The population of bacteria after I days is P(I) = 3700 * e^(0.11 * I) and percentage rate of change per hour is 0.4285%
What is exponential growth?
Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function.
Equation:The population of bacteria in the petri dish is growing exponentially at a rate of 11% per day. This means that the daily growth rate r is 0.11, or 11/100.
The formula for exponential growth is:
P(t) = P0 * e^(rt)
Where:
P(t) is the population after t days
P0 is the initial population
r is the growth rate per day
e is the mathematical constant approximately equal to 2.71828
Using the given information, we have:
P0 = 3700
r = 0.11
So, the formula for the population of bacteria after I days is:
P(I) = 3700 * e^(0.11 * I)
To find the percentage rate of change per hour, we need to convert the daily growth rate to an hourly growth rate. There are 24 hours in a day, so the hourly growth rate h is:
h = (1 + r)^(1/24) - 1
Substituting the value of r, we get:
h = (1 + 0.11)^(1/24) - 1
Simplifying this expression, we get:
h = 0.004285
So, the hourly growth rate is 0.4285%, or 0.004285 expressed as a decimal.
Therefore, the population of bacteria after I days is:
P(I) = 3700 * e^(0.11 * I)
And the percentage rate of change per hour is:
0.4285% (rounded to the nearest hundredth of a percent)
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The percentage rate of change per hour is approximately 0.46%.
How to calculate percentage?
The formula for exponential growth is:
N(t) = N0 * e raise to the power (r*t)
where:
N(t) is the population at time t
N0 is the initial population
r is the growth rate
e is the mathematical constant approximately equal to 2.71828
t is the time elapsed
In this case, we have:
N0 = 3700
r = 11% per day, or 0.11/24 = 0.0045833 per hour (since there are 24 hours in a day)
t is the time elapsed in days
To convert the time elapsed in days to hours, we can multiply t by 24. Therefore, the function for the population of bacteria after t days is:
f(t) = 3700 * e raise to the power (0.004583324t)
To round the coefficients in the function to four decimal places, we can use the round() function in Python:
f(t) = round(3700 * e**(0.004583324t), 4)
To determine the percentage rate of change per hour, we can calculate the percentage increase in the population per hour using the formula:
Percentage increase = (e raise to the power (r*h) - 1) * 100
where:
r is the growth rate per day
h is the time elapsed in hours
In this case, we have:
r = 11% per day, or 0.11/24 = 0.0045833 per hour
h = 1 hour
Plugging these values into the formula, we get:
Percentage increase = (e raise to the power (0.0045833*1) - 1) * 100 = 0.4646%
Therefore, the percentage rate of change per hour is approximately 0.46%.
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Scores of healthy adults on a neurological test form a normal distribution with mean = 100 and sd = 15. what conclusion can be inferred about an individual score that corresponds to a z value of 1.0?
A conclusion which can be inferred about an individual score that corresponds to a z-value of 1.0 is that: c.) it is likely to come from the healthy distribution.
What is a z-value?A z-value is also referred to as a z-score or standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.
In Statistics, z-values can either be positive or negative and it can be calculated by using this formula:
\(Z=\frac{x\;-\;u}{\delta}\)
Where:
x is the sample mean or observed data.u is the mean.δ is the standard deviation.Since the individual score that corresponds to a z-value of 1.0, we can reasonably infer and logically conclude that an individual score is likely to come from the healthy distribution.
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Complete Question:
Scores of healthy adults on a neurological test form a normal distribution with mean = 100 and SD = 15. What conclusion can be inferred about an individual score that corresponds to a z value of 1.0?
a.) it falls in the general region of the population
distribution
b.) it falls in the common region of the distribution
c.) it is likely to come from the healthy distribution
d.) it is unlikely to come from the healthy distribution
3.3142 pounds converted into kilograms
Answer:
7.30656029
Step-by-step explanation:
Answer:
1.50329583
Step-by-step explanation:
FORMULA
for an approximate result, divide the mass value by 2.20462262
I have no idea how to do this can someone help? See the picture below for the question and answers.
Answer:
The answer is 1 foot
Which expression is equivalent to 120x2 - 48x?
F 12(10X - 4)
G 12x(10x + 4)
H 12X(-10X - 4)
J 12x(10x - 4)
Once a month, volunteers from the Green Sea Club clean up litter at the beach. Last month, the volunteers picked up 8 pounds of trash in 4 hours. This month, the same group of volunteers will spend 3 hours picking up trash.
If they pick up trash at the same rate, how many pounds of trash should the volunteers pick up this month?
Answer:
Step-by-step explanation:
8 pounds.... 4hours
x pounds.... 3 hours
x=3 ×8 :4
x=24 :4
x=6 pounds of trash
The number of pounds of trash should the volunteers pick up this month is 6.
Calculation of the number of pounds:Since Last month, the volunteers picked up 8 pounds of trash in 4 hours. This month, the same group of volunteers will spend 3 hours picking up trash.
So here we can do
x=3 ×8 :4
x=24 :4
x=6
Hence, The number of pounds of trash should the volunteers pick up this month is 6.
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16. Label the following statements as true or false:
o Every real number is a rational number.
b) Every whole number is an integer.
c) Some irrational numbers are integers.
d) Some integers are natural numbers.
Answer:
A.) True
B.) True
C.) False
D.)True
Step-by-step explanation:
find the cube root of 1728
Answer:
12
Step-by-step explanation:
simple math.
Answer:
it is 12
I don't know how to type the process
What is the constant of variation,k,for the table?
The constant of variation, k for the given table is 0.0725 which is the third option.
There is a table given with values of x and y.
We have to find the value of the constant of variation, k for the table.
We can write the relationship of x and y as :-
y = kx
k = y/x
Hence,
Putting the value of x = 4 and y = 0.29 , we get
k = 4/0.29 = 0.0725
We can also use any other of the values of x and y and we will get the same result.
12/0.87 = 36/2.61 = 60/4.35 = 0.0725.
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answer this question:
Answer:
P>7
Step-by-step explanation:
the teacher has 3 red pens 8 black pens and 4 blue pens all the same size in his box what is the probability of reaching in without looking and picking out a red pen
1/3
1/15
1/4
1/5
Answer: 1/5
Step-by-step explanation:
So we have a total of 15 pens and 3 of those pens we know are red. The probability of randomly selecting a red pen would be 3/15 or simplified 1/5
Answer:
1/5
Step-by-step explanation:
** numbers of chances you can pick/total chances of that you can pick anything
--> # of chances you can pick red pens, in this case, is 3, since there are only 3 red pens -->3/total
--> in this case total should be every numbers of pens added --> 3+8+4 = 15
--> 3/15 -->simplify: 1/5
In which step did Tyrianne make an error?
1
(x+4)2 – 3 = 29
Answer:
There isn't really an error noticeable, because steps are listed. However, x = 11.5
Step-by-step explanation:
Work the problem in reverse
(x+4)2 - 3 = 29
+3 +3
(x+4)2 = 31
2x + 8 = 31
-8 -8
2x = 23
x = 11.5
I need help fast!!!! Can’t figure these out at all!
Answer: GH = 12
Step-by-step explanation:
Don't panic! Remember that a perpendicular bisector divides a segment equally in half. (If you're writing a proof, cite the "Definition of a perpendicular bisector)
It breaks down to: GH = HI
HI = 12
By the transitive property of segment congruence: GH = 12
Good luck!
Answer:
im sorry but i really cant see the image
Step-by-step explanation:
7 + 8p - 2r3
terms:
coefficients:
Answer:
terms= 3 (7, 8p and 2r3)
coefficients: 2 (8 and 2)
Step-by-step explanation:
note that a term of any expression:
■is a single number (7)
■or product of a number and one or more variables (8p and 4xyz)
Please mark as the brainliest.
Answer:
o resultado menos 8
um belo dia abençoado
Given: Triangle WTR with WT = 25 and WR = 40. Identify all possible lengths for TR.
40
17
15
42
52
67
65
14
Answer:
The possible lengths of TR : TR = 17, 40, 42, 52,
Step-by-step explanation:
Given: Triangle WTR with WT = 25 and WR = 40. Identify all possible lengths for TR.
To find the possible lengths of the third side of a triangle:
c - a< b > a + c
a = WT = 25
c = WR= 40
b = TR = ??
40 - 25 < b < 40 + 25
15 < b < 65
The possible lengths of TR has to be greater than 15 and less than 65, Hence: TR = 17, 40, 42, 52,
Round 8,937.2546 to the nearest
hundred.
Answer:
8,900
Step-by-step explanation:
Given Number: 8,937.2546
Determine the two consecutive multiples of 100 that bracket 8,937.2546
8,937.2546 is between 8,900 and 9,000
8,950 is the midpoint between 8,900 and 9,000
As illustrated on the number line, 8,937.2546 is less than the midpoint (8,950)
Therefore, 8,937.2546 rounded to the nearest hundred = 8,900
HELP ASAP!!! Solve for x if the figure is a rectangle. (Attachment) ignore my attempt
The value of x that makes the given image to be a rectangle is: x = 2.5
How to find the length of the diagonal of a rectangle?The length of the diagonals of a rectangle are equal and congruent to each other. It is also pertinent to note that the diagonals of a rectangle bisect each other at the center. Thus:
From the given parameters, we see that half of the diagonals have been labelled and as such we have:
8x - 3 = 4x + 7
Rearrange to have like terms on same side and so we have:
8x - 4x = 7 + 3
4x = 10
x = 10/4
x = 2.5
Thus, the value of x from the calculation above of the rectangle is 2.5
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I NEED HELP PLS!!
WHAT IS THE AREA OF THE POLYGON IN SQUARE UNITS?
A- 85 square units
B- 55 square units
C- 48 square units
D- 35 square units
A line is perpendicular to y = -1/5x + 1 and intersects the point negative (-5,1) what is the equation of this perpendicular line?
Answer: y = 5x + 26
Step-by-step explanation:
To find the equation of a line that is perpendicular to the given line y = -1/5x + 1 and passes through the point (-5, 1), we need to determine the slope of the perpendicular line. The given line has a slope of -1/5. Perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the perpendicular line will be the negative reciprocal of -1/5, which is 5/1 or simply 5. Now, we have the slope (m = 5) and a point (-5, 1) that the perpendicular line passes through.
We can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
Substituting the values, we get:
y - 1 = 5(x - (-5))
Simplifying further:
y - 1 = 5(x + 5)
Expanding the brackets:
y - 1 = 5x + 25
Rearranging the equation to the slope-intercept form (y = mx + b):
y = 5x + 26
Therefore, the equation of the perpendicular line that passes through the point (-5, 1) is y = 5x + 26.
The Mathletes Club is printing t-shirts for its 15 members. The printing company charges a certain amount for each shirt plus a setup fee of $20.
If the t-shirt order costs a total of $162.50, how much does the company charge for each shirt?
Answer:
it is $10.83
Step-by-step explanation:
What is the domain of the step function f(x) = [2x]- 1?
O {x|x2-1}
O {x|x ≥ 1}
O x x is an integer}
O {x|x is a real number}
Domain: {x | x is a real number}
Option D, "{x | x is a real number}" accurately represents the domain of the function.
The domain of the step function f(x) = [2x] - 1, where [2x] represents the greatest integer less than or equal to 2x, can be determined by considering the restrictions on the input values.
In this case, the step function is defined for all real numbers. However, the greatest integer function imposes a restriction. Since the greatest integer function only outputs integers, the input values (2x) must be such that they produce integer outputs.
For any real number x, the greatest integer less than or equal to 2x will always be an integer. Therefore, the domain of the function f(x) = [2x] - 1 is:
Domain: {x | x is a real number}
Option D, "{x | x is a real number}" accurately represents the domain of the function.
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. You are working for Yarra Valley Water as a data scientist and decide to use a polynomial of degree 4, that is, f(x) = a + aз³ + a2x² + α1x+ao, to model the daily water usage of a Melbournian family at time r for all r such that -12 ≤ x ≤ 12. x = -12 and x = 12 I correspond to 3am so f(12) = f(-12). We also also assume that 9am and 9pm (x = -6 and x = 6, respectively) are local maxima of the usage. In this question we assume that the total water consumption during the day equals 24.
(a) Write a linear system of equations describing the following properties:
[4]
(i) f(12) = f(-12),
(ii) x=- -6,6 are stationary points of f,
(iii) the total water consumption is 24.
(b) Using Gaussian elimination, find all solutions of the linear system obtained in (a).
[4]
(c) Find all functions ƒ that satisfy all of the data given in the description of the question. [7]
(d) Is it possible that the total water consumed during the night hours from 1am to 5am [3] is smaller than 2 (that is the average over these four hours is less than half of the daily average)?
If your answer is "yes" then you should give an example of such function f from (c). otherwise justify why it is not possible.
(a) Linear system of equations: \($f(-12) = f(12)$, $f^{'}(-6) = f^{'}(6)$, $f^{''}(-6) = f^{''}(6)$, $f(-6) + f(6) = 24$\)
To find the solutions, we first differentiate f and obtain f'(x) = 4a3x3+ 2a2x + α1.
Using the stationary point condition, we have f'(-6) = f'(6) = 0, which gives the following equations: 864a + 6α1 + 2a2 = 0 and -864a + 6α1 - 2a2 = 0Differentiating f' gives f''(x) = 12a3x2 + 2a2.
Using the second derivative test, we have f''(-6) < 0 and f''(6) > 0, which gives 72a - 12a2 < 0 and 72a + 12a2 > 0 respectively.
Adding these two equations gives 144a > 0 or a > 0.Using the condition f(-12) = f(12) gives the equation -20736a + 1728a3 - 144α1 + 4a2 = 0.
Finally, the condition for the total water consumption can be expressed as f(-6) + f(6) = 24, which gives -144a + 12a3 + 6α1 + 2a2 = 24The final system of linear equations is:
\($$\begin{matrix}-20736a + 1728a^3 - 144α_1 + 4a^2 &=& 0\\ 864a + 6α_1 + 2a^2 &=& 0\\ -864a + 6α_1 - 2a^2 &=& 0\\ -144a + 12a^3 + 6α_1 + 2a^2 &=& 24 \end{matrix}$$\)
(b) Solving the system of equations using Gaussian elimination:
\($$\begin{pmatrix} 1 & 0 & 0 & 0 & -\frac{1}{2} \\ 0 & 1 & 0 & 0 & \frac{5}{36} \\ 0 & 0 & 1 & 0 & \frac{25}{288} \\ 0 & 0 & 0 & 1 & \frac{15}{32} \\ \end{pmatrix}$$This gives a = $\frac{1}{288}$, α1 = $\frac{5}{6}$, a2 = $\frac{25}{576}$,\)
which can be used to find f using f(x) = $\frac{1}{288}(x^4+3x^3-25x^2+180x+288)$
(c) The solution to the linear system of equations in (a) gives the function \(f(x) = $\frac{1}{288}(x^4+3x^3-25x^2+180x+288)$.\)
Therefore, this is the only function that satisfies all the given data.
(d) It is not possible that the total water consumed during the night hours from 1am to 5am is smaller than 2 (that is the average over these four hours is less than half of the daily average).
Proof:If we let g(x) denote the amount of water used during the night hours, then the total water usage is 24 = f(-12) + g(x) + f(12). Note that f(-12) = f(12), which gives g(x) = 12. Hence, the average over the four hours is g(x)/4 = 3, which is greater than half of the daily average. Therefore, it is not possible for the average to be less than 2.
The question provides all the necessary data to determine the function f(x) that models the daily water usage of a Melbournian family. We are given that the function is a polynomial of degree 4, and that it passes through (12, f(12)) and (-12, f(-12)). We are also given that x=- -6,6 are stationary points of the function and that the total water consumption during the day equals 24. Using these conditions, we are able to write a system of linear equations that determines the coefficients of the polynomial.
We then use Gaussian elimination to solve the system and obtain the function f(x). Finally, we show that it is not possible for the total water consumed during the night hours from 1am to 5am to be smaller than 2, and that the function f(x) satisfies all the given data.
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Ashley went to a store and bought 3 items. Each item cost $21. How much did she spend
Answer:
$63
Step-by-step explanation:
helppppp meeeeee pleaseeeee
1 are you on ixl and 2 the answer is 17+17+20+16+15
how many squares whose sides are parallel to the axes and whose vertices have coordinates that are integers lie entirely within the region bounded by the line y
Solve for x 3(x-4)-6=9x
Answer:
x = -3
Step-by-step explanation:
3(x-4)-6=9x
Distribute
3x -12 -6 = 9x
Combine like terms
3x -18 = 9x
Subtract 3x from each side
3x -18-3x =9x-3x
-18 = 6x
Divide by 6
-18/6 = 6x/6
-3 = x
Answer:
X=-3
Step-by-step explanation:
1. There are 24 bottles of drinks in a box. How many bottles are there in 8 of such boxes?
A. 190
B. 182
C. 172
D. 192
Q19,20,21
In Exercises 19-24, convert to an equation in polar coordinates of the form r = f(0). 19. x² + y² = 5 20. x = 5 21. y = x² 22. xy = 1
19. An equation in polar coordinates of the form r = ±√5
20. An equation in polar coordinates of the form r = 5secθ
21. An equation in polar coordinates of the form r = secθtanθ
Given that,
We have to convert to an equation in polar coordinates of the form r = f(θ).
We use Jacobian properties to solve the equation.
19. x² + y² = 5
We know that,
x = rcosθ
y = rsinθ
x² + y² = r²cos²θ + r²sin²θ
x² + y² = r²(cos²θ + sin²θ)
x² + y² = r²(1)
x² + y² = r²
So, x² + y² = 5
r² = 5
Taking square root on both sides,
r = ±√5
Therefore, an equation in polar coordinates of the form r = ±√5
20. x = 5
We know that,
x = rcosθ
So,
x = 5
rcosθ = 5
r = 5secθ
Therefore, an equation in polar coordinates of the form r = 5secθ
21. y = x²
We know that,
x = rcosθ
y = rsinθ
rsinθ = r²cos²θ
Dividing r on both sides
sinθ = rcos²θ
r = \(\frac{sin\theta}{cos^2\theta}\)
r = secθtanθ
Therefore, an equation in polar coordinates of the form r = secθtanθ
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Can someone answer this question please please help me I really need it if it’s correct I will mark you brainliest .
Answer:
169.65 for volume.
Step-by-step explanation:
Volume = πr2h
= π×32×6
= 54π
= 169.64600329385 (unit^3)
I Hope this helps!!!
Answer:
339.12 squared (for surface area)
Step-by-step explanation:
radius=6
area of the circles is, 6*6= 36 * 3.14= 113.04
there are 2 circles so we multiply that by 2 to get 226.08
now to find the perimeter of a circle it is the radius * pi, so that would be 6*3.14= 18.84 now we have a height of 6 so we multiply that by 6 and get 113.04 now add up all our numbers and get 339.12
Elijah earns $200 for 8 hours of work.What is the rate (in dollars per item)
The mean mass of five men is 76 kg. The masses of four of the men are 72 kg, 74 kg, 75 kg and 81 kg. What is the mass of the fifth man
Answer:
78kg
Step-by-step explanation:
76×5= 380kg
380-72-74-75-81= 78kg