Answer:
Step-by-step explanation:
According to the Polynomial Remainder Theorem, if we have a polynomial P(x) divided by a binomial in the form of (<em>x</em> - <em>a</em>), then the remainder will be given by P(a).
And according to the Factor Theorem, if the remainder of P(x) / (<em>x</em> - <em>a</em>) is zero: that is, if P(a) = 0, then (<em>x</em> - <em>a</em>) is a factor of P(x).
We are given the polynomial:
And we know that it is divisible by:
We can rewrite our divisor as (<em>x</em> - (-2)). Hence, <em>a</em> = -2.
According to both the PRT and Factor Theorem, P(-2) must equal 0. Hence:
Substitute:
Solve for <em>k</em>. Simplify:
Hence:
The difference (faculty-student) in the sample proportions of those who believe that five minutes is not enough time for students to change classes typically varies about 0.096 from the true difference in proportions. Option D is correct.
<h3>What is the standard deviation?</h3>It is a measurement of statistical data dispersion. The degree to which the value varies is known as standard deviation.
The standard deviation of the sampling distribution is found as;
The difference in the sample proportions of those who think five minutes is not enough time for students to switch classrooms generally differs by roughly 0.096 from the actual difference in proportions.
Hence option D is correct.
To learn more about the standard deviation, refer to: brainly.com/question/16555520.
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