Math Answers

what is symbolic form of she did nit received a promotion or she did not received a salary increase

What is symbolic form of it is not true that, the students answered their activity or participated in the class discussion

Let E:=Exi+Eyj+Ezk  and H:=Hxi+Hyj+Hzk be two vectors assumed to have continuous partial derivatives (of second order at least) with respect to position and time. Suppose further that E and H satisfy the equations:

∇⋅E=0,∇⋅H=0,∇×E=−1/c. ∂H/∂t, ∇×H=1/c. ∂E/∂t

prove that E and H satisfy the equation

∇^2Ei =1/c^2. ∂^2Ei/∂t^2  and ∇^2Hi=1/c^2. ∂^2Hi/∂t^2

Here, i=x,y  or z.

Hint: Use the fact that∇×(∇×V)=∇(∇⋅V)−∇^V.

In one study it was found that  84%  of all homes have a functional smoke detector. Suppose this proportion is valid for all homes. Find the probability that in a random sample  of  150  homes, between  70 %  and  90%  will have a functional smoke detector.

A population comprises numbers 1,3,5,7,9 and 11. Consider all population of size two when sampling with replacement.

Find the

1. The mean of population

2. The standard deviation of the population.

3. The mean of the sampling distribution of means.

4. The standard deviation of the sampling distribution of means.

Calculate the confidence level that would be required to have the mean

assembly time estimated up to ±15 seconds assuming the sample size

is 120 minutes.

he weekly wages of 100 employees are given below. Find D4 and D8. Also find the wage

above which we have the richest 35% employees, correct to the nearest rupee.

Weekly Wages Below 50 50-100 100-150 150-200 200-250 250-300

No. of employees 10 70 80 100 150 90

Hint: Richest 35% employees earn above P65.

Ans.: D4= 170, D8 = 246.66, Richest 35% employees earn above Rs. 222.

The following table shows the income distribution of 600 families. Find the minimum income

of the riches 30% families. Also the limits of income of middle 50% of families, to the nearest

rupees.

Income Below

75

75-

150

150-

225

225-

300

300-

375

375-

400

400 &

above

No. of

families

69 137 225 46 88 25 10

Ans.: the richest 30 % families earns Rs. 222 and above per week , the middle 50% families

weekly income lies between 120 and 256.

The ages of 100 persons are tabulated below. Find Q1, Q3, D2, D8, P20 and P60. Above what age

we have the oldest 10% persons?

Age(in years) 10-20 20-30 30-40 40-50 50-60 60-70 70-80

No. of persons 16 20 21 28 10 3 2

Note: the oldest 10% are above P90.

Ans.: P20 = 22, P60=41.071, the oldest 10% persons are of the age 55 and above.

Calculate the quartiles, (i,e., Q1 and Q3,), deciles D3 and D7, Percentiles P10, P23 and P92 for the

following data. Also find the Quartile Range and Quartile Deviation.

Marks 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80

No. of Students 8 7 5 12 28 22 8 10