Afarmer has two types of milk, one that is 24% butterfat and another which is 18% butterfat. how much of each should he use to end up with 42 gallons of 20% butterfat

28 gallon of 24% butterfat and 14 gallon of 18% butterfat.

Step-by-step explanation:

Let x gallon of 24% butterfat mixed with the y gallon of 18% butterfat to obtain 42 gallon of 20% butterfat,

⇒ x + y = 42 ⇒ x = 42 - y (1),

Quantity of butterfat in x gallon + quantity of butterfat in y gallon = total quantity of butterfat,

⇒ 24% of x + 18% of y = 20% of 42

⇒ 0.24x + 0.18y = 0.20 × 42

⇒ 0.24x + 0.18y = 8.4

⇒ 24x + 18y = 840

⇒ 4x + 3y = 140  

From equation (1),

4(42-y) + 3y = 140

168 - 4y + 3y = 140

168 - y = 140

⇒ y = 28,

Again from equation (1),

x = 42 - y = 42 - 28 = 14,

Hence, 28 gallon of 24% butterfat and 14 gallon of 18% butterfat.

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.

.24

step-by-step explanation:

the probability is   .24

the first player had the highest probability of getting a silver marble

the game could be made fair by adding back the marble that was drawn after each draw