Answer:
20 mph
Step-by-step explanation:
Let speed of Train a = Va mph
Let speed of Train b = Vb mph
Va = Vb + 30
Let time taken for Train a = Ta
Let time taken for Train b = Tb
time taken = distance travelled/speed
Ta = 350/Va = 350/(Vb+30)
Tb = 140/Vb
But they both travel in the same amount of time.
So, Ta = Tb
![\frac{350}{v_{b} + 30}=\frac{140}{v_{b}}](https://tex.z-dn.net/?f=%5Cfrac%7B350%7D%7Bv_%7Bb%7D%20%2B%2030%7D%3D%5Cfrac%7B140%7D%7Bv_%7Bb%7D%7D)
Cross multiply
![350v_{b} = 140(v_{b} + 30)\\\\350v_{b} = 140v_{b} + 4200\\\\350v_{b} -140v_{b} = 4200\\\\210v_{b} = 4200](https://tex.z-dn.net/?f=350v_%7Bb%7D%20%3D%20140%28v_%7Bb%7D%20%2B%2030%29%5C%5C%5C%5C350v_%7Bb%7D%20%3D%20140v_%7Bb%7D%20%2B%204200%5C%5C%5C%5C350v_%7Bb%7D%20-140v_%7Bb%7D%20%3D%204200%5C%5C%5C%5C210v_%7Bb%7D%20%3D%204200)
Divide both sides by 210
![\frac{210v_{b} }{210} \frac{4200}{210} \\\\v_{b} = 20 mph](https://tex.z-dn.net/?f=%5Cfrac%7B210v_%7Bb%7D%20%7D%7B210%7D%20%5Cfrac%7B4200%7D%7B210%7D%20%5C%5C%5C%5Cv_%7Bb%7D%20%3D%2020%20mph)
Answer:
x = 6
Step-by-step explanation:
5x = 24 + 6
5x = 30
5x/5 = 30/5
x = 6
Given:
μ = 25 mpg, the population mean
σ = 2 mpg, the population standard deviation
If we select n samples for evaluation, we should calculate z-scores that are based on the standard error of the mean.
That is,
![z= \frac{x-\mu}{\sigma / \sqrt{n} }](https://tex.z-dn.net/?f=z%3D%20%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%20%2F%20%5Csqrt%7Bn%7D%20%7D%20)
The random variable is x = 24 mpg.
Part (i): n = 1
σ/√n = 2
z = (24 -25)/2 = -0.5
From standard tables,
P(x < 24) = 0.3085
Part (ii): n = 4
σ/√n = 1
z = (24 -25)/1 = -1
P(x < 24) = 0.1587
Part (iii): n=16
σ/√n = 0.5
z = (24 - 25)/0.5 = -2
P(x < 24) = 0.0228
Explanation:
The larger the sample size, the smaller the standard deviation.
Therefore when n increases, we are getting a result which is closer to that of the true mean.
You are looking for the slope and y intercept to complete the equation of the line.
The equation of a line is in something called slope intercept form. That looks like y = mx + b. m represents the slope (measure of how steep a line is, and in which direction it is going) and b represents the y intercept (y coordinate when x = 0). You need to find the slope and y intercept to complete the equation.
First, find the slope. The formula for slope is: m = (y2 - y1)/(x2 - x1) where m is the slope and (x1, y1) and (x2, y2) are points.
Pick any two points on the graph. I will use (-2, 0) and (0, 4). Now use these values to find the slope.
m = (4-0)/(0+2) = 4/2
m = 2
m = 2 means that for every two units the line goes up on the y axis, it moves one to the right on the x axis. 2 will go in your first box.
Now find the y intercept. The y intercept is where the line crosses the y axis - it is the y coordinate when x = 0. Here when x = 0, y = 4, so your y intercept is at 4. 4 goes into your second box.
The equation is y = 2x + 4
Answer:
K(x) =
( curvature function)
Step-by-step explanation:
considering the Given function
F(x) = ![-5x^2](https://tex.z-dn.net/?f=-5x%5E2)
first Determine the value of F'(x)
F'(x) = ![\frac{d(-5x^2)}{dy}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%28-5x%5E2%29%7D%7Bdy%7D)
F'(x) = -10x
next we Determine the value of F"(x)
F"(x) = ![\frac{d(-10x)}{dy}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%28-10x%29%7D%7Bdy%7D)
F" (x) = -10
To find the curvature function we have to insert the values above into the given formula
K(x) ![= \frac{|f"(x)|}{[1 +( f'(x)^2)]^{\frac{3}{2} } }](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B%7Cf%22%28x%29%7C%7D%7B%5B1%20%2B%28%20f%27%28x%29%5E2%29%5D%5E%7B%5Cfrac%7B3%7D%7B2%7D%20%7D%20%7D)
K(x) =
( curvature function)