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Use the table to determine the total of the servicecharge. Service charges for Gary Baxter's account were the basic charge, 8 bills paid, 1 overdraft, $450 cash advance, and 3 regional ATM transactions.
$\begin{array}{|lc|}\hline \text{ Online Banking Service }& \text{ Service Charge }\\ \text{ Basic Monthly Charge }& \$6.95\\ \text{ Bill Payment-first 5 N/C }& 0.50\\ \text{ Printed Statement }& 4.00\\ \text{ Replace Lost Card }& 5.00\\ \text{ Overdraft }& 25.00\\ \text{ International Wire Transfer }& 20.00\\ \text{ ATM Transaction Charges }\\ \text{ Local Network }& \text{ N/C }\\ \text{ Regional Network }& 1.00\\ \text{ National Network }& 2.00\\ \text{ Out-of-Network }& 3.00\\ \text{ Cash Advance }-2.00\mathrm{\%}\text{ of }\text{ Amt }& \$10.00\mathrm{Max}\\ \hline\end{array}$

The following advanced exercise use a generalized ratio test to determine convergence of some series that arise in particular applications, including the ratio and root test, are not powerful enough to determine their convergence.

The test states that if

 $\underset{n\to \mathrm{\infty }}{lim}\frac{a_{2n}}{a_n}<1/2$

then $\sum a_n$ converges,while if

$\underset{n\to \mathrm{\infty }}{lim}\frac{a_{2n+1}}{a_n}>1/2$,

then $\sum a_n$  diverges. Let ${\displaystyle a_n=\frac{1}{1+x}\frac{2}{2+x}\dots \frac{n}{n+x}\frac{1}{n}=\frac{(n-1)!}{(1+x)(2+x)\dots (n+x)}}$.

Show that $a_{2n}/a_n\le e^{-x/2}/2$  .

For which x > 0 does the generalized ratio test imply convergence of ${\displaystyle \sum _{n=1}^{\mathrm{\infty }}{a}_n}$?

Use the table to determine the total of the service charge. Sally Hudson's service charges: basic charge, 9 bills paid, lost card replacement, and 6 ATM transactions, 3 national and 3 out of network.
$\begin{array}{|lc|}\hline \text{ Online Banking Service }& \text{ Service Charge }\\ \text{ Basic Monthly Charge }& \$6.95\\ \text{ Bill Payment-first 5 N/C }& 0.50\\ \text{ Printed Statement }& 4.00\\ \text{ Replace Lost Card }& 5.00\\ \text{ Overdraft }& 25.00\\ \text{ International Wire Transfer }& 20.00\\ \text{ ATM Transaction Charges }\\ \text{ Local Network }& \text{ N/C }\\ \text{ Regional Network }& 1.00\\ \text{ National Network }& 2.00\\ \text{ Out-of-Network }& 3.00\\ \text{ Cash Advance }-2.00\mathrm{\%}\text{ of }\text{ Amt }& \$10.00\mathrm{Max}\\ \hline\end{array}$

During a given week, the museum had attendance as shown in the table at right. a. Numerically summarize the center and spread of attendance by finding the median and interquartile range (IQR). b. The museum management needs to tell the staff members their work schedules a week in advance. The museum wants to have approximately one staff member for every 150 visitors. How many staff members should be scheduled to workeach week? Explain your reasoning. c. Why is a scatterplot not an appropriate display of this data?
$\begin{array}{cc}Day& Attendance\\ 1& 870\\ 2& 940\\ 3& 731\\ 4& 400\\ 5& 861\\ 6& 680\\ 7& 593\end{array}$

The yield strength of CP titanium welds was measured for welds cooled at rates of ${10}^{\circ }\mathrm{C}\&\#x2F;\mathrm{s},{15}^{\circ }\mathrm{C}\&\#x2F;\mathrm{s},and{28}^{\circ }\mathrm{C}\&\#x2F;\mathrm{s}$. The results are presented in the following table. (Based on the article “Advances in Oxygen Equivalence Equations for Predicting the Properties of Titanium Welds,” D. Harwig, W. Ittiwattana, and H. Castner, The Welding Journal, 2001:126s-136s.)$amp;71.00amp;63.00amp;68.65amp;75.00amp;68.00amp;73.70amp;79.67amp;73.00amp;78.40amp;81.00amp;76.00amp;84.40amp;75.50amp;79.67amp;91.20amp;72.50amp;81.00amp;87.15amp;73.50amp;amp;77.20amp;78.50amp;amp;80.70amp;78.50amp;amp;84.85amp;88.40$
a. Construct an ANOVA table. You may give a range for the P-value. b. Can you conclude that the yield strength of CP titanium welds varies with the cooling rate?

${\displaystyle {\left(x^4{y}^5\right)}^{\frac{1}{4}}{\left(x^8{y}^5\right)}^{\frac{1}{5}}=x^{\frac{j}{5}}{y}^{\frac{k}{4}}}$
In the equation above, j and k are constants. If the equation is true for all positive real values of x and y, what is the value of $j-k$?
A)3
B)4
C)5
D)6

Advanced Math
Which one is a simplified expression for $A(A^{\prime }+B^{\prime })(B+C)(B+C^{\prime }+D)$