The life of a manufacturer's compact fluorescent light bulbs is normal, with mean 12,000 hours and standard deviation 2,000 hour

The risk of down syndrome, in terms of the percentage of births per year, is changing at a rate given by the equation r(x) = 0.004641x² - 0.3012x + 4.9 for the range 20 ≤ x ≤ 45, where x signifies the maternal age at delivery. To derive the risk function as a percentage of births relative to maternal age x, we integrate r(x), leading to the function f(x) = 0.001547x³ - 0.1506x² + 4.9x + c. When x is 30, f evaluates to 0.14%. This means that 0.001547(30³) - 0.1506(30²) + 4.9(30) + c equals 0.14. Solving gives 41.769 - 135.54 + 147 + c = 0.14, which simplifies to c = -53.089. As a result, we establish that f(x) = 0.001547x³ - 0.1506x² + 4.9x - 53.089 for 20 ≤ x ≤ 45. The graph corresponding to this function is illustrated below.

The formula that describes the sequence is

Step-by-step explanation:

The nth-term formula for a geometric sequence is , where

• a represents the first term of the sequence
• r signifies the common ratio between any two consecutive terms
• =

∵ The sequence is , -4, -24, -144,.......

∵ The first term is

∵ The second term is -4

∴

∵ The third term is -24

∴

∵ The fourth term is -144

∴

∵   = =   = 6

∴ There is a consistent ratio between two consecutive terms

∴ The sequence qualifies as a geometric sequence

∵ The formula for the nth term of the geometric sequence is

∵ a =

∵ r = 6

∴ The equation for the sequence is

The formula that can be employed to outline the sequence is

Learn more:

You can explore more about sequences in

The provided sequences pertain to every x. To determine the series, we start with the specified value a, and the values of both and are found accordingly. The calculation of the series comes from dividing the preceding value, yielding results for all x.

Answer:

Step-by-step explanation:

The question is

We let , so the equation becomes:

Where

By applying the quadratic formula, we arrive at:

Quadratic formula:

Substituting yields:

We let , thus x calculates to:

and

The solutions to the equation are (rounded to 2 decimal places) and (rounded to 2 decimal places)