Answer:
Null Hypothesis,
: p = 0.54
Alternate Hypothesis,
: p 0.54
Step-by-step explanation:
We are given that the company's promotional literature states that 78% of the chips fail in the first 1000 hours of their use. Also, a sample of 1500 computer chips revealed that 77% of the chips fail in the first 1000 hours of their use.
And the quality control manager wants to test the claim that the actual percentage that fail is different from the stated percentage, i.e;
Null Hypothesis,
: p = 0.78 {means that the actual percentage that fail is same as the stated percentage}
Alternate Hypothesis,
: p 0.78 {means that the actual percentage that fail is different from the stated percentage}
Gas is 2.45 per gallon. So if we pay $12 we get 12÷2.45 gallons:
12 ÷ 2.45 ≈ 4.90 gallons.
You get roughly 4.90 gallons.
Take his original weight and divide it by the 84% or 0.84 as a decimal. This works out to be 235 lbs.
Answer:
The velocity function is
.
The acceleration function is
.
When t = 44, the velocity is
.
When t = 44, the acceleration is
.
Step-by-step explanation:
We know that the position function is given by
![s(t)=5t^2+5t](https://tex.z-dn.net/?f=s%28t%29%3D5t%5E2%2B5t)
Velocity is defined as the rate of change of position or the rate of displacement. If you take the derivative of the position function you get the instantaneous velocity function.
![v(t)=\frac{ds}{dt}](https://tex.z-dn.net/?f=v%28t%29%3D%5Cfrac%7Bds%7D%7Bdt%7D)
Acceleration is defined as the rate of change of velocity. If you take the derivative of the instantaneous velocity function you get the instantaneous acceleration function.
![a(t)=\frac{dv}{dt}](https://tex.z-dn.net/?f=a%28t%29%3D%5Cfrac%7Bdv%7D%7Bdt%7D)
The instantaneous velocity function is given by
![v(t)=\frac{d}{dt} s(t)=\frac{d}{dt}(5t^2+5t)\\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\v(t)=\frac{d}{dt}\left(5t^2\right)+\frac{d}{dt}\left(5t\right)\\\\\mathrm{Apply\:the\:Power\:Rule}:\quad \frac{d}{dx}\left(x^a\right)=a\cdot x^{a-1}\\\\v(t)=10t+\frac{d}{dt}\left(5t\right)\\\\\mathrm{Apply\:the\:common\:derivative}:\quad \frac{d}{dt}\left(t\right)=1\\\\v(t)=10t+5](https://tex.z-dn.net/?f=v%28t%29%3D%5Cfrac%7Bd%7D%7Bdt%7D%20s%28t%29%3D%5Cfrac%7Bd%7D%7Bdt%7D%285t%5E2%2B5t%29%5C%5C%5C%5C%5Cmathrm%7BApply%5C%3Athe%5C%3ASum%2FDifference%5C%3ARule%7D%3A%5Cquad%20%5Cleft%28f%5Cpm%20g%5Cright%29%27%3Df%5C%3A%27%5Cpm%20g%27%5C%5C%5C%5Cv%28t%29%3D%5Cfrac%7Bd%7D%7Bdt%7D%5Cleft%285t%5E2%5Cright%29%2B%5Cfrac%7Bd%7D%7Bdt%7D%5Cleft%285t%5Cright%29%5C%5C%5C%5C%5Cmathrm%7BApply%5C%3Athe%5C%3APower%5C%3ARule%7D%3A%5Cquad%20%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%28x%5Ea%5Cright%29%3Da%5Ccdot%20x%5E%7Ba-1%7D%5C%5C%5C%5Cv%28t%29%3D10t%2B%5Cfrac%7Bd%7D%7Bdt%7D%5Cleft%285t%5Cright%29%5C%5C%5C%5C%5Cmathrm%7BApply%5C%3Athe%5C%3Acommon%5C%3Aderivative%7D%3A%5Cquad%20%5Cfrac%7Bd%7D%7Bdt%7D%5Cleft%28t%5Cright%29%3D1%5C%5C%5C%5Cv%28t%29%3D10t%2B5)
The instantaneous acceleration function is given by
![a(t)=\frac{dv}{dt} =\frac{d}{dt}(10t+5)\\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\a(t)=\frac{d}{dt}\left(10t\right)+\frac{d}{dt}\left(5\right)\\\\a(t)=10](https://tex.z-dn.net/?f=a%28t%29%3D%5Cfrac%7Bdv%7D%7Bdt%7D%20%3D%5Cfrac%7Bd%7D%7Bdt%7D%2810t%2B5%29%5C%5C%5C%5C%5Cmathrm%7BApply%5C%3Athe%5C%3ASum%2FDifference%5C%3ARule%7D%3A%5Cquad%20%5Cleft%28f%5Cpm%20g%5Cright%29%27%3Df%5C%3A%27%5Cpm%20g%27%5C%5C%5C%5Ca%28t%29%3D%5Cfrac%7Bd%7D%7Bdt%7D%5Cleft%2810t%5Cright%29%2B%5Cfrac%7Bd%7D%7Bdt%7D%5Cleft%285%5Cright%29%5C%5C%5C%5Ca%28t%29%3D10)
To find the velocity and acceleration when t = 44, we substitute this value into the velocity and acceleration functions
![v(44)=10(44)+5\\v(44)=445 \:\frac{ft}{s}](https://tex.z-dn.net/?f=v%2844%29%3D10%2844%29%2B5%5C%5Cv%2844%29%3D445%20%5C%3A%5Cfrac%7Bft%7D%7Bs%7D)
![a(44)=10\: \frac{ft}{s^2}](https://tex.z-dn.net/?f=a%2844%29%3D10%5C%3A%20%5Cfrac%7Bft%7D%7Bs%5E2%7D)
Answer:
34
Step-by-step explanation:
18 - (-16) double negatives equal a positive so
18 + 16 = 34