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leonid [27]
2 years ago
10

The ratio of the number of boys to the number of girls at a school is 4:5. If there are 120 boys, how many students are there al

together?
Mathematics
1 answer:
frutty [35]2 years ago
8 0

Answer: 270 students altogether

There are 150 girls.

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Solve the linear programming problem. Minimize and maximize Upper P equals negative 20 x plus 30 y Subject to 2 x plus 3 y great
Alika [10]

Answer:

Maximum = 540 at (6,14)

Minimum = 300 at (0,10) or (12,2).

Step-by-step explanation:

The given linear programming problem is

Minimize and maximize: P = 20x + 30y

Subject to constraint,

2x+3y\ge 30            .... (1)

2x+y\le 26            .... (2)

-2x+3y\le 30            .... (3)

x,y\geq 0

The related equation of given inequalities are

2x+3y=30

2x+y=26

-2x+3y=30

Table of values are:

For inequality (1).

x      y

0     10

15     0

For inequality (2).

x      y

0     26

13     0

For inequality (3).

x      y

0     10

15     0

Pot these ordered pairs on a coordinate plane and connect them draw the corresponding related line.

Check each inequality by (0,0).

2(0)+3(0)\ge 30\Rightarrow 0\ge 30    False

2(0)+(0)\le 26\Rightarrow 0\le 26     True

-2(0)+3(0)\le 30\Rightarrow 0\le 30    True

It means (0,0) is included in the shaded region of inequality (2) and (3), and (0,0) is not included in the shaded region of inequality (1).

From the below graph it is clear that the vertices of feasible region are (0,10), (6,14) and (12,2).

Calculate the values of objective function on vertices of feasible region.

Point           P = 20x + 30y

(0,10)           P = 20(0) + 30(10) = 300

(6,14)           P = 20(6) + 30(14) = 540

(12,2)           P = 20(12) + 30(2) = 300

It means objective function is maximum at (6,14) and minimum at (0,10) or (12,2).

7 0
3 years ago
Myra saved $15 a month for 18 months. She bought a book for $46.50 and a tennis racquet for $129.95. How much does she have left
Elis [28]

Answer:

A

Step-by-step explanation:

15*18=270.

270-46.50=223.5

223.5-129.95=93.55.

A. $93.55

7 0
3 years ago
Ben's making bow ties. How many 1/2 yard-long bow ties can he make if he has 18 feet of fabric
ira [324]

Answer:

12 bow ties

Step-by-step explanation:

1/2 yard = 1.5 feet = 1 bow tie

1.5 x 2 = 3 feet

1 yd = 2 bow ties

18/3 = 6 yards

6 x 2 = 12 bow ties

6 0
3 years ago
Brian works in the lab and feels an empty cylindrical flask with 200 cubic centimeters of liquid. The flask has a radius of 3 cm
Fittoniya [83]

Answer:

<h2>49.49%</h2>

Step-by-step explanation:

volume of liquid in the flask= 200 cm^3

radius of the flask = 3 cm

height of the  flask= 12 cm

volume of flask is given by =

putting values and solving we get =396 cm^3

therefore the volume unfilled= 396-200= 196cm^3

therefore % of volume unfilled= 196/396*100= 49.49%

6 0
3 years ago
Enter the y coordinate of the solution to this system of equations.
riadik2000 [5.3K]
-x-y=1
-y=1+x
y=-1-x

-1-x=-2x+9
-x=-2x+10
x=10

y=-1-10
y=-11
3 0
3 years ago
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