A colony of bacteria is grown under ideal conditions in a laboratory so that the population increases exponentially with time. At the end of 3 h there are 10,000 bacteria. At the end of 5 h there are 40,000 bacteria. How many bacteria were present initially?
Answers
There were approximately 1,562.5 bacteria present initially.
What is expression ?
In mathematics, an expression is a combination of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. An expression can represent a single value or a range of values, and can be evaluated to produce a result. Expressions can be simple, such as 3 + 4, or complex, involving multiple operations and variables. They are used in a variety of mathematical contexts, including algebra, calculus, and statistics.
According to given conditions :
We can use the exponential growth model to solve this problem. The model is:
\(N(t) = N0 * e^{(kt)}\)
where:
N(t) is the population at time t
N0 is the initial population
k is the growth rate constant
To solve for N0, we need to use the information given in the problem to find k, and then use that value to solve for N0.
From the problem, we know that:
N(3) = 10,000
N(5) = 40,000
Plugging these values into the exponential growth model, we get:
\(N(3) = N0 * e^{(3k)} = 10,000\\N(5) = N0 * e^{(5k)} = 40,000\)
Dividing the second equation by the first, we get:
\(N(5)/N(3) = e^{(2k)} = 4\)
Taking the natural logarithm of both sides, we get:
ln(4) = 2k
Solving for k, we get:
k = ln(4)/2
Now that we have k, we can use either of the two original equations to solve for N0. Using N(3) = 10,000, we get:
\(10,000 = N0 * e^{(3*ln(4)/2)}\)
Simplifying, we get:
\(N0 = 10,000 / e^{(3*ln(4)/2)}\)
N0 ≈ 1,562.5
Therefore, there were approximately 1,562.5 bacteria present initially.
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Related Questions
Please help ASAP
Compare -2.3 and -8/3 using symbols <, >, or =
Answers
Answer:
to compare -2.3 and -8/3, we need to put them in the same form. We can convert -8/3 to a decimal by dividing -8 by 3, which gives us -2.66667.
Now we can see that -2.3 is greater than -2.66667, so we can write -2.3 > -8/3.
Step-by-step explanation:
Don't worry I can help.
Mathmetics isn't easy. so study
Could you please help me with my problem?
Answers
Answer:
54
Step-by-step explanation:
food concession owner in a mall sold 120 beef, vegetable and pork sliders in 7 days. 20% of the sliders sold were beef and 15% were vegetable. How many pork sliders were sold?
Answers
The number of pork sliders sold is given as follows:
24 pork sliders.
How to obtain the number of pork sliders sold?The number of pork sliders sold is obtained applying the proportions in the context of the problem.
The total number of pork sliders is given as follows:
120 pork sliders.
The percentage of pork sliders sold is given as follows:
20%. (proportion of 0.2).
Hence the amount sold is given as follows:
0.2 x 120 = 24 pork sliders.
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In 2003, the average combined SAT score (math and verbal) for college-bound students in the United States was 1026. Suppose that approximately 45% of all high school graduates took this test and that 100 high school graduates are randomly selected from among all high school grads in the United States. Which of the following random variables has a distribution that can be approximated by a binomial distribution? Whenever possible, give the values for n and p.
a. The number of students who took the SAT
b. The scores of the 100 students in the sample
c. The number of students in the sample who scored above average on the SAT
d. The amount of time required by each student to complete the SAT
e. The number of female high school grads in the sample
Answers
Answer:
The random variables which has a distribution that can be approximated by a binomial distribution is:
c. The number of students in the sample who scored above average on the SAT.
Step-by-step explanation:
The binomial distribution in this scenario will be between the number of students in the sample who scored below average on the SAT and the number of students who scored above average. Variables that have a binomial distribution must meet these four conditions:
1: The observed number of students who sat for the SAT 'n' is not variable.
2: Each student's score (observation) is purely independent of each other, either above or below average scores.
3: Each student's score (observation) shows one of the two outcomes ("success" or "failure"). Those below average are "failures." Those above average are "successes."
4: The outcome probability of "success" 'p' for each student is the same.
devide 255 in the ratio 3:7:7:10
Answers
Answer:5
Step-by-step explanation:
5098
Help me please I need help x^2 - 8x + 16
Answers
The set of factors used to factor the given trinomial are -4 and -4. Therefore, option C is the correct answer.
The given trinomial is x²-8x+16.
Factors of 16 Sum of factors
-1 and -16 -1+(-16)=-17
-2 and -8 -2+(-8)=-10
-4 and -4 -4+(-4)=-8
The set of factors would used to factor the trinomial are -4 and -4.
Therefore, option C is the correct answer.
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This is due in like 45 minutes HELP
Answers
Answer:
what is the question....?
Answer:
Answer:We need to know the question!!
Applying the Right Triangle Altitude Theorem. Which similarity statement is true?
Answers
The true similarity statement are using Right Triangle Altitude Theorem :
ΔABD similar to ΔBCD
ΔABC similar to ΔADB
ΔABC similar to ΔBDC
Two triangles are said to be similar if the triangles are of the same shape but different size. The angles of the triangle will be equal and the sides are proportional.
By the Right Triangle Altitude Theorem,
If the altitude of a triangle is drawn to the hypotenuse of a right angled triangle, then the triangles formed by the division are similar to each other and both are similar to the original triangle.
Using this,
ΔABD similar to ΔBCD
ΔABC similar to ΔADB
ΔABC similar to ΔBDC
Hence the true statements are ΔABD similar to ΔBCD, ΔABC similar to ΔADB, ΔABC similar to ΔBDC.
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The complete question is given below.
PLEASE HELP FAST I’M HAVING A LITTE TROUBLE PLEASE GIVE THE RIGHT ANSWER
Answers
Answer:
C) 1/2 and 8
Step-by-step explanation:
-2x + y = 7 Eq. 1
6x + y = 11 Eq. 2
From Eq. 1:
y = 7 + 2x Eq. 3
From Eq. 2:
y = 11 - 6x Eq. 4
Equalyzing Eq. 3 and Eq. 4:
7 + 2x = 11 - 6x
2x + 6x = 11 - 7
8x = 4
x = 4/8
x = 1/2
From Eq. 3:
y = 7 +2* 1/2
y = 7 + 1
y = 8
Check:
From Eq. 2
6x + y = 11
6*1/2 + 8 = 11
3 + 8 = 11
Find the mean, median and mode of the data set. If there is no mode, enter the words "no mode". 140, 128, 124, 137, 143, 126, 130, 136
Answers
Answer:
mode = no mode. median = 133, mean = 133
Step-by-step explanation:
mode = most common value. all of the values appear once. so there is no mode.
median = arranging the data in numerical order, then finding middle value.
there are 8 values. we have 4 on one side (124, 126, 128, 130) and 4 on the other (136, 137, 140, 143).
median is halfway between 130 and 136. that is 133.
mean = add up the values/ how many there are
adding them up, you get 1064. there are 8 values.
mean = 1064/8 = 133
The conditional statement below is true. If possible, write the biconditional statement.
If 2x = 18, then x = 9.
Answers
The biconditional statement for the given conditional statement would be:
2x = 18 if and only if x = 9.
The given conditional statement "If 2x = 18, then x = 9" can be represented symbolically as p → q, where p represents the statement "2x = 18" and q represents the statement "x = 9".
To form the biconditional statement, we need to determine if the converse of the conditional statement is also true. The converse of the original statement is "If x = 9, then 2x = 18". Let's evaluate the converse statement.
If x = 9, then substituting this value into the equation 2x = 18 gives us 2(9) = 18, which is indeed true. Therefore, the converse of the original statement is true.
Based on this, we can write the biconditional statement:
2x = 18 if and only if x = 9.
The biconditional statement implies that if 2x is equal to 18, then x must be equal to 9, and conversely, if x is equal to 9, then 2x is equal to 18. The biconditional statement asserts the equivalence between the two statements, indicating that they always hold true together.
In summary, the biconditional statement is a concise way of expressing that 2x = 18 if and only if x = 9, capturing the mutual implication between the two statements.
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F(x)=(x+2)^2 (x-3) graph the function
Answers
The value of the equation f ( x ) is
f ( x ) = x³ + x² - 8x - 12
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
f ( x ) = ( x + 2 )²( x -3 ) be equation (1)
Now , on simplifying the equation , we get
f ( x ) = ( x + 2 )²( x -3 )
f ( x ) = ( x² + 4x + 4 ) ( x - 3 )
Now , multiplying each term with ( x - 3 ) , we get
f ( x ) = ( x - 3 ) x² + ( x - 3 ) 4x + ( x - 3 ) 4
f ( x ) = x³ - 3x² + 4x² - 12x + 4x - 12
On simplifying the equation ,we get
f ( x ) = x³ + x² - 8x - 12
Now , the value of the equation f ( x ) = x³ + x² - 8x - 12
On graphing the equation , we get
The graph of the equation f ( x ) = x³ + x² - 8x - 12 is shown below
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An ammunition producer claims his best product has an average lifespan of exactly 18 years. A skeptical product evaluator asks for evidence (data) that might be used to evaluate this claim. The product evaluator was provided data collected from a random sample of 50 people who used the product. Using the data, an average product lifespan of 15 years and a standard deviation of 8 years was calculated. Select the 90%, confidence interval for the true mean lifespan of this product.
Answers
Answer:
The 90% confidence interval for the true mean lifespan of this product is between 13.1 and 16.9 years.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 50 - 1 = 49
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 49 degrees of freedom(y-axis) and a confidence level of \(1 - \frac{1 - 0.9}{2} = 0.95\). So we have T = 1.6766
The margin of error is:
\(M = T\frac{s}{\sqrt{n}} = 1.6766\frac{8}{\sqrt{50}} = 1.9\)
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 15 - 1.9 = 13.1 years
The upper end of the interval is the sample mean added to M. So it is 15 + 1.9 = 16.9 years
The 90% confidence interval for the true mean lifespan of this product is between 13.1 and 16.9 years.
Can anyone help ?
Kim rolls a dice and flips a coin.
a) Calculate the probability that she
gets a 2 and a head.
b) Work out the probability that she
gets an even number and a tail.
What would b be
Answers
Answer:
a) 1 / 12
b) 1 / 4
Step-by-step explanation:
The events are independent since they do not affect each other. The total probability of two independent events is the product of the probabilities of the two events.
a) When rolling a die, there are 6 outcomes, the numbers 1 - 6. There is only 1 outcome where you can get a 2. Therefore, the probability of rolling a two is 1/6.
When flipping a coin, there are two ways it can land: heads or tails. And there is one outcome with heads. The probability of getting head would be 1 / 2.
To find the the total, you multiply the probabilities of the two events: 1 / 6 * 1 / 2 = 1 / 12
b) As stated before, when rolling a die, there are 6 outcomes, the numbers 1 - 6. There are 3 outcomes where she can roll an even number: the numbers 2, 4, or 6. So, the probability of rolling an even number is 3 / 6 or 1 / 2.
When flipping a coin, there are two ways it can land: heads or tails. And there is one outcome with tails. The probability of getting tails would be 1 / 2.
Now, you multiply the two probabilities to get the total probability: 1 / 2 * 1 / 2 = 1 / 4
3 to 2 if there are 120 children who like pizza, how many total
Answers
Answer:
320
Step-by-step explanation:
Is the 3 to 2 part to part? Out of every 5 people, 3 prefer pizza and 2 do not. We can us this to set up a proportion.
3/5 = 120/x The 3 represent the part that like pizza over the whole of 5. The second ratio is showing the actual number of people that liked pizza over the total number of people.
What would be multiply 3 by to get 120? 40. So, we will multiply 5 times 40 to get the total number of people. 5 x 40 = 200
identify point in region of inequalities
Answers
We want to picture the inequalities
\(y<\text{ - x -3}\)and
\(y>\frac{4}{5}x\text{ +5}\)First, we consider the lines y= -x -3 and and y=(4/5) x +5 . Since the first line has a negative slope, this means that its graph should go downwards as x increases and since the other line has a positive slope, this means that its graph should go upwards as x increases. This leads to the following picture
Now, the expression
\(y<\text{ -x -3}\)means that the y coordinate of the line should be below the red line. Also, the expression
\(y>\frac{4}{5}x+5\)means tha the y coordinate should be above the blue line. If we combine both conditions, we find the following region
so we should look for a point that lies in this region
We are given the points (-1,9), (-6,2), (9,-9) and (-8,-5).
We see that the yellow region is located where the x coordinate is always negative. So, this means that we discard (9,-9).
so we should test the other points. Since -8 is the furthest to the left, let us calculate the value of each line at x=-8.
\(\text{ -(-8) -3 = 8 -3 = 5}\)so, in this case the first expression is accomplished since -5 < 5. And
\(\frac{4}{5}\cdot(\text{ -8)+5= =}\frac{\text{ -7}}{5}=\text{ -1.4}\)However note that -5 < 1.4, and it should be greater than -1.4 to be in the yellow region. So we discard the point (-8,-5) .
We can check , iusing the graph, that the lines cross at the point (-40/9, 13/9) which is about (-4.44, 1.44). This means that for the point to be on the yellow region, it should be on the left of -4.44. Since the only point that we are given that fulfills this condition is (-6, 2), this should be our answer. We check that
\(\text{ -(-6)-3=3>2}\)and
\(\frac{4}{5}\cdot(\text{ -6)+5 = }\frac{1}{5}=0.2<2\)so, the point (-6,2) is in the yellow region
Which of the numbers below is greater than 313.587?
A) 314
B) 313.59
C) 313
D) 313.58
Answers
Answer:
314
Step-by-step explanation:
Because 314 is bigger than 313.587
A movie theater has a seating capacity of 187. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 1338, How many children, students, and adults attended?
___ children attended.
___ students attended.
___ adults attended.
Answers
Answer:
A) children attended=98 b) students attended=60 c)adults attended=49
Step-by-step explanation:
system%28a%2Bc%2Bx=207%2Cc%2Fa=2%2C5c%2B7x%2B12a=1498%29
Simplify and solve the system.
-
a%2B2a%2Bx=207
3a%2Bx=207
x=207-3aandc=2a
-
The revenue equation can be written in terms of just one variable, a.
10a%2B7%28207-3a%29%2B12a=1498
Solve for a;
use it to find x and c.
FURTHER STEPS
-
10a%2B1449-21a%2B12a=1498
a%2B1449=1498
a=98-49
highlight%28a=49 -------adults
-
c=2a
c=2%2A49
highlight%28c=98 -------children
-
x=207-a-c
x=207-49-98
highlight%28x=60 ---------students
Which is an equation of the line through (0,0) and (-3,-7)?
O A. y=-7x
O B. y= 2
O C. y = 2
O D. y=-3x
Answers
Answer:
y=7/3x
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-7-0)/(-3-0)
m=-7/-3
m=7/3
y-y1=m(x-x1)
y-0=7/3(x-0)
y=7/3(x)
y=7/3x
Equation of the line through (0,0) and (-3,-7) is y=7/3x
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
We need to find the equation of the line through (0,0) and (-3,-7)
m=-7/-3=7/3
Now let us find the y intercept
-7=7/3(-3)+b
b=0
So the equation is y=7/3x
Hence, equation of the line through (0,0) and (-3,-7) is y=7/3x
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Find the volume of a pyramid with a square base, where the side length of the base is
10.6
in
10.6 in and the height of the pyramid is
12.3
in
12.3 in. Round your answer to the nearest tenth of a cubic inch.
Answers
Answer:
V = 460.68
Step-by-step explanation:
V=(lwh)/3
Volume = (1/3) * base area * height
In this case, the base of the pyramid is a square with a side length of 10.6 inches, so the base area can be calculated as:
Base area = side length * side length
Let's calculate the base area first:
Base area = 10.6 in * 10.6 in
Next, we'll substitute the values into the volume formula:
Volume = (1/3) * (10.6 in * 10.6 in) * 12.3 in
Calculating this expression will give us the volume of the pyramid. Rounding the answer to the nearest tenth of a cubic inch will provide the final result.
The charge-to tap time (m) for carbon steel in one type of open-hearth furnace is to be determined for each heat in a sample n. If the investigator believes that almost all times in the distribution are between 320 and 440, what sample size would be appropriate for estimating the true time to within 5 min confidence level of 95%
Answers
The sample size appropriate for estimating the true time to within 5 min confidence level of 95% is 139
How to solve for sample sizeWe have to get the range of the values in this distribution
The range is given as: 440 - 320
= 120
through the range rule, we would have to solve for the standard deviation
= 120 / 4
= 30
At the 95 percent level of confidence, the critical value of Z is solved as 1.96
To get the value of n which is the sample size, we would have to use the Margin of error formula
\(ME = z*\frac{sd}{\sqrt{n} }\)
ME = 5
\(5 = 1.96 * \frac{30}{\sqrt{n} }\)
n = 138.2976
n is approximately 139
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{x + 3y =- 5
{9x + 3y = 3
Answers
Answer:
1. y-intercept(s):
(0,−53)
x-intercept(s):
(−5,0)
2. x-intercept(s):
(13,0)
y-intercept(s):
(0,1)
Step-by-step explanation:
Use inductive reasoning to predict the most probable next number in the list.
3, 9, -3, 3, -9, -3, -15, -9, -21, ?
Need Help
Answers
Answer: -27
Step-by-step explanation: Use inductive reasoning to predict the most probable next number in the list.
3, 9, -3, 3, -9, -3, -15, -9, -21, ?
We can start by looking at the differences between consecutive terms in the list:
9 - 3 = 6 -3 - 9 = -12 3 - (-3) = 6 -9 - 3 = -12 -3 - (-9) = 6 -15 - (-3) = -12 -9 - (-15) = 6 -21 - (-9) = -12
Notice that the differences alternate between positive 6 and negative 12. This suggests that the pattern involves adding 6, then subtracting 12, and then adding 6 again. Applying this pattern to the last term in the list (-21), we get:
-21 + 6 = -15 -15 - 12 = -27 -27 + 6 = -21
Therefore, we predict that the most probable next number in the list is -27.
How many cubic feet of warehouse space are needed for 350 boxes 11in. by 8in. by 12in?
Answers
Answer:
214 cubic feet (rounded to the nearest cubic foot)
Step-by-step explanation:
Step 1 Determine the volume of 1 box
Volume of a box or rectangular prism = dimensions multiplied by each other
Here, the given dimensions are 11 in by 8 in by 12 in
So the volume of one box would be 11 x 8 x 12 = 1056 cubic inches
Step 2 Determine volume of all 350 boxes
Volume of 1 box = 1056
So volume of all 350 boxes = 1056 x 350 = 369600 cubic in
Step 3 Convert cubic in to cubic ft
To convert to cubic feet we divide the amount of cubic inches by 1728 (this is because there are 1728 cubic inches in 1 cubic foot)
369600 / 1728 = 214 cubic feet (to the nearest cubic foot)
214 cubic feet of warehouse space is required for 350 boxes with the dimensions of 11in by 8in by 12in
A florist currently makes a profit of $20 on each of her celebration bouquets and sells an average of 30 bouquets every week. She noticed that when she reduces the price such that she earns $1 less in profit from each bouquet, she then sells three more bouquets per week. The relationship between her weekly profit, P(x), after x one-dollar decreases is shown in the graph below.
A graph for p of x is a downward open parabola with its vertex at (5, 725) and passes through the points (negative 10, 0), and (20, 0).
Use the graph to complete each statement about this situation.
The maximum profit the florist will earn from selling celebration bouquets is $.
The florist will break-even after one-dollar decreases.
The interval of the number of one-dollar decreases for which the florist makes a profit from celebration bouquets is ( , ).
Answers
Answer:
The maximum profit the florist will earn from selling celebration bouquets is $725.
The florist will break-even after one-dollar decreases when her profit is zero. From the graph, this occurs at x = 10. So the florist will break-even after 10 one-dollar decreases.
The interval of the number of one-dollar decreases for which the florist makes a profit from celebration bouquets is (0, 10). This is because the profit is positive for values of x between 0 and 10, and becomes negative after 10.
Step-by-step explanation:
A cube is a three-dimensional geometric figure, hollow or solid, contained by six equal square sides. The maximum capacity of a cube is calculated with the formula, V = s3, where V = volume and s = side length. Which of the following situations best models the maximum capacity of a cube shaped box with a side length of 4x inches? Select all that apply.
A)V = 4 3 · x3 cubic inches
B)V = 64 x3cubic inches
C)V = (4 x) 3 cubic inches
D)V = 64 x cubic inches
E)V = 4 x cubic inches
Answers
Answer:
good luck with that you trooper
Step-by-step explanation:
What linear equation represents the graph of a horizontal line, parallel to the x-axis, that travels through the point (0,4)? Use the grid or a piece of paper if needed. LY 2 1 X 5 2 2 0 1 2 3 4 1 -2
Answers
It's important to know that all horizontal lines can be represented as y = k, where k is a real number.
In this case, we know that the horizontal line passes through (0,4).
Therefore, the equation of the line is y = 4.
$120; Markup: 35%
What's the final price? pls show how u got the answer...
Answers
Answer: 162
Step-by-step explanation:
So you will need to find the Markup. The original cost is $120.
Divide the number by 100 is 1.2. $1.2 is 1% of the $120.Now times the number by 35. $1.2 x 35 is $42.Finally, add the number. 120 + 42 = 162.I hope this is the answer you are looking for.
find the square root of 7
Answers
The value of the square root of 7 is,
⇒ √7 = 2.645
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
WE have to given that;
To find the value of the square root of 7 .
Since, the square root of 7 is,
⇒ √ 7
⇒ 2.645
Thus, The value of the square root of 7 is,
⇒ √7 = 2.645
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Answer the question plz
Answers
7. 360 - 70 - 80 - 85 = 125
Answer:
1) A- 95
2) B- 125
Step-by-step explanation:
1) 50 + 35+x = 180
85 +x = 180
x = 180- 85
= 95
2) 70 +80 + 85+d = 360
235 + d = 360
d = 360 - 235 = 125
I Hope im right!