IM 3 Exam STUDY REVIEW

• 176

• 173

• 178

• 179

Answer explanation

To convert 20121 in base 3 to base 10, calculate: 2*(3^4) + 0*(3^3) + 1*(3^2) + 2*(3^1) + 1*(3^0) = 2*81 + 0*27 + 1*9 + 2*3 + 1*1 = 162 + 0 + 9 + 6 + 1 = 178. Thus, the correct answer is 178.

Convert 79011 to base 7

Answer explanation

To convert 79011 to base 7, repeatedly divide by 7 and record the remainders. The correct conversion yields 446232 in base 7, confirming that the answer is \(446232_{seven}\).

Tags

CCSS.4.NBT.A.1

Answer explanation

To convert the binary number 1001110100 to octal, group the binary digits in sets of three from right to left: 001 001 110 100. This corresponds to 1 1 6 4 in octal, giving us 1164_{eight} as the correct answer.

Convert 52433 to base 16

Answer explanation

To convert 52433 to base 16, divide by 16 repeatedly and record the remainders. The remainders give the digits in reverse order. The correct conversion results in CCD1_{sixteen}, confirming it as the right choice.

Determine if p, q, r, and s are true or false. Then, use that information to figure out if the symbolic statement is true or false.

p: The capital of Tennessee is Madison.

q: A dog is a mammal.

r: Nashville State is the largest college in the world.

s: A rectangle has four right angles.

• True

• False

Answer explanation

p is false, q is true, r is false, and s is true. The only true statements are q and s, which confirms the symbolic statement is true. Therefore, the correct answer is True.

Tags

CCSS.6.EE.B.6

Which symbol represents negation?

Answer explanation

The symbol for negation is represented by \( \sim \). It is commonly used in logic to indicate the opposite of a statement, while the other symbols represent different mathematical concepts.

Tags

CCSS.HSS.CP.A.1

A statement that has the opposite meaning, as well as an opposite truth value is called what?

• Logic

• Pyramid

• Disjunction

• Negation

Answer explanation

A statement that has the opposite meaning and truth value is known as 'negation'. It effectively reverses the truth of the original statement, making 'negation' the correct answer.

Tags

CCSS.L.11-12.6

CCSS.L.9-10.6

CCSS.W.11-12.2D

CCSS.W.8.2D

CCSS.W.9-10.2D

What is a compound statement using the word "and" called?

• Juxtaposition

• Colorado

• Conjunction

• Negation

Answer explanation

A compound statement using 'and' is called a conjunction. It connects two or more statements, indicating that all conditions must be true for the overall statement to be true.

Tags

CCSS.L.3.1H

CCSS.L.4.2C

CCSS.L.5.1E

CCSS.L.7.1B

CCSS.L.9-10.2A

What is the symbol used to represent Disjunction?

Answer explanation

The symbol used to represent Disjunction in logic is \( \vee \). This operator indicates a logical 'OR' between two statements, distinguishing it from other symbols like \( \wedge \) for conjunction and \( \sim \) for negation.

Tags

CCSS.HSS.CP.A.1

What is the truth value for #10 ?

• True

• False

Answer explanation

The truth value for #10 is False because the statement or condition being evaluated does not hold true. Therefore, the correct answer is False.