John needs to divide the sample in half once the number of bacteria has reached 1000. How many hours after the initial time must be divide the sample?
Answers
Answer:
Option A
Step-by-step explanation:
The complete question is attached here
The rate of increase of bacterial population be K
As we know
[tex]Y = Y_0 * e^{kT}[/tex]
where Y is the final population. In this case it is 1000
K is the rate of increase of population i.e 3 times per hour
T is the time in hours
Y0 is the initial population = 5
Substituting the given values, we get -
[tex]1000 = 5 *e^{3*T}\\200 = e^{3*T}[/tex]
Taking log on both sides, we get -
ln [tex]200[/tex] = ln [tex]e^{3T}[/tex]
[tex]2.718 * 2.301 = 3T[/tex]
T = 2.084 hours
hence, option A is correct
The number of hours required after the initial time must be divide the sample by John is 2.084 hours.
What is an exponential function?Exponential function is the function in which the function growth or decay with the power of the independent variable. The curve of the exponential function depends on the value of its variable.
The exponential function with dependent variable y and independent variable x can be written as,
[tex]y=ba^x+c[/tex]
Here, a, b, and c are the real number
John needs to divide the sample in half once the number of bacteria has reached 1000.
The table of this bacterial growth is,
Time(hours) Number of bacteria
0 5
1 15
2 45
The rate of increasing the bacteria each hour is,
[tex]x=\dfrac{15}{5}=3\\x=\dfrac{45}{15}=3[/tex]
Thus, the exponential rate is 3.
Now the number of reached is 1000, and the initial population was 5. Therefore, for the time t, the exponential function can be given as,
[tex]1000=5e^{3t}\\\dfrac{1000}{5}=e^{3y}\\200=e^{3y}[/tex]
Taking log both the sides as,
[tex]\ln (200)=\ln e^{3t}\\2.301=0.434({3t})\\t=2.084[/tex]
Hence, the number of hours required after the initial time must be divide the sample by John is 2.084 hours.
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Related Questions
6x+2 = 5x+18 PLS QUICKKKK
Answers
Answer:
16
Step-by-step explanation:
Equation : 6x+2=5x+18
Like Terms : x + 2 = 18
Like Terms Again : x = 16
Answer:
6x+2=5x+18
6x-5x=18-2
X=16
Step-by-step explanation:
First you need to group numbers of like terms in one side. Then when you take the other number to the other side of equal sign changes it's form eg +6 change to - 6
A rectangular picture is twice as long as it is wide. If the
area of the picture is 288 in^2, what are its dimensions?
The dimensions of the picture are_____ in long by_____ in wide.
Answers
Answer:
24 in long by 12 in wide.
Step-by-step explanation:
l=2w
288=(2w)×w
288=2w^2
144=w^2
12=w
width is 12 inches. Plug that in to find length...
l=2×12
l=24
The perimeter of a semicircle is 46.26 meters. What is the semicircle's diameter?
Answers
Answer:
diameter = 18 m
Step-by-step explanation:
46.26 = 1/2π(diameter) + diameter
46.26 = 1.57d + d = 2.57d
d = 46.26/2.57 = 18 m
Can someone help me with this please
Answers
Hope it helps!
Math-way app for problems like number 2
Have a nice day:)
Fill in the number to find the sum . 2/10 + /100= 50/100 a. 30 b. 10 c. 28 d. 52
Answers
Answer:
2/10 + 30/100 = 50/100
Step-by-step explanation:
First, you want to multiply 2/10 by 10, to get the same common denominator in both numbers, you would get 20/100. Then, its pretty simple from there, you just add the number that gets you to 50, which is 30, 20 + 30 =50. I Hope This Helps :)
The required missing number is 30. So, the correct answer is (a) 30.
Arithmetic is a branch of mathematics that deals with the study of numbers, their properties, and their operations. It involves the basic operations of addition, subtraction, multiplication, and division.
Here,
To find the missing number, we can use the fact that 50/100 is equivalent to 1/2.
So, we need to find a number that, when added to 2/10, gives 1/2 as the sum.
We can write this as an equation:
2/10 + x/100 = 1/2
Multiplying both sides by 100 to eliminate the denominator, we get:
20 + x = 50
Subtracting 20 from both sides, we get:
x = 30
Therefore, the missing number is 30. So, the correct answer is (a) 30.
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I have a question for special product patterns.
It is in the attached image.
Answers
If sin(38°) and cos(52°) does that add up to 90°?
Answers
Answer:
38 plus 52 is in fact 90, but Sin and Cos will be different.
Step-by-step explanation:
Honestly I haven't learned Sin or Cos
but actually 38+52=90 but putting sin and cos will definitely differ
I need help with this math problem.
Answers
Answer:
Answer and steps in picture.
what is 6,720 divided by 14??
Answers
480 because 6,720 divided by 14 is 480
HELP PLEASE : For numbers 3 & 4, draw a triangle for each to find the missing side.
Answers
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Answer: 1) b = 2
2) c = 20
Explanation:
I hope this helped!
<!> Brainliest is appreciated! <!>
- Zack Slocum
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Answer:
3) b = 2.24
4) c = 15.62
Step-by-step explanation:
Pythagorean formula:
a² + b² = c²
3)
a² + b² = c²
2² + b² = 3²
4 + b² = 9
b² = 5
b = 2.24
4)
a² + b² = c²
10² + 12² = c²
100 + 144 = c²
244 = c²
c = 15.62
I’ll give you brain list if you solve it
Answers
Answer:
1000$ is the correct ans I think ?
hey i need some help
Answers
Please help!!!!!!!!!!!!!!!!!!!
Answers
Answer:
there are infinitely many solutions
Step-by-step explanation:
1/2(b + 14) is the same as (b + 14) / 2
Tim has 39 pairs of headphones and 13 music players. Tim wants to sell all of the headphones and music players in identical packages.
Answers
Answer: Well, I think a package is 1 pair of headphones and 1 music player and if it is the answer will be 13 because there are only 13 music players
Step-by-step explanation: Sorry if this is wrong. I just don't fully understand the question :)
The distance between itahari and Damak is
42 km. Mr. Dhamala travelled 18.325 km by a
bus / 15.675 km by a toxi and the re
remaining dis-
tance by a motorbike How many km did he
travelled ky motorbike?
Answers
Answer:
8 km by motorbike.
Step-by-step explanation:
The distance between itahari and Damak is 42 km.
Mr. Dhamala travelled 18.325 km by a bus / 15.675 km by a taxi and the remaining distance by a motorbike.
Let he covered x distance by motorbike. So,
Remaining distance = Total distance -(distance covered by bus + distance by taxi)
= 42 -(18.325 +15.675 )
= 42-34
= 8 km
So, he travelled 8 km by motorbike.
I WILL GIVE BRAINILYEST!!!This is a graded discussion:
Modules
Mathematical Modeling Discussion
Syllabus
Grades
99 Co
5.272 a
People
0.31 MeV B 99.80%
Office 365
1.48 Mev B-
1.1732 MeV Y
0365 Email
1.3325 MeV Y
The rate of decay of a radioactive substance depends upon the
amount present initially. The mass y (mg) of the radioactive substance
cobalt-60 present in a sample at time < (years) is represented by the
-0.13151
exponential equation y = 50 e
Answer the following questions in complete sentences.
1. How does the exponential equation above compare to the equation
for simple interest that is compounded continuously? Explain the
similarities. What is the initial amount of cobalt-60 in the sample?
2. How much cobalt-60 is left after 8.4 years? Show your work
3. What would be the y-intercept of the graph? What does it
represent?
4. After how many years will the amount of cobalt-60 left be 6.25
mg? Explain what happens to the cobalt-60 after 50 years?
5. Discuss some real-world" examples and uses of cobalt-60
Answers
Answer:1.40
2.20
3.100
4.39
5.7
7
Step-by-step explanation:
One face of a prism is in the shape of an isosceles triangle with a base of 15 inches. The perimeter of the triangle is 47
inches. How long is each of the equal sides of the triangle?
Provide your answer below:
inches
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SUBMIT
Content attribution
Answers
Answer:
16 Inches
Step-by-step explanation:
.........................
The sum of three numbers is 30. The third number is twice the second, and is also 2 less than 3 times the first. What are the three numbers?
Answers
Answer:
First: 6 Second: 8 Third:16
Step-by-step explanation:
First number:x
Second number: 1.5x-1
Third number: 3x-2
x+1.5x-1+3x-2=30
5.5x-3=30
5.5x=33
x=33/5.5=6
So First =6
Second= 1.5(6)-1=8
Third " 3(6)-2=16
Repeated-measures and matched-subjects experiments
Repeated measures experiments measure the same set of research participants two or more times, while matched-subjects experiments study participants who are matched on one or more characteristics. Which of the following are true for both a repeated-measures experiment and a matched-subjects experiment when used to compare two treatment conditions?
A. If the researcher has n number of participants to use in the experiment, then the degrees of freedom will be the same in a repeated-measures experiment or in a matched-subjects experiment.
B. The researcher must compute a pooled variance to compute a t statistic.
C. The researcher must compute an estimated standard error for the mean difference score to compute a t statistic.
D. Participants in both types of experiments are all measured the same number of times.
A matched-subjects experiment produced at statistic with a df of 13. How many subjects participated in this study?
a. 13.
b. 28.
c. 26.
d. 14.
For a repeated-measures experiment comparing two treatment conditions, the t statistic has a df of 17. How many subjects participated in this study?
a. 18.
b. 17.
c. 36.
d. 34.
Answers
A company has 500 employees, and 60% of them have children. Suppose that we randomly select 4 of these
employees.
Which of the following would find the probability that exactly 3 of the 4 employees selected have children?
Answers
The probability that exactly 3 of the 4 employees selected will have children is given by binomial distribution formula ⁴C₃(0.60)³(0.40)
What is a Binomial Distribution?
The binomial distribution is a type of probability distribution that predicts the likelihood of obtaining one of two outcomes given a set of inputs. It summarizes the number of tries where each trial has the equal chance of producing the same result.
The formula for Binomial Distribution is given by
P ( x ) = ⁿCₓ pˣq⁽¹⁻ˣ⁾
where
n = number of trials
x = number of successes
p = probability of getting a success in one trial
q = probability of getting a failure in one trial
q = 1 - p
Given data ,
Let the total number of employees be = 500
Now , the probability of success of selecting employees having children is given by p = 0.60
So , the value of q = 1 - p
q = 1 - 0.60
q = 0.40
So , The probability that exactly 3 of the 4 employees selected will have children is given by binomial distribution formula
where,
P ( x ) = ⁿCₓ pˣq⁽¹⁻ˣ⁾
where
n = number of trials
x = number of successes
p = probability of getting a success in one trial
q = probability of getting a failure in one trial
q = 1 - p
Substituting the values in the equation , we get
P ( x ) = ⁴C₃(0.60)³(0.40)
On simplifying the equation , we get
P ( x ) = 4 x 0.246 x 0.4
P ( x ) = 0.3456
Therefore , the value of P ( x ) is 0.3456
Hence , The probability that exactly 3 of the 4 employees selected will have children is given by binomial distribution formula ⁴C₃(0.60)³(0.40)
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The length of a rectangular garden is 3 m greater than the width.the area of the garden is 70 m^2. Find the dimensions of the garden
Answers
Cause my dad came back with the milk
Answer:
Step-by-step explanation:
A = L x W
so you know that the length is 3m longer than the width, so you could use a formula to represent that
w = L + 3
you then substitute the second equation into the first to solve for L
70 = L x (l +3)
70 = L^2 + 3l
you could then rearrange the formula and solve for l using the quadratic formula
0 = L^2 + 3l - 70
l = -3 +- (square root (3)^2 - 4(1)(70)) / 2(1)
l = -3 +- (square root 9 + 280) / 2
l = -3 +- (square root 289) / 2
l = -3 +- 17 / 2
then you solve for the two separate roots
l = -3 + 17 /2
l = 14 / 2
l = 7
or
l = -3 - 17 / 2
l = -20 / 2
l = -10
since a length cannot be negative, this root is not viable. therefore l = 7
to solve for w you would use
w = l + 3
w = 7 + 3
w = 10
hope this helps. :)))
What is the measure of ZB, in degrees?
Answers
This triangle is an isosceles triangle so two sides are equal, angle A and angle C are equal so 74+74=148 and then a triangle equals 180 degrees so you subtract the angles of A and C to find B. 180-148=32
What is the 20th term of the linear sequence below?
1, 7, 13, 19, 25, ...
Answers
Answer:
115
Step-by-step explanation:
1, 7, 13, 19, 25...
1, 1+6, 1+6+6, 1+6+6+6, 1+6+6+6+6...
In 2nd number, 1 plus one 6
In 3rd number, 1 plus two 6s
:
In 20th, 1 plus nineteen 6s
1 + 6 × 19 = 115
help pls
hannah is making a fleece tie blanket. it is 36 inches long. each tie will be 3/4 of an inch wide. how many times will she have
Answers
Proportionately, the number of times that Hannah will have to tie the blanket is 48 times.
What is proportion?Proportion is the relationship between two numerical values or variables. It shows the share or portion of a variable to the whole number.
Proportions are expressed as ratios, usually using fractions, decimals, or percentages.
Data and Calculations:The length of the fleece tie blanket = 36 inches
The width of each tie = 3/4 inches
The proportion of 3/4 inches to an inch = 0.75 (3/4)
The number of times to tie the blanket = 48 times (36/0.75)
Thus, the number of times that Hannah will tie the blanket is 48 times.
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Determine the value of a.
Answers
what is the area of a square that is 2 feet length and 7 1/4 feet width
Answers
Hope this helps :)
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Answers
it's not possible
I think -7 is the right answer but it's not possible actually
Answer:
c. -7
Step-by-step explanation:
(x+57) + (63+67) = 180
(x+57) + 130 = 180
x + 187 = 180
x = 180-187
x = -7
why did I make it equal to 180?
all the angles in a triangle always equal 180 :)
I don’t understand this at all helppp
Answers
Answer:
I don’t think it’s a right triangle
Step-by-step explanation:
5^2 + 8^2 should equal 12^2 for it to be a right triangle.
HELP FAST
A house costing $500,000 with a 15-year mortgage and an APR of 4.5% would
have what monthly payment?
Answers
Answer:
3825
Step-by-step explanation:
Which is the sum of 14t/10t^2 + 5t^2+40t/10t^2
Answers
Answer:
7t/5^3 + 5t^2 + 4t^3
Step-by-step explanation: