6. The number of bacteria N in a culture is given by the model N(t) = 250e 0.0156 where t is the time in hours.
Find how many hours it takes for the original population to double. Round your answer to the nearest hundredth
of an hour.
i just need to know how to work this out!! please help
Answers
Answer:
t ≈ 44.43 hours
Step-by-step explanation:
Expression that models the population of a bacteria after time 't' is,
N(t) = [tex]250(e^{0.0156t})[/tex]
Here initial population = 250
And N(t) = Population after 't' hours
t = duration
We have to find the duration in which bacterial population gets doubled.
N(t) = 2×250 = 500
From the given expression,
500 = [tex]250(e^{0.0156t})[/tex]
[tex]e^{0.0156t}=2[/tex]
[tex]\text{ln}(e^{0.0156t})=\text{ln}(2)[/tex]
0.0156t[ln(e)] = 0.693147
0.0156t = 0.693147
t = [tex]\frac{0.693147}{0.0156}[/tex]
t = 44.432
t ≈ 44.43 hours
Related Questions
Write the equation of a circle that has a diameter of 12 units if its center is at (4,7).
PLZ HELP ASAP! I will give you BRAINLIEST
Answers
9514 1404 393
Answer:
(x -4)^2 +(y -7)^2 = 36
Step-by-step explanation:
The equation of a circle with radius r and center at (h, k) is ...
(x -h)^2 +(y -k)^2 = r^2
When the diameter is 12, the radius is 6 (half the diameter). Then for your center point, the equation is ...
(x -4)^2 +(y -7)^2 = 36
Ted has the following triangle dimensions.
side length of 8
side length of 14
side length of 23
How many triangles can he construct?
He can construct only one triangle.
He can construct two triangles.
He can construct three triangles.
He cannot construct a triangle.
Answers
Answer:
He cannot construct a triangle
Step-by-step explanation:
In order to construct a triangle the two shorter sides added together have to be greater than the longest side if that makes sense
So basically 8+14 has to be greater than 23 in order for it to be side lengths of a triangle
8+14=22
22 is not greater than 23 therefore he cannot create a triangle
AnsweFREE 50 POINTS FOR MEEE
Step-by-step explanation:
its D :)
What is the area of rectangle CDEF?ILL GIVE BRAINLIEST
Answers
Answer:
180 is the answer
Step-by-step explanation:
To find out areas of rectangles, you have to count the left side of the rectangle which is (12) and then count the bottom of the rectangle which is (15)
Then multiply 12 times 15 to find out the area
15 x 12= 180
what do you mean CDEF
and can I get brainliest?
what is 18 out of 65%
Answers
Answer:
11.7
Step-by-step explanation:
Wayne is hanging a string of lights 45 feet long around the three sides of his patio, which is adjacent to his house. The length of his patio, the side along the house, is five feet longer than twice its width. Find the length and width of the patio.
Answers
Answer:
The length and width of the patio are 18¹/₃ feet and 6²/₃ feet respectively.
Step-by-step explanation:
Let L and W be the length and width of the patio respectively. Since the patio is a rectangle, its perimeter, P = 2(L + W). This perimeter equals the length of string of lights which is 45 ft.
Now, the length of his patio, the side along the house, is five feet longer than twice its width implies that L = 2W + 5.
Substituting L into P, we have
P = 2(L + W)
= 2(2W + 5 + W)
= 2(3W + 5)
= 6W + 5
Since P = 45 feet,
6W + 5 = 45
6W = 45 - 5
6W = 40
W = 40/6
W = 20/3 feet
W = 6²/₃ feet
Since L = 2W + 5, substituting W = 20/3 into L, we have
L = 2W + 5
= 2(20/3) + 5
= 40/3 + 5
taking the L.C.M, we have
= (40 + 15)/3
= 55/3 feet
= 18¹/₃ feet
So, the length and width of the patio are 18¹/₃ feet and 6²/₃ feet respectively.
50 points
Help if you know.
Thanks.
Answers
Answer:
RhombusStep-by-step explanation:
Refer to attached
You can easily calculate that each of the sides have the length:
AB= BC = CD = AD = [tex]\sqrt{1^2+4^2} = \sqrt{17}[/tex]Parallel sides have equal slopes:
m = - 4 for AB and CDm = - 1/4 for AD and BCDiagonals are perpendicular as their slopes are negative reciprocal:
m = 1 for ACm = -1 for BDSo we see the quadrilateral ABCD has two pairs of parallel sides, all sides are equal and the diagonals are perpendicular.
This is the definition of the rhombus.
Please answer 1-5.ASAP.
Answers
Answer:
Step-by-step explanation:
1) Function: y = 5x - 2
2) Slope: 1/2 Y-Int: 4
3) Function: y = 6
4) Slope: -4 Y-Int: 1
5) Function: y = -2x/3
Answer:
Step-by-step explanation:
(1). y = 5x - 2
(2). m = [tex]\frac{1}{2}[/tex] , b = 4
(3). y = 6
(4). m = - 4 , b = 1
(5). y = - [tex]\frac{2}{3}[/tex] x
12. The base angles of an isosceles triangle are represented by (5x + 10) and 50°. Find x.
Answers
Answer:
x = 8
Step-by-step explanation:
Base angles of isoceles triangle are equal
5x + 10 = 50
5x = 40
x = 8
4 points
4.) How could we determine who has the greater total change in the
amount of juice in their carton?
Felicia pours juice from a carton into a glass. Every time she fills the glass, the
amount of juice in the carton changes by -0.44 L. She fills her glass 2 times in
all. Bernadette has a different carton of juice that is the same size. Every time she
fills her glass, the amount of juice in her carton changes by -0.42 L. She fills her
glass 2 times in all. Who has
the greater total change in the amount of juice in
their carton?
A. 2 3/4 multiplied by (-0.44) and 2 2/3 multiplied by (-0.42)
B. 2 3/4 divided by -0.44 and 2 2/3 divided by -0.42
Answers
Answer:
A is the answer you sent on the question on carton
the distance an asteroid travel is directly proportional to the amount of time it travels if an asteroid travels 112,000 miles in 2 hours how far will it travel in 24 hours
Answers
Answer:
1,344,000
Step-by-step explanation:
since 2 hours have gone by divide 112,000 by 2 you will get 56,000 meaning the asteroid is going 56,000 Miles Per Hour now Multiply 56,000(MPH) by 24 (Hours)
You're Answer: 1,344,000
Which equation for a line with a slope of -3 and a y intercept of 4? Multiple Choice Answer: y=-4+3, y= - 3/4x+4, y=-3x+4, y= - 4\3x-3. HElP QUICKLY
Answers
y=-3x+4
dedont be suspicoes
A MOP TO CLEAN CULO
c
c
c
c
c
Franky and Francesca applied to the same college. They looked up the average SAT score of students admitted to that college. Franky’s SAT score was 140 points above the average score. Francesca’s SAT score was 40 points below the average score. Which expression represents the difference in their scores?
❘-40 - 140❘
-❘140❘ - ❘40❘
-❘140❘ + ❘-40❘
❘140 - 40❘
Answers
Answer:
❘-40 - 140❘
Step-by-step explanation:
Given that,
Franky’s SAT score was 140 points above the average score.
Francesca’s SAT score was 40 points below the average score.
We need to find the expression that represents the difference in their scores. It can be calculated as follows :
d = ❘-40 - 140❘
= -180
Hence, the correct option is (A) "❘-40 - 140❘".
Solve for each variable x & y.
Answers
Answer:
x=4 and y=7. did this help
need help again... asap
Answers
Answer:
9/41
Step-by-step explanation:
cos=adjacent/hypotenuse
adjacent=9
hypotenuse=41
−2x+y=0, −7x+3y=2 adding
Answers
Answer:
X= -2, y=-4
Step-by-step explanation:
hard to explain it
Can someone help me quickly?
Jamila has a recipe for biscuits.
To make 12 biscuits
250 g oats
125 g butter
100 g sugar
2 tablespoons syrup
Jamila makes 36 biscuits.
Wok out how much butter she needs.
Answers
Answer:
Jamila need's 375g of butter
Step-by-step explanation:
12 biscuits , but she wants to make 36,
12x3 = 36 so times to rest of the ingredients by 3
250x3=750g Oats
125x3=375g Butter
100x3=300g Sugar
2x3= 6 tablespoons of syrup
Jamila needs 375 g of butter to make 36 biscuits.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
If the recipe makes 12 biscuits and Jamila wants to make 36 biscuits, she needs to triple the recipe.
To triple the amount of butter, we can multiply 125 g by 3:
125 g x 3 = 375 g
Therefore,
Jamila needs 375 g of butter to make 36 biscuits.
Learn more about expressions here:
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Help ASAP. This is vital to my math grade. I will award 100 points and Brainly to whoever can give me the correct slope. I need this question correct in order to pass my math class. This is for a dual enrollment class. This is timed
Answers
Answer:
-2/2
Step-by-step explanation:
I think the slope is -2/2 I hope I got this right, sorry if I got it wrong. Anyway, you solve this by plotting your two points, then doing rise over run (down 2 and over to the right).
Your welcome :D.
Answer:
Slope: -1
Step-by-step explanation:
( 3, -6) and (5, -8)
m= (y2-y1)/(x2-x1)
m = ( -8 + 6)/ (5-3)
m = (-2)/2
m = -1
Find the volume of a pyramid with a square base, where the perimeter of the base is
17 cm and the height of the pyramid is 15 cm. Round your answer to the nearest
tenth of a cubic centimeter.
Answers
Answer:
90.3125 cm³
Step-by-step explanation:
Since the perimeter of the bottom square is 17, you can divide by four to find out what the lenght of each side is.
17/4=4.25 cm
We know the height of pyramid is 15 cm
The formula for the volume of a square pyramid is
V=a²(h/3)
V=a2(h/3)=4.252·15/3=90.3125 cm³
please help me with this and explain. It’s due in a bit :/
Answers
Answer:
choice D
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
they have similar angles and similar sides, and the description choice D gives is also correct
find the mean of the given data. 147 141 120 124 128
Answers
660/4 =132
hope that helps xo
I divided by 5 because there are 5 items in the set of data.
Hope this helped!!
complete the square to solve 3x^2+12x=9
A. x=3+√6
B. x=2+√7
C. x=-2+√7
D. x=-2+√13
Answers
(
b
2
)
2
(
b
2
)
2
in order to create a new term. Solve for
x
x
by using this term to complete the square.
Exact Form:
x
=
±
√
7
−
2
x
=
±
7
-
2
Decimal Form:
x
=
0.64575131
…
,
−
4.64575131
…
Step-by-step explanation:
3 {x}^{2} + 12x - 9 = 0
[tex] \frac{ - (12) \binom{ + }{ - } \sqrt{ {12}^{2} - 4(3)( - 9)} }{2(3)} [/tex]
The graph of f(x) = 1/x has been transformed to create the graph of g(x) = a/x
What is the value of a?
2
-3
3
-2
Answers
Answer:
2/x
Step-by-step explanation:
The easy way:
take point (2,1) on graph g
subst the values into g(x)=a/x
1=a/2
a=2
thus -> 2/x
The value of a is 2 for the transformed function g(x) = a/x.
What is a graph?
A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
The value of a is calculated as,
Take point (2,1) on graph g and substitute the values into g(x)=a/x
1=a/2
a=2
Therefore, the value of a is 2 for the transformed function g(x) = a/x.
To know more about graphs follow
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Example :
3X+4 X=2
3(2)+4
6+4
10
1. 2X-5 X= 7
2. X2 - 15 X= 5
3. X/9 +6 X = 81
4. 8X -4. X = 13
Answers
Answer:
1) 9
2) -5
3) 15
4) 100
those are the answers
9514 1404 393
Answer:
91015100Step-by-step explanation:
As in the example, put the value where the variable is and do the arithmetic.
1. 2·7 -5 = 9
2. 5^2 -15 = 10
3. 81/9 +6 = 15
4. 8·13 -4 = 100
Your calculator can do the math.
What is 3(4r-2)+8x+ 18 equal
Answers
Answer:
12r+8x+12
Step-by-step explanation:
3(4r-2)+8x+18
12r-6+8x+18
12r+8x-6+18
12r+8x+12
Kim was sitting in row 5, seat 8 at a soccer game when she discovered her ticket was for row 2, seat 3. Write a rule to describe the translation needed to put her in the proper seat.
Answers
Answer:
Step-by-step explanation:
We can assume we are seeing these seats as points on a graph with her current position being (8, 5) and her destination being (3, 2). Using these values Kim would need to follow the following rules...
Move 3 positions down to point/seat (8, 2)
Move 5 positions to the left to point/seat (3,2)
Following these instructions, she would correctly transition to the correct seat.
Your friend Mel says he has an easier way to solve this problem. Here are the first steps in his method.
First, isolate all of the x-terms on the left side. This leaves a constant on the right that isn't equal to 0.
Factor the GCF out of the terms on the left side.
If there's a whole-number factor on the left side, divide both sides by that number. Notice that after you do this, one factor on the left is just x.
Apply Mel's steps to your equation in question 1. (5 points)
The original equation is 2x^2 +6x+4=24 ft.^2
Answers
Simplifying
2x2 + 6x + 4 = 24
Reorder the terms:
4 + 6x + 2x2 = 24
Solving
4 + 6x + 2x2 = 24
Solving for variable 'x'.
Reorder the terms:
4 + -24 + 6x + 2x2 = 24 + -24
Combine like terms: 4 + -24 = -20
-20 + 6x + 2x2 = 24 + -24
Combine like terms: 24 + -24 = 0
-20 + 6x + 2x2 = 0
Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + 3x + x2) = 0
Factor a trinomial.
2((-5 + -1x)(2 + -1x)) = 0
Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:
Simplifying
-5 + -1x = 0
Solving
-5 + -1x = 0
Move all terms containing x to the left, all other terms to the right.
Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5
Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5
Combine like terms: 0 + 5 = 5
-1x = 5
Divide each side by '-1'.
x = -5
Simplifying
x = -5
Answer:
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:
-5 + -1x = 0
-5 + -1x = 0
Move all terms containing x to the left, all other terms to the right.
-5 + 5 + -1x = 0 + 5
Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5
Combine like terms: 0 + 5 = 5
-1x = 5
x = -5
Step-by-step explanation:
Ruben adds some water to a glass of juice. The ratio of water to juice in his glass in now 4:6. Which fraction below represents this ratio? A 3/5 C 2/3 B 3/2 D 2/5
Answers
Answer:
C
Step-by-step explanation:
since we're being told to convert the ratio to fraction then it is C. note that 4 ratio is also the same as dividing 4 by 6
Solving Logarithmic Equations
不
Identify the solution set of 3 In 4 = 2 In x.
o {6}
O {-8, 8}
o {8}
DONE
(8)
Answers
Answer:
Step-by-step explanation:
3ln(4) = 2ln(x)
ln(4³) = ln(x²)
4³ = x²
(2²)³ = x²
2⁶ = x²
x = ±√2⁶ = ±2³ = ±8
However, the argument of a logarithm must be positive, so x=8.
The solution set of the equation is {8, -8}, but we can discard the negative solution as it is not physically meaningful in this context. So, the final solution set is {8}. Option D is correct.
To solve the equation, we can use the logarithmic identity that states:
n * log(a) = log(aⁿ)
Using this identity, we can rewrite the equation as:
In(4³) = In(x²)
Simplifying both sides using the natural logarithm properties, we get:
In(64) = In(x²)
Taking the exponential of both sides, we have:
[tex]e^{In 64} = e^{In x^2}\\64 = x^2[/tex]
Taking the square root of both sides, we get:
x = ±8
However, we must check if either of these solutions makes the argument of the natural logarithm negative, which is not allowed. Since the argument of the natural logarithm is positive for both x = 8 and x = -8, both solutions are valid.
Therefore, the solution set of the equation is {8, -8}, but we can discard the negative solution as it is not physically meaningful in this context. So, the final solution set is {8}.
Learn more about logarithmic function here:
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ITS A ANGLE QUESTON PLS HELP
Answers
This is a right angles triangle
(6x6)/2
18
Hope this helps :>From CambridgePlease give brainliestAnswer:
18 cm²
Step-by-step explanation:
The area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
Here b = 6 and h = 6 , then
A = [tex]\frac{1}{2}[/tex] × 6 × 6 = 3 × 6 = 18 cm²
Is -6 a solution for the equation 3(2x - 8)= -4(-6 +21)?
Answers
Answer:
YeS, it is a solution
Step-by-step explanation:
Here, we want to check if -6 is a solution to the question
What we have to do is to replace x by -6
If what we have on the left equals that on the right, then -6 is a solution
Thus, we have it that;
3(2(-6) -8)
= 3(-12-8)
= 3(-20) = -60
for the right hand side
-4 (15) = -60
This means both sides are equal and that -6 is a solution