Assume that after t hours on the job, a factory worker can produce 100te^-.5t units per hour. How many units does the worker produce during the first three hours?

Answers

Answer 1
The number of units produced by the worker during t hours of work can be modelled by the following function:

[tex]N(t)=100t e^{(-0.5t)} [/tex]

To find the number of units produced during first 3 hours, we can substitute 3 for t. This will give us the number of units produced by the worker during first 3 hours.

[tex]N(3)=100(3) e^{-0.5(3)} = 67[/tex]

Thus the worker will produce 67 units during the first 3 hours of the work. 
Answer 2

Final answer:

To find the number of units that the worker produces during the first three hours, we need to calculate the integral of the production function from 0 to 3. The production function is given as 100te^-0.5t. Using the power rule and the exponential rule of integration, we can find that the worker produces approximately -300e^-1.5 units during the first three hours on the job.

Explanation:

To find the number of units that the worker produces during the first three hours, we need to calculate the integral of the production function from 0 to 3.
The production function is given as 100te^-0.5t.
To integrate this function, we can use the power rule and the exponential rule of integration.

First, let's apply the power rule. The integral of t^n is (t^(n+1))/(n+1).In this case, we have t*e^-0.5t. So, applying the power rule, we get (t^(1+1))/(1+1) = (t^2)/2.Next, we apply the exponential rule. The integral of e^at is (1/a)e^at.Here, we have e^-0.5t. So, applying the exponential rule, we get (1/(-0.5))e^-0.5t = -2e^-0.5t.Now, let's combine the two results. The integral of 100te^-0.5t can be written as 100 * ((t^2)/2) * (-2e^-0.5t).Simplifying, we get -100te^-0.5t.

Now, we can plug in the values from 0 to 3 in the integral and calculate the result.

First, plug in the value t=3 in the integral: -100(3)e^-0.5(3) = -300e^-1.5.Then, plug in the value t=0 in the integral: -100(0)e^-0.5(0) = 0.Finally, subtract the result from step 2 from the result from step 1: -300e^-1.5 - 0 = -300e^-1.5.

Therefore, the worker produces approximately -300e^-1.5 units during the first three hours on the job.


Related Questions

WILL GIVE BRAINLIEST ANSWER
What is the area of Triangle PQR on the grid?


2 square units
3 square units
4 square units
8 square units

Answers

PQ = 2 units

height = 4 units

 area = 2*4 = 8/2 = 4 square units

The area of a triangle is base×height/2:
2×4/2=4 square units

19 tens + 11 tens equal

Answers

19*10= 190 11*10=110 190+110=300
19 tens is also equal to 19 · 10, which equals 190.

11 tens is equal to 11 · 10, which equals 110.

190 + 110 = 300.

So, 19 tens + 11 tens is equal to 300 (or 30 tens).

a 25000 gallon swimming pool is being filled. Two hundred and fifty gallons are in it after 30 minutes. How many hours will it take to fill the pool?

Answers

In 30 minutes, 250 gallons are filled in the swimming pool. In the same rate in 1 hours (which means 60 minutes), 500 gallons will be filled.

Let x be the number of hours it will take to fill the entire swimming pool which has the capacity of 25,000 gallons.

We need to set up a proportion like given below:

[tex] \frac{Number \; of \; Hours }{Amount \; of\; water \; in\; gallons} =\frac{x}{25,000} =\frac{1}{500} [/tex]

Solving the equation for x:

[tex] \frac{x}{25000} =\frac{1}{500} \\ Multiply \; 25000\; on\; both\; sides\; of\; the \; equation\\ \\ 25000 \times \frac{x}{25000} =\frac{1}{500} \times 25000\\ Simplify \; on \; both \; sides\\ \\ x \; = \; \frac{25000}{500} \; = 50 \; hours [/tex]

Conclusion:

The number of hours that will take to fill the pool is 50 hours !

If 8 cakes cost £4.00 how much would 3 cakes cost?

Answers

Hello!

To calculate how much 3 cakes would cost, we must first find the cost of each individual cake.

To do this, we must divide the cost of 8 cakes by 8 cakes.

4.00 ÷ 8 = 0.5

This means that each individual cake costs $0.50. Multiply this by 3 to find the cost of 3 cakes.

0.50 × 3 = 1.50

Therefore, 3 cakes would cost $1.50.
your answer would be $1.50

what value of c makes the statement true? -2x^3(cx^3+x^2)=-10x^6- 2x^5

Answers

c must equal 5

-2x^3(5x^3+x^2)= -10x^6 - 2x^5

answer
c = 5

Can someone please answer this question here are the answers to the question:

A. 1,209 square feet
B. 1,298 square feet
C. 869 square feet
D. 699 square feet

Answers

Answer: 1298 square feet

------------------------------------------------------

Work Shown:

Area of Rectangle on the Left = length*width = c*d = 24*20 = 480
Area of Rectangle in the center = length*width = c*b = 24*10 = 240
Area of Rectangle on the Right = length*width = c*e = 24*17 = 408

Area of top triangle = (base*height)/2 = b*a/2 = 10*17/2 = 170/2 = 85
Area of bottom triangle = (base*height)/2 = b*a/2 = 10*17/2 = 170/2 = 85

Add up the individual areas to get:
480+240+408+85+85 = 1298

The units are in square feet since this is dealing with area.

This box is 3/4 inches long, 1/2 inches wide, and 1/4 inches deep. What is the volume of the box ?

Answers

Answer:

The volume of the box is 0.09375 inches cube.

Step-by-step explanation:

Given : This box is 3/4 inches long, 1/2 inches wide, and 1/4 inches deep.

To find : What is the volume of the box ?          

Solution :

The dimension of the box is,

Length = [tex]l=\frac{3}{4}[/tex] inches

Breadth = [tex]b=\frac{1}{2}[/tex] inches

Height = [tex]h=\frac{1}{4}[/tex] inches

The formula of volume of the box is

[tex]V=l\times b\times h[/tex]

[tex]V=\frac{3}{4}\times \frac{1}{2}\times\frac{1}{4}[/tex]

[tex]V=\frac{3}{4\times 2\times 4}[/tex]

[tex]V=\frac{3}{32}[/tex]

[tex]V=0.09375in^3[/tex]

Therefore, The volume of the box is 0.09375 inches cube.

The volume of the box is 3/32 cubic inches.

Given

This box is 3/4 inches long, 1/2 inches wide, and 1/4 inches deep.

The volume of the box;

The volume of the box is given by-product of length, width, and height.

The volume of the box is determined by the following formula;

[tex]\rm Volume \ of \ box =Height\times Width \times length[/tex]

Substitute all the values in the formula;

[tex]\rm Volume \ of \ box =Height\times Width \times length\\\\\rm Volume \ of \ box =\dfrac{3}{4}\times \dfrac{1}{2} \times \dfrac{1}{4}\\\\\rm Volume \ of \ box =\dfrac{3}{32} \ cubic \ inches[/tex]

Hence, the volume of the box is 3/32 cubic inches.

To know more about the Volume of the box click the link given below.

https://brainly.com/question/13749063

What is the factor pairs of 78

Answers

1 x 42, 2 x 21, 3 x 14, or 6 x 7
These are the factor pairs of 78.

If guy walks from his house to school and back,how far does he walk?

Answers

He walked the same distance to school and back home.
I hope this helped! :-)

Final answer:

The total distance walked by someone from home to school and back depends on the distance covered in each direction, for example, if a person walks 2 kilometers to school and 2 kilometers back, the total distance walked is 4 kilometers.

Explanation:

The total distance walked by the guy from his house to school and back depends on the exact distance he covers in each direction. If he walks 2 kilometers to school and 2 kilometers back, then the total distance walked would be 4 kilometers.

Joe went to the hobby shop and bought 2 model sports cars at $8.95 each and some paints. If he spent a total of $23.65, what was the cost of the paints

Answers

We have 2 cars at $8.85 each. So we have 8.85 * 2 = $17.70

If we know he spent 23.65, we can do 23.65 - 17.70 = 5.95

So the paint must have cost $5.95.
$5.75  add the cars times 2, ans subtract that from the total cost

I NEED HELP ON QUESTION #4

Answers

No, they are not equivalent.

9w ×0 is already 0.
0 - 12 = -12

-12 doesn't equal 9w - 12.

Hope this helps!

When 8 is added to the number that is produced by doubling the number x, the result is equal to 8 times the number that is 5 less than x. What is the value of x?
can someone help me i am confused

Answers

2x+8 = 8(x-5)
expand the rhs to get
2x+8 = 8x-40
now we minus 2x and add 40 to make one side without the unknown and the other with the unknown. you have
48 = 6x
x = 48/6
   = 8

Answer:

It is 8

Step-by-step explanation:


1) Simplify x + 2x by adding the like terms.

x

2x

3x

2) Simplify y - y + y + y by adding the like terms.2y

3y

4y

5y
4x

Answers

1) 3x
2)2y
hope this helps you!

if you vertically compress the absolute value parent function f(x)=|x| by a factor of 3 what is the equation of the new function

Answers

Answer:

The equation for new function is [tex]y=\frac{1}{3}|x|[/tex]

Step-by-step explanation:

We have been given the absolute value parent function f(x) = |x| and this function is vertically compressed by a factor 3.

If we multiply the function with a constant (say a) then the parent function will get stretch/compressed vertically.

We have below conditions for vertical stretch and compression.

a > 1 => vertically stretch

0 < a < 1 => vertically compression

Hence, in order to vertical compression by a factor 3, we have to multiply the whole function by 1/3

Therefore, the equation for new function is [tex]y=\frac{1}{3}|x|[/tex]

Answer:

g(x) = 1/3 |x| !

Step-by-step explanation:

I hope this helps!

Select the graph that represents the following: -5

Answers

I think graph number (d)
The correct answer is:  [D]:  {the last answer choice provided.} .
____________________________________________________

Caluculate the distance kris walks in 8 days if she walks 7/8 mile each day

Answers

8x7=56
56 ÷ 8 = 7

Kris walked 7 miles in 8 days
The way to answer this is quit easy if in one day Kris walks 7/8 mile you will jave to mult. by 8



7/8×8=42/8( you can reduce is needed)

Answer this question: a family of 4 people consumes 5000 grams of fish every week. how much fish will the family consume in an year? find the answer in kilograms.

Answers

1 year = 52 weeks
1 week = 5000 grams
5000g x 52weeks = 260,000g
260,000g = 260 kg

The family consumes 260 kilograms of fish in a year.
1 year = 52 weeks 
1 week = 5000 grams
5000g x 52weeks = 260,000g
260,000g = 260 kg

Therefore family consumes 260 kilograms of fish in a year

which expression is equivalent to (5y+4) - 2 (7 - 2)

A. y-10
B. 9y+18
C.3y - 10
D. 9y-10

Answers

I think the answer is D.

3 and 1/3x + 5.3 = -2. What is x?

Answers

There you go! X = 10.95
You need to solve for x
3 1/3x + 5.3 = -2
subtract 5.3 from both sides
3 1/3x = -7.3
write the mixed number as an improper fraction
10/3x = -7.3
rewrite
10x/3 = -7.3
multiply both sides by 3
10x = -21.9
divide both sides by 10
x = -2.19

To check:
3  1/3x + 5.3 = -2
3  1/3(-2.19) + 5.3 =?= -2
-7.3 + 5.3 =?= -2
-2 = -2
This proves that -2.19 is the answer

Hope this helps

A particular fruit's weights are normally distributed, with a mean of 611 grams and a standard deviation of 28 grams. The heaviest 2% of fruits weigh more than how many grams? Give your answer to the nearest gram.

Answers

The answer to the nearest gram is 538gm

Can someone help my sister Kathy with this

Answers

The three tenth values that would cause the inequality to be true would be 4, 5, and 6 because each make the other decimal greater than 24.34.

I hope this helped! :-)

Lisa needs to score at least 12 points on her next turn to win the game. Write an inequality to represent the number of points Lisa needs to win the game

Answers

L will be the number of points Lisa needs to win the game. She needs at least, so you know the sign will include "or equal to". Now, she can score over 12 points to win on her next turn, so we'll be using ≥.
L ≥ 12  will be the inequality for this situation.

Final answer:

Lisa needs to score at least 12 points to win, so the inequality to represent this scenario is 'p >= 12', where 'p' is the number of points she scores on her next turn.

Explanation:

To represent the number of points Lisa needs to win the game with an inequality, we can let p stand for the points she will score on her next turn.

Since she needs to score at least 12 points, the inequality would be p \">= 12".

This reads as 'p is greater than or equal to 12,' meaning Lisa needs to score 12 or more points to win.

the soccer club has planned a trip to a tournament . the cost of the van is $192. when 2 students who are not members of the club join the trip , thw transportation cost per person drops by $3.20. how mant soccer club members are gpoing to the tournament

Answers

Answer:

10 soccer club members are going to the tournament.

Step-by-step explanation:

Let x be the number of soccer club members who are going to the  tournament,

Given,

The cost of transportation of x students = $ 192

⇒ The cost of transportation of 1 student = [tex]\frac{192}{x}[/tex]

⇒ The cost of transportation of (x+2) student = [tex]\frac{192}{x-2}[/tex]

According to the question,

[tex]\frac{192}{x}-\frac{192}{x+2}=3.20[/tex]

[tex]192(\frac{1}{x}-\frac{1}{x+2})=3.20[/tex]

[tex]192(\frac{x+2-x}{x(x+2)})=3.20[/tex]

[tex]\frac{384}{x^2+2x}=3.20[/tex]

[tex]3.2x^2+6.4x=384[/tex]

[tex]3.2x^2+6.4x-384=0[/tex]

By the quadratic formula,

[tex]x=\frac{-6.4\pm \sqrt{40.96+4915.2}}{6.4}[/tex]

[tex]\implies x = \frac{-6.4\pm 70.4}{6.4}[/tex]

[tex]\implies x = 10\text{ or } x = -12[/tex]

Since, the number can not be negative,

Hence, 10 soccer club members are going to the tournament.

Final answer:

To find the number of soccer club members going to the tournament, we set up an equation based on the total cost of the van and the drop in cost per person when two additional students join. Solving the quadratic equation reveals that the number of soccer club members is 10.

Explanation:

The question asks us to determine the number of soccer club members going to the tournament given that the cost of the van is $192 and that the cost per person drops by $3.20 when 2 additional students join the trip. Let's denote the number of club members as 'x'. Before the 2 students join, the cost per person is $192 / x. After they join, the cost per person becomes $192 / (x + 2), which is $3.20 less than the original cost per person, so:

192 / x - 192 / (x + 2) = $3.20

Multiplying through by x(x + 2) to clear the denominators gives us:

192(x + 2) - 192x = 3.20x(x + 2)

This simplifies to:

192x + 384 - 192x = 3.20x^2 + 6.4x

The term 192x cancels out on both sides, so we have:

384 = 3.20x^2 + 6.4x

To solve for 'x', we divide both sides by 3.20:

120 = x^2 + 2x

Now we solve the quadratic equation x^2 + 2x - 120 = 0. Factoring this equation, we get (x + 12)(x - 10) = 0. Thus, x can be -12 or 10. However, since we can't have a negative number of club members, the number of soccer club members is 10.

1. A cake in the shape of a circus tent is used as a centerpiece at a celebration. The cake consists of a cylinder and a cone. The cylinder has a diameter of 12 inches and a height of 14 inches. The cone has a height of 6 inches. What is the volume of the cake? Round your answer to the nearest tenth of a cubic inch. Use 3.14 to approximate pi. Show your work.
(Please show me how you get your answers)
I nEED HELP!

Answers

Let us divide the shape of the cake into two parts:

1) The cylindrical part.
2) The cone of the tent.

Note: In order to find the total volume of the cake, we have to add the volumes of both of the above-mentioned part.


1.
The volume of the cylinder = [tex] \pi *r^{2}*h[/tex] --- (A)

We have the height = h = 14 inches.
Radius = r = Diameter / 2 = 12/2 = 6 inches.

and [tex]\pi [/tex]= 3.14

Put the above values in equation (A);
(A) => The volume of the cylinder = (3.14) * (6 x 6) * (14) = 1582.56 inches cubed

2. 
The volume of the cone = [tex]\pi *r^{2}* \frac{h}{3} [/tex] --- (B)

Since the cake is in "circus tent" shape, therefore, the radius of the cone should be equal to the radius of the cylinder.

Radius of the cone = r = 6 inches.
Height of the cone = h = 6 inches.

and [tex]\pi [/tex]= 3.14

Put the above values in equation (B);
(B) => The volume of the cone = (3.14) * (6 x 6) * (6 / 3) = 226.08 inches cubed

The volume of the cake = Volume of the cylinder + Volume of the cone
[tex]V_{cake}[/tex]  = 1582.56 + 226.08 = 1808.64 inches cubed

Ans: The volume of the cake = 1808.64 
[tex]in^{3}[/tex]

-i

X over five equals three over four

Answers

X is equal to 3.75
Hope this helps :)

Final answer:

The equation 'x over five equals three over four' is solved by cross-multiplying to get 4x = 15, and then dividing both sides by four to find x = 3.75.

Explanation:

The equation presented by the student 'x over five equals three over four' translates to the algebraic equation x/5 = 3/4. Solving this involves finding the value of x that makes the equation true. To solve for x, we can cross-multiply to get 4x = 15, and then divide both sides of the equation by four to isolate x, giving us x = 15/4 or x = 3.75. Thus, the solution to the equation x/5 = 3/4 is x = 3.75.

A law firm has nine senior and six junior partners. A committee of three partners is selected at random to represent the firm at a conference. What is the probability that at least one of the junior partners is on the​ committee?

Answers

67% chance of having a junior partner on the committee if rounded up or 66.66....... chance

What is the area of this figure?

Answers

Palelogram area:
 Knowing the base and the height, the area of the parallelogram is calculated by its formula:
 A1 = b * h
 Where
 b: base
 h: height.
 We have then
 b = root ((- 4 - (- 10)) ^ 2+ (2-2) ^ 2) = 6
 h = root ((- 7 - (- 7)) ^ 2+ (3-2) ^ 2) = 1
 A1 = (6) * (1) = 6 units ^ 2
 Rectangle area
 A2 = L * W
 Where
 L: long
 W: Wide
 We have then:
 L = root ((1 - (- 2)) ^ 2 + (- 3 - (- 4)) ^ 2) = 3.16227766
 W = root ((- 4 - (- 2)) ^ 2+ (2 - (- 4)) ^ 2) = 6.32455532
 A2 = (3.16227766) * (6.32455532)
 A2 = 20 units ^ 2
 The total area is the sum of both ares:
 A = A1 + A2
 A = 6 + 20
 A = 26 units ^ 2
 Answer:
 the area of this figure
 A = 26 units ^ 2

Algebra problem #1 help (pic included)

Answers

To find the answer of this problem, we need to plug in and multiply the numbers.

16 - 4 (0)(-6)
= 16 - 0 (-6)
= 16

16 would be the answer.

Hope this helps!

Anna plants peas in 3/8 of her garden and herbs in 1/8 of it . She divides The rest of the garden into 6 sections. What fraction of the original garden is each section

Answers

The six sections would be 1/12

The six sections would be 1/12


A scooter can travel 72 mi per gallon of gasoline and holds 2.3 gal. the function d(x)-72x represents the distance d(x), in miles, that the scooter can travel with x gallons of gasoline. How many miles can the scooter go with a full tank of gas ?

Answers

The scooter can go 165.6 miles
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