Bright Bulb light bulb company is planning a study to assess the average life expectancy of their light bulbs. They know the standard deviation is σ = 400 hours. They want a 95% confidence interval with a margin of error of 50 hours. What sample size do they need?

Sample size = 246 .

Step-by-step explanation:

We are given that Bright Bulb light bulb company is planning a study to assess the average life expectancy of their light bulbs. For this they know;

Standard deviation, = 400 hours         Confidence interval = 95%

Margin of error = 50 hours

We know that Margin of error formula is given by;

    Margin of Error =   where = 5%

                   50       =  1.96 *  

                       =   = 15.68

                      n  =   = 245.86 ≈ 246

So, sample size needed will be 246 bulbs.

x² + 3x + 7 = 0       [ax² + bx + c]

a = 1

b = 3

c = 7

quadratic formula:

    (+/- is this ±)

plug in the numbers into the variables

your answer is a

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places