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2 years ago

Need help solveing this for class!

Mathematics

1 answer:

Mandarinka [93]2 years ago

7 0

According to graphical and analytical methods, the value of the input variable associated with point of intersection between f(x) and g(x) is 1.5. (Correct choice: C)

<h3>How to determine the point of interception between two linear functions</h3>

Linear functions are polynomials with a grade of 1 and described by the following form:

y = m · x + b (1)

Where:

x - Independent variable
m - Slope
y - Dependent variable
b - Intercept

Please notice that horizontal lines have a slope of 0.

There are two forms to estimate the coordinates of the point of intersection of the two functions: (i) graphical, (ii) analytical. According to the first method, the value of the input variable is approximately 1.5.

And according to the second method, we have the functions f(x) = 1 and g(x) = (4/3) · x - 1. Then, we must solve the following formula to determine the input variable of the point of interception:

1 = (4/3) · x - 1

(1/3) · x = 1/2

x = 3/2

x = 1.5

The value of the input variable is approximately 1.5.

To learn more on systems of linear equations: brainly.com/question/27664510

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From the question we are told that

The first sample size $n_1 = 30$

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The second standard deviation is $s_2 = 45$

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Generally the standard error is mathematically represented as

$SE = \sqrt{\frac{s^2}{n_1} + \frac{s^2}{n_2} }$

=> $SE = \sqrt{\frac{1888.34}{30} + \frac{1888.34}{45} }$

=> $SE = 10.24$

Generally the margin of error is mathematically evaluated as

$E = Z_{\frac{\alpha }{2} } * SE$

$E = 1.645* 10.24$

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Generally the 90% confidence interval is mathematically represented as

$\=x_1 -\=x_2 -E < \mu_1 -\mu_2 < \=x_1 -\=x_2 +E$

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The null hypothesis is $H_o : \mu_1 = \mu_2$

The alternative hypothesis $H_a : \mu_1 < \mu_2$

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$t = \frac{\= x_1 - \=x_2 }{SE}$

=> $t = \frac{323-356}{10.24}$

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The p-value is obtained from the student t distribution table at degree of freedom of 73 at 0.05 level of significance

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Here the level of significance is $\alpha = 5\% = 0.05$

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