How do you solve the system of linear equations by graphing X+y=7 -x+y=-7

Mathematics

1 answer:

morpeh [17]4 years ago

8 0

Answer:

x = 7 and y = 0

Step-by-step explanation:

We can either solve by substitution method or by elimination method or both method . We will solve by both the elimination and substitution method.

X+y=7 ---------------------------------------------------(1)

-x+y=-7 -------------------------------------------------(2)

Subtract equation (2) from equation(1)

2x = 14

Divide both-side of the equation by 2

2x/2 = 14/2

x = 7

Substitute x = 7 into equation (1)

x+y=7

7 + y = 7

Subtract 7 from both-side of the equation

7-7 + y = 7-7

y = 0

x = 7 and y =0

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The weights of ice cream cartons are normally distributed with a mean weight of 1313 ounces and a standard deviation of 0.50.5 o

asambeis [7]

Answer:

a) We are interested on this probability

$P(X>13.17)$

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:

$P(X>13.17)=P(\frac{X-\mu}{\sigma}>\frac{13.17-\mu}{\sigma})=P(Z>\frac{13.17-13}{0.5})=P(z>0.34)=0.367$

b) $P(\bar X >13.17)$

The new z score is given by:

$z =\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And replacing we got:

$P(\bar X >13.17)=P(Z> \frac{13.17-13}{\frac{0.5}{\sqrt{36}}})= P(Z>2.04) =0.0207$

Step-by-step explanation:

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".

Part a

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:

$X \sim N(13,0.5)$