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2sinx/sin3x + tanx/tan3x =1 . prove this
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During a normal weekday, customers arrive randomly at a local branch of ScotiaBank in the downtown Toronto at an average rate of 5 per 3 minutes.

Question . What is the probability that there are 10 customers arriving at this branch during the next 3 minutes?
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How to determine the volume of the function f(x) = 3/2sin(x) rotated around the x-axis from (0, pi). The slice is a semi-circle. Thank you!
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child ratio- If you have a room measuring 10.01m by 6.07m and each child needs 2.5m play space how many children would the room hold
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Let A={1,1/2,1/4,1/8,…} and B={ 1/2,3/4,7/8,…}. Explain why supA=supB=1?
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Show that f(x)=x^2 is not uniformly continuous on R.
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I have data from participants who rate emotional content of pictures. Specifically, people see 20 pictures of abstract paintings (one at a time) and are asked, "what emotions is expressed in the picture?" There are 5 response options: anger, fear, sadness, happiness, and none. The key info here is that for each picture people choose only one of the emotion choices. I then add number of pictures rated as expressing anger, fear, sadness etc. and have 5 continuous variables. The 5 continuous variable are obviously not independent because if someone rated X pictures as expressing anger and Y as expressing happiness, then they could not choose more than 20-(X+Y) pictures as expressing fear or sadness; hence the variables have negative correlations. My question now is, how can I examine correlations among these emotions if they are not completely independent of one another?
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On the set lunch menu of a restaurant, there are 4 types of rice, 3 types of noodles and 2 types of congee for customers to choose. If Lilian selects one of them from the menu, how many choices does she have?
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A right circular cone contains some fluid. The height of the water level is 9 cm. Now, an additional 37pi cubic cm of fluid is poured into the cone.(Let the height rise of water level be x cm.)
(a) Find the rise of the water level.
(b) Find the percentage increase of the surface area in contact with the fluid.
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if the perimeter of an equilateral triangle is 72 m,then its area is
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