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3 years ago

Is 3( x + 4 ) equivalent to 3x + 12?

Mathematics

2 answers:

pochemuha3 years ago

6 0

Yes the equations are equivalent

liberstina [14]3 years ago

4 0

Yes they are. The distribution rule means that the 3 distributes to the x and 4. 3 times x is 3x. 3 times 4 is 12.

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What is the acceleration of a truck if the force on the truck is 325 N and the mass is 1,300 kg

horrorfan [7]

Answer:

Step-by-step explanation:

5 0

3 years ago

3. Tickets to a show cost $5.50 for adults and 54.25 for students. A family is purchasing2

bulgar [2K]

Step-by-step explanation:The cost of an adult ticket to the show is $5.5

The cost of a student ticket to the show is $4.25

A family is purchasing 2 adult tickets and 3 student tickets. This means that the total cost of 2 adult tickets would be

2 × 5.5 = $11

It also means that the total cost of 3 student tickets would be

3 × 4.25 = $12.75

The total cost of 2 adult tickets and 3 student tickets would be

11 + 12.75 = $23.75

If the family pays $25, the exact amount of change they should receive is

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7 0

3 years ago

The scale factor of the blueprint of a gymnasium to the actual gymnasium is 1in/15ft . The area of the floor on the blueprint is

miskamm [114]

B) 25, 650 ft^2
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4 0

4 years ago

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

If you have 24 square pieces of wood, and you divided each in half. Then, you divided each of those in half. How many square pie

hichkok12 [17]

The answer is 96
24 pieces of wood all cut in half so multiply by 2
24x2=48
Now cut 48 pieces in half so multiply by 2
48x2=96

3 0

3 years ago