Answer:
y = negative 2 (x minus one-half)
Step-by-step explanation:
The equation of a line is given as:
y = mx + c, where m is the slope and c is the intercept on the y axis.
The equation of a line going through (0, 1) and (1, - 1) is calculated using:
![y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\ y-1=\frac{-1-1}{1-0}(x-0)\\ y-1=-2x\\y=-2x+1](https://tex.z-dn.net/?f=y-y_1%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%28x-x_1%29%5C%5C%20y-1%3D%5Cfrac%7B-1-1%7D%7B1-0%7D%28x-0%29%5C%5C%20y-1%3D-2x%5C%5Cy%3D-2x%2B1)
The solution of two lines is at their point of intersection. The equation of the line that would not have any solution with y = -2x + 1 would be a line that is parallel to y = -2x + 1. Since the two lines would be parallel to each other, their would be no intersection and therefore no solution.
Two lines are said to be parallel to each other if they have the same slope. The slope of y = -2x + 1 is gotten by comparing with y = mx + c, therefore the slope m = -2. From the options the only line with a slope m = -2 is y = -2(x -1/2). Therefore y = -2(x -1/2) is parallel to y = -2x + 1 and would have no solution
1/3 because in the decimal form is 0.33333 repeating
The expected value is
![E[X]=\displaystyle\sum_xx\,P(X=x)=\frac1{11}\sum_{x=0}^{10}x=\dfrac{0+1+\cdots+9+10}{11}=\dfrac{55}{11}=\boxed{5}](https://tex.z-dn.net/?f=E%5BX%5D%3D%5Cdisplaystyle%5Csum_xx%5C%2CP%28X%3Dx%29%3D%5Cfrac1%7B11%7D%5Csum_%7Bx%3D0%7D%5E%7B10%7Dx%3D%5Cdfrac%7B0%2B1%2B%5Ccdots%2B9%2B10%7D%7B11%7D%3D%5Cdfrac%7B55%7D%7B11%7D%3D%5Cboxed%7B5%7D)
The standard deviation is the square root of the variance, which is
![V[X]=E[(X-E[X])^2]=E[X^2]-E[X]^2](https://tex.z-dn.net/?f=V%5BX%5D%3DE%5B%28X-E%5BX%5D%29%5E2%5D%3DE%5BX%5E2%5D-E%5BX%5D%5E2)
where
![E[X^2]=\displaystyle\sum_xx^2\,P(X=x)=\frac1{11}\sum_{x=0}^{10}x^2=\dfrac{0^2+1^2+\cdots+9^2+10^2}{11}=\dfrac{385}{11}=35](https://tex.z-dn.net/?f=E%5BX%5E2%5D%3D%5Cdisplaystyle%5Csum_xx%5E2%5C%2CP%28X%3Dx%29%3D%5Cfrac1%7B11%7D%5Csum_%7Bx%3D0%7D%5E%7B10%7Dx%5E2%3D%5Cdfrac%7B0%5E2%2B1%5E2%2B%5Ccdots%2B9%5E2%2B10%5E2%7D%7B11%7D%3D%5Cdfrac%7B385%7D%7B11%7D%3D35)
so that
![V[X]=35-5^2=10](https://tex.z-dn.net/?f=V%5BX%5D%3D35-5%5E2%3D10)
making the standard deviation
![\sqrt{V[X]}=\sqrt{10}\approx\boxed{3.16}](https://tex.z-dn.net/?f=%5Csqrt%7BV%5BX%5D%7D%3D%5Csqrt%7B10%7D%5Capprox%5Cboxed%7B3.16%7D)
Answer:
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Step-by-step explanation:
Answer:
$1170
Step-by-step explanation:
Let x and y represent the numbers of economy and deluxe seats sold. The constraints are ...
And the objective function we want to maximize is ...
p = 40x +35y
__
I find it convenient to graph the equations and locate the objective function line as far from the origin as possible. The graph is shown, along with the solution.
Here, it's even simpler than that. The profit per seat is the greatest for economy seats, so Roland's should sell as many of those as they can. The only limit is that 6 seats must be deluxe. The remaining 30-6=24 can be economy. So, the profit will be maximized for ...
24 economy seats and 6 deluxe seats
The corresponding profit will be ...
24(40) +6(35) = 1170
The maximum profit from one tour is $1170.