Answer: 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
Answer:
D
Step-by-step explanation:
Answer:
Step-by-step explanation:
The surface area of the square prism is obtained by using the following formula:
![A_{s} (t) = 4\cdot l(t)\cdot h(t) + 2\cdot [l(t)]^{2}](https://tex.z-dn.net/?f=A_%7Bs%7D%20%28t%29%20%3D%204%5Ccdot%20l%28t%29%5Ccdot%20h%28t%29%20%2B%202%5Ccdot%20%5Bl%28t%29%5D%5E%7B2%7D)
The rate of change of the surface area can be found by deriving the function with respect to time:
![\frac{dA_{s}}{dt} = 4\cdot [h(t)\cdot \frac{dl}{dt} + l(t)\cdot \frac{dh}{dt}] + 2\cdot l(t)\cdot \frac{dl}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7BdA_%7Bs%7D%7D%7Bdt%7D%20%3D%204%5Ccdot%20%5Bh%28t%29%5Ccdot%20%5Cfrac%7Bdl%7D%7Bdt%7D%20%2B%20l%28t%29%5Ccdot%20%5Cfrac%7Bdh%7D%7Bdt%7D%5D%20%2B%202%5Ccdot%20l%28t%29%5Ccdot%20%5Cfrac%7Bdl%7D%7Bdt%7D)
Known variables are summarized below:
The rate of change is:
![\frac{dA_{s}}{dt} = 4\cdot [(9\,km)\cdot (-7\,\frac{km}{min} )+(4\,km)\cdot (10\,\frac{km}{min} )] + 2\cdot (4\,km)\cdot (-7\,\frac{km}{min} )](https://tex.z-dn.net/?f=%5Cfrac%7BdA_%7Bs%7D%7D%7Bdt%7D%20%3D%204%5Ccdot%20%5B%289%5C%2Ckm%29%5Ccdot%20%28-7%5C%2C%5Cfrac%7Bkm%7D%7Bmin%7D%20%29%2B%284%5C%2Ckm%29%5Ccdot%20%2810%5C%2C%5Cfrac%7Bkm%7D%7Bmin%7D%20%29%5D%20%2B%202%5Ccdot%20%284%5C%2Ckm%29%5Ccdot%20%28-7%5C%2C%5Cfrac%7Bkm%7D%7Bmin%7D%20%29)
