i have 537 cookies and i need to divide them into 12 equal groups. how many cookies are in each group

Mathematics

1 answer:

katrin [286]3 years ago

5 0

If you divide 537 in to 12 groups. each group would have 44 cookies and you would have 9 left.

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Food and clothing are shipped to victims of a natural disaster. Each carton of food will feed 13 people, while each carton of c

lutik1710 [3]

Answer:

233 cartons of food; 467 cartons of clothing

Step-by-step explanation:

This linear programming problem can be formulated as two inequalities (in addition to the usual constraints that the variables be non-negative). One of these expresses the constraint on weight. Let f and c represent numbers of food and clothing containers, respectively.

40f +25c ≤ 21000

The other expresses the limit on volume.

20f + 5c ≤ 7000

_____

Feasible Region vertex

We can subtract the boundary line equation of the first inequality from that of 5 times the second to find f:

5(20f +5c) -(40f +25c) = 5(7000) -21000

60f = 14000

f = 233 1/3

The second boundary line equation can be rearranged to find c:

c = 1400 -4f = 466 2/3

The nearest integer numbers to these values are ...

(f, c) = (233, 467)

The other vertices of the feasible region are associated with one or the other variable being zero: (f, c) = (0, 840) or (350, 0).

Check of Integer Solution

Trying these in the constraint inequalities gives ...

40·233 +25·467 = 20,995 < 21000
20·233 +5·467 = 6995 < 7000

Selection of the Answer

The answer to the question will be the feasible region vertex that maximizes the number of people helped. That is, we want to maximize ...

p = 13f + 6c

The values of p at the vertices are ...

p = 13·233 + 6·467 = 5831

p = 13·0 + 6·840 = 5040

p = 13·350 + 6·0 = 2100

The most people are helped when the plane is filled with 233 food cartons and 467 clothing cartons.

7 0

3 years ago

Write an equation of the line containing the point (3,5) and perpendicular to the line 4x-3y=5

ICE Princess25 [194]

Answer:

Step-by-step explanation:

In order to write the equation of the line perpendicular to the given line, we first have to know what the slope of the given line is, and there's no way to tell by looking at it in its current form, which is standard. We need to solve that equation for y to determine the slope of that line. Solving for y:

$-3y=-4x+5$ and

3y = 4x - 5 (just change all the signs so our y term isn't negative anymore...yes, you're "allowed" to do that!) and

$y=\frac{4}{3}x-\frac{5}{3}$ So we can see now that the slope of this line is 4/3. That means that the perpendicular slope is -3/4. Passing through the given point (3, 5):