Math Answers

 Show that the equation 𝑦 = 𝑥𝑒 𝑥 is a solution of the differential equation: 𝑦 ′ − 𝑦 − 𝑒 𝑥 = 0

1. A bag contains five yellow sweets, three green sweets and one purple sweet. A sweet is taken out

of the bag and replaced. Another sweet is taken out.

(a) Find the probability of neither sweet is green.

(b) Find the probability that the two sweets are different colours

y'=cos(x+y)

USE DE MOIVRE'S THEOREM TO EVALUATE (SQUARE ROOT OF 3 MINUS 1)^5. EXPRESS YOUR ANSWER IN THE STANDARD FORM A+BI

1.     There are 41 candidates approved to be allotted as the F.D.R.E. council of cabinets. Historic facts of the candidates are shown below, 8 were served as former cabinet members,14 were university presidents, 15 served as members of P.R.H., 2 served in former cabinet and as P.R.H, 4 served as university presidents and members of former cabinet, 6 were served as university presidents and members of P.R.H, 1 served in all the three positions. The find the number of candidates:

a.      Served in none of the three positions?

b.     Only university presidents?

c.      At least one of the three positions?

d.     Exactly two positions?

The average weight of newborns is 2150 grams. The standard deviation is 480 grams. Assume the variable is normally distributed. If a newborn is selected at random, find the probability that

a) The newborn will weigh less than 2846 grams.

b) The newborn will weigh between 3118 and 4038 grams.

c) What is the 60th percentile of the weights?

d) If a sample of 40 newborns were selected, find the probability that the sample mean is greater than 3330 grams.

 Identify the appropriate distribution function if we want to select 20 random numbers between 0 and 9.

Suppose the mean of the student completed the quiz is 30 minutes. Find the probability of a student completed the quiz in less than 20 minutes.

1.   Assume that the exam result of Data Science class fits a normal distribution. Furthermore, the mean exam result  is 82, and the standard deviation is 17.2. What is the percentage of students scoring 90 or more in the exam?

Prove that all the real of the form a+b√2 a,b element of Z forms a ring