Question

1. a chemist determines the constant s for a particular solution. he calculates s using the following formula: s = \\(\frac{p - 1}{t + 1}\\) where p is the total concentration of the solution and t is the conductivity of the solution. under which of the following conditions would s be equal to 0? a) when p = 0 or t = 0 b) when p = 0 or t = 1 c) when p = 1 or t = 0 d) when p = 1 or t=-1 108. in one exhibit, all mammals have striped fur, solid - black fur, or solid - brown fur. there are twice as many mammals with solid - black fur as solid - brown fur, and the number of mammals with striped fur is two less than the combined number of solid - black and solid - brown mammals. if there are 88 mammals in total in the exhibit, how many have solid - brown fur? a) 15 mammals b) 20 mammals c) 22 mammals d) 46 mammals

Explanation:

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Step1: Recall the condition for a fraction to be zero

A fraction $\frac{a}{b}$ is zero when the numerator $a = 0$ and the denominator $b
eq0$. Given $S=\frac{p - 1}{t}$, for $S = 0$, we need $p-1 = 0$ and $t
eq0$.

Step2: Solve for $p$

If $p - 1=0$, then $p = 1$. And $t$ can be any non - zero value. Among the options, when $p = 1$ and $t
eq0$ (in option C, $t = 0$ is incorrect as it would make the fraction undefined, but the idea is that for the fraction to be zero the numerator must be zero and denominator non - zero), the closest correct condition for $S$ to be zero is when $p = 1$ and $t$ is non - zero. Here we assume the intention is to have a non - zero denominator in a general sense of fraction evaluation.

Step1: Define variables

Let the number of mammals with solid brown fur be $x$. Then the number of mammals with solid black fur is $2x$, and the number of mammals with striped fur is $(x + 2x)-2=3x - 2$.

Step2: Set up an equation

The total number of mammals is 88. So, $x+2x+(3x - 2)=88$.

Step3: Simplify the left - hand side of the equation

Combining like terms, we get $6x-2 = 88$.

Step4: Add 2 to both sides

$6x-2 + 2=88 + 2$, which gives $6x=90$.

Step5: Solve for $x$

Dividing both sides by 6, we have $x=\frac{90}{6}=15$.

Answer:

C. When $p = 1$ and $t
eq0$ (closest option is C where $p = 1$ is given, though $t = 0$ in C makes the formula undefined in a strict sense, but the numerator condition for zero fraction is met)

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