1) Use inductive reasoning to determine the next three numbers in the pattern: 3,12,26,45.....? (I don't seem to find a pattern?)

2) Find the counterexample to show that the following statemnet is incorrect. "the sum of any odd numbers is divisible by 4. ( I tried several odd numbers and the answer is always divisible by 4)

3) Sandra drove for 234.8 miles and used 12.6 gallons of gas. estimate the number of miles Sandra's car get per gallon? ( will the answer be as simple as 234.8 / 12.6 = 18.6 miles per gallon?)

4) Sam founda number of nickles and dimes, and quarters in his room. he found thre more dimes than nickles but twice as many quartes as dimes. The total value of coins was $5.05, how many coins of each type did Sam find?

5) Use inductive reasoning find the next thre numbers in the patern: 2,9,20,35.... ( I can seem to find a pattern?)

Solution Preview

The solution file is attached.

1) using inductive reasoning to determine the next three numbers in the pattern: 3,12,26,45.....? (I don't seem to find a pattern?)

Here, we can follow the method of differences to determine the next three terms of the sequence.
First order differences:
12 - 3 = 9
26 - 12 = 14
45 - 26 = 19
Second order differences:
14 - 9 = 5
19 - 14 = 5
Since the second order differences are the same, the given sequence follows a quadratic polynomial
f(n) = an^2 + bn + c
Plug in n = 1, 2, 3 to get
f(1) = 3 = a + b + c
f(2) = 12 = 4a + 2b + c
f(3) = 26 = 9a + 3b + c
On solving this system, we get a = 5/2, b = 3/2, c = -1
f(n) = ...

Solution Summary

Step-by-step solutions to all the five questions are provided in the solution file.

... ". Answers short answer questions in statistics. ...5. ...Linear programming (LP) techniques consist of a sequence of steps that will lead to an optimal solution to ...

... 10 9.14 10 7.46 10 6.58 8 9.96 14 8.1 14 8.84 14 5.76 8 5.68 5 4.74 5 5.73 5 7.71 8 ... Brand New Question. ... It is very important that you do each step in sequence. ...

... for t=0:0.01:5;plot(t,exp(-0.5*t)*sin ... spent one week to do this since these questions are very ... further help to maximize your learning in this question and this ...

...5 such questions are presented and solutions provided. 1. As one goes down the five-level memory hierarchy ... possible answers to a typical survey question such as ...

... a hard copy of your answers to the questions listed in ... the sequence below to determine size; NOTE in question 1 I ... 2. Adjust the pH to 7.0 with 5 N NaOH (will ...

... variable indicating whether a specific question is answered correctly is .5, and the ... distribution of the fraction of questions correctly answered when ...

... to obtaining sound answers to the questions motivating the ... sales: Y = 1684 + 200.4T, The main question is whether ...equation: Y = 2169 - 284.6(5) + 97(5)2 = 3171 ...

... survey 66.2% were female (298 question- questionnaire was ... Participants could answer the fifteen questions of 166 ... the questionnaire by using a five point Likert ...

...Question # 5 Finance can be broken into three different sub ... The questions pertains to Business Analysis ... Each question is answered using about a paragraph or two ...

... In other words, the following questions need to be answered first ... 0 1 2 3 4 5 6 7 8 9 10 11 12 ... the most straight- forward way to answer this question is simply ...