The population will reach 15,000 after approximately 156.24 minutes.
To find the initial size of the culture, we can use the exponential growth formula:
[tex]N = N0 * e^(rt)[/tex]
Where:
N = final count after a certain time
N0 = initial count
r = growth rate
t = time in minutes
e = Euler's number (approximately 2.71828)
We are given two data points:
At 20 minutes: N = 900
At 35 minutes: N = 1100
Using these points, we can set up two equations:
[tex]900 = N0 * e^(20r) ---(1)[/tex]
[tex]1100 = N0 * e^(35r) ---(2)[/tex]
To solve this system of equations, we can divide equation (2) by equation (1):
[tex]1100 / 900 = (N0 * e^(35r)) / (N0 * e^(20r))[/tex]
Simplifying:
[tex]1.2222 = e^(35r) / e^(20r)[/tex]
[tex]e^(a - b) = e^a / e^b:[/tex]
[tex]1.2222 = e^((35-20)r)[/tex]
Taking the natural logarithm (ln) of both sides:
[tex]ln(1.2222) = ln(e^((35-20)r))[/tex]
ln(1.2222) = (35-20)r
Now we can solve for r:
r = ln(1.2222) / 15
Using a calculator, we find:
r ≈ 0.0461
Now we can substitute the value of r into equation (1) to find N0:
[tex]900 = N0 * e^(20 * 0.0461)[/tex]
[tex]N0 = 900 / e^(0.922)[/tex]
N0 ≈ 697.86
Therefore, the initial size of the culture was approximately 697.86.
To find the doubling period, we can use the formula:
doubling period = ln(2) / r
doubling period = ln(2) / 0.0461
Using a calculator, we find:
doubling period ≈ 15.03 minutes
Therefore, the doubling period is approximately 15.03 minutes.To find the population after 60 minutes, we can use the formula:
[tex]N = N0 * e^(rt)[/tex]
[tex]N = 697.86 * e^(0.0461 * 60)[/tex]
Using a calculator, we find:
N ≈ 1579.83
Therefore, the population after 60 minutes is approximately 1579.83.
To find when the population will reach 15,000, we can rearrange the formula:
[tex]N = N0 * e^(rt)[/tex]
15,000 = N0 [tex]* e^(0.0461 * t)[/tex]
Dividing both sides by N0 and taking the natural logarithm:
ln(15,000/N0) = 0.0461 * t
Now we can solve for t:
t = ln(15,000/N0) / 0.0461
Substituting the value of N0 we found earlier:
t = ln(15,000/697.86) / 0.0461
Using a calculator, we find:
t ≈ 156.24 minutes
Therefore, the population will reach 15,000 after approximately 156.24 minutes.
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answer easy question quick
Answer:
Step-by-step explanation:
a) 9.80- 98/10
b) 7.3- 73/10
a) 7/100- 0.07
b) 82/10- 8.2
Hope this helps
Fraction:
a) 98/100
b) 73/10
Decimal:
a) 0.07
b) 8.2
What is your dream career and why ?
Answer:
Step-by-step explanation:
Professional dancers cause I’ve danced since I was 3 and I’ve always wanted to do it. And I wanna model on the side
Answer:
Detective/Forensics scientist
Step-by-step explanation:
I want to be a detective/ forensic scientist because I am interested in science and investigating.
Should i trust the links people say "Their is an imagine in this link that contains the answer" usually these links are from sus profiles. So should i use it or no?
Answer:
no don't ever click on links okay.
Step-by-step explanation:
PLEASE HELP ME ASAP I SWEAR IT WOULD BE A BIG HELP.
Jethro has sat 5 tests.
Each test was marked out of 100 and Jethro's mean mark for the 5 tests is 74
Jethro has to sit one more test that is also to be marked out of 100
Jethro wants his mean mark for all 6 tests to be at least 77
Work out the least mark that Jethro needs to get for the last test.
This paper will discuss the mathematics involved in determining the least mark that Jethro needs to get for the last test in order to end up with a mean mark of 77 over all 6 tests.
Jethro has sat 5 tests and each test was marked out of 100. Therefore, Jethro’s marks for the 5 tests can be represented by x1, x2, x3, x4, and x5. Jethro’s mean mark for the 5 tests is 74, which can be represented by the mathematical equation: (x1 + x2 + x3 + x4 + x5) / 5 = 74.
Jethro needs to sit one more test that is also marked out of 100 and he wants his mean mark for all 6 tests to be at least 77. Therefore, the least mark that Jethro needs to get for the last test can be found by rearranging the equation to: (x1 + x2 + x3 + x4 + x5 + x6) / 6 = 77. This can be written in its simplified form as: 6x6 = 77(x1 + x2 + x3 + x4 + x5).
In order to find the least mark that Jethro needs to get for the last test, x6, the other terms must be known. Since Jethro has already sat the 5 tests the marks for these tests are known, so they can be added together. This results in: x6 = 77(x1 + x2 + x3 + x4 + x5) / 6. Therefore, Jethro needs to get a mark of at least 77.6 (rounded to the nearest tenth) on the last test in order to end up with a mean mark of 77.
y−3=5(x−2) what is the slope?
Answer:
y=5(x-2)+3 or y= 5x+7
Step-by-step explanation:
no links
The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $4 and each adult ticket sells for $8. The auditorium can hold a maximum of 110 people. The drama club must make at least $570 from ticket sales to cover the show's costs. Also, they must sell at least 20 student tickets and a maximum of 70 adult tickets. If xx represents the number of student tickets sold and yy represents the number of adult tickets sold, write and solve a system of inequalities graphically and determine one possible solution.
Answer:
hgfxjdt
Step-by-step explanation:
Factor 9z^2 - 6x +1.
pls will mark you brainiest
Answer:
It is not factorable
Step-by-step explanation:
The expression is not factorable with rational numbers.
Answer:
This is not factorable.
Step-by-step explanation:
This is not factorable.
What is the value of x in the equation below?
12 – 2(x-1)=6
Hey I'm Chloe Can you Help Me, I will give Brainlest, Thank you :)
Stefan sells Jin a bicycle for $104 and a helmet for $17. The total cost for Jin is 110 % of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin?
Answer:
Stefan spent 108.9$ and made 12.1$
Step-by-step explanation:
Hey I'm Aiden I can help you, I will take Brainlest, Your welcome :)
take 10% of 121 and subtract it from 121 and you get the price he paid and made
Will Mark Brainliest To First Correct Answer.
Properties of Kites on IXL. I Only need to get one more correct and dont want to get reset...
Step-by-step explanation:
[tex]ei = \sqrt{ {45}^{2} - {27}^{2} } = \\ = \sqrt{2025 - 729} = \\ = \sqrt{1296} = \\ = 36[/tex]
Which number line shows - graphed?
Answer:
The second one down is the answer
Step-by-step explanation:
Stop and Shop sells 6 cases of Pepsi for $21.60. What is the constant of proportionality?
Answer: $3.60 per case
Step-by-step explanation: $21.60 divided by 6 = 3.60
MARKING BRAINLIEST TO FIRST PERSON WHO IS CORRECT!
I need help with #13
Answer:
True
False
False
Step-by-step explanation:
If p(x)= 2^x, what is the value of p(3) - p(2)?
Answer:
4
Step-by-step explanation:
p(3) = 2³ = 8
p(2) = 2² = 4
8-4 = 4
An experiment was performed to test whether caffeine in Coca-Cola would improve performance on an intelligence test. One randomly chosen group of subjects was given an 8 oz. cup of Coca-Cola containing caffeine to drink 10 minutes before taking the intelligence test. Another randomly chosen group was given an 8 oz. cup of decaffeinated Coke to drink 10 minutes before taking the test. Neither group had any food or drink for three hours before the experiment began. What are the levels or conditions of the independent variable
Answer:
8 oz of cocacola drink containing caffeine
8 oz of Decaffeinated Coke
Step-by-step explanation:
Th independent variables is that variable which causes a change in the output or the dependent or response variable. In the scenario described above, the type of drink Given to the participants is the independent variable
The Independent variable is the type of drink Given to the subjects with two levels ;
Levels :
cocacola drink containing caffeine
Decaffeinated Coke
Therefore, we can conclude that, there are two levels Of the jndependent variable, which are stated above.
Find the potential function f for the field F.
F = -1/x i+1/y j-1/z k
The potential function for the given field is f = ln |y| - ln |z| - ln |x| + C, where C is a constant of integration.
Given field is F = (-1/x) i+ (1/y) j- (1/z) k
The potential function f is given by
∂f/∂x = -1/x .........(1)∂f/∂y = 1/y .........(2)∂f/∂z = -1/z .........(3)
Using the equation (1)
we get
f = -ln |x| + C1
Using the equation (2)
we get
f = ln |y| + C2
Using equation (3) we get
f = -ln |z| + C3
On adding the above three equations we get
f = ln |y| - ln |z| - ln |x| + C
where C = C1 + C2 + C3 is a constant of integration.
Therefore, the potential function for the given field is f = ln |y| - ln |z| - ln |x| + C, where C is a constant of integration.
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Mother put 22 apples in each basket. How many baskets did she use for 390 apples?
Answer:
To find the no. of baskets used to put 390 apples we have to divide 390/22 which is 17.7272727273,
so to put 390 apples we need approximately 18 baskets.
hope this answer helps you...
Martina runs 6 miles in 50 minutes. At the same rate, how many miles would she run in 35 minutes?
Answer:
4.2 miles
Step-by-step explanation:
Martina runs 6 miles in 50 minutes, we have to find the rate at which she is running. Put it in a fraction [tex]\frac{6}{50}[/tex] or she runs 6 miles every 50 minutes. When we divide we get that she is running, 0.12 miles evrey minute. The question askes us how far Matina will run in 35 minutes, so we multiply 0.12 by 35, and we get that she will run 4.2 miles.
Show all steps please!
Suppose you are told that 3.59% of Wendigos are less than 273cm tall while only 4.01% are taller than 326.25 cm tall. Find the mean and standard deviation of the heights of Wendigos.
The mean of the heights of Wendigos ≈ 302.523 cm, and the standard deviation ≈ 14.165 cm.
To obtain the mean and standard deviation of the heights of Wendigos, we can use the information given about the percentiles.
Let's denote the mean as μ and the standard deviation as σ.
Step 1: Finding the Z-scores
First, we need to find the Z-scores corresponding to the given percentiles.
For the lower percentile:
Z = (X - μ) / σ = -1.880
For the upper percentile:
Z = (X - μ) / σ = 1.880
Step 2: Finding the corresponding values using Z-scores
Next, we need to find the values corresponding to the Z-scores using a standard normal distribution table or a calculator.
For the lower percentile:
Z = -1.880 corresponds to a cumulative probability of 0.0359
For the upper percentile:
Z = 1.880 corresponds to a cumulative probability of 0.9601
Step 3: Calculating the values
Using the cumulative probabilities obtained, we can find the corresponding values.
For the lower percentile:
X = Z * σ + μ
273 = -1.880 * σ + μ
For the upper percentile:
X = Z * σ + μ
326.25 = 1.880 * σ + μ
Step 4: Solving the equations
We now have a system of equations with two unknowns (μ and σ).
273 = -1.880 * σ + μ (Equation 1)
326.25 = 1.880 * σ + μ (Equation 2)
We can solve this system of equations to find the values of μ and σ.
Subtracting Equation 1 from Equation 2, we get:
326.25 - 273 = 1.880 * σ + μ - (-1.880 * σ + μ)
53.25 = 3.760 * σ
Dividing both sides by 3.760, we get:
σ ≈ 14.165
Substituting this value of σ into Equation 1, we can solve for μ:
273 = -1.880 * 14.165 + μ
273 + 1.880 * 14.165 = μ
μ ≈ 302.523
Therefore, mean is approximately 302.523 cm, and the standard deviation is approximately 14.165 cm.
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Which function matches the table?
Answer:
B. f(x) =3
Step-by-step explanation:
sbwveivdebeudh
A recent stocktake measured the price of BBQs at a large hardware store. From the stocktake, it was determined that the price was normally distributed with a mean of 500 dollars and a standard deviation of 50 dollars. Twenty per cent of the BBQs would cost more than what price? Select from the answers below.
575.5
542
526
459
The price at which twenty percent of the BBQs would cost more is $542 and it follows a normal distribution.
In this case, we are given that the price of BBQs at a large hardware store follows a normal distribution with a mean of $500 and a standard deviation of $50. We want to find the price at which twenty percent of the BBQs would cost more.
To solve this problem, we need to find the value, denoted as x, for which 20% of the BBQs are priced higher. This can be done by finding the z-score corresponding to the 20th percentile and then converting it back to the original scale.
The z-score is calculated using the formula:
z = (x - μ) / σ,
where μ is the mean and σ is the standard deviation.
To find the z-score corresponding to the 20th percentile, we can use a standard normal distribution table or a statistical calculator. The z-score corresponding to the 20th percentile is approximately -0.84.
Now we can use the z-score to find the corresponding value in the original scale:
-0.84 = (x - 500) / 50.
Solving for x, we get:
-0.84 * 50 = x - 500,
-42 = x - 500,
x = 500 - 42,
x = 458.
So, twenty percent of the BBQs would cost more than $458. However, since we need to choose from the given options, the closest price to $458 is $459.
Therefore, the answer is $459.
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A person visits the store and picks up five kg vegetables for did he buy?
£6.25. Which vegetable
Tomato - £1.50 per kg Carrot - £1.75 per kg Cabbage - £2 per kg Beetroot - £1.25 per kg
One hundred tickets, numbered 1, 2, 3, …, 100, are sold to 100 people for a drawing. Four different prizes are awarded, including a grand prize (a trip to Tahiti). How many ways are there to award the prizes if a) the person holding ticket 47 wins one of the prizes? b) the people holding tickets 19 and 47 both win prizes?
Solution :
It is given that four different prizes were awarded. So,
a). 4 ways for person 47 to win a prize
99 ways to give out the 2nd prize
98 ways to give the 3rd prize
97 ways to give the last prize
∴ P(99,3) = 99 x 98 x 97
b). 1 way to give person 47 their prize
1 way to give person 19 their prize
98 ways to give out the 3rd prize
97 ways to give out the last prize
So, P(98,2) = 98 x 97
The mean score in a physics test is 75% with the standard deviation 6.5%. Suppose that the scores in the test are approximately normally distributed. What is the probability that a randomly selected student scores more than 82%? Round your answer for 4 decimal places.
__________
The probability that a randomly selected student scores more than 82% on the physics test, we can use the standard normal distribution and the given mean and standard deviation.
The z-score formula is given by z = (x - μ) / σ, where z represents the z-score, x is the observed value, μ is the mean, and σ is the standard deviation. In this case, the observed value is 82%, the mean is 75%, and the standard deviation is 6.5%. Plugging these values into the formula, we calculate the z-score as z = (0.82 - 0.75) / 0.065 = 1.0769.
Next, we need to find the area to the left of the z-score in the standard normal distribution table or using a calculator. The area to the left of 1.0769 corresponds to the probability of scoring less than 82%. Let's assume this area is P(z < 1.0769).
The probability of scoring more than 82%, we subtract P(z < 1.0769) from 1: P(z > 1.0769) = 1 - P(z < 1.0769).
Using a standard normal table or a calculator, we can find P(z < 1.0769) to determine the probability.
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SHOW WORK PLEASE! I WILL GIVE YOU BRAINLIEST IF YOU SHOW! DONT USE LINKS PLEASE!!!
A single number cube is rolled twice and the two numbers are added.
PART A:
How can you determine the total number of possible outcomes
Answer:
well if you where talking about the dice the awnser is 6 and if you are tlking about the shirts then you can do 3 times 3 i thik is the right awnser
Step-by-step explanation:
1. a dice is a cube a cube has 6 sides a single number dice is a dice that only has numbers that are by themselves so the awnser can only be on the dice 6 to 9 so now we know that it is 6 now 6 times 2 is 12 because it got rolled twice
2.
Your parents gave you $0.35 on Sunday and then gave you twice as much money on Monday as they did on Sunday. On Tuesday, they gave you twice as much money as they gave you monday. The pattern continued for a week. How much money did your parents give you on Saturday??
Answer:
$22.40 im pretty sure its right
Step-by-step explanation:
sorry if im late and mark me brainliest if im right
If there is 0.25 probability that a child in New York gets the flu and a 0.30 probability that a child in Los Angeles gets the flu, what is the probability that both will get the flu?If there is 0.25 probability that a child in New York gets the file and a 0.30 probability that a child in Los Angeles gets the flu, what is the probability that both will get the flu? O 0.075 O 0.275 O 0.25 O 0.55
Answer:
(.25)(.30) = .075 probability that both children will get the flu
The probability that both a youngster in New York and a kid in Los Angeles will get this season's virus can be determined by duplicating the singular probabilities. Consequently, the likelihood that both will get influenza is 0.075.
To find the probability of the two occasions happening, we duplicate the probabilities of every occasion. Considering that the probability of a kid in New York getting this season's virus is 0.25 (or 25%) and the probability of a youngster in Los Angeles getting influenza is 0.30 (or 30%), we multiply these probabilities: 0.25 * 0.30 = 0.075. This implies there is a 0.075 probability, or 7.5%, that both a youngster in New York and a kid in Los Angeles will get influenza.
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A woman bought a bag of rice 5700 naira and in 3 weeks later, she could only buy 2/4 of the bags for 5700 naira. Find the percentage?
Answer: 100% increase
Step-by-step explanation:
You need the find the cost per bag in those weeks.
Three weeks ago, she could buy a bag for N5,700.
Three weeks after that, she could only buy half a bag for the same amount. A bag therefore costs:
= 5,700 ÷ 2/4
= N11,400
The percentage increase is:
= (11,400 - 5,700) / 5,700
= 100%
In the lexicographic ordering of the permutations of the set {A,B,C,D,E,F,G,H} , what is the next permutation after GAEDBHFC? (Assume the usual alphabetic order of letters.)
a. HAEFBDCG b. GAEDCBFH c. DEHBFGCA d. None of the other answers is correct. e. FDAEGBCH
In the lexicographic ordering of the permutations of the set {A,B,C,D,E,F,G,H} , the next permutation after GAEDBHFC will be GAEDBHFD.
What is lexicographic ordering?
Lexicographic ordering or dictionary ordering is a way of ordering elements based on their alphabetical or numerical values.
To find the next permutation in the lexicographic ordering, we need to find the smallest possible permutation that is greater than GAEDBHFC by considering the order of the letters.
Let's analyze the given permutation:
GAEDBHFC
To find the next permutation, we start from right to left and look for the first occurrence of a letter that can be replaced by a greater letter. In this case, the first such occurrence is "C" (after "H").
Next, we need to find the smallest letter that is greater than "C" from the remaining letters. From the letters {C, D, E, F, G, H}, the smallest greater letter than "C" is "D".
Now, we swap "C" with "D":
GAEDBHFD
After swapping, we need to sort the remaining letters in ascending order to obtain the smallest permutation. The remaining letters are {B, E, F, G, H}. Sorting them gives:
GAEDBHFD
Therefore, the next permutation after GAEDBHFC is GAEDBHFD.
The correct answer is:
b. GAEDBHFD
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A birthday cake is being made using a cylindrical baking pan. The radius of the pan is 4 inches, and the height is 5 inches.
Which formula represents the correct way to calculate the volume of the cake?
O V = (4)(5)
O V = r(4)(5)
O V = $(5) (4)
O V = $(4)?(5)
Answer:
the formula represent the correct way is π(4)^2 (5)
Step-by-step explanation:
The formula that represent the correct way to calculate is given below:
As we know that
Volume = πr^2 h
where
r denotes the radius i.e. 4 inches
And, h denotes the height i.e. 5 inches
Now placed these values to the above formula
So,
= π(4)^2 × 5
= 80π in^3
Hence, the formula represent the correct way is π(4)^2 (5)
Answer: the answer is D.
Step-by-step explanation: