What number occurs the most often? What is this kind of average called? mode e. What is this average called? f. Calculate the mean of these numbers. g. Now that you have the mean, say which temperatures are above and which below the mean. Above :

Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to \( t \). \( x^{\prime}=5 x-6 y+\sin t \) \( y^{\prime}=3 x-y-\cos t \) Eliminate \( x \) and solve the remaining differential equation for \( y \). Choose the correct answer below. A. \( y(t)=C_{1} e^{2 t}+C_{2} t e^{2 t}+\frac{19}{40} \cos t+\frac{7}{40} \sin t \) B. \( y(t)=C_{1} e^{-2 t} \cos 3 t+C_{2} e^{-2 t} \sin 3 t+\frac{19}{40} \cos t+\frac{7}{40} \sin t \) C. \( y(t)=C_{1} e^{-2 t}+C_{2} t e^{-2 t}+\frac{19}{40} \cos t+\frac{7}{40} \sin t \) D. \( y(t)=C_{1} e^{2 t} \cos 3 t+C_{2} e^{2 t} \sin 3 t+\frac{19}{40} \cos t+\frac{7}{40} \sin t \) E. The system is degenerate.

Find the base of 'a parallelogram with a height of 10.5 feet and an area of \( 189 \mathrm{ft}^{2} \).

Find the standard deviation of the sampling distribution of sample means using the given information. Round to one decimal place, if necessary. \[ \mu=61 \text { and } \sigma=10 ; n=64 \]

A manufacturer produces chairs for a retail store according to the formula, \( M=12 P+100 \), where \( M \) is the number of units produced and \( P \) is the retail price of each chair. The number of units sold by the retail store is given by \( N=-3 P+970 \), where \( N \) is the number of units sold and \( P \) is the retail price of each chair. What are all the values of \( P \) for which the number of units produced is greater than or equal to the number of anits sold?

\( \frac { a ^ { 3 } - 125 } { a - 5 } = a ^ { 2 } + \square a + 25 \)