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As there are a total of 10 marbles in the bag, then the probability of picking a red marble is 5/10. When the next marble is selected, there are only 9 marbles left in the bag since the red marble has not...

Here, we're using the product rule (and the chain rule for the e^-x): y=(x²+1)(e^-x) dy/dx=(2x)(e^-x)+(x²+1)(-1)(e^-x) Then we simplify to get...

We can see that the function is a sum of three terms so we can deal with each term separately and add them up. The term 8x³ and 5 are relatively straightforward and follow the standard rules fo...

dx=du/6 => (u-5)/6=x So the integral is now (2((u-5)/6)-3)(u^1/2) du/6 Which through simplifying becomes (1/36)(2u-28)(u^1/2)du = (1/36)(2u^3/2 -28u^1/2)du After integrating becomes (1/36)(4(u^5/2)/5 -...

Step 1: (5t+3)/4 = 1 Step 2: (5t+3)= 1 x 4 Step 3: 5t + 3 = 4 Step 4: 5t = 4 - 3 Step 5: 5t = 1 Answer: t = 1/5