Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (The pair of variables have a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The number of hours 6 students spent for a test and their scores on that test are shown below. Hours spent studying, x Test score, y 1 3 4 6 (a) x=2 hours (c) x = 14 hours (b) x = 2.5 hours (d) x = 1.5 hours 40 43 52 48 61 67 Find the regression equation. (Round the slope to three decimal places as needed. Round the y-intercept to two decimal places as needed.)

Q: v2 dv

A:

Q: Evaluate. (Be sure to check by differentiating!) √3+4x² 8 + 4x dx, x# - 2

A:

Q: aluate. v2

A: Integration: ∫-12(-x2+x+2)dxWe know∫xndx=xn+1n+1

Q: dy ー1

A: Given:

Q: Find the formula for dz Xx2

A: Given z=fx,y where x=est and y=s2t3 It is asked to find ∂z∂s.

Q: |4x dA R.

A:

Q: S- 3+ Vx

A:

Q: Evalucte (x²_ 2x+ dx atb+C Soln:

A: given,       ∫x3-2x+1xdx

Q: 1 4x +3 dr

A:

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.