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1 answer:
Answer:
<em>See below</em>
Step-by-step explanation:
In this example we are to consider the equation 2x - 5 = 4x + 12, and are asked to solve for x. Well let us take the first approach, a mathematical one;
Now consider the explanation, " talking over a phone to a friend. "
First you would subtract 2x on either side of the equation, canceling the 2x on one side, and subtracting 2x from 4x on the other, resulting in the simplified equation - 5 = 2x + 12. Subtracting 12 from either side we cancel the 12 on one side, and subtract - 12 and - 5 on the other. We now get - 17 = 2x. Dividing 2 on either side, x = - 8.5!
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Answer:
(a) C: 0.0465 ; reject the null hypothesis
(b) B: 0.3409 ; fail to reject the null hypothesis
Step-by-step explanation:
Firstly, the decision rule based on P-value to reject the null hypothesis or fail to reject the null hypothesis is given by;
- If the P-value of test statistics is less than the level of significance, then we have sufficient evidence to reject our null hypothesis.
- If the P-value of test statistics is more than the level of significance, then we have insufficient evidence to reject our null hypothesis due to which we fail to reject our null hypothesis.
(a) Now, we are given alternate hypothesis, : p < 3/5
Also, z test statistics is -1.68. Since this is a left tailed test, so P-value is given by;
P-value = P(Z < -1.68) = 1 - P(Z 1.68)
= 1 - 0.95352 = <u>0.0465</u>
Since, the P-value of test statistics is less than the level of significance as 0.0465 < 0.05, so we have sufficient evidence to reject our null hypothesis due to which <u>we reject the null hypothesis.</u>
(b) Now, we are given alternate hypothesis, : p > 0.383
Also, z test statistics is 0.41. Since this is a right tailed test, so P-value is given by;
P-value = P(Z > 0.41) = 1 - P(Z 0.41)
= 1 - 0.6591 = <u>0.3409</u>
Since, the P-value of test statistics is more than the level of significance as 0.3409 > 0.05, so we have insufficient evidence to reject our null hypothesis due to which <u>we fail to reject the null hypothesis.</u>
Answer:
x = -1 +/-2i
Step-by-step explanation:
Write the equation in standard form to find the roots, also known as the solutions, zeros, or x-intercepts, of the quadratic.
x² + 2x + 5 = 0
Use the quadratic formula by substituting a= 1, b = 2 and c = 5.