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3 years ago

A dog breeder plans to mix two types of food to make a mix of low cost

Mathematics

1 answer:

lys-0071 [83]3 years ago

5 0

Answer:

3.75 bags of ChowChow
0.75 bags of Kibble

Step-by-step explanation:

The constraints on protein, minerals, and vitamins give rise to the inequalities ...

40c +30k ≥ 150 . . . . . . required protein

20c +20k ≥ 90 . . . . . . required minerals

10c +30k ≥ 60 . . . . . . . required vitamins

And we want to minimize 10c +12k.

The graph shows the vertices of the feasible region in (c, k) coordinates. The one that minimizes cost is (c, k) = (3.75, 0.75).

To minimize cost, the daily feed should be ...

3.75 bags of ChowChow
0.75 bags of Kibble

Daily cost will be $46.50.

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Use induction to prove: For every integer n > 1, the number n5 - n is a multiple of 5.

nignag [31]

Answer:

we need to prove : for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

1) check divisibility for n=1, $f(1)=(1)^{5}-1=0$ (divisible)

2) Assume that $f(k)$ is divisible by 5, $f(k)=(k)^{5}-k$

3) Induction,

$f(k+1)=(k+1)^{5}-(k+1)$

$=(k^{5}+5k^{4}+10k^{3}+10k^{2}+5k+1)-k-1$

$=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k$

Now, $f(k+1)-f(k)$

$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-(k^{5}-k)$

$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-k^{5}+k$

$f(k+1)-f(k)=5k^{4}+10k^{3}+10k^{2}+5k$

Take out the common factor,

$f(k+1)-f(k)=5(k^{4}+2k^{3}+2k^{2}+k)$ (divisible by 5)

add both the sides by f(k)

$f(k+1)=f(k)+5(k^{4}+2k^{3}+2k^{2}+k)$

We have proved that difference between $f(k+1)$ and $f(k)$ is divisible by 5.

so, our assumption in step 2 is correct.

Since $f(k)$ is divisible by 5, then $f(k+1)$ must be divisible by 5 since we are taking the sum of 2 terms that are divisible by 5.

Therefore, for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

3 0

3 years ago

What is the probability that a marble chosen at random is

Brums [2.3K]

Answer:

$P=\frac{6}{11}$

Step-by-step explanation:

The probability can be defined as the ratio between the possible events and the total number of outcomes.

In this case, according to the image attached, the total number of outcomes is 11, because they are 11 marbles in total.

Now, the specific event is all shaded marbles or labeled with a multiple of 3. With this specific characteristics 6 marbles, because there are 5 shaded marbles and 6 is a multiple of 3. So, the possible events are 6.

Therefore, the probability is

$P=\frac{6}{11}$

The right answer is the last choice.

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3 years ago

Read 2 more answers

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tangare [24]

Answer:

See Below

Step-by-step explanation:

First, isolate x. To do that add 3.5 to each side

x - 3.5 = -3.1

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I dont understand this question.Help?

Maurinko [17]

the first step Andre made was

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And the first step Diego made was

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Alinara [238K]

What exactly is it asking for

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