Daily Practice Questions

Explanation: Getting to the Answer: Write the expression in words first: points per blue ring (5) times number of darts in blue ring ( x ), plus points per red ring (10) times number of darts in red ring (6 − x ). Now, translate the words into numbers, variables, and operations: 5 x + 10(6 − x ). This is not one of the answer choices, so simplify the expression by distributing the 10 and then combining like terms: 5 x + 10(6 − x ) = 5 x + 60 − 10 x = 60 − 5 x . This matches (D) .

Explanation: The reaction enthalpy ($\Delta H$) is calculated by summing the energy required to break bonds in the reactants and the energy released when forming bonds in the products. Based on the stoichiometry of $2 \text{Na}(g) + \text{Cl}_2(g) \rightarrow 2 \text{NaCl}(s)$, the expression must account for breaking two moles of Na atoms (requiring $2w$), one mole of $\text{Cl}_2$ bonds (requiring $x$), and forming two moles of NaCl lattice (releasing $2y + 2z$). Choice (C) correctly reflects these coefficients, whereas choices with incorrect multipliers for the sodium or chlorine terms fail to match the balanced equation's molar ratios.

Explanation: The passage indicates that subjectivism influenced Rodin but also restricted his ability to innovate further, implying that while he embraced new ideas, this mindset ultimately hindered his creative evolution. Thus, option C best summarizes the effect described.

Explanation: This problem models exponential decay using the differential equation $\frac{dy}{dt} = ky$, where $y$ is the amount of contaminant remaining. Since 20% is removed in the first minute, 80% remains ($y(1) = 0.8y_0$), allowing us to solve for the decay constant $k$. To find the time required to remove 98% of the contaminant, we set the remaining amount to 2% of the initial value ($y(t) = 0.02y_0$) and solve for $t$, which yields approximately 18 minutes. Choices like 2 or 5 minutes are incorrect because they underestimate the time needed for the contaminant level to drop from 80% remaining to just 2% remaining in an exponential process.

Explanation: Statement (1) says $x > 0$ and Statement (2) says $x < 1$. Since the question asks if $x < 1$, Statement (2) directly confirms this with a "yes," while Statement (1) provides no information about whether $x$ is less than or greater than 1. Because each statement independently yields a definitive answer, EACH statement ALONE is sufficient.

Explanation: To solve 12 – 6x > 0, subtract 12 from both sides to get –6x > –12. Dividing both sides by –6 (a negative number) reverses the inequality, yielding x < 2.