How do you write 8.16 × 101 in standard form?
1 answer:
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Answer:
144500
Step-by-step explanation:
(1.7 x 10^4) x (8.5 x 10^-2)
= (1.7 x 10000) x (8.5 x 0.01)
=( 17/10 x 10000/1) x (17/2 x 1/100)
=17000/1 x 17/200
=289000/2
=1445000
When you divide a fraction by another fraction, it is the same thing as multiplying that fraction by its reciprocal.
The reciprocal is the 'flipped' version of a fraction where the numerator becomes the denominator and the denominator becomes the numerator.
for example, the reciprocal of 9/10 is 10/9
Knowing this information 4/5÷9/10 is the same as 4/5×10/9
Now we can solve...
Answer= 8/9
The reciprocal is the 'flipped' version of a fraction where the numerator becomes the denominator and the denominator becomes the numerator.
for example, the reciprocal of 9/10 is 10/9
Knowing this information 4/5÷9/10 is the same as 4/5×10/9
Now we can solve...
Answer= 8/9
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
