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3 years ago

Expand & simplify 6(g + 4) + 5(8+3) +4

Mathematics

1 answer:

Karo-lina-s [1.5K]3 years ago

5 0

Answer: 6 g + 83

Step-by-step explanation: That is how far it can go.

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A lab animal may eat any one of three foods each day. Laboratory records show that if the animal chooses one food on one trial,

Tresset [83]

Answer:

The probability that it will choose food #2 on the second trial after the initial trial = 0.3125

Step-by-step explanation:

Given - A lab animal may eat any one of three foods each day. Laboratory records show that if the animal chooses one food on one trial, it will choose the same food on the next trial with a probability of 50%, and it will choose the other foods on the next trial with equal probabilities of 25%.

To find - If the animal chooses food #1 on an initial trial, what is the probability that it will choose food #2 on the second trial after the initial trial?

Proof -

By the given information, we get the stohastic matrix

$H = \left[\begin{array}{ccc}0.5&0.25&0.25\\0.25&0.5&0.25\\0.25&0.25&0.5\end{array}\right]$

As we know that,

The matrix is a Markov chain $x_{k+1} = Hx_{k}$

Let

The initial state vector be

$x_{0} = \left[\begin{array}{ccc}1\\0\\0\end{array}\right]$

we choose this initial vector because given that If the animal chooses food #1 on an initial trial.

Now,

$x_{1} = Hx_{0} \\ = \left[\begin{array}{ccc}0.5&0.25&0.25\\0.25&0.5&0.25\\0.25&0.25&0.5\end{array}\right]\left[\begin{array}{ccc}1\\0\\0\end{array}\right] \\= \left[\begin{array}{ccc}0.5\\0.25\\0.25\end{array}\right]$

∴ we get

$x_{1} = \left[\begin{array}{ccc}0.5\\0.25\\0.25\end{array}\right]$

Now,

$x_{2} = Hx_{1} \\ = \left[\begin{array}{ccc}0.5&0.25&0.25\\0.25&0.5&0.25\\0.25&0.25&0.5\end{array}\right]\left[\begin{array}{ccc}0.5\\0.25\\0.25\end{array}\right] \\= \left[\begin{array}{ccc}0.25+0.0625+0.0625\\0.125+0.125+0.0625\\0.125+0.0625+0.125\end{array}\right]\\= \left[\begin{array}{ccc}0.375\\0.3125\\0.3125\end{array}\right]$

∴ we get

$x_{2} = \left[\begin{array}{ccc}0.375\\0.3125\\0.3125\end{array}\right]$

∴ we get

The probability that it will choose food #2 on the second trial after the initial trial = 0.3125

4 0

3 years ago

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the corre

luda_lava [24]

Answer:

Match the number of statement with the same number of reasons.

Step-by-step explanation:

Here are the statements

Points R, S, T, Q on circle O

measure of RS+ST=RT

measure of RT+TQ=RQ

3.RS+ST+TQ=RQ

Here are the reasons

1.Given

2. Arc Addition

3. Subsitution

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3 years ago

What is the value of 35 to the second power

valina [46]

35 to the second power would be the same as multiplying 35 by itself so.....
Ex. 35 to the second power would be

35x35

35 to the third power would be

35x35x35

35 to the fourth power would be

35x35x35x35

And etc.

35x35=1,225

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3 years ago

On December 1, there were 52 more tickets to the Spring Fling unsold than sold. At that time, the sold tickets represented 30% o

Andru [333]

156 tickets .........................

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3 years ago

In the expression 5x + 3xy - 7yz +

julia-pushkina [17]

Answer: 2

Step-by-step explanation:

8 0

4 years ago

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