Final answer:
The student's question involves solving algebraic and quadratic equations, as well as analyzing statistical distributions. The quadratic formula is employed to find the roots of quadratic equations, while the shape of the distribution and standard deviation are key concepts in statistics.
Step-by-step explanation:
The student appears to be asking for assistance with a set of mathematical expressions and equations, including solving quadratic equations using the quadratic formula. These problems typically require manipulation of algebraic expressions, understanding of statistical concepts, and application of mathematical formulas to find unknown variables.
To solve a quadratic equation using the quadratic formula, you would follow these steps:
- Rearrange the equation to have 0 on one side (e.g., t² + 10t - 2000 = 0).
- Identify the coefficients a, b, and c in the standard form at² + bt + c.
- Substitute those coefficients into the quadratic formula, which is t = (-b ± √(b² - 4ac)) / (2a).
- Solve for t by simplifying the expression under the square root and then by performing the addition or subtraction and division.
To address questions about statistical distributions, one would need to analyze the collected data and use graphs like histograms to determine the general shape of the curves and compare distributions. In statistical analysis, s often represents the standard deviation, which measures the amount of variation or dispersion in a set of values.