Question

1. if φ is defined such that aφb = b(a + b), what is the value of 5φ4?

○a) 13
○b) 14
○c) 36
○d) 45

1. hakim, lisa, and oscar all play instruments. hakim plays the same instrument as oscar. lisa plays the violin.

i. hakim and lisa play the same instrument.
ii. oscar plays the violin.
iii. hakim and oscar play the flute.
○a) i only
○b) ii only
○c) i and iii only
○d) none of the above must be true.

1. the charge of an atom can be found by comparing the number of protons with the number of electrons in that atom. what is the charge of an atom with 56 protons and 54 electrons?

○a) +2
○b) +1
○c) 0
○d) - 2

1. which of the following numbers has no prime factors in common with 60?

○a) 9
○b) 24
○c) 49
○d) 69

Explanation:

81.

Step1: Identify values of a and b

Given \(a\varphi b=b(a + b)\), for \(5\varphi4\), \(a = 5\) and \(b=4\).

Step2: Substitute values into formula

Substitute \(a = 5\) and \(b = 4\) into \(b(a + b)\), we get \(4\times(5 + 4)\).

Step3: Calculate the result

First, calculate inside the parentheses: \(5+4=9\). Then, \(4\times9 = 36\).

We know Hakim plays the same instrument as Oscar and Lisa plays the violin. But there is no information connecting Hakim - Oscar's instrument to Lisa's. So, we cannot conclude that Hakim and Lisa play the same instrument (I is not necessarily true), we cannot conclude that Oscar plays the violin (II is not necessarily true), and we cannot conclude that Hakim and Oscar play the flute (III is not necessarily true).

Protons have a charge of + 1 and electrons have a charge of - 1. The net charge of an atom is the number of protons minus the number of electrons. Given 56 protons and 54 electrons, the charge is \(56-54=+2\).

Answer:

C. 36

82.