P=115-n
115-n+4.25n=358.75
3.25n=243.75
N=75
P=40
(40,75)
The answer is D
Answer: ![5.7\ cm](https://tex.z-dn.net/?f=5.7%5C%20cm)
Step-by-step explanation:
Given
Rectangle has an area of ![19.38\ cm^2](https://tex.z-dn.net/?f=19.38%5C%20cm%5E2)
Suppose rectangle length and width are
and ![w](https://tex.z-dn.net/?f=w)
If each side is increased by ![1.50\ cm](https://tex.z-dn.net/?f=1.50%5C%20cm)
Area becomes ![A_2=35.28\ cm^2](https://tex.z-dn.net/?f=A_2%3D35.28%5C%20cm%5E2)
We can write
![\Rightarrow lw=19.38\quad \ldots(i)\\\\\Rightarrow (l+1.5)(w+1.5)=35.28\\\Rightarrow lw+1.5(l+w)+1.5^2=35.28\\\text{use (i) for}\ lw\\\Rightarrow 19.38+1.5(l+w)=35.28-2.25\\\Rightarrow l+w=9.1\quad \ldots(ii)](https://tex.z-dn.net/?f=%5CRightarrow%20lw%3D19.38%5Cquad%20%5Cldots%28i%29%5C%5C%5C%5C%5CRightarrow%20%28l%2B1.5%29%28w%2B1.5%29%3D35.28%5C%5C%5CRightarrow%20lw%2B1.5%28l%2Bw%29%2B1.5%5E2%3D35.28%5C%5C%5Ctext%7Buse%20%28i%29%20for%7D%5C%20lw%5C%5C%5CRightarrow%2019.38%2B1.5%28l%2Bw%29%3D35.28-2.25%5C%5C%5CRightarrow%20l%2Bw%3D9.1%5Cquad%20%5Cldots%28ii%29)
Substitute the value of width from (ii) in equation (i)
![\Rightarrow l(9.1-l)=19.38\\\Rightarrow l^2-9.1l+19.38=0\\\\\Rightarrow l=\dfrac{9.1\pm\sqrt{(-9.1)^2-4(1)(19.38)}}{2\times 1}\\\\\Rightarrow l=\dfrac{9.1\pm\sqrt{5.29}}{2}\\\\\Rightarrow l=\dfrac{9.1\pm2.3}{2}\\\\\Rightarrow l=3.4,\ 5.7](https://tex.z-dn.net/?f=%5CRightarrow%20l%289.1-l%29%3D19.38%5C%5C%5CRightarrow%20l%5E2-9.1l%2B19.38%3D0%5C%5C%5C%5C%5CRightarrow%20l%3D%5Cdfrac%7B9.1%5Cpm%5Csqrt%7B%28-9.1%29%5E2-4%281%29%2819.38%29%7D%7D%7B2%5Ctimes%201%7D%5C%5C%5C%5C%5CRightarrow%20l%3D%5Cdfrac%7B9.1%5Cpm%5Csqrt%7B5.29%7D%7D%7B2%7D%5C%5C%5C%5C%5CRightarrow%20l%3D%5Cdfrac%7B9.1%5Cpm2.3%7D%7B2%7D%5C%5C%5C%5C%5CRightarrow%20l%3D3.4%2C%5C%205.7)
Width corresponding to these lengths
![w=5.7,\ 3.4](https://tex.z-dn.net/?f=w%3D5.7%2C%5C%203.4)
Therfore, we can write the length of the longer side is ![5.7\ cm](https://tex.z-dn.net/?f=5.7%5C%20cm)
<span>True, as a postulate is the assumption of existence.</span>
Answer:
![P(X](https://tex.z-dn.net/?f=%20P%28X%3C3.7%29)
And we can use the cumulative distribution function given by:
![F(x) = \frac{x-a}{b-a} , a \leq X \leq b](https://tex.z-dn.net/?f=%20F%28x%29%20%3D%20%5Cfrac%7Bx-a%7D%7Bb-a%7D%20%2C%20a%20%5Cleq%20X%20%5Cleq%20b)
And for this case we can write the probability like this:
![P(X](https://tex.z-dn.net/?f=%20P%28X%3C3.7%29%3D%20F%283.7%29%20%3D%20%5Cfrac%7B3.7-3.5%7D%7B3.8-3.5%7D%20%3D0.667)
And then the final answer for this case would be ![\frac{2}{3}=0.667](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D%3D0.667)
Step-by-step explanation:
For this case we define our random variable X "price of gasoline for a city in the USA" and we know the distribution is given by:
![X \sim Unif (a=3.5, b=3.8)](https://tex.z-dn.net/?f=%20X%20%5Csim%20Unif%20%28a%3D3.5%2C%20b%3D3.8%29)
And for this case the density function is given by:
![f(x) = \frac{x}{b-a}= \frac{x}{3.8-3.5}=, 3.5 \leq X \leq 3.8](https://tex.z-dn.net/?f=%20f%28x%29%20%3D%20%5Cfrac%7Bx%7D%7Bb-a%7D%3D%20%5Cfrac%7Bx%7D%7B3.8-3.5%7D%3D%2C%203.5%20%5Cleq%20X%20%5Cleq%203.8)
And we want to calculate the following probability:
![P(X](https://tex.z-dn.net/?f=%20P%28X%3C3.7%29)
And we can use the cumulative distribution function given by:
![F(x) = \frac{x-a}{b-a} , a \leq X \leq b](https://tex.z-dn.net/?f=%20F%28x%29%20%3D%20%5Cfrac%7Bx-a%7D%7Bb-a%7D%20%2C%20a%20%5Cleq%20X%20%5Cleq%20b)
And for this case we can write the probability like this:
![P(X](https://tex.z-dn.net/?f=%20P%28X%3C3.7%29%3D%20F%283.7%29%20%3D%20%5Cfrac%7B3.7-3.5%7D%7B3.8-3.5%7D%20%3D0.667)
And then the final answer for this case would be ![\frac{2}{3}=0.667](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D%3D0.667)