Math Answers

Testing for a disease can be made more efficient by combining samples. If the samples from two people are combined and the mixture tests​ negative, then both samples are negative. On the other​ hand, one positive sample will always test​ positive, no matter how many negative samples it is mixed with. Assuming the probability of a single sample testing positive is 0.15​, find the probability of a positive result for two samples combined into one mixture. Is the probability low enough so that further testing of the individual samples is rarely​ necessary?

14119 € was deposited on 4.4.2006 in a bank account. The interest rate was 3,5 % (p.a.) and the tax at source rate was 30 %. The bank added the accrued interest to the capital at the end of each year. Calculate the accumulated value of the investment on 4.4.2010 when the account was closed.

Create a simplified expression for the perimeter of this rectangle. Horizontally it is labelled 3x-11, and vertically it is labeled x+9. What do I do??

Find a particular solution of y''+y=sinx, using the method of undetermined coefficients

Solve by the method of variation of parameter y''+y=secx

Solve by the method of variation of of parameter y''+y=secx

21. Find the values of my for which the system is not a Cramer's system.

(a)-2x+m²y=m

x-my=1-m

(b) mx+y=2

x+my=-2

22.(a) Mr. Benny is now 3 times as old as his son. In 13 years' time he will be twice as old as his son,Find Mr. Benny's present age.

(b) Two buses are 200 kilometers apart. They are traveling towards each other, the first bus is traveling 40km per hour while the second bus is traveling 60km per hour. When and where will they meet?

23.Two consecutive intergers are such that their reciprocatals add to 9/10. Find the two integers.

16. Solve in |R:

(a) 2(3y-2)+3(4-3y)>12-(5y+7)

(b) 2(k+2)+3(2k-3)<or=2

17.(a) if x=1-3t and y=2t-1.

Find the value of t such that x=y.

(b) solve for real value of x the equation,

(m+1)x²-(m+3)x+3-m=0.

When m=-1.

18.Given the parametric equations:

x=t-1/t

y=2(t+2)/t²

Find the coordinates of the point where,

(a) t=-2

(b) t=-1

19.solve in |R:

(a) 4(m+5)-6(2m+3)=3(m+14)-2(5-m)+9

(b) 3(k-1)-4(k+6)=10(k+5)

Show that x^5 +4x=1 has exactly one solution on [0,1]

Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that each baby will be a​ girl, but assume that the method has no​ effect, so the probability of a girl is 0.5. Assume that the groups consist of 17 couples.