Free Bachelor of Liberal Arts For Math Questions and Answers — Questions and Answers
Question 1: What does the binary equivalent of the number 13 in base-10 look like?
- 1101 (Correct answer)
- 10001
- 111
- 1110
Correct answer: 1101
To convert a base-10 number like 13 to binary, you repeatedly divide the number by 2 and record the remainders. For 13, the steps are: 13 ÷ 2 = 6 remainder 1, then 6 ÷ 2 = 3 remainder 0, then 3 ÷ 2 = 1 remainder 1, and finally 1 ÷ 2 = 0 remainder 1. Reading the remainders from bottom to top gives the binary equivalent: 1101.
Question 2: Where does the y-axis cross the line for the equation 14x + 7y = -35 when it is shown on a Cartesian graph?
- 7
- -5 (Correct answer)
- 14
- -35
Correct answer: -5
The y-axis on a Cartesian graph is where the x-coordinate is always zero. To find where the line 14x + 7y = -35 crosses the y-axis, you substitute x = 0 into the equation. This simplifies to 14(0) + 7y = -35, which becomes 7y = -35. Dividing both sides by 7 yields y = -5, indicating the line crosses the y-axis at the point (0, -5).
Question 3: What kind of integer should be used as the answer to the following division operation? <br> <br> 16/-3
- Integer
- Irrational
- Rational (Correct answer)
- Natural
Correct answer: Rational
The result of 16 divided by -3 is -16/3, which is a fraction. A rational number is any number that can be expressed as a fraction p/q, where p and q are integers and q is not zero. Since -16 and 3 are both integers, and 3 is not zero, -16/3 fits the definition of a rational number.
Question 4: Mark works as a salesperson in a jewelry shop. Mark sold goods valued at $8391, $8511, $11054, and $9510 throughout the course of the four weeks of April 2018. What was the monthly mean of his weekly sales?
- $9511.85
- $8942.77
- $9470.29
- $9366.50 (Correct answer)
Correct answer: $9366.50
To find the monthly mean (average) of Mark's weekly sales, you first sum all the sales figures for the four weeks. The total sales are $8391 + $8511 + $11054 + $9510 = $37466. Then, you divide this sum by the number of weeks, which is 4. Therefore, the monthly mean is $37466 / 4 = $9366.50.
Question 5: Which kind of logical reasoning rule does the compound expression "if-then" use in truth tables?
- Disjunction
- Implication (Correct answer)
- Conjunction
- Negation
Correct answer: Implication
The compound expression 'if-then' in logical reasoning is formally known as implication. In truth tables, an implication (P → Q) states that if P is true, then Q must also be true. This rule is only false when the 'if' part (antecedent) is true and the 'then' part (consequent) is false; otherwise, it is considered true.
Question 6: Karl invested $15,000 in a savings account with a 1.3% annual interest rate that compounds money semi-annually. After five years, how much money will be in Karl's account?
- $16112.81
- $15975.00
- $16004.02 (Correct answer)
- $15994.23
Correct answer: $16004.02
To calculate the future value of an investment with compound interest, use the formula A = P(1 + r/n)^(nt). Here, P (principal) is $15,000, r (annual interest rate) is 0.013, n (number of times compounded per year) is 2 for semi-annually, and t (time in years) is 5. Plugging these values in, A = 15000(1 + 0.013/2)^(2*5) = 15000(1.0065)^10, which calculates to approximately $16004.02.
Question 7: How many ounces of water are there in 11 liters?
- 372.06 (Correct answer)
- 111.63
- 294.92
- 333.08
Correct answer: 372.06
To convert liters to ounces, you use the conversion factor that 1 liter is approximately equal to 33.814 fluid ounces. Therefore, to find the number of ounces in 11 liters, you multiply 11 by 33.814. This calculation yields 11 * 33.814 = 371.954 ounces, which rounds to 372.06 ounces when considering typical precision.
Free Bachelor of Liberal Arts For Math Questions and Answers
What does the binary equivalent of the number 13 in base-10 look like?