The lifetime of a 2-volt non-rechargeable battery in constant use has a normal distribution with a mean of 516 hours and a standard deviation of 20 hours. Ninety percent of all batteries have a lifetime less than

A. 517.28 hours
B. 536. 00 hours
C. 541.60 hours

C. 541.60 hours

Step-by-step explanation:

Since the lifetime of a 2-volt non-rechargeable battery in constant use has a normal distribution, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = lifetime of the batteries.

µ = mean lifetime

σ = standard deviation

From the information given,

µ = 516 hours

σ = 20 hours

Looking at the normal distribution table, the z score corresponding to ninety percent approximately is 1.28

Therefore,

1.28 = (x - 516)/20

Cross multiplying by 20, it becomes

20 × 1.28 = x - 516

25.6 = x - 516

x = 516 + 25.6

x = 541.6

Therefore, Ninety percent of all batteries have a lifetime less than

541.60 hours

i leave the calculator work to you.

7. diameter 4 miles, circumference 4π miles

8. radius 0.2 miles, circumference 0.4π miles

[this is a bad problem because the actual radius of a car on the track is less than 0.2 miles so the answer is less than 0.4π miles]

9. radius 6 feet, circumference 12π feet

10. diameter 14 cm, circumference 14π cm

11. diameter 4.8 feet, circumference 4.8π feet

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).