Can someone write the standard form for this?

Which notation best represents the phrase “no more than 200”

Lilit [14]

Answer:

X<_200

Step-by-step explanation:

We know that if the number connot be more than 200 then the number is less than or equal to 200

7 0

3 years ago

6) Two boats set off from X at the same

lord [1]

Answer:

The distance between the two boats after 2.5 hours is 57 m.

Step-by-step explanation:

The distance covered by each boat after 2.5 hours are:

speed = $\frac{distance}{time}$

distance = speed x time

For boat A, speed = 14 km/h and time = 2.5 hrs.

So that,

distance = 14 x 2.5

= 35 km

For boat B, speed = 18 km/h and time = 2.5 hrs.

So that,

distance = 18 x 2.5

= 45 km

The distance between the two boats after travelling 2.5 hours can be determined by applying the cosine rule. Let the distance be represented by x, so that:

$a^{2}$ = $b^{2}$ + $c^{2}$ - 2bc Cos A

$x^{2}$ = $45^{2}$ + $35^{2}$ - 2(45 x 35) Cos $90^{o}$

= 2025 + 1225 - 3150 (0)

= 3250

x = $\sqrt{3250}$

= 57.0088

x = 57.0 m

The distance between the two boats after 2.5 hours is 57 m.

4 0

3 years ago

The Fine Line Pen Company makes two types of ballpoint pens: a silver model and a gold model. The silver model requires 1 minute

tresset_1 [31]

Answer:

Optimal production = 600 gold pens

Revenue = 600*7 = $4200 gold pens

Step-by-step explanation:

The Fine Line Pen Company makes two types of ballpoint pens: a silver model and a gold model.

A. The silver model requires 1 minute in a grinder and 3 minutes in a bonder.

B. The gold model requires 3 minutes in a grinder and 4 minutes in a bonder.

Because of maintenance procedures,

C. the grinder can be operated no more than 30 hours per week and

D. the bonder no more than 50 hours per week.

The company makes

E. $5 on each silver pen and

F. $7 on each gold pen.

How many of each type of pen should be produced and sold each week to maximize profits?

Solution:

We will solve the problem graphically, with number of silver pens, x, on the x axis, and number of gold pens, y, on the y axis, i.e.

1. From A and C, the maximum number of silver pens

x <= 30*60 / 1 = 1800 and

x <= 50*60 /3 = 1000 ....................(1) bonder governs

2. from A & D, the maximum number of gold pens

y <= 30*60 / 3 = 600 .....................(2) grinder governs

y <= 50*60 / 4 = 750

3. From D,

x + 3y <= 30*60 = 1800 ...................(limit of grinder) ..... (3)

3x + 4y <= 50*60 = 3000 .................(limit of bonder) .......(4)

Need to maximize profit,

Z(x,y) = 5x+7y, represented by parallel lines y = -5x/7 + k such that all constraints of (3) and (4) are satisfied.

The maximum is obtained when Z passes through (360,480), i.e. at intersection of constraints (3) and (4). Using slope intercept form,

(y-480) = -(5/7)(x-360)

or y=-(5/7)x + (737+1/7) [the purple line] which violates the red line, so not a solution.

Next try the point (0,600)

(y-600) = -(5/7)(x-0), or

y = 600 - (5/7)x [the black line]

As we can see all point on the black (in the first quadrant) satisfy the constraints, so it is a feasible solution, and is the optimal solution, with a revenue of

Revenue = 600*7 = 4200 gold pens