The Large square represents one whole.<br> 3.74

Answer and Step-by-step explanation: A line of best fit is the best approximation of the given data. It is used to show the relation of two variables and it can be determined, more accurately, by the Least Square Method.

To use the method, follow the steps:

1) Calculate the mean of the two variables:

$X = \frac{\Sigma x_{i}}{n}$

$Y=\frac{\Sigma y_{i}}{n}$

2) The Slope of the line is given by:

$m=\frac{\Sigma (x_{i}-X)(y_{i}-Y)}{\Sigma (x_{i}-X)^{2}}$

3) The y-intercept is found by the formula:

$b=Y-mX$

For the ripening of bananas, the least square method gives the line:

y = -0.142x + 5.56

The rate of change of a line equation is its slope, so

Rate of change = -0.14

The rate of change of ripening time with respect to exposure time is -0.14, which means the more expose the fruit is, the less time it needs to ripe.

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7 0

3 years ago

Problem 7.1 (10 points) Let pXnqn"0,1,... be a Markov chain with state space S " t1, 2, 3u and transition probability matrix P "

12345 [234]

Answer:

The responses to the given can be defined as follows:

Step-by-step explanation:

For point a:

fixing probability vector that is $W = [a b c]$

$\therefore$

relation: $WT =W$

$\to 0.5a+0.3b+0.2c=a ..................(1)\\\\ \to 0.4a+0.4b+0.3c=b..............(2)\\\\ \to 0.1a+0.3b+0.5c=c.................(3)$

solving the value:

$a=0.3387 \\\\ b=0.3710\\\\ c=0.2903$

Therefore the stationary distribution $\pi =[0.3387 \ 0.3710\ 0.2903]$

For point b:

$\pi$ will be limiting distribution if $\pi_j=\lin_{n\to \infity} (X_n=\frac{j}{X_0}=i) \Sigma_{\sqrt{j}} n_j=1$

$\pi$ satisfies the above condition so, it is limiting the distribution.

3 0

3 years ago

A baseball is hit with an initial upward velocity of 70 feet per second from a height of 4 feet above the ground. The equation h

Katyanochek1 [597]

To solve you need to set the equation equal to 6 (the height at which the player caught the ball.

6 = -16t^2 + 70t + 4

Next put the equation in standard form by subtracting 6 from both sides

-16t^2 + 70t - 2 = 0

This equation can be simplified by dividing by 2

-8t^2 + 35t - 1 = 0

This equation cannot be factored, but we can use the quadratic formula to find a value for x. Using the equation above we can find the values for a=-8, b = 35 and c = -1.

using the quadratic formula we can solve for x

-b +/- sqrt(b^2 - 4ac)
-------------------------------
2a

The solutions are

0.03 and 4.35. as 0.03 seems an unrealistic time to hit and catch a baseball we would expect the time to be 4.35 seconds.

8 0

4 years ago

The Large square represents one whole. 3.74 - 1.53 = ?