answer:In Maple, the default expansion order can be modified using the environment variable called Order. To change it to 3, for instance, you should execute the following command: ```maple Order := 3: ``` After this, when you use the right-click context-menu action for series, the new default order (3 in this case) will be reflected. For further information, consult the help page for Order in Maple.

answer:Given the 95% confidence interval of (5.48, 8.72) messages per year, we can conclude that: - It is 95% confident that the average number of messages sent by LinkedIn users using the new recommendation algorithm will be higher than the average number of messages sent by LinkedIn users using the regular recommendation algorithm. - Specifically, the average number of messages sent by LinkedIn users using the new algorithm will be approximately 6 to 9 messages more per year than the average number of messages sent by LinkedIn users using the regular algorithm. Therefore, the correct statement is: d. On average, all LinkedIn users would send more messages with the new algorithm than with the old algorithm.

answer:1. The area, A, can be calculated using the formula for the area of a triangle with two angles and a side: A = frac{1}{2} a b sin(C), where a and b are the sides adjacent to angles C and 10 {}^{circ} respectively. First, we find the third angle, C = 180 {}^{circ} - 102 {}^{circ} - 10 {}^{circ} = 68 {}^{circ}. Now, let's compute the side b using the law of sines: frac{b}{sin(10 {}^{circ})} = frac{6.5}{sin(68 {}^{circ})}. After calculating, the area is approximately 3.48 square units. 2. The circumradius, R, can be found using the formula R = frac{a}{2 sin(A)}, where a is the side opposite angle A. Let A = 102 {}^{circ}, then R = frac{6.5}{2 sin(102 {}^{circ})}. Calculating this, we get the circumradius to be about 3.32 units. 3. The inradius, r, can be expressed in terms of the area and the semiperimeter, s: A = r(s - a)(s - b)(s - c), where a, b, and c are the sides of the triangle. Since we know A and s, we can solve for r. The semiperimeter is s = frac{a + b + c}{2}, which we can compute using the lengths found earlier. The inradius is approximately 0.5 units. 4. The semiperimeter, s, is already given as 6.91 units. Therefore, the triangle's area is 3.48 square units, the circumradius is 3.32 units, the inradius is 0.5 units, and the semiperimeter is 6.91 units.

answer:To express 4/4.5 in its simplest form, we first convert 4.5 to a mixed number, then find the equivalent fraction. Here's the simplification process: 4.5 = 4 + 0.5 = 4 + 1/2 = 9/2 Now, we can rewrite the original fraction: 4/4.5 = 4/(9/2) To simplify, we multiply the numerator and denominator by the denominator's reciprocal: 4/4.5 = 4/1 * 2/9 = 8/9 Therefore, the fraction 4/4.5 in simplest form is 8/9.