Answer:
The expression is: [tex]P(t) = 693e^{0.3662t}[/tex]
The initial number of strands is 693
Step-by-step explanation:
A bacterial culture is known to grow at a rate proportional to the amount present.
This means that the bacterial model can be modeled by the following equation:
[tex]P(t) = P(0)e^{rt}[/tex]
In which P(0) is the initial population, and r is the growth rate.
After one hour, there are 1000 strands of bacteria
This means that [tex]P(1) = 1000[/tex], So
[tex]P(0)e^{r} = 1000[/tex]
[tex]P(0) = \frac{1000}{e^{r}}[/tex]
After four hours, 3000 strands.
This means that P(4) = 3000. So
[tex]P(0)e^{4r} = 3000[/tex]
Since [tex]P(0) = \frac{1000}{e^{r}}[/tex], we have that:
[tex]\frac{1000}{e^{r}}e^{4r} = 3000[/tex]
[tex]\frac{e^{4r}}{e^{r}} = \frac{3000}{1000}[/tex]
[tex]e^{4r-r} = 3[/tex]
[tex]e^{3r} = 3[/tex]
[tex]\ln{e^{3r}} = \ln{3}[/tex]
[tex]3r = \ln{3}[/tex]
[tex]r = \frac{\ln{3}}{3}[/tex]
[tex]r = 0.3662[/tex]
The initial population is:
[tex]P(0) = \frac{1000}{e^{0.3662}} = 693[/tex]
The expression is:
[tex]P(t) = 693e^{0.3662t}[/tex]
The equation becomes [tex]y=694(1.44)^t[/tex]. The initial number of strands is 694.
An exponential growth is in the form:
y = abˣ
where y, x are variables, a is the initial value of y and b is the multiplier.
Let y represent the number of strands after t hours.
After one hour, there are 1000 strands of bacteria:
1000 = ab¹
ab = 1000 (1)
After four hour, there are 3000 strands of bacteria:
3000 = ab⁴
ab⁴ = 3000 (2)
Dividing equation 2 by 1:
b³ = 3
b = 1.44
ab = 1000
a = 1000/b = 1000/1.44 = 694
The equation becomes [tex]y=694(1.44)^t[/tex]
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Cho surveyed a random sample of 60 students in the school's library about whether they read the newest magazine. Fifteen of the 60 students said they read the newest magazine. Cho determined that 360 students visit the library each day.
Based on the survey, how many of the 360 students can he expect to read the newest magazine?
Answer:
90 students.
Step-by-step explanation:
Given that Cho surveyed a random sample of 60 students in the school's library, of which 15 said they read the newest magazine, and that a total of 360 students attend the library every day, to determine how many of the 360 students can have expect to read the newest magazine the following calculation should be performed:
60 = 100
15 = X
15 x 100/60 = X
1,500 / 60 = X
25 = X
Thus, 25 percent of the students in the sample read the newest magazine. Since 25% of 360 is 90 (360 x 0.25), that is the number of students he can expect to have read the magazine.
Jamie has $70 in a savings account. The interest rate is 5%,
compounded annually.
To the nearest cent, how much will he have in 2 years?
*pls hurry . *
Answer:
$77
Step-by-step explanation:
10% of 70$ is $7
$70+$7=$77
Find the scale factor
(-3,-12)--->(-2,-8)
(-6,-15)--->(-4,-10)
(-9,-12)--->(-6,-8)
Answer:
2/3 is the scale factor of the sequence
There are 14 boys and 9 girls in miss Keller's music class. what is the ratio of boys to girls
Answer:
14:9
Step-by-step explanation:
you cant simplify so just put : in between the numbers and boom! ur ratio is 14 to 9 or 14:9
hope this helps :D
A city’s elevation is 140.2 feet below sea level. Between which two integers does this elevation lie?
Answer:
The elevation lies between -140 and -141.
Step-by-step explanation:
The elevation lies between -140 and -141.
Verify that the following function is a probability mass function, and determine the requested probabilities.
fx = (8/7(1/2)x
x = 0, 1, 2, ...
A. P(X = 2).
B. P(X ≤ 2).
C. P(X > 2).
D. P(X ≥ 1).
Is the function a probability mass function?
Answer:
yes
Step-by-step explanation:
Karen used one-third of her total stamps on a campaign for charity. Karen used 60 stamps on the campaign
Answer:
She has 180 stamps in total
Step-by-step explanation:
Answer:
180 stamps
Step-by-step explanation:
if she used 60 stamps and that was only a thrid of it, then all you have to do is multiply by 3
Formula: 60·3=180
A ball thrown in the air has a height of h(t)
- 16t^2 + 50+ + 3 feet after t seconds.
Part A: What is the average rate of change for h(t) between t=0 and t = 2?
A. 36 seconds per second
B. -36 feet per second
C.-18 Seconds per second
D. 18 feet per second
PART B.Is the average of the height of the ball increasing or decreasing.
Answer:
(D) 18ft per second
Step-by-step explanation:
the average of the height of the ball is increasing from t=0 to t=2.
A recent survey was conducted to compare the cost of solar energy to the cost of gas or electric energy. Results of the survey revealed that the distribution of the amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of $123 and a standard deviation of $9. If nothing is known about the shape of the distribution, what percentage of homes will have a monthly utility bill of less than $105
Answer:
At most 25% of homes will have a monthly utility bill of less than $105.
Step-by-step explanation:
Chebyshev Theorem
The Chebyshev Theorem can also be applied to non-normal distribution. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.
At least 89% of the measures are within 3 standard deviations of the mean.
An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].
In this question, we have that:
The mean is $123.
The standard deviation is $9.
What percentage of homes will have a monthly utility bill of less than $105
105 = 123 - 2*9
So 105 is two standard deviations below the mean.
We have that, by the Chebyshev Theorem, at least 75% of the measures will be within 2 standard deviations from the mean, so at most 25% of the measures will be more than two standard deviations of the mean(greater than 141 ou lesser than 105).
So at most 25% of homes will have a monthly utility bill of less than $105
Suppose a car travels 174 miles in 3 ours. How far will it travel in 6 hours?
Answer: 348 miles
Step-by-step explanation:
The car will travel 174 miles in 3 hours, if you multiply 174 x 2, the car will travel 348 miles in 6 hours.
2. The sum of two numbers is 52. The
difference of the two numbers is 6.
What are the numbers?
Answer:
29 and 23
Step-by-step explanation:
Step 1: rewrite the sentences as equations:
equation 1: x+y=52
equation 2: x-y=6
Step 2: add those two equations together to get:
2x=58
x=29
Step 3: substitute x in one of the first equations to get y:
29-y=6
y=23
Step 4: Check with the other equation:
x+y=52
29+23=52✔
How much water should he use?
enough
lololololololololololol
Answer:
6.25 cups
Step-by-step explanation:
Find the mean, median mode(s), range, standard deviation, and variance of the data: 21, 15, 16, 25, 13, 18 5, 3, 2, 6, 5, 2, 5 Eight car sales men sold cars at a dealership. Here is the distribution of cars sold last month: 6, 45, 52, 43, 48, 41, 50, and 48. Find the mean, median mode(s), range, standard deviation, and variance of the data: Which measure of central tendency best represents the data
Answer:
Kindly check explanation
Step-by-step explanation:
Given tbe data :
21, 15, 16, 25, 13, 18 5, 3, 2, 6, 5, 2, 5
Ordered data : 2, 2, 3, 5, 5, 5, 6, 13, 15, 16, 18, 21, 25
Mean, m = Σx /n
Σx = 136
n = sample size = 13
m = Σx / n = 136 / 13 = 10.46
Mode, = 5 (most frequently occurring with frequency of 5)
Median = 1/2(n+1)th term = 1/2(14) = 7th term = 6
Range = maximum - minimum = [25 - 2] = 23
Variance : (V) = Σ(x - m)²/n-1
V = [(2-10.46)^2 + (2-10.46)^2 + (3-10.46)^2 + (5-10.46)^2 + (5-10.46)^2 + (5-10.46)^2 + (6-10.46)^2 + (13-10.46)^2 + (15-10.46)^2 + (16-10.46)^2 + (18-10.46)^2 + (21-10.46)^2 + (25-10.46)^2] / (13-1)
= 745.2308 / 12
= 62.10
Standard deviation = sqrt(V) = sqrt(62.10) = 7.88
2.)
X : 6, 45, 52, 43, 48, 41, 50, 48
Reordered data, X: 6, 41, 43, 45, 48, 48, 50, 52
Mean, m = Σx /n
Σx = 333
n = sample size = 8
m = Σx / n = 333 / 8 = 41.625
Median = 1/2 (n+1)th term = 46.5
Range = 52 - 6 = 46
Mode = 48 (highest occurring frequency of 2)
Variance (V) = Σ(x - m)²/n-1
V = [(6-41.625)^2 + (41-41.625)^2 + (43-41.625)^2 + (45-41.625)^2 + (48-41.626)^2 + (48-41.625)^2 + (50-41.625)^2 + (52-41.625)^2] / 5
= 1541.862251 / 7
= 220.27
Standard deviation = sqrt(Variance)
Standard deviation = sqrt(220.26603)
Standard deviation = 14.84
The median
what is the difference between 6 and 2 1/5.
Answer:
3.8
Step-by-step explanation:
6 - 2 1/5 = 6 - 11/5
= 6-2.2
=3.8
The difference between the 6 and 2 1/5 will be 3.8
What is a fraction?A fraction represents a part of a number or any number of equal parts. There is a fraction, containing numerator(upper value) and denominator(lower value). When the numerator is less than the denominator, the fraction is called proper fraction, otherwise it is called improper fraction. A proper fraction is also called fraction which is less than 1. A mixed fraction contains a sum of whole number and a proper fraction.
So, WE need to find the difference between the 6 and [tex]2 \frac{1}{5}[/tex].
First we need to convert the mixed fraction into simple fraction.
[tex]2 \frac{1}{5}[/tex] = 11/5
Therefore, the difference between them will be;
6 - [tex]2 \frac{1}{5}[/tex] = 6 - 11/5
= 6 - 2.2
= 3.8
Hence, the difference between the 6 and [tex]2 \frac{1}{5}[/tex] will be 3.8
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A beachfront hotel is planning for its summer busy season. It wishes to estimate with 95% confidence the average number of nights each guest will stay in a single visit. Using a sample of guests who stayed last year, the average number of nights per guest is calculated at 5 nights. The standard deviation of the sample is 1.5 nights. The size of the sample used is 120 guests and the beachfront hotel desires a precision of plus or minus 0.5 nights.
Required:
a. What is the standard error of the mean in the lakefront resort example?
b. Within what range below can the resort expect with 95% confidence for the true population mean to fall?
Answer:
0.1369
(4.732, 5.268)
Step-by-step explanation:
Given that:
Mean, m = 5
Standard deviation, s = 1.5
Error margin, E = 0.5
Sample size, n = 120
Zcritical at 95% = 1.96
Standard Error of the mean (S. E) :
S. E = s /sqrt(n)
S. E = 1.5 / sqrt(120
S.E = 1.5 / 10.954451
S. E = 0.1369306
S. E = 0.1369
Confidence interval (C. I)
Mean ± (Zcritical * S.E)
5 ± (1.96 * 0.1369)
Lower boundary = 5 - 0.268324 = 4.731676
Upper boundary = 5 + 0.268324 = 5.268324
(4.732, 5.268)
Part A
Darren has already earned $80 mowing lawns. He earns $20 per lawn. He needs at least $135 for a new string trimmer. Write
an inequality to determine how many more lawns Darren will need to mow to have at least $135, where n represents the
number of lawns he needs to mow
O A) SO + 20n < 135
OB) 80 + 20 2135
O c) SOn + 20 2 135
OD SOn + 20 <135
Answer:
A
Step-by-step explanation:
Brandon is 5 years older than his brother Hermie. There combined age is 23. How old is Brandon?
Find Brandon's age using the following equation:
2 + (x + 5) = 23
A
9
14
15
Answer:
9
Step-by-step explanation:
9 +5 = 14
14 +9 = 23
Factor the common expression: 2x + 4 =
Answer:
2(x+2)
Step-by-step explanation:
Hope it helps you
Which soap deal has the lowest price per ounce?
$5.50 for 13.0 oz
$5.75 for 14.0 oz
$3.45 for 3.5 oz
$5.25 for 12.0 oz
what is the slope intercept form of 7x-5y=15?
Answer:
y=7/5x-3 is the slope intercept form
1. Graph y = x?. Try and do it without using the table
y = x^2 is a quadratic equation. A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared. This what a graph like dat would look like.
How much is a 2/9 pound plus 1/9 pound?
Answer:
1/3 pound.
Step-by-step explanation:
2/9 pound +1/9 pound = (2+1)/9 pound.
This can be simplified to 3/9 pound, or 1/3 pound.
Let me know if this helps!
Answer:
33.333 percent
Step-by-step explanation:
A spinner with 8 equal sections labeled 1 through 8 landing on a number less than 9
Answer:
1
Step-by-step explanation:
The probability of that happening is 1. It must always be < 9. The only way it is not true is if you choose not to spin.
Jillian’s school is selling tickets for a play. The tickets cost $10.50 for adults and $3.75 for students. The ticket sales for opening night totaled $2071.50. The equation 10.50 a plus 3.75 b equals 2071.50, where a is the number of adult tickets sold and b is the number of student tickets sold, can be used to find the number of adult and student tickets. If 82 students attended, how may adult tickets were sold?
adult tickets
Answer:
1035.75
Step-by-step explanation:
Answer:
your answer is 168 adult tickets
Step-by-step explanation:
Just got 100 on edge
can someone help me? its due in 10 minutes.
Answer:
The first option is correct.
Answer:
A= ×/87=43/100
I'm terrible in explaining this, but the answer is A. x = 37.41. Since you cross-multiply and divide. 87×43=3741 and 3741÷100=37.41
Write 36 + 60 as a product using the GCF as one of the factors.
Answer:
12(3+5)
Step-by-step explanation:
You factor out 12 because it is the GCF, then you divide 36 and 60 by 12.
36 + 60 as a product using the GCF as one of the factors is 12(3 + 5).
What are GCF and distributive property?The GCF of two or more than two numbers is the highest number that divides the given two numbers completely.
We also know that distributive property states a(b + c) = ab + ac.
Given, 36 + 60 now the common factors of 36 and 60 are 2, 3, 6, 12
∴ The GCF of 36 and 60 is 12.
So, 36 + 60 as a product can be written as
36 + 60.
12(3 + 5).
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HELP!!
Construct the graph of the direct proportion y=kx for k=0
Answer:
Shown in picture UnU
Which number line diagram represents the solution to the inequality?
A
B
C
D
Answer:
C
Step-by-step explanation:
PLZ HELP NEED THIS TO BE RIGHT AS YOU CAN GET IT
Answer of this qn is. option D hope it helps
9X - 5X + 18 = 2X +34
Answer:
x=8
Step-by-step explanation: