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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?

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.

(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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