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2 years ago

Is (2, 3) a solution to this system of equations? 2x + 5y = 19 X + 16y = 5 yes no

Mathematics

1 answer:

chubhunter [2.5K]2 years ago

3 0

Answer:

Step-by-step explanation:

To check if (2,3) is a solution to the system of equations, we simply have to plug the coordinate points into the two equations and see if it is valid.

$2*2+5*3=\\4+15=\\19\\\\19=19$

(2,3) belongs in the first equation.

$2+16*3=\\2+48=\\50\\\\50\neq 5$

(2,3) does not belong in the second equation.

Therefore, (2,3) is not a solution to this system of equations.

I hope this helps! Let me know if you have any questions :)

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. The psychology club is having a self-proclaimed psychic come to their campus fund-raising event to demonstrate his abilities.

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3 years ago

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Answer:

We conclude that seniors skip more than 2% of their classes at 0.01 level of significance.

Step-by-step explanation:

We are given that a professor wishes to discover if seniors skip more classes than freshmen. Suppose he knows that freshmen skip 2% of their classes.

He randomly samples a group of seniors and out of 2521 classes, the group skipped 77.

Let p = percentage of seniors who skip their classes.

So, Null Hypothesis, $H_0$ : p $\leq$ 2% {means that seniors skip less than or equal to 2% of their classes}

Alternate Hypothesis, $H_A$ : p > 2% {means that seniors skip more than 2% of their classes}

The test statistics that will be used here is One-sample z proportion statistics;

T.S. = $\frac{\hat p-p}{{\sqrt{\frac{\hat p(1-\hat p)}{n} } } } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of seniors who skipped their classes = $\frac{77}{2521}$

n = sample of classes = 2521

So, test statistics = $\frac{\frac{77}{2521} -0.02}{{\sqrt{\frac{\frac{77}{2521}(1-\frac{77}{2521})}{2521} } } } }$

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The value of the test statistics is 3.08.

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3 years ago

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