Bachelor of Liberal Arts For Math Flashcards
7 cards from real B.L.A.; occasionally A.L.B. Bachelor of Liberal Arts practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
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What does the binary equivalent of the number 13 in base-10 look like?
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.
Where does the y-axis cross the line for the equation 14x + 7y = -35 when it is shown on a Cartesian graph?
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).
What kind of integer should be used as the answer to the following division operation? 16/-3
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.
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?
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.
Which kind of logical reasoning rule does the compound expression "if-then" use in truth tables?
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.
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?
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.
How many ounces of water are there in 11 liters?
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.