What is the length of the hypotenuse of the right angle defined by the points (-3,-1),(1,-1),and (1,2)?A)square root of 3
B)square root of 3
C) 2 timessquare root of 3
D)5

Answers

Answer 1
Answer: To find the length of the triangle first find the two coordinates with a common x coordinate, (1,-1) and (1,2). Now find the difference between their y coordinates, -1 and 2. This means that the length of the triangle is 3.
To find the width of the triangle first find the two coordinates with a common y coordinate, (-3,-1) and (1,-1). Now find the difference between their x coordinates, -3 and 1. This means that the width of the triangle is 4. 
By Pythagoras' theorem, we know that hypotenuse = \sqrt{ width^(2) + length^(2) }. Inserting our newfound values into this equation, we an find thelength of the hypotenuse:
hypotenuse = \sqrt{ 4^(2) +3^(2)} hypotenuse = √(16+9) hypotenuse =  √(x) 25hypotenuse = 5
Therefore, your answer is D0 5. To visualise this question better, you can plot the points on a graph. 

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Which of the following have a rate of change of 3?

Answers

31 is the rats or change

Apply the laws of exponents, calculate the result and express the result in scientific notation, and as a decimal: (8.1*10^-4)^2Format your answer like this: The result of the scientific notation is __*10^--. The result as a decimal is _.

Answers

Answer:

  • the result in scientific notation is 6.561×10⁻⁷
  • the result as a decimal is 0.000 000 656 1

Explanation:

The rules of exponents say the exponent outside parentheses applies to each factor inside parentheses.

... (8.1*10^-4)^2 = 8.1^2 × (10^-4)^2

... = 65.61 × 10^-8

... = 6.561 × 10^-7 . . . . adjust to scientific notation with one digit left of the decimal point

The exponent of -7 means the decimal point in the decimal number is 7 places to the left of where it is in scientific notation. That is ...

... 6.561 × 10^-7 = 0.0000006561

The breakfast cafe uses 3 1/4 lb of coffee per day. How much coffee does it use ina 7 day week?​

Answers

Quantity of coffee used per day by breakfast cafe =

= 3 (1)/(4)  \: lb

Quantity of coffee it will use in a seven day week =

= 3 (1)/(4)  * 7

=  ((4 * 3) + 1)/(4)  * 7

=  (13)/(4)  *  (7)/(1)

=  (91)/(4)

= 22 (3)/(4)  \: lb

Therefore , a breakfast cafe will use =

22 (3)/(4)  \: lb \: of \: coffee \: in \: a \: seven \: day \: week \: .

Final answer:

By multiplying the daily coffee consumption of 3 1/4 lbs by 7, we find that the cafe uses 22 3/4 lbs of coffee in a week.

Explanation:

In a week, the cafe's coffee consumption is calculated by multiplying its daily usage of 3 1/4 lbs by 7 (the number of days in a week). This computation yields 22 3/4 lbs as the total weekly coffee consumption. This process involves multiplying the daily quantity by the number of days to obtain the weekly total. Therefore, the cafe utilizes 22 3/4 lbs of coffee throughout a 7-day week. This method of determining weekly coffee usage is crucial for managing inventory and ensuring that the cafe meets the demands of its customers efficiently. By understanding their weekly consumption, the cafe can effectively plan and stock their coffee supply.

Learn more about Mathematical Multiplication here:

brainly.com/question/1582368

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I need help please with the work?

Answers

Answer with Step-by-step explanation:

m<A=m<J=20

In JOE,

80+20+m<O=180[Angles of a trinagle]

m<O=80=m<M

m<E=m<Y=80

1/4 times 2 equals??

Answers

Answer:

1/2

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

1/4 = 0.25 x 2 = 0.5 = 1/2

Three friends — let’s call them X, Y , and Z — like to play pool (pocket billiards). There are some pool games that involve three players, but these people instead like to play 9-ball, which is a game between two players with the property that a tie cannot occur (there’s always a winner and a loser in any given round). Since it’s not possible for all three of these friends to play at the same time, they use a simple rule to decide who plays in the next round: loser sits down. For example, suppose that, in round 1, X and Y play; then if X wins, Y sits down and the next game is between X and Z. Question: in the long run, which two players square off against each other most often? Least often? So far what I’ve described is completely realistic, but now we need to make a (strong) simplifying assumption. In practice people get tired and/or discouraged, so the probability that (say) X beats Y in any single round is probably not constant in time, but let’s pretend it is, to get a kind of baseline analysis: let 0 < pXY < 1 be the probability that X beats Y in any given game, and define 0 < pXZ < 1 and 0 < pY Z < 1 correspondingly. Consider the stochastic process P that keeps track of

Answers

Answer:

Step-by-step explanation:

(a) If the state space is taken as S = \{(XY),(XZ),(YZ)\} , the probability of transitioning from one state, say (XY) to another state, say (XZ) will be the same as the probability of Y losing out to X, because if X and Y were playing and Y loses to X, then X and Z will play in the next match. This probability is constant with time, as mentioned in the question. Hence, the probabilities of moving from one state to another are constant over time. Hence, the Markov chain is time-homogeneous.

(b) The state transition matrix will be:

P=\begin{vmatrix} 0 & p_(XY) & (1-p_(XY))\n p_(XZ)& 0& (1-p_(XZ))\n p_(YZ)&(1-p_(YZ)) & 0\end{vmatrix},

where as stated in part (b) above, the rows of the matrix state the probability of transitioning from one of the states S = \{(XY),(XZ),(YZ)\} (in that order) at time n and the columns of the matrix state the probability of transitioning to one of the states S = \{(XY),(XZ),(YZ)\} (in the same order) at time n+1.

Consider the entries in the matrix. For example, if players X and Y are playing at time n (row 1), then X beats Y with probability p_(XY), then since Y is the loser, he sits out and X plays with Z (column 2) at the next time step. Hence, P(1, 2) = p_(XY). P(1, 1) = 0 because if X and Y are playing, one of them will be a loser and thus X and Y both together will not play at the next time step. P(1, 3) = 1 - p_(XY), because if X and Y are playing, and Y beats X, the probability of which is1 - p_(XY), then Y and Z play each other at the next time step. Similarly,P(2, 1) = p_(XZ), because if X and Z are playing and X beats Z with probabilityp_(XZ), then X plays Y at the next time step.

(c) At equilibrium,

vP = v,

i.e., the steady state distribution v of the Markov Chain is such that after applying the transition probabilities (i.e., multiplying by the matrix P), we get back the same steady state distribution v. The Eigenvalues of the matrix P are found below:

:det(P-\lambda I)=0\Rightarrow \begin{vmatrix} 0-\lambda & 0.6 & 0.4\n 0.975& 0-\lambda& 0.025\n 0.95& 0.05& 0-\lambda\end{vmatrix}=0

\Rightarrow -\lambda ^3+0.9663\lambda +0.0337=0\n\Rightarrow (\lambda -1)(\lambda ^2+\lambda +0.0337)=0

The solutions are

\lambda =1,-0.0349,-0.9651. These are the eigenvalues of P.

The sum of all the rows of the matrixP-\lambda I is equal to 0 when \lambda =1.Hence, one of the eigenvectors is :

\overline{x} = \begin{bmatrix} 1\n 1\n 1 \end{bmatrix}.

The other eigenvectors can be found using Gaussian elimination:

\overline{x} = \begin{bmatrix} 1\n -0.9862\n -0.9333 \end{bmatrix}, \overline{x} = \begin{bmatrix} -0.0017\n -0.6666\n 1 \end{bmatrix}

Hence, we can write:

P = V * D * V^(-1), where

V = \begin{bmatrix} 1 & 1 & -0.0017\n 1 & -0.9862 & -0.6666 \n 1 & -0.9333 & 1 \end{bmatrix}

and

D = \begin{bmatrix} 1 & 0 & 0\n 0 & -0.9651 & 0 \n 0 & 0 & -0.0349 \end{bmatrix}

After n time steps, the distribution of states is:

v = v_0P^n\Rightarrow v = v_0(VDV^(-1))^n=v_0(VDV^(-1)VDV^(-1)...VDV^(-1))=v_0(VD^nV^(-1)).

Let n be very large, say n = 1000 (steady state) and let v0 = [0.333 0.333 0.333] be the initial state. then,

D^n \approx \begin{bmatrix} 1 & 0 & 0\n 0& 0 &0 \n 0 & 0 & 0 \end{bmatrix}.

Hence,

v=v_0(VD^nV^(-1))=v_0(V\begin{bmatrix} 1 & 0 & 0\n 0 &0 &0 \n 0& 0 & 0 \end{bmatrix}V^(-1))=[0.491, 0.305, 0.204].

Now, it can be verified that

vP = [0.491, 0.305,0.204]P=[0.491, 0.305,0.204].