Question

1. if ★ is defined such that a★b = b(a + b), what is the value of 5★4?

a) 13
b) 14
c) 36
d) 45

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

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 elect

Explanation:

Step1: Identify values for a and b

In the expression \(6
abla4\), \(a = 6\) and \(b = 4\).

Step2: Substitute into the formula

Given \(a
abla b=b(a + b)\), substitute \(a = 6\) and \(b = 4\): \(4\times(6 + 4)\).

Step3: Calculate the result

First, calculate the sum inside the parentheses: \(6+4 = 10\). Then, multiply by 4: \(4\times10=40\). But there seems to be a mis - type in the problem setup as the result doesn't match the options. Assuming the formula is correct, we re - check.
If we assume the formula is \(a
abla b=b(a + b)\), for \(a = 6\) and \(b = 4\), we have \(4\times(6 + 4)=40\). However, if we assume the formula is \(a
abla b=a(b + a)\) (a possible mis - transcription), then for \(a = 6\) and \(b = 4\), we have \(6\times(4 + 6)=6\times10 = 60\). Let's go with the original formula \(a
abla b=b(a + b)\).
For the second part:
We know Hakim plays the same instrument as Oscar. But we have no information about what instrument Lisa plays in relation to the others other than the statements.
Statement I: Just because Hakim and Oscar play the same instrument doesn't mean Hakim and Lisa play the same instrument.
Statement II: Oscar plays the violin, but we don't know if Hakim plays the violin.
Statement III: Hakim and Oscar play the flute, but we have no information about Lisa. So none of the statements must be true.

Answer:

1. None of the options are correct with the correct calculation using \(a

abla b=b(a + b)\) (if there is a mis - type in the options).

1. D. None of the above must be true.