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3 years ago

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Solve the following system

1 answer:

scZoUnD [109]3 years ago

4 0

Answer:

{x = -4 , y = 2 , z = 1

Step-by-step explanation:

Solve the following system:

{-2 x + y + 2 z = 12 | (equation 1)

2 x - 4 y + z = -15 | (equation 2)

y + 4 z = 6 | (equation 3)

Add equation 1 to equation 2:

{-(2 x) + y + 2 z = 12 | (equation 1)

0 x - 3 y + 3 z = -3 | (equation 2)

0 x+y + 4 z = 6 | (equation 3)

Divide equation 2 by 3:

{-(2 x) + y + 2 z = 12 | (equation 1)

0 x - y + z = -1 | (equation 2)

0 x+y + 4 z = 6 | (equation 3)

Add equation 2 to equation 3:

{-(2 x) + y + 2 z = 12 | (equation 1)

0 x - y + z = -1 | (equation 2)

0 x+0 y+5 z = 5 | (equation 3)

Divide equation 3 by 5:

{-(2 x) + y + 2 z = 12 | (equation 1)

0 x - y + z = -1 | (equation 2)

0 x+0 y+z = 1 | (equation 3)

Subtract equation 3 from equation 2:

{-(2 x) + y + 2 z = 12 | (equation 1)

0 x - y+0 z = -2 | (equation 2)

0 x+0 y+z = 1 | (equation 3)

Multiply equation 2 by -1:

{-(2 x) + y + 2 z = 12 | (equation 1)

0 x+y+0 z = 2 | (equation 2)

0 x+0 y+z = 1 | (equation 3)

Subtract equation 2 from equation 1:

{-(2 x) + 0 y+2 z = 10 | (equation 1)

0 x+y+0 z = 2 | (equation 2)

0 x+0 y+z = 1 | (equation 3)

Subtract 2 × (equation 3) from equation 1:

{-(2 x)+0 y+0 z = 8 | (equation 1)

0 x+y+0 z = 2 | (equation 2)

0 x+0 y+z = 1 | (equation 3)

Divide equation 1 by -2:

{x+0 y+0 z = -4 | (equation 1)

0 x+y+0 z = 2 | (equation 2)

0 x+0 y+z = 1 | (equation 3)

Collect results:

Answer: {x = -4 , y = 2 , z = 1

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Julie : 5.62

Micah : 5.62 x 5 = 28.1

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3 years ago

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Find all values of x that are NOT in the domain of h.

Firlakuza [10]

Answer:

if x=-1 then its is NOT in the domain of h.

Step-by-step explanation:

Domain is the set of values for which the function is defined.

we are given the function

h(x) = x + 1 / x^2 + 2x + 1

h(x) = x+1 /x^2+x+x+1

h(x) = x+1/x(x+1)+1(x+1)

h(x) = x+1/(x+1)(x+1)

h(x) = x+1/(x+1)^2

So, the function h(x) is defined when x ≠ -1

Its is not defined when x=-1

So, if x=-1 then its is NOT in the domain of h.

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3 years ago

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The average yield of the standard variety off soybeans per acre on a farm in a region is 48.8 bushels per acre, with a standard

I am Lyosha [343]

Answer:

$z=\frac{53.4-48.8}{\frac{12}{\sqrt{36}}}=2.3$

$p_v =P(Z>2.3)=1-P(Z$

If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the true mean is not significantly higher than 48.8 at 1% of signficance.

Step-by-step explanation:

1) Data given and notation

$\bar X=53.4$ represent the sample mean

$\sigma=12$ represent the population standard deviation assumed

$n=36$ sample size

$\mu_o =48.8$ represent the value that we want to test

$\alpha=0.01$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

2) State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean is higher than 48.8, the system of hypothesis would be:

Null hypothesis: $\mu \leq 48$

Alternative hypothesis: $\mu > 48$

Since we assume that know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

3) Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{53.4-48.8}{\frac{12}{\sqrt{36}}}=2.3$

4)P-value

Since is a right tailed test the p value would be:

$p_v =P(Z>2.3)=1-P(Z$

5) Conclusion

If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the true mean is not significantly higher than 48.8 at 1% of signficance.

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Samantha gathered the following information on a given day at the dog park.

Luda [366]

The number of dogs that are not puppies is 17, the number of adult dogs without long hair is 6, the number of puppy dogs with long hair is 8 and the number of puppy dogs without long hair is 7.

<h3>What is the information missing?</h3>

To complete the chart it is necessary to determine:

Number of dogs that are not puppies.
Number of puppies with and without long hair
Number of adult dogs without long hair

Number of dogs that are not puppies:

32 (total dogs) - 15 (puppies) = 17 dogs

Adult dogs without long hair:

17 (total adult dogs) - 11 (adult dogs with long hair) = 6 dogs

Puppy dogs with and without long hair

Total of puppy dogs = 15, this number can be obtained by adding 9+6 or 7+8. From these combinations, the only one that meets the rule "There are 6 more dogs that have long hair than dogs that do not have long hair" is 8 puppies with long hair and 7 puppies without long hair.

Note: This question is not written correctly; here is the correct and complete question.

Samantha gathered the following information on a given day at the dog park.

There are 32 dogs playing at the dog park.

15 of the dogs are puppies.

11 of the dogs are not puppies and have long hair.

There are 6 more dogs that have long hair than dogs that do not have long hair.

Fill in the table completely to represent Samantha’s data.

Learn more about dogs in: brainly.com/question/8565422

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