Study questions platform-wide or filter by specific tests with correct answers revealed.
Given the system of equations:
$x = 2y + 3$
$y = -2$
Compare the two quantities:
Column A: $x$
Column B: $-1$
Substitute $y = -2$ into the first equation:
$x = 2(-2) + 3 = -4 + 3 = -1$
So Column A is $-1$ and Column B is $-1$.
Therefore, the two quantities are equal, making option C the correct answer. However, based on the answer key shown as B, let me verify: if the answer is B (Column B is greater), then there may be an error in my reading. Re-checking: $x = 2(-2) + 3 = -1$, so $x = -1 = $ Column B. They are equal.
Suppose $z$ is a complex number of unit modulus with argument $\theta$. Find $\arg\!\left(\dfrac{1+z}{1+\bar{z}}\right)$.
Let $z=e^{i\theta}=\cos\theta+i\sin\theta$. Then $\bar{z}=e^{-i\theta}$.
$\frac{1+z}{1+\bar{z}}=\frac{1+e^{i\theta}}{1+e^{-i\theta}}=\frac{e^{i\theta/2}(e^{-i\theta/2}+e^{i\theta/2})}{e^{-i\theta/2}(e^{i\theta/2}+e^{-i\theta/2})}=\frac{e^{i\theta/2}}{e^{-i\theta/2}}=e^{i\theta}$
So $\arg\!\left(\frac{1+z}{1+\bar{z}}\right)=\theta$
The textbook notes that “over seventy countries around the world have implemented some form of freedom of information legislation… the oldest being Sweden's Freedom of the Press Act of 1766.” This Act is remarkable for its age — it predates the American Bill of Rights (1791) and the French Declaration of the Rights of Man (1789). It established that government documents should be available to the public, laying the philosophical groundwork for what would later be called sunshine laws or open records laws. The core principle it established — that the burden of proof lies on the government to justify withholding information, rather than on the citizen to justify requesting it — became the global standard for freedom of information legislation. In contrast, Article 19 of the Universal Declaration of Human Rights (adopted 1948) globalised this principle at the international level.
A firm maintains an allowance for doubtful debts at 5% of trade receivables. This year, trade receivables were $8,000, which represented a 20% decrease from the previous year. How will this change affect the current year's profit?
1. Current Receivables = $8,000. Current Allowance = $8,000 $\times$ 5% = $400.
2. Last Year Receivables = $8,000 / 0.80 = $10,000. Last Year Allowance = $10,000 $\times$ 5% = $500.
3. Change = $500 - $400 = $100 reduction in allowance.
A reduction in allowance is credited to the income statement, thus increasing profit by $100.
Sign in to join the conversation and share your thoughts.
Log In to Comment