The lifetimes of a certain brand of photographic are normally distributed with a mean of 210 h and a standard deviation of 50 h. What percent of lights will need to be replaced within 235 h? Show Work

69.15% of lights will need to be replaced within 235 h.

Step-by-step explanation:

We are given that the lifetimes of a certain brand of photographic are normally distributed with a mean of 210 h and a standard deviation of 50 h.

Let X = the lifetimes of a certain brand of photographic

The z-score probability distribution for the normal distribution is given by;

                              Z  =    ~ N(0,1)

where, = population mean lifetime = 210 h

            = standard deviation = 50 h

Now, the percent of lights that will need to be replaced within 235 h is given by = P(X 235 h)

      P(X 235 h) = P( ) = P(Z 0.50) = 0.6915 or 69.15%

The above probability is calculated by looking at the value of x = 0.5 in the z table which has an area of 0.6915.

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).

1. x> -5

2. x< 8

step-by-step explanation:

1. 2x> -10

divide by 2 from both sides of equation.

2x/2> -10/2

simplify, to find the answer.

-10/2=-5

x> -5 is the correct answer.

2. 3x< 24

divide by 3 from both sides of equation.

3x/3< 24/3

simplify, to find the answer.

24/3=8

x< 8 is the correct answer.

i hope this you, and have a wonderful day!