the number of bacteria in a container increases at the rate of R(t) bacteria per hour. If there are 1000 bacteria at time t=0 , which of the following expressions gives the number of bacteria in the container at time t=3 hours?

Answers

Answer 1

The expression for the total number of bacteria at t = 3 hours, given an initial 1000 bacteria at t = 0, is: [tex]\[ 1000 + \int_0^3 R(x) \, dx \][/tex]

To find the number of bacteria in the container at time t = 3 hours, given that the rate of increase is [tex]$ R(t) $[/tex] bacteria per hour and there are 1000 bacteria at time t = 0, you can use the following steps:

Start with the initial condition :

You are given that there are 1000 bacteria at t = 0.

So, the initial condition is [tex]$ N(0) = 1000 $,[/tex] where N(t) represents the total number of bacteria at time t.

Integrate to find the change in number of bacteria over time :

Since the rate of increase is R(t), the total increase in bacteria from time t = 0 to t = t is given by integrating R(t) with respect to time.

This integral provides the cumulative increase in bacteria:

[tex]\[ \int_0^t R(x) \, dx. \][/tex]

Add the initial bacteria to the increase :

Since there are already 1000 bacteria at t = 0, the total number of bacteria at time t is given by:

[tex]\[ N(t) = 1000 + \int_0^t R(x) \, dx. \][/tex]

Find the expression for t = 3 hours :

To find the total number of bacteria at t = 3 hours, you substitute t = 3 into the expression derived in step 3:

[tex]\[ N(3) = 1000 + \int_0^3 R(x) \, dx. \][/tex]

Thus, the expression [tex]$ 1000 + \int_0^3 R(x) \, dx $[/tex] gives the number of bacteria in the container at time t = 3 hours.

Question :

the number of bacteria in a container increases at the rate of R(t) bacteria per hour. If there are 1000 bacteria at time t=0 , which of the following expressions gives the number of bacteria in the container at time t=3 hours?

Answer 2

The correct expression that gives the number of bacteria in the container at time t = 3 hours is D. [tex]1000 + \int_0^3 R(t) \, dt[/tex]

The problem asks us to find the number of bacteria in a container at t = 3 hours, given that the number of bacteria increases at a rate of R(t) bacteria per hour and there are 1000 bacteria at time t = 0.

To solve this, we need to integrate the rate function R(t) to find the total change in the number of bacteria over the interval from t = 0 to t = 3.

1. Initial number of bacteria:

At t = 0, the number of bacteria is 1000.

2. Change in number of bacteria:

The rate of change of the number of bacteria is given by R(t) bacteria per hour.

To find the total number of bacteria added over the time interval from t = 0 to t = 3, we need to integrate R(t) from 0 to 3.

Total change in number of bacteria = [tex]\int_0^3 R(t) \, dt[/tex]

3. Total number of bacteria at t = 3 hours:

This is the sum of the initial number of bacteria and the total change in the number of bacteria over the 3 hours.

Number of bacteria at t = 3 hours = [tex]1000 + \int_0^3 R(t) \, dt[/tex]

Complete Question:

The number of bacteria in a container increases at the rate of R(t) bacteria per hour. If there are 1000 bacteria at time t=0, which of the following expressions gives the number of bacteria in the container at time t=3 hours?

(A) R(3)

(B) 1000+R(3)

(D) [tex]$1000+\int_0^3 R(t) d t$[/tex]

Related Questions

What are the relationships among radii, chords, tangents, and inscribed angles?

Answers

The relationship between these four sectors are:

The plural of radius is what we call radii. For any line that joins the center or is joining the center to any point in the circumference of a circle is what we call radii.
Note:
If there is an infinite line from the center to circumference then is it called infinite radii.

For any line that joins or is joining two points on the circumference of a circle is known as chord and any line touching the circle is what we call as tangent to the circle.

Lastly, the intersection of bisector angles is known as in-center or inscribed.

Below are attached pictures of figures

Evaluate the expression
4^2+6⋅5^2−3^3÷3^2.

Answers

[tex]4^2 + 6 \times 5^2- 3^3 \div 3^2.[/tex]

Evaluate exponents:
[tex]=16 + 6 \times 25- 27 \div 9[/tex]

Evaluate multiplication and division:
[tex]= 16 + 150- 3[/tex]

Evaluate addition and subtraction:
[tex]= 163[/tex]

There are five green marbles numbered 1-5 and there are 4 yellow marbles numbered 1-4. what is the probability of picking a green or odd numbered marble

Answers

{g,g,g,g,g,y,y,y,y}

5+4=9

P(odd/green)=3/9 = 1/3 = .33 or 33% approximately

10q-3r=14 write a formula for g (r) in terms of r

Answers

Answer:

3/10r +7/5

Step-by-step explanation:

10q−3r=14

10q=3r-14

10q=3r/10 +14/10

q=3/10r+7/5

Final answer:

To find g(r) in terms of r, the equation 10q-3r=14 is manipulated algebraically to isolate q as g(r)=(14+3r)/10.

Explanation:

The student's question involves solving a linear equation for a variable. This is a standard algebraic task often encountered in high school mathematics. The student is given the equation 10q-3r=14 and is asked to write a formula for g(r) in terms of r, implying a need to solve for q as a function of r, which can be named g(r).

To isolate q, we perform algebraic manipulations:

First, add 3r to both sides of the equation to get 10q = 14 + 3r.Next, divide both sides of the equation by 10 to solve for q, which gives us q = (14 + 3r) / 10.Last, we rename q as g(r) which results in the final function: g(r) = (14 + 3r) / 10.

This function represents q in terms of r, and g(r) is thereby defined.

hey can you please help me posted picture of question

Answers

All the statements are true except the 1st one.

The parent absolute function is y = |x| and its has only one x-intercept which occurs at x = 0

The rest statements are true. As x value gets closer to 0, the y values also gets closer to zero.

So, correct statements are options 2,3,4

A map has the scale 2 centimeters = 1 kilometer. on a map, the area of a forest preserve is 3.8 square centimeters. what is the area of the actual forest preserve

Answers

we know that
the scale is 2 cm/1 km
on a map, the area of a forest preserve is 3.8 cm²
assuming it has a square shape
the length side of the square is √3.8 cm
so
if 2 cm on a map-----------------> is a 1 km in the actual
√3.8 cm------------------------> x
x=√3.8/2 km

the area of the actual forest preserve is
(√3.8/2)*(√3.8/2)----> 3.8/4---> 0.95 km²

the answer is
0.95 km²

Final answer:

To find the actual area of the forest preserve, the map area of 3.8 cm² is multiplied by the scale ratio squared (0.25 km²/cm²), resulting in an actual area of 0.95 km².

Explanation:

The area of the actual forest preserve can be calculated by using the scale given, which is 2 centimeters = 1 kilometer. First, we need to convert the area on the map into the actual area using this scale. Since the scale is linear and the area is measured in square units, we need to square the scale ratio to convert the area on the map to the actual area.

To do this conversion we consider that the scale of 2 cm : 1 km means that every 1 cm on the map is equivalent to 0.5 km (since 2 cm is 1 km). Therefore, for the area, we get the following ratio: (1 cm² = 0.5 km) × (1 cm² = 0.5 km), which simplifies to 1 cm² = 0.25 km². Now, we can find the actual area of the forest preserve by multiplying the 3.8 cm² area on the map by the value of each square centimeter in real-life units, which is 0.25 km².

Actual area = Map area × Scale ratio squared
= 3.8 cm² × 0.25 km²/cm²
= 0.95 km².

Therefore, the forest preserve has an actual area of 0.95 square kilometers.

PLEASE HELP ME OUT ON THIS CRITICAL HARD QUESTION!!!!!!!! NEEDS THINKING!!!! MARK THE BRAINIEST

Answers

You are getting into stats and I have to warn you that the condition of my stats knowledge is almost as limited as what I know about Biology which is practically nothing. But let's see if we can do something about this.

The first thing you have to do is make sure that the sales reps face the same conditions. Geography is going to matter. Start with the simple stuff. Does it matter whether or not the sales representatives were in the city of the country? If in the country, do the people have money enough to buy what is being sold? If in the city, what is the employment situation like? Make sure that you are comparing Apples and Apples.

What about crops? Do they matter? What about livestock does it matter? What do these rural areas need? Is he selling what they need? It's going to be harder to sell something in Detroit or Flint than it is San Francisco?

Did people experience a devastating winter? Especially in the Northeast? If they did, their heating bills are going through the roof. Literally. More money on heating less on whatever he's selling.

In short he has to consider conditions. Perhaps training will make no difference. There's other things that people have to live through. Maybe this was just a bad year. (It certainly was where I live. We got nothing but snow into mid April and East winds which are strong, cold, miserable and very nasty.)

Credit scores. I'd be well aware of any credit stats that I can obtain. What are people doing with their credit cards. You may be able to sell the stuff on credit, but will you ever receive payment that you can rely on or are these people one step away from bankruptcy? Is it different in the rural areas than in the cities? I can tell you I would hate to have it known that I disregard my credit cards in the town I live in (700 people). It would be cash only for everything.

Single or married? What's the demographics of the areas he's trying to sell in. We're retired. We don't take well to door to door sales people. Retired people have very little money to throw away on things we don't need. People on 3000 a month live very differently from those on 10000 a month.

Finally what's the competition like? Sears going under is a huge warning. Where do people get the products you are selling? This is especially important in rural areas. We have made over 170 mail purchases (we won't do that any more -- postage rates are just prohibitive).

If he has a sales force of 1000 people in 2 regions, he should think about moving some of them to other regions. Don't use this point.

Many of the things I've pointed out require a study before the the training is administered. You have to separate out what mitigates the efforts of the sales force and what they have little or no control over.

Consider a box with a square base that has a volume of 64 cubic inches and a height of 4 inches. What is the volume of a similar box whose square base has an area of 4 square inches?

Answers

We know that the square base of the new box is 4 sq. in. This means that each side has to equal 2 in., because A = l*w and 4 = 2x2; we also know that since it is a square, both sides have to be equal, so it must be a 2x2 square and not a 4x1 rectangle.

That being said, the first box had dimensions of 4x4x4 - and this is confirmed by the volume being 64 sq. in. and the height being told to us as 4 in. as well as the square base having to have equal sides.

Because of this, since the question states "similar," all of the dimensions have to be reduced by the same factor. Since the square base was reduced by 1/2, we can assume the height is also reduced by 1/2, thus giving us a height of the new box as 2 in.

So, the volume of the new box is 2x2x2, which equals 8 sq. in.

The length of the shorter base in an isosceles trapezoid is 4 in, its altitude is 5 in, and the measure of one of its obtuse angles is 135°. Find the area of the trapezoid.

Answers

The answer is 45.

Ask me if you still don't understand it because I didn't write any explanation.

Answer:

Step-by-step explanation:

Find the general form of the complete partial fraction decomposition of the integrand. use it to determine whether or not a term of each type listed below occurs in the complete partial fraction decomposition. select true if it does occur and false if it does not.

Answers

The answer is int(x^2-4x / X = 3).

(-2q^4)(-8q^3b^6)
help I need to simplify this problem

Answers

Multiply the constants. Multiply the variables according to the rules of exponents.
[tex](-2q^{4})(-8q^{3}b^{6}) = ((-2)(-8))q^{(4+3)}b^{6}\\\\=16q^{7}b^6}[/tex]

a soccer ball has the same diameter as a lenght of a cube shaped box. if the diameter of the soccer ball is 12 inches what volume inside that is not filled by a soccer ball

Answers

diameter is the length, width, and height of the box, therefore, volume of box is length x width x height= 12 x 12x 12= 1728
volume of ball is (4/3) x pi x radius cubed =288 pi
then answer is 1728 - 288 pi

Please rate me don't just say thanks

The volume of box which is not used is (1728 - 288π) inch³.

What is Volume?

Volume is a three-dimensional quantity used to calculate a solid shape's capacity. That means that the volume of a closed form determines how much three-dimensional space it can fill.

If the diameter of the soccer ball is 12 inches.

So, Volume of box

= length x width x height

= 12 x 12 x 12

= 1728 inch³

and, Volume of ball

= 4/3 πr³

= 4/3π (6)³

= 864/3 π

= 288 π inch³

So, the volume of box which is not used

= 1728 - 288π

Learn more about Volume here:

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if a certain type of bacteria quadruples every 15 minutes, how many bacteria will be presents after 90 minutes if the initial population was 5 bacteria?

HELP ME FOR 97 POINTS !!!!

Answers

For this case we have an equation of the form:
y = A (b) ^ (t / n)
Where,
A: initial amount
b: growth rate
t: time
n: number of time periods
Substituting values we have:
y = 5 * (4) ^ (90/15)
y = 20480
Answer:
will be presents after 90 minutes about:
y = 20480 bacteria

what if the value of x? show all work

Answers

For this case we can make use of the Pythagorean theorem.
We have then:
(root (117)) ^ 2 = x ^ 2 + 6 ^ 2
Clearing x we have:
x ^ 2 = (root (117)) ^ 2 - 6 ^ 2
Rewriting:
x = root (117-36)
x = root (81)
x = 9
Answer:
The value of x is given by:
x = 9 cm

Identify the problem with the following study.

It was found that a third of all people in the United States live in urban centers. This finding is based on a study involving 3 randomly selected individuals.

reported results

small sample

missing data

loaded question

Answers

If the question is, why is this study faulty? Then you can answer it.
We know nothing about what was asked. (How could it be much more than "Where do you live?" The last one is wrong.

Is there missing data? We don't know. So the second last one is not the best answer.

The sample is too small. So far that's your best answer.

The results cannot be at fault. How can saying 2/3 of the people answered that they lived in the country.

B <<<<<< second one down <<<<< Answer

What is the sum of the first 51 consecutive odd positive integers?

Answers

We call:

[tex] a_{n} [/tex] as the set of the first 51 consecutive odd positive integers, so:

[tex]a_{n} = \{1, 3, 5, 7, 9...\} [/tex]

Where:
[tex]a_{1} = 1[/tex]
[tex]a_{2} = 3 [/tex]
[tex]a_{3} = 5 [/tex]
[tex]a_{4} = 7 [/tex]
[tex]a_{5} = 9 [/tex]
and so on.

In mathematics, a sequence of numbers, such that the difference between two consecutive terms is constant, is called Arithmetic Progression, so:

3-1 = 2
5-3 = 2
7-5 = 2
9-7 = 2 and so on.

Then, the common difference is 2, thus:

[tex]a_{n} = \{ a_{1} , a_{1} + d, a_{1} + d + d,..., a_{1} + (n-2)d+d\} [/tex]

Then:

[tex]a_{n} = a_{1} + (n-1)d[/tex]

So, we need to find the sum of the members of the finite series, which is called arithmetic series:

There is a formula for arithmetic series, namely:

[tex] S_{k} = ( \frac{a_{1} + a_{k}}{2} ).k[/tex]

Therefore, we need to find:
[tex] a_{k} = a_{51} [/tex]

Given that [tex]a_{1} = 1[/tex], then:

[tex]a_{n} = a_{1} + (n-1)d = 1 + (n-1)(2) = 2n-1 [/tex]

Thus:
[tex]a_{k} = a_{51} = 2(51)-1 = 101[/tex]

Lastly:

[tex] S_{51} = ( \frac{1 + 101}{2} ).51 = 2601[/tex]

HOW CAN YOU WRITE THE EQUATION OF A LINE THAT IS PARALLEL AND/OR PERPENDICULAR TO ANOTHER LINE USING A POINT ON THAT LINE.?

Answers

The point-slope equation of a line is useful for this purpose. It is often seen in the form
y -k = m(x -h)
for a line of slope m through the point (h, k).

You can add k to this equation to put it in a form more like slope-intercept form:
y = m(x -h) +k

Either of these can be used to write the equation of a parallel or perpendicular line through the point (h, k). The slope "m" of a parallel line will match that of the given line.

The slope "m" of a perpendicular line will be the negative reciprocal of the slope of the given line. That is, if you are given a line with slope "s", the slope of the perpendicular line will be m = -1/s.

WILL MARK BRAINLEST * PLEASE HELP AND FAST :)

Answers

A stem and leaf plot is an abbreviated way of presenting data by grouping the data based on the leading number. In this plot, the minimum number is 54 (5|4), and the maximum is 96(9|6).

The range of a data set is the largest value minus the smallest value; the range for this data set would be 96-54, or 42.

The range of this stem and leaf plot is 42.

20 pt question on angles plz help

Answers

just set it up as 2x +5 =5x-25
and you should get x=10

congruent means that bot S and T are the same degrees
so we can set S and T equal to each other and solve:

2x +5 = 5x-25

subtract 2x from each side:

5 = 3x-25

add 25 to each side:

30 = 3x
divide both sides by 3 to get x

x = 30 / 3
x = 10
now we know x so replace x with 10 and solve for S

S = 2(10) +5 = 20+5 = 25

angle S = 25 degrees

A ________ is a numerical quantity computed from the data of a sample and is used in reaching a decision on whether or not to reject the null hypothesis.
a. significance level
b. critical value
c. test statistic
d. parameter

Answers

The answer for the completion exercise shown above is the second option (option b), which is:

b. critical value.

Therefore, you have that the text is: "A critical value is a numerical quantity computed from the data of a sample..."

This numeral quantity is used in statitics. Then, if the absolute value is greater that the quantity defined before, the null hypothesis must be rejected.

hey can you please help me posted picture of question

Answers

From the graph we can observe that G(x) is obtained by shifting F(x) 3 units to the left and 1 unit upwards.

Thus, both horizontal and vertical translations are involved. Horizontal translation of 3 units to left can be obtained by adding 3 to x in the equation and vertical translation of 1 can be obtained by adding 1 to the entire function.

So,

G(x) = F(x+3) + 1

G(x) = (x+3)² + 1

Thus the correct answer is option C

Q # 9 Find the circumference

Answers

Circumfernce: C=2*Pi*r
Pi=3.14
Radius of the circumference: r=3 m
C=2*3.14*(3 m)
C=18.84 m

Answer: First option 18.84 m

Experts/ace/geniuses helppp asapp

Answers

Point E is the correct answer! :D

[tex] \sqrt{10}=3.1622... [/tex]
therefore if you round the 3.1622... it would be closer to 3.2 so point F is actually correct

The number pi goes on forever with no repeating pattern; therefore, it is rational. A) True or B) False

Answers

false, it's irrational.

False, Because it is an Irrational number.

What is Rational number?

A number which can be written in the form of fraction p / q , where q is non zero, are called Rational numbers.

We have to given that;

The number π goes on forever with no repeating pattern.

Therefore, it is rational.

Since, We know that;

Number π cannot be expressed as the ratio of one number to another

Hence, in other words, Number π is an 'irrational' number that goes on forever, never repeating itself.

Hence, Statements in false, Because it is an Irrational number.

Learn more about the rational numbers visit:

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A statistician observes the number of heads that occur when a coin is tossed 1000 times

Answers

A coin wouldn't be a coin without two sides

How to find the answers to nine and ten? Please show your work.

Answers

Nine
Comment
The figure consists of 2 figures, a rectangle and a trapezoid. You should break them up and find the area of each separately and add to get the total.

Rectangle.
Area = L * W
L = 40 yd
W = 25 yd.
Area = 40 * 25 = 1000 square yards.

Trapezoid
B1 = 40 yards
B2 = 65 yards
H = 55 - 25 yards
H = 30 yards
Area = (B1 + B2)* H / 2
Area = (40 + 65)*30 / 2 Add the 2 bases together.
Area = ( 105) * 30 / 2 You can divide either the 30 or the 105 by 2. Do the 30
Area = (105) *15
Area = 1575 square yards.

Find the total Area
Total Area = rectangle + trapezoid
Total Area = 1000 + 1575
Total Area = 2575 <<<<< Answer

Ten
Comment
Assume the other side has no windows or doors. Both sides consist of 1 triangle and 1 rectangle.

Problem A
Rectangle
Area = l * w
L = 28 feet
W = 8.5 feet
Area = 28 * 8.5
Area = 238 square feet.

Triangle
Area = 1/2 Base * Height
Base = 28 feet
Height = 12.5 - 8.5
Height = 4
Area = 1/2 * 28 * 4
Area = 56 square feet.

Total Area (1 Side)
Total Area (1 Side) = 56 + 238
Total Area (1 side) = 394

Total Area (Both sides)
Total Area (both sides) = 2 * 294
Total Area (both sides) = 588 square feet.

Problem B
Comment
You have 588 square feet. First figure out the number of bundles and then calculate the cost.

Bundles
Bundles = Total Square Feet (Rounded up) / 100
Bundles = 588 / 100 = 5.88 bundles.
But you cannot buy 0.88 bundles So you have to round up, otherwise you'll have a bit of the building uncovered.

You may not care in reality, but the question does. So your answer is that you have 6 bundles.

Cost
1 bundle costs 75 dollars.
6 bundles cost x

1/6 = 75 / x
x = 6 * 75
x = 450 dollars <<<<< Answer 10B

PLZ HELP ASAP FEATURES OF A CIRCLE FROM ITS EXPANDED EQUATION LAST ONE

Answers

We have the following equation:
x2 + y2 + 6y - 72 = 0
Rewriting we have:
x2 + y2 + 6y = 72
Complete squares we have:
x2 + y2 + 6y + (6/2) ^ 2 = 72 + (6/2) ^ 2
x2 + y2 + 6y + (3) ^ 2 = 72 + (3) ^ 2
x2 + y2 + 6y + 9 = 72 + 9
x2 + (y + 3) 2 = 81
So, the center is:
(0, -3)
The radio is:
r = 9
Answer:
(0, -3)
r = 9

what is the difference? (x+5)/(x+2)-(x+1)/(X^2+2x)

Answers

[tex] \frac{x+5}{x+2} - \frac{x+1}{x^{2}+2x } = \frac{x^{2}+4x-1 }{ x^{2} +2x} [/tex]

Answer:

[tex]\text{The difference is }\frac{x^2+4x-1}{x(x+2)}[/tex]

Step-by-step explanation:

Given two expression, we have to find the difference of these two.

[tex]\frac{x+5}{x+2}-\frac{x+1}{x^2+2x}[/tex]

[tex]=\frac{x+5}{x+2}-\frac{x+1}{x(x+2)}[/tex]

[tex]\text{Taking (x+2) common from the denominator }[/tex]

[tex]=\frac{1}{x+2}((x+5)-\frac{x+1}{x}[/tex]

[tex]=\frac{1}{x+2}(\frac{x(x+5)-(x+1)}{x})[/tex]

[tex]=\frac{1}{x+2}(\frac{x^2+5x-x-1}{x}[/tex]

[tex]=\frac{1}{x+2}(\frac{x^2+4x-1}{x})[/tex]

[tex]=\frac{x^2+4x-1}{x(x+2)}[/tex]

which is required difference.

Amy had $26 dollars to spend on school supplies. After buying 10 pens, she had $14.30 left. How much did each pen cost including tax?

Answers

11.70 is what wouldve been spent without adding tax, if you add tax you wouldve spent around $12-$12.50

Here, we need to find the cost of each pen, including tax. Since, information about tax was not given, so we will not consider this.

Total money Amy had = $ 26.

She is left with $ 14.30. The money she spent will be -

Total money - Money left = Money spent

$ 26 - $ 14.30 = $ 11.70

Total money she spent on 10 pens = $ 11.70

So, money spent on = $ 11.70 ÷ 10 = $ 1.17

So, the cost of each pen will be = $ 1.17

The circle shown here has area πr2. If its radius is tripled in length its new area will be

Answers

[tex]\bf \textit{area of a circle}\\\\ A=\boxed{\pi r^2}~~ \begin{cases} r=radius\\ -----\\ r=\stackrel{tripled}{3r} \end{cases}\implies A=\pi (3r)^2\implies A=\pi (3^2r^2) \\\\\\ A=9\boxed{\pi r^2}\impliedby \textit{9 times the original area}[/tex]

Other Questions

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