Example Question - solving for n
Here are examples of questions we've helped users solve.
Finding the Value of n in an Exponential Equation
<p>Given the equation:</p> <p>(x<sup>n</sup>)<sup>3</sup> = \frac{x<sup>18</sup>}{x<sup>-6</sup>}</p> <p>We can simplify the right side:</p> <p>\frac{x<sup>18</sup>}{x<sup>-6</sup>} = x<sup>18 - (-6)</sup> = x<sup>18 + 6</sup> = x<sup>24</sup></p> <p>Now we have:</p> <p>(x<sup>n</sup>)<sup>3</sup> = x<sup>24</sup></p> <p>Using the power of a power rule, the left side becomes:</p> <p>x<sup>3n</sup> = x<sup>24</sup></p> <p>Since the bases are the same, we can set the exponents equal to each other:</p> <p>3n = 24</p> <p>Now solve for n:</p> <p>n = \frac{24}{3} = 8</p> <p>The value of n is 8.</p>
Solving for n in a Binomial Test
The image presents a question related to a binomial test: For a binomial test, if p = 1/2, p*n = 35 and q*n = 35, what is the value of n? Here, p is the probability of success on a single trial, and q is the probability of failure (q = 1 - p). Since we know p, we can find q: q = 1 - p = 1 - 1/2 = 1/2 With the formulas p*n and q*n equaling 35, we have: p*n = 35 q*n = 35 Since both p and q are equal to 1/2, and both p*n and q*n are equal to 35, we can solve for n: (1/2)*n = 35 n = 35 / (1/2) n = 35 * 2 n = 70 Thus, the value of n is 70.
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