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kifflom [539]
3 years ago
5

What are the values of m and n in the matrix addition below?

Mathematics
1 answer:
Aleksandr [31]3 years ago
6 0

ANSWER

The correct answer is m=45,n=12.

<u>EXPLANATION</u>

We were given the matrix equation;

\left[\begin{array}{cc}n-1&6\\-19&m+3\end{array}\right] +\left[\begin{array}{cc}-1&0\\16&-8\end{array}\right] =\left[\begin{array}{cc}10&6\\-3&40\end{array}\right].


We must first simplify the Left Hand Side of the equation by adding corresponding entries.


\left[\begin{array}{cc}n-1+-1&6+0\\-19+16&m+3-8\end{array}\right]=\left[\begin{array}{cc}10&6\\-3&40\end{array}\right].


That is;


\left[\begin{array}{cc}n-2&6\\-3&m-5\end{array}\right]=\left[\begin{array}{cc}10&6\\-3&40\end{array}\right].

Since the two matrices are equal, their corresponding entries are also equal. we equate corresponding entries and solve for m and n.


This implies that;


n-2=10


We got this equation from row one-column one entry of both matrices.


n=12


Also, the row three-column three entries of both matrices will give us the equation;


m-5=40


m=45


Hence the correct answer is m=45,n=12.


The correct option is option 2






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Translate each algebraic expression to a verbal phrase
GaryK [48]

Answer:

1.  A number decreased by seven.

2. A number increased by nine.

3. The product of six and a number, divided by eight.

4. The product of three and a number increased by five is equal to twenty.

5. The product of two and a number increased by eight is equal to twenty-three.

Step-by-step explanation:

1.   x-7

A number decreased by seven.

2. y+9

A number increased by nine.

3. 6m/8

The product of six and a number, divided by eight.

4. 3y+5 =20

The product of three and a number increased by five is equal to twenty.

5. 2(x+8)= 23

The product of two and a number increased by eight is equal to twenty-three.

3 0
3 years ago
If the filling equipment is functioning properly what is the probability that the volume of oil in a randomly selected barrel wi
Sophie [7]

Answer:

P(X>55.4)=P(\frac{X-\mu}{\sigma}>\frac{55.4-\mu}{\sigma})=P(Z>\frac{55.4-55}{0.5})=P(Z>0.8)

P(Z>0.8)=1-P(Z\leq 0.8)

P(Z>0.8)=1-0.788=0.212

Step-by-step explanation:

Assuming this previous info : "Trucks carry barrels of crude oil from a port in Texas to a distributer in New Mexico on long  trailers. Filling equipment is used to fill the barrels with the oil. When functioning properly,  the actual volume of oil loaded into each barrel by the filling equipment at the port is  approximately normally distributed with a mean of 55 gallons and a standard deviation of 0.5  gallons. If the mean is greater than 55.4 gallons, the filling mechanism is overfilling."

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the amount filling of a population, and for this case we know the distribution for X is given by:

X \sim N(55,0.5)  

Where \mu=55 and \sigma=0.5

We are interested on this probability

P(X>55.4)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X>55.4)=P(\frac{X-\mu}{\sigma}>\frac{55.4-\mu}{\sigma})=P(Z>\frac{55.4-55}{0.5})=P(Z>0.8)

And we can find this probability using the complement rule:

P(Z>0.8)=1-P(Z\leq 0.8)

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.  

P(Z>0.8)=1-0.788=0.212

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3 years ago
What is 546 divided by 25 in long division
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    ·_21.21
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    l50↓
    -----
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It takes Dariya 35 seconds to download 5 songs from the Internet. How can the number of seconds it would take Dariya to download
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Answer:

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Step-by-step explanation:

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7x7=49 seconds

6 0
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Read 2 more answers
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andreyandreev [35.5K]
Solve for w:
p = (1.2 w)/h^2
(1.2 w)/h^2 = (6 w)/(5 h^2):
p = (6 w)/(5 h^2)
p = (6 w)/(5 h^2) is equivalent to (6 w)/(5 h^2) = p:
(6 w)/(5 h^2) = p
Multiply both sides by (5 h^2)/6:
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