FREE Bachelor of Liberal Arts For Math Questions and Answers
Which kind of logical reasoning rule does the compound expression "if-then" use in truth tables?
In a truth table, the compound statement 'if-then' is expressed using the logical reasoning rule known as implication. Implication is denoted by the symbol "→" or "⇒", and it represents a conditional statement where the truth of one proposition (the antecedent) implies the truth of another proposition (the consequent). The implication rule determines the truth value of the compound statement based on the truth values of its components.
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?
To calculate the amount of money in Alan's account after 5 years with compound interest, we can use the formula for compound interest:
A = P * (1 + r/n)^(n*t)
Where:
A = the final amount
P = the principal amount (initial deposit)
r = the annual interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the number of years
n this case, Alan placed $15,000 in the account, the annual interest rate is 1.3% (or 0.013 in decimal form), and the interest is compounded semiannually (n = 2) over a period of 5 years.
Plugging in the values into the formula:
A = 15000 * (1 + 0.013/2)^(2*5)
A = 15000 * (1.0065)^10
A ≈ 15000 * 1.06767823
A ≈ 16004.02
Therefore, the amount of money in Alan's account after 5 years would be approximately $16,004.02.
What does the binary equivalent of the number 13 in base-10 look like?
The corresponding value for the base-10 number 13 in the binary system is 1101. In binary, each digit represents a power of 2, starting from the rightmost digit with 2^0. In this case, the binary representation of 13 is 1101, which can be broken down as follows:
1 * 2^3 (8)
‥ 1 * 2^2 (4)
‥ 0 * 2^1 (0)
‥ 1 * 2^0 (1)
=13
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?
To find the mean value of Bruce's weekly sales in April 2018, we need to calculate the average of the four values.
Mean value = (Sum of all values) / (Number of values)
Sum of weekly sales = $8391 + $8511 + $11054 + $9510 = $37366
Number of values = 4
Mean value = $37366 / 4 = $9366.50
Therefore, the mean value of Bruce's weekly sales in April 2018 was $9366.50.
What kind of integer should be used as the answer to the following division operation?
16/-3
To find where the line intersects the y-axis, we need to determine the value of y when x is equal to zero. Let's substitute x = 0 into the equation and solve for y.
14(0) + 7y = -35
0 + 7y = -35
7y = -35
y = -35/7
y = -5
Therefore, the line intersects the y-axis at y = -5.
How many ounces of water are there in 11 liters?
To convert liters to ounces, we need to know the conversion factor. One liter is approximately equal to 33.814 ounces.
So, to find the number of ounces in 11 liters of water, we can multiply 11 by the conversion factor:
11 liters * 33.814 ounces/liter ≈ 372.06 ounces
Therefore, there are approximately 372.06 ounces in 11 liters of water.