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qwelly [4]
3 years ago
11

Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 4x -

5y = 24 2x + 3y = -10 one and only one solution infinitely many solutions no solution Find the solution, if one exists. (If there are infinitely many solutions, express x and y in terms of the parameter t. If there is no solution, enter NO SOLUTION.)
Mathematics
1 answer:
zepelin [54]3 years ago
3 0

Answer:it has one and only one solution.

Step-by-step explanation:

The given system of equations is expressed as

4x - 5y = 24 - - - - - - - - - - - - -1

2x + 3y = -10 - - - - - - - - - - - - - 2

We would eliminate x by multiplying equation 1 by 1 and equation 2 by 2. It becomes

4x - 5y = 24

4x + 6y = - 20

Subtracting, it becomes

- 11y = 44

Dividing the left hand side and the right hand side of the equation by

- 11, it becomes

- 11y/- 11 = 44/- 11

y = - 4

Substituting y = - 4 into equation 2, it becomes

2x + 3 × - 4 = -10

2x - 12 = - 10

2x = - 10 + 12

2x = 2

Dividing the left hand side and the right hand side of the equation by

2, it becomes

2x/2 = 2/2

x = 1

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tatyana61 [14]

Using the normal distribution, there is a 0.4826 = 48.26% probability that the sample mean is between 15 and 16 grams per day.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean \mu and standard deviation \sigma is given by:

Z = \frac{X - \mu}{\sigma}

  • The z-score measures how many standard deviations the measure is above or below the mean.
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For this problem, the parameters are given as follows:

\mu = 15, \sigma = 3, n = 40, s = \frac{3}{\sqrt{40}} = 0.4743

The probability is the <u>p-value of Z when X = 16 subtracted by the p-value of Z when X = 15</u>, hence:

X = 16:

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{16 - 15}{0.4743}

Z = 2.11

Z = 2.11 has a p-value of 0.9826.

X = 15:

Z = \frac{X - \mu}{s}

Z = \frac{15 - 15}{0.4743}

Z = 0

Z = 0 has a p-value of 0.5.

0.9826 - 0.5 = 0.4826 = 48.26% probability that the sample mean is between 15 and 16 grams per day.

More can be learned about the normal distribution at brainly.com/question/15181104

#SPJ1

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Answer:

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Step-by-step explanation:

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