Answer:

**Answer:**

1/3 + 1/4 = 4/12 + 3/12 = 7/12

7/12 = both brothers ate 7 crackers out of 12 crackers

there were 5 crackers left on the plate means 5/12 crackers left on the plate

answer: 12 crackers at the beginning

**Step-by-step explanation:**

Whats y=1/4x-12, solve for x

What is the relationship between gross pay and net pay

John has five apples and he gives two to his friend how many apples does John have left

Write equations for the vertical and horizontal lines passing through the point (-3,0).

4/5 divided by 1/10?

What is the relationship between gross pay and net pay

John has five apples and he gives two to his friend how many apples does John have left

Write equations for the vertical and horizontal lines passing through the point (-3,0).

4/5 divided by 1/10?

−

5

y

=

14

Find

x

when

y

=

2

**Answer:**

4

**Step-by-step explanation:**

The **distance **between the **midpoints **of the first **segment **and the third **segment **is __2k/3__. Hence, __option A__ is the right choice.

The **mid-point** of a **line segment** is the **point **from which the **distance **to both ends of the **line segment** is **equal**.

In the question, we are given a **line segment** of **length **k units, which is divided into 3 equal parts.

We are asked to find the **distance **between the **midpoints **of the first and third **segments**.

Firstly, we divide the **line segment** at **points **k/3 and 2k/3, to get three **equal **parts of **lengths **k/3 each.

Now, the **mid-point** of the first **segment **= (0 + k/3)/2 = k/6.

The **mid-point** of the third **segment **= (2k/3 + k)/2 = 5k/6

Therefore, the **distance **between the **midpoints **of the first **segment **and the third **segment **is (5k/6 - k/6) = 4k/6 = __2k/3__. Hence, __option A__ is the right choice.

Learn more about **midpoints** at

#SPJ2

Line segment of length k is divided into 3 equal parts.

so first segment is 0-k/3 and third segment is 2/3k-k

so mid-pt of 1st = k/6 and 3rd = 5/6k

so the distance in between = 5/6k-k/6 = 4/6k = 2/3k

ans is A

There is more argon in the air.

a. Formulate an LP model for this problem.

b. Sketch the feasible region.

c. What is the optimal solution?

**Answer:**

Let X1 be the number of decorative wood frame doors and X2 be the number of windows.

The profit earned from selling each door is $500 and the profit earned from selling of each window is $400.

The Sanderson Manufacturer wants to maximize their profit. So for this model, the objective function is

Max: 500X1 + 400X2

Now the total time available for cutting of door and window are 2400 minutes.

so the time taken in cutting should be less than or equal to 2400.

60X1 + 30X2 ≤ 2400

The total available time for sanding of door and window are 2400 minutes. Therefore, the time taken in sanding will be less than or equal to 2400. 30X1 + 45X2 ≤ 2400

The total time available for finishing of door and window is 3600 hours. Therefore, the time taken in finishing will be less than or equal to 3600. 30X1 + 60X2 ≤ 3600

As the number of decorative wood frame door and the number of windows cannot be negative.

Therefore, X1, X2 ≥ 0

so the questions

**a)**

The LP mode for this model is;

Max: 500X1 + 400X2

Subject to:

60X1 + 30X2 ≤ 2400

]30X1 +45X2 ≤ 2400

30X1 + 60X2 ≤ 3600

X1, X2 ≥ 0

**b)** Plot the graph of the LP

Max: 500X1+ 400X2

Subject to:

60X1 + 30X2 ≤ 2400

30X1 + 45X2 ≤ 2400

30X1 + 60X2 ≤ 3600

X1,X2

≥ 0

In the **uploaded image** of the graph, the** shaded region** in the graph is the **feasible region**.

**c)** Consider the following corner point's (0,0), (0, 53.33), (20, 40) and (40, 0) of the feasible region from the graph

At point (0, 0), the objective function,

500X1 + 400X2 = 500 × 0 + 400 × 0

= **0**

At point (0, 53.33), the value of objective function,

500X1 + 400X2 = 500 × 0 + 400 × 53.33 = **21332 **

At point (40, 0), the value of objective function,

500X1 + 400X2 = 500 × 40 + 400 × 0 =** 20000**

At point (20, 40), the value of objective function

500X1 + 400X2 = 500 × 20 + 400 × 40 = **26000 **

The maximum value of the objective function is

**26000** at corner point** ( 20, 40 )**

Hence, the optimal solution of this problem is

**X1 = 20, X2 = 40 **and the objective is **26000**

**Answer:**

13 pages : 1/2 hour Multiply both sides by 2

26 pages : 1 hour ------>> 26 pages/hr

Flip over 26 pages/hr ----->>> hr / 26 pages = 1 hr / 26 pages

Split up the fraction: (1/26) hr / page

**Answer:**

26

**Step-by-step explanation:**

13 in 1/2 hour

13:1/2

26:1

Answer:

0.4 ; 0.6125

Step-by-step explanation:

Given the following :

Bag 1 : 75 red ; 25 blue

Bag 2: 60 red ; 40 blue

Bag 3: 45 red ; 55 blue

Probability = (required outcome / Total possible outcomes)

A) since the probability of choosing each bag is equal :

BAG A:

P(choosing bag A) = 1 / total number of bags = 1/3 ; P(choosing blue marble) = number of blue marbles / total number of marbles = 25/100

HENCE, choosing a blue marble from bag A : = (1/3 × 75/100) = 25/300

BAG B:

P(choosing bag B) = 1/3 ;

P(choosing blue marble) = number of blue marbles / total number of marbles = 40/100

HENCE, choosing a blue marble from bag A : = (1/3 × 40/100) = 40/300

BAG C:

P(choosing bag C) = 1/3

P(choosing blue marble) = number of blue marbles / total number of marbles = 55/100

HENCE, choosing a blue marble from bag A : = (1/3 × 55/100) = 55/300

= (25/300) × (40/300) × (55/300) = (25 + 40 + 55)/300 = 120/300 = 0.4

2) What is the probability that the marble is blue when the first bag is chosen with probability 0.5 and other bags with equal probability each?

BAG A:

P(choosing bag A) = 0.5 ; P(choosing blue marble) = number of blue marbles / total number of marbles = 25/100

HENCE, choosing a blue marble from bag A : = (0.5 × 75/100) = (0.5 * 0.75) = 0.375

BAG B:

P(choosing bag B) = (1-0.5) / 2 = 0.25 ;

P(choosing blue marble) = number of blue marbles / total number of marbles = 40/100

HENCE, choosing a blue marble from bag A : = (0.25 × 40/100) = (0.25 × 0.4) = 0.1

BAG C:

P(choosing bag C) = (1 - (0.5+0.25)) = 0.25

P(choosing blue marble) = number of blue marbles / total number of marbles = 55/100

HENCE, choosing a blue marble from bag A : = (0.25 × 55/100) = 0.25 × 0.55 = 0.1375

= 0.1375 + 0.1 + 0.375 = 0.6125