 10 20 30 40 50 60 70 80 90
Time (minutes)
(a) How large is the circular area of the spill 30 minutes after it was first observed? Give your answer in terms of π.
square feet
(b) If the cost to clean the oil spill is proportional to the square of the diameter of the spill, express the cost, C, as a
function of the radius of the spill, r. Use a lower case k as the proportionality constant.
C(r) =
(c) Which of the following expressions could be used to represent the amount of time it took for the radius of the spill to
increase from 20 feet to 60 feet?
r(60) - r(20)
Or¹(80-30)
r(80) - r(30)
r-1(80) - r−1(30)
r-1(60) - r¹(20)
Chapter 1 Solutions
Thinking Mathematically, Books a la Carte Plus MyLab Math -- Access Card Package (7th Edition)
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Discrete Distributions: Binomial, Poisson and Hypergeometric | Statistics for Data Science; Author: Dr. Bharatendra Rai;https://www.youtube.com/watch?v=lHhyy4JMigg;License: Standard Youtube License