A kite has 4 equal sides. If 5 was added to each side, the new perimeter will be 56 inches. Find the side length of the original
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Answer:
The 90% confidence interval for the mean time to graduate with a bachelor’s degree is (4.32, 4.84).
Yes, this confidence interval contradict the belief that it takes 4 years to complete a bachelor’s degree.
Step-by-step explanation:
The (1 - <em>α</em>)% confidence interval for population mean <em>μ, </em>when the population standard deviation is not known is:
The information provided is:
Compute the critical value of <em>t</em> for 90% confidence interval and (n - 1) degrees of freedom as follows:
*Use a <em>t</em>-table for the probability.
Compute the 90% confidence interval for population mean <em>μ</em> as follows:
Thus, the 90% confidence interval for the mean time to graduate with a bachelor’s degree is (4.32, 4.84).
If a hypothesis test is conducted to determine whether it takes 4 years to complete a bachelor’s degree or not, the hypothesis will be:
<em>Hₐ</em>:<em> </em>The mean time it takes to complete a bachelor’s degree is 4 years, i.e. <em>μ </em>= 4.
<em>Hₐ</em>:<em> </em>The mean time it takes to complete a bachelor’s degree is different from 4 years, i.e. <em>μ </em>≠ 4.
The decision rule based on a confidence interval will be:
Reject the null hypothesis if the null value is not included in the interval.
The 90% confidence interval for the mean time to graduate with a bachelor’s degree is (4.32 years, 4.84 years).
The null value, i.e. <em>μ </em>= 4 is not included in the interval.
The null hypothesis will be rejected at 10% level of significance.
Thus, it can be concluded that that time it takes to complete a bachelor’s degree is different from 4 years.
Answer:
Step-by-step explanation:
( g ° f )(x) = ( x + 7 )² = x² + 14x + 49
20 + 3(x² + 14x + 49) = - 34
20 + 3x² + 42x + 147 = - 34
3x² + 42x + 201 = 0 ⇔ x² + 14x + 67 = 0
D = 196 - 268 = - 72 < 0
There is no any roots in set of real numbers.
The values of x in set of complex numbers are:
=
±
= - 7 ± 3√2 i