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3 years ago

Which ordered pair (x, y) is a solution to the following system of equations?

Mathematics

2 answers:

Rudik [331]3 years ago

7 0

Answer: (-6, 4)

Step-by-step explanation:

You can use the Elimination method:

- Multiply the the first equation by -3 and the second one by 5.

- Add both equations.

- Solve for y:

$\left \{ {{(-3)(5x+4y=-14(-3)} \atop {5(3x+6y)=6(5)}} \right.\\\\\left \{ {{-15x-12y=42} \atop {15x+30y=30}} \right.\\-------\\18y=72\\y=4$

- Susbtittute y=4 into any of the original equations and solve for x:

$3x+6(4)=6\\3x=6-24\\3x=-18\\x=-6$

Then the ordered pair is:

(-6, 4)

Irina18 [472]3 years ago

4 0

<u>Answer:</u>

(-6, 4)

<u>Step-by-step explanation:</u>

We are given the following two equations and we are to solve them:

$5x+4y=-14$ --- (1)

$3x+6y=6$ --- (2)

Using the substitution method:

From equation (2):

$3 x = 6 - 6 y \\\\ x = \frac { 6 - 6 y } { 3 } \\ \\ x = 2 - 2 y$

Substituting this value of x in equation (1) to get:

$5 ( 2 - 2 y ) + 4 y = -14 \\\\ 10 - 10 y + 4 y = -14 \\\\ 1 0 + 14 = 6 y \\\\ y = \frac { 24 } { 6 } \\ \\ y = 4$

Putting this value of y in equation (2) to find the value of x:

$3 x + 6 ( 4 ) = 6 \\\\ 3x + 24 = 6 \\\\ 3x = 6 - 24 \\\\ x = \frac { -18 } { 3 } \\\\ x = -6$

Therefore, (-6, 4) is the solution to the given system of equations.

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Answer:

$P(5.5$

And we can find this probability using the normal standard distribution or excel and we got:

$P(-2.769$

Step-by-step explanation:

For this case we assume the following complete question: "The pucks used by the National Hockey League for ice hockey must weigh between 5.5 and 6 ounces. Suppose the weights of pucks produced at a factory are normally distributed with a mean of 5.86 ounces and a standard deviation of 0.13ounces. What percentage of the pucks produced at this factory cannot be used by the National Hockey League? Round your answer to two decimal places. "

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 weights of a population, and for this case we know the distribution for X is given by:

$X \sim N(5.86,0.13)$