Answer:
740
Step-by-step explanation:
Answer:
Y=-4x-5
Step-by-step explanation:
-21=-4(4)+b
-21=-16+b
b=-5
y=-4x-5
Answer:
∑ (-1)ⁿ⁺³ 1 / (n^½)
∑ (-1)³ⁿ 1 / (8 + n)
Step-by-step explanation:
If ∑ an is convergent and ∑│an│is divergent, then the series is conditionally convergent.
Option A: (-1)²ⁿ is always +1. So an =│an│and both series converge (absolutely convergent).
Option B: bn = 1 / (n^⁹/₈) is a p series with p > 1, so both an and │an│converge (absolutely convergent).
Option C: an = 1 / n³ isn't an alternating series. So an =│an│and both series converge (p series with p > 1). This is absolutely convergent.
Option D: bn = 1 / (n^½) is a p series with p = ½, so this is a diverging series. Since lim(n→∞) bn = 0, and bn is decreasing, then an converges. So this is conditionally convergent.
Option E: (-1)³ⁿ = (-1)²ⁿ (-1)ⁿ = (-1)ⁿ, so this is an alternating series. bn = 1 / (8 + n), which diverges. Since lim(n→∞) bn = 0, and bn is decreasing, then an converges. So this is conditionally convergent.
Answer:
$316.46
Step-by-step explanation:
total cost = 109.5% = 109.5% x $289 = $316.46 (2dp)
Topic: Percentages
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If each player will receive 7/8 of a cup, and there are a total of 20 cups of lemonade, then the number of servings that can be made is equal to:
20 cups divided by (7/8 cup per player)
20 / (7/8) = 20 * (8/7) = 160/7 = 22 and 6/7 (round down since we're looking for complete servings)
This means that 22 complete servings can be made.
