The number of bacteria at the beginning of an experiment was 30 and the bacteria grow at an hourly rate of 1.4 percent. Using the model given by () = 0e, estimate the number of bacteria, rounded to the nearest whole number after 20 hours.

Answers

Answer 1

Answer:

Answer:

The estimated number of bacteria after 20 hours is 40.

Step-by-step explanation:

This is a case where a geometrical progression is reported, which is a particular case of exponential growth and is defined by the following formula:

$n(t) = n_(o)\cdot \left(1+(r)/(100) \right)^(t)$ (1)

Where:

$n_(o)$ - Initial number of bacteria, dimensionless.

$r$ - Increase growth of the experiment, expressed in percentage.

$t$ - Time, measured in hours.

$n(t)$ - Current number of bacteria, dimensionless.

If we know that $n_(o) = 30$ , $r = 1.4$ and $t = 20\,h$ , then the number of bacteria after 20 hours is:

$n(t) = 30\cdot \left(1+(1.4)/(100) \right)^(20)$

$n(t) \approx 39.616$

$n(t) = 40$

The estimated number of bacteria after 20 hours is 40.

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Answers

i thing the answer is D the last chart

At the new light bulb plant, 9 out of 25 light bulbs produced are defective. If the daily production is 4400 light bulbs, how many are defective?

Answers

1584 lightbulbs would be defective out of 4400

The base of a right rectangular prism has an area of 173.6 square centimeters and a height of 9 centimeters. What is the volume, in cubic centimeters, of the right rectangular prism?

Answers

Answer:

D) 1562.4 cubic centimeters

Step-by-step explanation:

volume = area of the base × height

volume = 173.6cm² × 9 cm

volume = 1562.4 cm³

Find the equation of the line through (-4,6) that is parallel to the line y=-5x+2

Answers

Answer:

The equation of the line, using the point-slope form, through (-4,6) that is parallel to the line will be:

$y=-5x-14$

Step-by-step explanation:

We know that the slope-intercept form is

$y=mx+b$

Where m is the slope and b is the y-intercept

Given the equation

$y=-5x+2$

comparing with the slope-intercept form

slope = m = -5

y-intercept = b = 2

We know that the parallel lines have the same slopes.

so, the slope of the parallel line will be: -5

Thus, the equation of the line, using the point-slope form, through (-4,6) that is parallel to the line will be:

$y-y_1=m\left(x-x_1\right)$

$y-6 = -5(x-(-4)$

$y-6 = -5 (x+4)$

$y-6 = -5x-20$

$y=-5x+6-20$

$y=-5x-14$

Answer:

y=-x+2

Step-by-step explanation:

i already did it and your welcome in advance

Sanderson Manufacturing produces ornate, decorative wood frame doors and windows. Each item produced goes through three manufacturing processes: cutting, sanding, and finishing. Each door produced requires 1 hour in cutting, 30 minutes in sanding, and 30 minutes in finishing. Each window requires 30 minutes in cutting, 45 minutes in sanding, and 1 hour in finishing. In the coming week Sanderson has 40 hours of cutting capacity available, 40 hours of sanding capacity, and 60 hours of finishing capacity. Assume all doors produced can be sold for a profit of $500 and all windows can be sold for a profit of $400.Required:
a. Formulate an LP model for this problem.
b. Sketch the feasible region.
c. What is the optimal solution?

Answers

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

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

Solve the following system of equation by using the method of substitution. x + 2y = -1 and 2x – 3y =12

Answers

Answer:

x = 3

y = -2

Step-by-step explanation:

x + 2y = -1

2x – 3y =12

Using substitution means that in one equation you solve for a variable. In this case, the first equation would be easier to solve for x since there are no coefficients.

x = -2y - 1

Now, we plug in the value of x into the second equation, and solve for y.

2 (-2y - 1) - 3y = 12

-4y - 2 - 3y = 12

-7y - 2 = 12

-7y = 14

y = -2

Since we have a numerical value of y, we can use it to solve for x by plugging it into one of the original equations.

x + 2(-2) = -1

x - 4 = - 1

x = 3

If you'd like to check the answer, plug in both values you got to the original equations!