# Questions & Answers

### Assume that a procedure yields a binomial distribution.

With n=6 trials and a probability of success of p=0.5 . Use a binomial probability table to find the probability that the number of successes x is

### Find the points on the cone z^2 = x^2 + y^2 that are closest to the point (2,2,0).

This question aims to explain the concepts of maxima and minima. Formulas to calculate the extreme values of the function. Further, it explains how

### Let x represent the difference between the number of heads and the number of tails obtained when a coin is tossed n times. What are the possible values of X?

The aim of this question is to understand the key concept of a random variable using the coin toss experiment which is the most basic binomial

### Prove that if n is a positive integer, then n is even if and only if 7n + 4 is even.

The purpose of this question is to prove that $n$ is a positive and even integer if and only if $7n + 4$ is also even. Even numbers can be equally

### A man 6 feet tall walks at a rate of 5 feet per second away from a light that is 15 feet above the ground.

When he is $10$ feet from the base of the light, at what rate is the tip of his shadow moving? When he is $10$ feet from the base of the light, at

### Find the parametric equation of the line through a parallel to b.

JUMP TO TOPICExpert AnswerExample 1SolutionExample 2Solution (a=begin{bmatrix}3\-4end{bmatrix}, b=begin{bmatrix}-7\8end{bmatrix}) This question aims

### Find, correct to the nearest degree, the three angles of the triangle with the given vertices. A(1, 0, -1), B(3, -2, 0), C(1, 3, 3).

The main objective of this question is to find the three angles of a triangle given three vertices. The angles can be found using the dot product of

### Find the differential of each function. (a) y=tan (7t), (b) y=3-v^2/3+v^2

The main purpose of this question is to find the differential of each given function. A function is a fundamental mathematical concept that describes

### Determine if the columns of the matrix form a linearly independent set. Justify each answer.

(begin{bmatrix}1&4&-3&0\-2&-7&4&1\-4&-5&7&5end{bmatrix}) The main objective of this question is to determine

### Solve the equation explicitly for y and differentiate to get y’ in terms of x.

JUMP TO TOPICExpert AnswerExample 1SolutionExample 2SolutionExample 3Solution (dfrac{1}{x}+dfrac{1}{y}=1). The main objective of this question is to

### Find the vectors T, N, and B at the given point. r(t)=< t^2,2/3 t^3,t > and point < 4,-16/3,-2 >.

This question aims to find the Tangent, Normal, and Binormal vectors by using the given point and a function. Consider a vector function,

### Find a nonzero vector orthogonal to the plane through the points P, Q, and R, and area of the triangle PQR.

Take note of the following points: $P(1,0,1) , Q(-2,1,4) , R(7,2,7)$ Find a nonzero vector orthogonal to the plane through the points $P, Q$, and