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# Tutor profile: Grant S.

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Grant S.
Mathematics Major from South Dakota State University
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## Questions

### Subject:Calculus

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Question:

Find the derivative of \$\$y=sin(3x^2+2x+1)\$\$.

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Grant S.

We will use the chain rule to solve for this derivative. To use the chain rule we will first take the derivative of the outside term, in this case, \$\$sin\$\$. Then we multiply it by the derivative of the inside term, in this case, \$\$3x^2+2x+1\$\$ Applying this we have \$\$y' = cos(3x^2+2x+1) (6x+2)\$\$.

### Subject:Statistics

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Question:

There are 4 green beads, 6 red beads, and 10 blue beads in a jar. Assuming the beads are drawn at random, what is the probability that 2 red beads will be selected in a row without replacement?

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Grant S.

Let's start with the probability that one red bead is selected. Which would be calculated as, \$\$6/(4+6+10) = 6/20\$\$ or \$\$3/10\$\$. Now we will incorporate the second red bead. The problem indicates that the first red bead drawn would not be replaced. This now means there are now only 5 red beads and only 19 total beads left in the jar. So the probability of drawing another red bead would be \$\$5/19\$\$ To calculate the overall probability that these two events happen in a row, we will multiply their independent probabilities. So we have \$\$(3/10)(5/19)=15/190\$\$. Simplifying we have \$\$3/38\$\$,

### Subject:Algebra

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Question:

Solve the system of linear equations: \$\$(1) 4x + 5y = 29\$\$ \$\$(2) 2x + y = 10 \$\$

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Grant S.

We will use elimination to solve this system of equations. First multiply equation (2) by 2, \$\$2(2x + y = 10)\$\$ \$\$= 4x+2y=20.\$\$ Then subtract our new form of equation (2) from equation (1) and we have \$\$ 4x + 5y = 29\$\$ \$\$-(4x+2y =20)\$\$ Combining like terms, the \$\$x\$\$s cancel and we are left with \$\$3y=9\$\$. \$\$y=3\$\$ We have now solved for one of the two variables. Now substitute \$\$y=3\$\$ back into either of the original equations to solve for \$\$x\$\$. Substituting into equation (2) we have \$\$2x+3=10\$\$ \$\$2x=7\$\$ \$\$x=7/2\$\$ or \$\$3.5\$\$

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