Kim Walrath has a nutritional deficiency and is told to take at least 2500 mg of​ iron, 2400 mg of vitamin​ B-1, and 1800 mg of vitamin​ B-2. One Maxivite pill contains 40 mg of​ iron, 8 mg of vitamin​ B-1, an 5 mg of vitamin​ B-2 and costs

$0.05.One Healthovite pill provides 10 mg of​ iron, 12 mg of vitamin​ B-1, and 15 mg of vitamin​ B-2 and costs ​$0.09.

Complete parts​ (a) and​ (b) below.

​(a) What combination of Maxivite and Healthovite pills will meet​ Kim's requirement at lowest​ cost? What is the lowest​ cost?

The best combination is? pills of Maxivite and? pills of Healthovite.

​(Round to the nearest whole number as​ needed.)

The lowest cost is ​$?

​(Round to the nearest cent as​ needed.)

​(b) In your solution for part​ (a), does Kim receive more than the minimum amount she needs of any​ vitamin? If​ so, which vitamin is​ it?

Select the correct answer​ below, and if​ necessary, fill in the answer boxes to complete your choice.

A.Yes. She receives?mg more iron than she​ requires,?mg more vitamin​ B-1 more than she​ requires,? and? mg more vitamin​ B-2 than she requires.

B. No. She does not receive more than she requires of any vitamin.

In general, if p is the number of predictor variables and k is the number of groups for the outcome variable in a DA, how many different discriminant functions can be obtained to differentiate among
groups? (This question assumes that the X predictor variables have a determinant that is nonzero; that is, no individual Xi predictor variable can be perfectly predicted from scores on one or more other X
predictor variables.)

Can a closed linear map be unbounded?

Let ? = {?1, ?2, ?3, … … … … ?? } ?? ? = {?1, ?2, ?3, … … … … ?? } Prove by induction that the number of injective functions ? from ? ?? ? is ?!

Solve the initial value problem below using the method of Laplace transforms.

y''+7y'+12y=-7cost-9sint

y(pi/2)=1 y'(pi/2)=0

a computer retail store has 11 personal computers in stock. a buyer wants to purchase 4 of them. unknown to either the retail store or the buyer, 4 of the computers in stock have defective hard drives. assume that the computers are selected at random.
in how many different ways can the 4 computers be chosen
what is the probability that exactly one of the computers will be defective
what is the probability that at least one of the computers selected is defective

(a) Show that a group that has only a finite number of subgroups must be a finite group.

(b) Let G be a group that has exactly one nontrivial, proper subgroup. Show that G must be isomorphic to Zp2 for some prime number p. (Hint: use part (a) to conclude that G is finite. Let H

be the one nontrivial, proper subgroup of G. Start by showing that G and hence H must be cyclic.)

Q) if a fraction λ of the population susceptible to a disease that provides immunity against reinfection moves out of the region of an epidemic, the situation may be modeled by system
S'=-βSI-λS
I'=βSI-α I.
Show that both S and I approach zero as t→∞.

Where,
S=The susceptible population
I=infected individuals
β=infection rate

Find the original source where Fibonacci presented his puzzle about modeling rabbit populations. Discuss this problem and other problems posed by Fibonacci and give some information about Fibonacci himself.

prove that a ring R is a field if and only if (R-{0}, .) is an abelian group