Final answer:
The solution to the equation 2x + 3 = 17 is x = 7. For x = 1, the corresponding z-score in a normal distribution with mean of 5 and a standard deviation of 6 is approximately -0.67. The exponent rule is demonstrated with 3².35, which is equivalent to 3 to the power of 7.
Step-by-step explanation:
If we are given the equation 2x + 3 = 17, we can solve for x by first subtracting 3 from both sides of the equation, which gives us 2x = 14. Then, by dividing both sides by 2, we find that x = 7. This is a basic algebraic operation involving solving linear equations. For the conclusion, we have determined the value of x that satisfies the equation.
Now, if we suppose x = 1, then we are looking to find the value of z in a statistical context, assuming a normal distribution with a mean (μ) of 5 and a standard deviation (σ) of 6. The formula for converting an x-value to a z-score is z = (x - μ) / σ. Plugging in the values, we get z = (1 - 5) / 6, which simplifies to z = -4/6 or z ≈ -0.67, rounded to two decimal places.
Finally, regarding rules for exponents, if we have an expression like 3².35, we can understand it as using the rule xPx9 = x(p+q). In this scenario, it would be the same as calculating 37, which is the multiplication of seven threes.