[2.13] Let S be a nonempty set in R". Show that S is convex if and only if for each integer k > 2, the following holds true: X1,..., Xg € S implies that £11,x; €S, where E1A; = 1 and i, 20 for j= 1,., k. =1 and å; 20 for j = 1,.., k.

Q: 5. 8. 45°

A: Solve for value x

Q: 4. 108 45 C B.

A: As per guideline we have to solve only one since all question are different

Q: 4.5.23 how do we figure out to solve it ?

A: The given polynomial is p (t) = 7 + 20 t2 + 8 t3 and the basis is given as { 1, 2t , -2 + 4t2 , -12t…

Q: 2. 3. 8. 5.

A:

Q: 14. 10 19

A: 14 Consider the sine angle property is, sinx=perpendicularhypotenuse

Q: 58.6 - 9.27

A: Given that the expression is  58.6-9.27.

Q: 2. 6. 1.

A:

Q: 6.4 3

A:

Q: Find lim (x,y)→(12,3) xy cos(x – 4y). OS 1. –36 2. 36 3. 3 4. 0

A:

Q: T. 9

A: Given: To determine: ST→ & tan∠S

Q: 18. 32 13

A:

Q: 14. 115"

A:

Q: 8 14

A:

Q: %3D 6.

A: Please see the explanation below

Q: ne distance between the points on the gi

A:

Q: 29 14

A: It's trigonometric question so I'm providing hand written solution for better understanding.

Q: 2.3 1/p; (1-P)/p².

A: X~geom(p)

Q: 9. 12 54

A: Will use basic trigonometry to solve this. Particularly we will use sine of x.

Q: Find the circumference of each circle. Leave your answer in terms of T.

A: The circumference of a circle with radius r is 2πr.

Q: Match the given parametric equations with one of the parametric curves. x-3- sint, y = 5+ cost O A.

A: To sketch the given parametric equation :- x = 3 -sin t  and  y = 5+cos t

Q: 10. 6. 3.

A: we have to find the radius of circle from the given figure

Q: 7. 45

A:

Q: 3. alogM

A: We have to find the value of: alogaM Let us substitute, logaM=y Then we get, ay=M

Q: 13. 34 18

A:

Q: 11 11 4. 64

A: Given: simplify the expression

Q: 10 4 2.

A: Solution-

Q: 4. 15 33,

A:

Q: 2. 27

A:

Q: Approximate the area under the curve y = x² from x = with 4 subdivisions. 1 to x = 3 using a Right…

A:

Q: 50.19

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.