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3 years ago

14

How many solution does this linear system have 2x-y=7 y=2x+3

1 answer:

Arisa [49]3 years ago

8 0

Answer:

NO SOLUTION

Step-by-step explanation:

We can make this problem easier to understand if we write the system vertically:

2x-y=7

y=2x+3

and then rewrite the first problem in the form y = mx + b:

2x-y=7 ↔ y + 7 = 2x ↔ y = 2x + 7

y=2x+3

Note how these two equations have the same slope, but different y-intercepts. This tells us that the two lines are parallel, which in turn tells us that they never intercept one another.

Thus, this system has NO SOLUTION.

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A manufacturer of golf equipment wishes to estimate the number of left-handed golfers. A previous study indicates that the propo

never [62]

Answer:

A sample of 997 is needed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

The margin of error is of:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

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This means that $\pi = 0.08$

98% confidence level

So $\alpha = 0.02$ , z is the value of Z that has a p-value of $1 - \frac{0.02}{2} = 0.99$ , so $Z = 2.327$ .

How large a sample is needed in order to be 98% confident that the sample proportion will not differ from the true proportion by more than 2%?

This is n for which M = 0.02. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.02 = 2.327\sqrt{\frac{0.08*0.92}{n}}$

$0.02\sqrt{n} = 2.327\sqrt{0.08*0.92}$

$\sqrt{n} = \frac{2.327\sqrt{0.08*0.92}}{0.02}$

$(\sqrt{n})^2 = (\frac{2.327\sqrt{0.08*0.92}}{0.02})^2$

$n = 996.3$

Rounding up:

A sample of 997 is needed.

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Answer:

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