Using an exponential function, the rate of growth is 20.482%, the number of bacteria after two hours is 12048.21 and the doubling time of the bacteria is 3.7 hours
Exponential FunctionExponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function.
A) The rate of growth can be calculated as
Data;
P = 8300A = 10000r = ?x = 1 hourWriting this in an exponential function;
A = P(1 + r)ˣ
10000 = 8300(1 + r)¹
r = 0.2048
r = 20.482%
B)
Substituting the values into the function above
x = 2
A = 8300(1 + 0.2048)²
A = 12048.21
C)
For the bacterial to double, the time will be
2 = (1 + 0.2048)ˣ
x = 3.7 hours
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2 = x
3 26
How do i solve this equation
Answer:
do the butterfly method if you don't know how to do that comment and I'll show you a screenshot
using a slope formula find the slope pf the line theough the points (0,0) and (2,6)
Step-by-step explanation:
slope formula: (y2-y1)/(x2-x1)at the point (0,0), it is known that x=0 and y=0.at the point (2,6), it is known that x=2 and y=6.slope: (6-0)/(2-0) =6/2 =3Find the smallest length that can be divided exactly into equal sections of length 5m,8m and 12m
As the LCM of 5, 8, and 12, which is 60 so it is the smallest length that can be divided exactly into equal sections of length 5 m, 8 m, and 12 m.
What is an LCM example?The acronym LCM stands for the least common multiple or factor of any two or more specified integers. The least common multiple for the numbers 16 and 20 is 80, hence the LCM of those two numbers will be, for instance, 2 x 2 x 2 x 2 x 5 = 80.
What is the LCM of 4 and 8?8 is the LCM of 4 and 8. The LCM is the number that can be divided by the provided numbers equally. You can discover the least common multiple of 4 and 8 by looking at the common multiples. 4 is a multiple of 8, 12, 16, 20, 24, etc.
finding prime factors of the given numbers by repeated division method in order to find the LCM;
2 | 5,8,12
5 | 5,4,6
2 | 1,4,6
2 | 1,2,3
3 | 1,1,3
0 | 1,1,1
so we get 2x5x3x2=60
As the LCM of 5, 8, and 12, which is 60 so it is the smallest length that can be divided exactly into equal sections of length 5 m, 8 m, and 12 m.
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The shortest length which can be split into equal segments of length 5 meters, 8 meters, or 12 meters is 120.
What does "section" signify in terms of forms and purposes?Your form may be divided into sections with the help of sections, as the name suggests. This enables your users to input responses that might be categorized. The fact that sections divide your form into distinct screens is another significant benefit. For instance, a first screen shows section 1. When concealed lines in external views cannot adequately represent a part's inner design, sections are employed. The internal components can be viewed more clearly by imagining cutting through the thing and removing a section of it.
Briefing:Finding the LCM by repeatedly dividing the supplied integers to get their prime components:
2 | 5,8,12
2 | 5,4,6
2 | 5,2,3
3 | 5,1,3
5 | 5,1,1
1 | 1,1,1
So we get 2*2*2*3*5*1 = 120
The lowest length that could be divided into precisely equal segments in lengths 5 m, 8 m, and 12 m is 120, which equals the LCM of 5, 8, & 12.
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.............................
The answer is 1,200
First you need to add . + . to get 1.5M and then you need to subtract the rest ( 1.5M - one million four hundred ninety-eight thousand eight hundred )
So then you get 1,200
Hope this helped!
"How do we transform System A into System B?
Equation [A1] → Equation [B1]
Equation [A2]→ Equation [B2]
Equation [A1]+Equation [A 2] → Equation [B 2]
Equation [A2]+ Equation [A 1] → Equation [B 1]"
The transformation of System A into System B is:
Equation [A2]+ Equation [A 1] → Equation [B 1]"
The correct answer choice is option D
How can we transform system A into System B ?To transform System A into System B as 1 × Equation [A2] + Equation [A1]→ Equation [B1] and 1 × Equation [A2] → Equation [B2].
System A:
-3x + 4y = -23 [A1]
7x - 2y = -5 [A2]
Multiply equation [A2] by 2
14x - 4y = -10
Add the equation to equation [A1]
14x - 4y = -10
-3x + 4y = -23 [A1]
11x = -33 [B1]
Multiply equation [A2] by 1
7x - 2y = -5 ....[B2]
So therefore, it can be deduced from the step by step explanation above that System A is ultimately transformed into System B as 1 × Equation [A2] + Equation [A1]→ Equation [B1] and 1 × Equation [A2] → Equation [B2].
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4 7/8 + (2 1/6). It’s fractions by the way.
Answer:
7 and 1/24
Step-by-step explanation:
4 7/8 + 2 1/6
First when adding fractions, we want to have a common denominator. To do that, we must multiply the fractions until we get a desired denominator. We can find LCM.
The LCM of 6 and 8 is 24, so we must multiply accordingly.
We can put this into improper fraction form:
39/8 + 13/6
Then multiply accordingly. Multiply by 3 on both sides for the first fraction, and multiply by 4 on both sides for the second to get a denominator of 24.
117/24 + 52/24
Now, we can add the fractions.
169/24
Simplify
7 and 1/24
An airplane cruises 1 kilometer in
1
12
of a minute. What is its cruising speed?
Simplify your answer and write it as a proper fraction, mixed number, or whole number.
kilometers per minute
Answer: It is 12 kilometers per minute
Step-by-step explanation:
in the problem that you'll need to simplify your answer and write it as a proper fraction, mixed number, or whole number so I can confirm this is 100% correct.
Step-by-step explanation:
What is the equation of the line that passes through the point (2,-6) and has a slope of -3?
A marching band needs to raise $13,500 for a trip to the Rose Bowl. The director told the band members that one-third of the amount that has been raised so far is equal to half of the amount that is still needed. How much more money needs to be raised for the trip?
Answer: $5400
Step-by-step explanation:
x = amount raised so far
13500 - x = amt. still needed
x/3 = (13500 - x)/2
2x = 3(13500 - x)
2x = 40500 - 3x
5x = 40500
x = 40500/5 = 8100 (amt. raised so far)
13500 - 8100 = 5400 (amt. still needed)
Find the probability of rolling a sum greater than 7 given that you rolled an odd number first.
Answer:
I think the answer is 1/2. Given the first die was odd, you rolled either a 1,3, or 5. Now on the second roll only a 6,4, or a 2 will give you a sum of 7. Given that is half of the sample space of the second die, it is 1/2?
Step-by-step explanation:
Determine the equation of the parabola that opens up, has vertex (7, 7), and a focal
diameter of 16.
Answer:
Step-by-step explanation:
Question: Determine the equation of the parabola that opens up, has vertex (7,7), and a focal diameter of 16 . This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts.
Answer: ((x2)−14x+87)/16
Step-by-step explanation:
focal diameter = 16,
4a=16;
a=4.
(h,v)=(7,7-a)
==> (h,v)=(7,3)
the equation of the parabola = ((x-7)^2)=16(y-3)
=> y = ((x^2)-14x+87)/16.
Find the Maclaurin series of the following functions. Step by Step Please
The Maclaurin series of xcos(-x) up to n = 3 is
[tex]m(x)= xcos(-x)= x-\frac{1}{2}x^3+\frac{1}{24}x^5-\frac{1}{720}x^7+\frac{1}{40320}x^9+\ldots \:[/tex]
The function is given in the question as
m(x) = xcos(-x)
Taylor (Maclaurin) series of xcos(x) up to n=5
A Maclaurin series is given by f(x),
[tex]f\left(x\right)=f\left(a\right)+\frac{f^'\left(a\right)}{1!}\left(x-a\right)+\frac{f^{''}\left(a\right)}{2!}\left(x-a\right)^2+\frac{f^{'''}\left(a\right)}{3!}\left(x-a\right)^3+\ldots[/tex]
[tex]f\left(x\right)=f\left(0\right)+\frac{f^'\left(0\right)}{1!}\left(x\right)+\frac{f^{''}\left(0\right)}{2!}\left(x\right)^2+\frac{f^{'''}\left(0\right)}{3!}\left(x\right)^3+\ldots[/tex]
We need to do to get the desired polynomial is to calculate the derivatives, evaluate them at the given point, and plug the results into the given formula.
f⁽⁰⁾(x) = f(x) = xcos(x)
Evaluate the function at the point: f(0)=0
1st derivative: f(1)(x)=(f(0)(x))′=(xcos(x))′=−xsin(x)+cos(x)
1st derivative at the given point: (f(0))′=1
2nd derivative: f(2)(x)=(f(1)(x))′=(−xsin(x)+cos(x))′=−xcos(x)−2sin(x)
Evaluate the 2nd derivative at the given point: (f(0))′′=0
3rd derivative: f(3)(x)=(f(2)(x))′=(−xcos(x)−2sin(x))′=xsin(x)−3cos(x)
Evaluate the 3rd derivative at the given point: (f(0))′′′=−3
Now, use the calculated values to get a polynomial:
[tex]m(x)=0+\frac{1}{1!}x+\frac{0}{2!}x^2+\frac{-3}{3!}x^3+.....[/tex]
[tex]m(x)=x-\frac{1}{2}x^3+\frac{1}{24}x^5-\frac{1}{720}x^7+\frac{1}{40320}x^9+\ldots \:[/tex]
Thus, the Maclaurin series of xcos(-x) up to n = 3 is
[tex]m(x)= xcos(-x)= x-\frac{1}{2}x^3+\frac{1}{24}x^5-\frac{1}{720}x^7+\frac{1}{40320}x^9+\ldots \:[/tex]
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If f(1)=7, f(5)=-3, f(11)=-9, g(7)=11, g(-3)=6 and g(-9)=1, then find g(f(11))
Answer:
1
Step-by-step explanation:
g(f(11))
It says in the problem that f(11) = -9
So:
g(-9)
It says again in the problem that g(-9) = 1
So the answer is 1
The function f(x) = 2x3 + 3x2 + 2x – 1 is divided by (x – 1) .
Step-by-step explanation:
here is your answer hope it helps you plaz mark me as brainlist
You decide to buy a refurbished computer for $550.00 plus 6% sales tax. BB Electronics allow you to take out a no-interest loan for 12 months, and after that the interest rate is a 13.25% APR. You must make payments of $25/month, and if you miss one payment you are assessed a late fee of $29.00 plus 13.25% APR interest beginning from the date of purchase. How much is due the first month?
order the fraction to least to greatest 2/3 3/7 4/8
Find the probability of exactly three
successes in six trials of a binomial
experiment in which the probability of
success is 50%.
The probability exactly three successes in six trials is 31.30%
What is Binomial Distribution?A binomial distribution can be defined as the probability of a success or failure outcome in an experiment or survey that is repeated multiple times.
The probability distribution of a binomial distribution is given by :
P(x = k) = n! /k!(n - k)! P^x(1 - P)^(n - k)
In our case :
n = 6
P = 50/100 = 0.5
Now we want the probability that:
x = 3
This is because the question states that we want the probability that the number of successes are exactly 3.
We do the substitution in the probability distribution function as follows :
P(x = 3) = 6!/3!(6 - 3)! × 0.5³ × (1 - 0.5)³
= 0.3125
= 31.25%
= 31.30%
Hence, the probability of exactly three successes in six trials of a binomial experiment in which the probability of success is 50 is 31.30%
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HELP PLEASE I NEED IT
Answer:=
Step-by-step explanation:
In a clothing store, 50% of the customers buy a shirt, 30% of the customers
buy a pair of pants, and 15% of the customers buy both a shirt and a pair of
pants.
If a customer is chosen at random, what is the probability that he or she buys
a shirt or a pair of pants?
A. 0.20
B. 0.18
C. 0.65
D. 0.80
Answer:
.20
Step-by-step explanation:
because customers are always right
5. Find the value of x. Round the length to the nearest tenth. 18 yd 309 2?.
By Trigonometric formula - Tan(∅) = [tex]\frac{opposite}{adjacent}[/tex] , we got that answer - x= 10.4 yard (On rounding to tenth place)
what are trigonometric equations?An equation containing one or more trigonometric ratios of unknown angles is known as a trigonometric equation. In terms of angles, it is written as ratios of the sine, cosine, tangent, secant, and cotangent angles. A trigonometric equation is, for instance, cos2 x + 5 sin x = 0.
For angle 30 degrees adjacent side is 18 yard and opposite side is x.
=> Tan(∅) = [tex]\frac{opposite}{adjacent}[/tex]
=> Tan(30) = [tex]\frac{x}{18}[/tex]
=> x=Tan 30 (18)
=> x= 10.39
=> x= 10.4 yard (On rounding to tenth place)
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m/3 - 6 = 4
solve for m
Answer:
m=10
Step-by-step explanation:
m/3-6=4
30/3=10
10-6=4
Apply the distributive property to simplify the expression
8(12x – 20)
I believe the answer must be 96x-160
Because we have to multiply 8x12 which is 96. and there is x next to it. so keep the x as it is.
and next to it is minus ( - ) sign so keep it as it is.
now we have to multiply 8x20 which is 160.
so if we write it together it will be:
so if we write it together it will be:96x - 160.
Thank you
rotate (2,-3) 270 degree counterclockwise around (1,-2) then translate (x-2,y+5)
The image point of the transformation is (-1, 6)
How to determine the image of the transformation?The coordinate of the point is given as
(2, -3)
The transformations are given as
270 degree counterclockwise around (1,-2) Translation by (x-2,y+5)The rotation is around the point (1,-2)
So, the point becomes
Point = (2 - 1, -3 + 2)
Evaluate
Point = (1, -1)
The 270 degrees rotation has the algebraic rule of its rotation to be changed from (x, y) to (-y, x) i.e. (x, y) => (-y, x)
So, we have
(x, y) = (1, 1) after the rotation
The translation is given as
(x - 2, y + 5)
So, we have
(x, y) = (1 - 2, 1 + 5)
Evaluate
(x, y) = (-1, 6)
Hence, the coordinates of the image is (-1, 6)
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Please help!!!!
Write an equation in point-slope form that passes through the points (2, 4) and (-3, -6).
Answer:
uh let's see
Step-by-step explanation:
2,4 and -3,-6
y2-y1/
x2-x1
-6-4
-3-2
-10/-5 = 2
slope is 2
u do the rest I'm tired
10 less than the product of 8 and b
Step-by-step explanation:
8b-10
hope it helps. please mark brainliest
Answer: The correct answer is (8*b) - 10
Step-by-step explanation:
When translating word problems into equations, the term "product" denotes multiplication, and "less than" denotes subtraction.
This wording "10 less than the product of 8 and b" tells us to multiply 8 and b, then subtract 10:
(8*b) - 10
Find the area of a shaded portion 10 km 20 km 20km
The area of the shaded region will be 150 square kilometers.
What is Parallelogram? What is triangle?In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -
∠x + ∠y + ∠z = 180°
There are different types of triangles such as -
equilateral triangle , scalene triangle , isosceles triangle etc.
Given is a 2- D figure as shown in the image.
The area of the shaded region will be -
A[shaded] = A [square] - {A [Δ1] + A [Δ2] + A [Δ3]}
A[shaded] = (20 X 20) - [{1/2 x 10 x 10} + {1/2 x 10 x 20} + {1/2 x 10 x 20}]
A[shaded] = 400 - [50 + 100 + 100]
A[shaded] = 400 - 250
A[shaded] = 150 square kilometers
Therefore, the area of the shaded region will be 150 square kilometers.
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The vertex angle of an isosceles triangle measures
15 degrees more than one of its base angles. How
many degrees are there in a base angle of the
triangle?
The required three angle is 55 , 55 and 70
What is an angle ?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.
Let each of the base angle of isosceles triangle = x
Vertex angle = (x+15)
Sum of the angle = 180
x + x + (x + 15) = 180
3x + 15 = 180
3x = 180 - 15
x = 165 / 3
x = 55
Each base angel = 55
Vertex angle = x + 15
= 55 + 15
= 70
Required three angles = 55 , 55 and 70
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Solve for x. Leave your answer in simplest radical form.
Answer:
√122
Step-by-step explanation:
first we have to find the missing side with x on the 5 and 9 triangle by using the theorem
a^2+b^2=c^2
9^2+5^2=c^2
81+25=c^2
106=c^2
√106=c
and now we can use this as a side to find x
4^2+√106^2=x^2
16+106=x^2
122=x^2
√122=x
Hopes this helps please mark brainliest
Suppose megan wants to run more sprints and laps. How many of each could she run so that her total sprints and total laps are in the ratio that the coach wanted?
Answer:
2
Step-by-step explanation:
Using division, what is the quotient (2x3 - 2x - 12) ÷ (x - 2)?
2x² + 4x-6 +
2x² - 4x + 6
1
X 2)
Answer: 2x²+4x+6
Step-by-step explanation:
[tex]\displaystyle\\\frac{2x^3-2x-12}{x-2} =\\\\\frac{2(x^3-x-6)}{x-2}=\\\\ \frac{2(x^2-8+8-x-6)}{x-2} =\\\\\frac{2(x^3-2^3-x+2)}{x-2} =\\\\\frac{2((x^3-2^3)-(x-2))}{x-2}=\\\\\frac{2((x-2)(x^2+2x+2^2)-(x-2))}{x-2} =\\\\\frac{2(x-2)(x^2+2x+4-1)}{x-2}=\\\\2(x^2+2x+3)=\\\\2x^2+4x+6[/tex]