Allison’s cupcake and cookie budget for her party is $105. She would like to have at least 40 cupcakes and cookies combined, and would like to have at most 5 more cupcakes than cookies. If cupcakes sell for $2.50 and cookies for $1.50, which system of inequalities could help Allison determine possible numbers of cupcakes (a) and cookies (b) that she should buy? ( a ≥ 0 , b ≥ 0 )

a + b ≥ 40

a + 5 ≤ b

2.50a + 1.50b ≤ 105

Step-by-step explanation:

We are told she would like to have at least 40 cupcakes and cookies combined.

If a is number of cupcakes and b is number of cookies, then this inequality is;

a + b ≥ 40

Secondly, we are told she would like to have at most 5 more cupcakes than cookies.

Thus, the inequality is;

a + 5 ≤ b

Lastly, we are told that cupcakes sell for $2.50 and cookies for $1.50

Thus, the inequality is;

2.50a + 1.50b ≤ 105

Finally, the 3 inequalities are;

a + b ≥ 40

a + 5 ≤ b

2.50a + 1.50b ≤ 105

step-by-step explanation:

i found the life tables for the year 2012. 

life table of males at age 30. probability of dying between ages x and x+1

total population:  

29–30 . . . . . . . . . . . . 0.001030

30–31 . . . . . . . . . . . . 0.001061

males:  

29–30 . . . . . . . . . . . . 0.001420

30–31 . . . . . . . . . . . . 0.001448

white population

29–30 . . . . . . . . . . . . 0.001005

30–31 . . . . . . . . . . . . 0.001037

white males

29–30 . . . . . . . . . . . . 0.001372

30–31 . . . . . . . . . . . . 0.001399

non hispanic white population

29–30 . . . . . . . . . . . . 0.001083

30–31 . . . . . . . . . . . . 0.001116

non hispanic white males

29–30 . . . . . . . . . . . . 0.001477

30–31 . . . . . . . . . . . . 0.001503

jacob, non hispanic white male. 30 years old.

probability that jacob lives to be 30 years old. 

since the given probabilities are probabilities of dying, i think we simply subtract it from 1 to get the probability of living. we will use the probability of non hispanic white male.

                                          probability of living to be 30 y.o.

29 - 30 : 1 - 0.001477 = 0.998523

30 - 31 : 1 - 0.001503 = 0.998497