1/5 or -1/9 would both be correct
suppose a population of bacteria in a petri dish has a doubling time of 6 hours. how long will it take for an initial population of 8000 bacteria to reach 12000? round your answer to two decimal places, if necessary.
For an initial Bacteria population of 8000 to reach 12000 bacteria it will take almost 4 hours.
Bacterial culture growth is defined as an increase in the number of bacteria within a population rather than an increase in the size of individual cells. Bacterial population growth occurs geometrically or exponentially. In each cycle of division (generation), the cell develops into 2 cells, then 4 cells, then 8 cells, then 16 cells, then 32 cells. The time required for generation formation, generation time (G), can be calculated using the following formula:
G = 1/n = [tex]\frac{t}{3.3logb/B}[/tex]
where B is the number of bacteria at the start of observation, b is the number of bacteria present after period t, and n is the number of generations. This relationship indicates that the average generation time is constant and the rate of bacterial population growth is proportional to the number of bacteria at any given time point. This relationship holds only during periods of exponential population growth called logarithmic growth.
According to the question:
2^(t/6) = 12000/8000 = 1.5
t = 6log1.5/log2
= 3.6 hours
Round up, since in 4 hours it will double to 12,000.
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5x-180x² factor completely
Answer:
-5(36x-1)x
Step-by-step explanation:
a cable company must provide service for 6 houses in a particular neighborhood. they would like to wire the neighborhood in a way to minimize the wiring costs (or distance). what is the minimal length of the network required to span the entire neighborhood?
The minimal Length of network to cover the entire neighborhood is 1200 yard , the correct option is (d) .
In the question ,
a table of of distance between the 6 cities is given ,
we have to find the minimal length in which all the neighbor hood can be connected .
From the table we can see that ;
the minimum distance to connect the house 1 to house 2 = 100 yards.
the minimum distance to connect the house 3 is from 2 to 3 = 300 yards.
the minimum distance to connect the house 4 is from 2 to 4 = 250 yards.
the minimum distance to connect the house 5 is from 4 to 5 = 300 yards.
the minimum distance to connect the house 6 is from 4 to 6 = 250 yards.
On adding all the distance ,
we get , the minimum distance = 100 + 300 + 250 + 300 + 250 = 1200 yards .
Therefore , the minimal length of the network is 1200 yards .
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a circle is inside a square. the radius of the circle is decreasing at a rate of 1 meter per day and the sides of the square are increasing at a rate of 2 meters per day. when the radius is 4 meters, and the sides are 18 meters, then how fast is the area outside the circle but inside the square changing? the rate of change of the area enclosed between the circle and the square is square meters per day.
Thus, the area is decreasing at a rate 12+20*π
What is area?The mathematical concept of "area" describes how big a region is on a planar or curved surface. A surface area is the area of an open surface or the border of a three-dimensional object, whereas a plane region's or plane's area's refers to a shape's or planar lamina's area.
Here,
Assume the circle's radius is r and the square's sides are s each.
The issue informs us that the radius is expanding at a pace of 2 m/hour. Dr/dt thus equals 2.
Four sides are shrinking simultaneously as the sides get smaller. ds/dt = -1 is the rate of change.
(why? because 4m/4 sides equals 1.
Find the area's formula right now. The region between the circle and the square is
A(t) = s^2 - π* r^2.
S(t) and R(t) are both time functions, thus you may compute a derivative with respect to t for both sides of the
equation. It follows that A'(t) = 2*s*s'(t) - 2**r*r' (t)
When r = 5 and s = 24/4 sides = 6, we are interested in the pace at which the area changes. Consequently, you
A'(t) = 2*6*(-1) - 2*π*5*2 = -12 - 20*π = -(12+20*π)
Thus, the area is decreasing at a rate 12+20*π
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big bobs bakery charges $9 for 1/2 dozen donuts. what is the price per dozen?
The charge per dozen donuts will be $18 according to the given ratio.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
As per the given,
Big bobs bakery charges $9 for 1/2 dozen donuts.
$9 for 1/2 dozen donuts
For one dozen,
$9 x 2 = $18
Hence "The above ratio will result in a fee of $18 for a dozen donuts.".
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I need help with this question
Answer:
not really sure but it could be a
Lily measures the circumference of three pillars.
Complete the table to show Lily’s measurements, the actual measurements, the difference between the measurement and the actual, and the percent error.
By using the concept of percentage, the complete table has been shown below
What is percentage?
Suppose there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage. For example 13% means [tex]\frac{13}{100}[/tex]. Here 13 is expressed as a fraction of 100.
For marble
Lily's Measurement = 90 cm
Actual Measurement = 90 + 10 = 100 cm
Absolute difference = 10 cm
Percent error = [tex]\frac{10}{100} \times 100[/tex] = 10 %
For granite
Lily's Measurement = 65 cm
Actual Measurement = 50 cm
Absolute difference = 15 cm
Percent error = [tex]\frac{15}{50} \times 100[/tex] = 30 %
For concrete
Lily's Measurement = 30 + 6 = 36 cm
Actual Measurement = 30 cm
Absolute difference = 6 cm
Percent error = [tex]\frac{6}{30} \times 100[/tex] = 20 %
Marble Granite Concrete
Lily's
Measurement 90 cm 65 cm 36
Actual
Measurement 100 cm 50 cm 30
Absolute
Difference 10 cm 15 cm 6
Percentage
Error 10% 30% 20%
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Complete Question
The table has been attached
Muhammad bought 4 movies for a total of $25. At this rate, what is the cost of 12 movies?
Answer:
$75
Step-by-step explanation:
25÷4= 6.25
6.25×12= 75
The total of 12 movies would be $75.
[tex]4 * 3 = 12[/tex]
[tex]25*3=75[/tex]
Thus, you're answer is $75.
2(x- 4) + 3x- 17 for x = 3
Answer:
-10
Step-by-step explanation:
i just did it
The Excel Cable Company has a monthly fee of $32.00 and an additional charge of $8.00 for each premium channel. The Best Cable Company has a monthly fee of $26.00 and an additional charge of $10.00 for each premium channel. The Horton family is deciding which of these two cable companies to subscribe to. For which number of premium channels will be the total monthly subscription fee for the excel and best cable companies be the same
Answer:
We can set up the following equation:
Excel Cable Company fee = Best Cable Company fee
32 + 8x = 26 + 10x
Here, x represents the number of premium channels. We can solve for x by subtracting 26 from both sides and then dividing both sides by 2 to get:
6 + 6x = 10x
6 = 4x
x = 6/4
x = 1.5
Therefore, the total monthly subscription fee for the Excel and Best cable companies will be the same for 1.5 premium channels. Note that this is not a whole number, so it is not possible for the subscription fees to be the same for a whole number of premium channels
Answer: 3 channels
Step-by-step explanation:
The ECC has an initial fee of $32.00 with a $8.00 fee for each channel, so we can label that as Total = 8(x) + 32.00.
The BCC has an initial fee of $26.00 with a $10.00 fee for each channel, so we can label that as Total = 10(x) + 26.00.
Since we want to find how many premium channels each company needs till the monthly subscription rate will be equal, we can set those equal to eachother.
8x + 32.00 = 10x + 26.00
2x = 6
x = 3, so when each company has 3 premium channels used, the prices will be the same.
there are 51 houses on a street. each house has an address between 1000 and 1099, inclusive. show that at least two houses have addresses that are consecutive integers.
according to the question,
given data in the question'
there are 51 houses on a street'
each hoses has an address between 1000 and 1099
There are 51 residences and 1000 possible addresses, according to the pigeon hole principle. There must be at least one address between each house in order for there to be no houses with consecutive addresses. To do this, only give houses even numbers (leaving odd addresses as the buffer address)
Giving houses even numbers (leaving odd addresses as the buffer address) There are now 1000=50 addresses that can be used.
According to the pigeon hole principle, there must be at least one box that contains at least N
k things if N objects are put into k boxes.
Because of this, it is impossible to assign 50 distinct addresses to 51 separate homes without utilising a single consecutive integer.
So, at least one instance of a home must have consecutive integers, which.
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There are 2 houses that have at least consecutive integers .
What is meant by the pigeonhole principle?According to the pigeonhole principle, at least one container must hold more than one item if n things are placed into m containers, where n > m.
Why is pigeonhole principle important?According to the pigeonhole principle, if there are more pigeons than there are pigeonholes, then at least one pigeonhole must hold more than one pigeon. Although the underlying idea is clear, the ramifications are staggering. The explanation is that the principle establishes the reality (or absence) of a certain phenomena.
There are potential residences and addresses. There must be at least one address between each house in order for there to be no houses with consecutive addresses. To do this, only give houses even numbers (leaving odd addresses as the buffer address)
Houses are given even numbers, leaving odd addresses as the buffer address. As a result, we now have
50
addressable addresses
According to the "pigeon hole concept," if items are put into boxes, then there must be at least one box that contains at
[N/k]object.
As a result, it is impossible to assign distinct addresses to several dwellings without using at least one consecutive number.
Since there must be at least two homes with consecutive integer addresses, there must be at least one instance of consecutive integer addresses for houses.
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please help!!
Ray BX is an angle bisector of angle ABC. If m∠ABX = 2y+10, and m∠ABC = 10y-4, calculate the measure of angle XBC.
The measure of angle XBC is 18°.
Given that, ray BX is an angle bisector of angle ABC.
What is an angle bisector?The angle bisector in geometry is the ray, line, or segment which divides a given angle into two equal parts.
Here,
m∠ABX = 2y+10, and m∠ABC = 10y-4
Now, m∠ABC = m∠ABX + m∠XBC
m∠ABX = m∠XBC
⇒ 10y-4 = m∠ABX+m∠ABX
⇒ 10y-4 = 2∠ABX
⇒ 10y-4 = 2(2y+10)
⇒ 10y-4 = 4y+20
⇒ 10y-4y = 20+4
⇒ 6y = 24
⇒ y=4
So, m∠XBC=2y+10
= 18°
Therefore, the measure of angle XBC is 18°.
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Please help!!! i need this done by tonight!! 30 points!!
The symbol ∠ is used to denote an angle. The symbol m ∠ is sometimes used to denote the measure of an angle.
What is angle for example?The two hands together make different sets of lines from a common point. These sets of lines from a common point is called angle. The two hands form different angles every minute of the time. A clock forms an example of angles in real life.When the angle between two lines is it is said to be zero angle. The angle between twAn angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle. The word angle comes from a Latin word named 'angelus,' meaning “corner or rays becomes when both the rays are in the same direction.Tape random straight lines across students' tables to create lots of angles where the tape overlaps. Then ask your students to sit around the table with a marker, and encourage them to classify as many angles as they could. After classifying angles, your pupils can then move on to measuring them.x = 15
∠H = 82
∠I = 49
∠G = 49
Note that side HG and side HI are congruent ( indicated by the little dashed line ) which means that their opposite angles are congruent ( ∠I and ∠G to be more specific. )
Angles in a triangle add up to equal 180°
Hence, 3x + 37 + 2 ( 4x - 11 ) = 180 ( note that the 2 in 2(4x - 11) came from angles I and G being congruent )
We now solve for x
3x + 37 + 2 ( 4x - 11 ) = 180
step 1 distribute the 2 to the 4x and -11
2 + 4x = 8x
-11 * 2 = -22
we now have 3x + 37 + 8x -22 = 180
step 2 combine like terms
3x + 8x = 11x
37 - 22 = 15
we now have 11x + 15 = 180
step 3 subtract 15 from each side
15 - 15 cancels out
180 - 15 = 165
we now have 11x = 165
step 4 divide each side by 11
11x / 11 = x
165 / 11 = 15
we're left with x = 15
Our final step is to find the measures of ∠G, ∠H and ∠I
We can do this by simply replacing x with 15 in their given expression
∠H = 3x + 37
* substitute 15 with x *
3 ( 15 ) + 37
3 * 15 = 45
45 + 37 = 82
Hence, ∠H = 82
∠I = 4x - 11
* substitute x with 15 *
4(15) - 11
4 * 15 = 60
60 - 11 = 49
Hence, ∠I = 49
Like stated previously ∠G and ∠I are congruent
Hence, ∠G = 49
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which list orders the fractions from least to greatest 2/3, 7/12, 17/24, 3/4 ?
Answer:
The bigger the denominator the less the value will be.
Just for clarification of what he said.
y=3x-4 what's the answer pleas and thank you
Answer:
-12 (?)
Step-by-step explanation:
You have to multiply to find out what Y =
3x-4
A positive x a negative = a negative number (the negative sign doesn't effect how you multiply only changes the answer to a negative)
3 x (-4) =
-12
so Y = -12 ( 3 x -4 )
Write an equation of the line passing through point $p\left(-2,\ \ \ 6\right)$ that is parallel to the line $x=-5$.
The equation of a line passing through point P(-2,6) and parallel to x = -5 is x = - 2.
Slope: The pace at which the y-axis changes in relation to the x-axis is known as the slope.
Because tan90° is undefinable, the slope of a vertical line is also undefinable.
First, a line with the equation x = -5 is a vertical line that crosses the y-axis at x = -5 for all values of y from zero to infinity, with no defined slope.
For every real value of y, a line that is perpendicular to the line at x = -5 and contains coordinate points P(-2,6) is also a vertical line at x = -2.
Thus, it has the equation x = -2.
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An equilateral triangle has a side measure of 10 in. What is the measure of each of the angles of the triangle?.
The angle of an equilateral triangle is 60°.
Equilateral triangle:
An equilateral triangle is a triangle with all three sides of equal length , corresponding to what could also be known as a "regular" triangle. An equilateral triangle is therefore a special case of an isosceles triangle having not just two, but all three sides equal. An equilateral triangle also has three equal.
Here we have to find each angle of the triangle.
Data given:
sides of an equilateral triangle = 10inches
As it is clear from the definition that the angle of an equilateral triangle is equal.
Let's consider the triangle as ABC.
∠A + ∠B + ∠C = 180°
As the angle are equal so we take
∠A = ∠B = ∠C
So we have;
3∠A = 180°
∠A = 60°
Therefore the angle of the triangle is 60°.
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what is the quotient of 10/16 ÷ 5/16
Answer: 2
Step-by-step explanation:
Answer:
Step-by-step explanation:
The answer is 2.
(10/16)/(5/16)=2
10/5=2
16/16=1
2/1=2
PLS HELP
Solve for y.
3y + 5y = 64
Answer:
y=8
Step-by-step explanation:
3y+5y=64
8y=64
y=8
Answer: Y=8
Step-by-step explanation:
Add 3y + 5y which equals 8y
Divide the 8y by 64
64/8 = 8
So y = 8
Can someone please help me. I dont want to mess up i only got one try. (15 pts)
there are water lilies on a lake. each day, the amount of water lilies doubles. after 20 days, there are so many water lilies that the entire lake is covered. after how many days was half of the lake covered?
We are aware that by day 20, the blossom will have covered half of the lake, or 1/2. It doubles the following day to become 1, which equals the entire lake. Knowing that the following day is 21.
Given that:
Each day, the amount of water lilies doubles. after 20 days, there are so many water lilies that the entire lake is covered.
we have something that doubles so 2 times something
after 20days = 20 × 2 = 40
However, we are aware that by day 20, the blossom will have covered half of the lake, or 1/2. It doubles the following day to become 1, which equals the entire lake. Knowing that the following day is 21.
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Work out
Give your
(5 x 10^3) x (9 x 10^7)
answer in standard form.
Answer:
To find the product of 5 x 10^3 and 9 x 10^7, we need to multiply the two numbers. The first step is to multiply the two numbers without the exponents, which gives us 5 x 9 = 45. Next, we need to add the exponents to find the exponent of the final product. 10^3 and 10^7 have exponents of 3 and 7, respectively, so the final exponent is 3 + 7 = 10. This means that the final product is 45 x 10^10, or 4.5 x 10^11 in standard form.
Step-by-step explanation:
If you took a 3 and 4, what are the two different fractions you could make?
Answer:
Step-by-step explanation:
If you took a 3 and 4 the two fractions you could make are 3/4 and 4/3
If 2x2 – 28x = –98, then x could equal which of the following?
The value of x in the quadratic equation is as follows:
x = 7 and x = 7
How to solve quadratic equation?A quadratic equation is a polynomial equation in one unknown that contains the second degree, but no higher degree, of the variable.
The standard form of a quadratic equation is ax² + bx + c = 0, when a ≠ 0.
Let's solve for x in the quadratic equation 2x² – 28x = –98.
2x² – 28x = –98
2x² – 28x + 98 = 0
divide through by 2
x² - 14x + 49 = 0
The two numbers you can add get -14 and multiply to get 49 are -7 and -7.
Hence,
x² - 14x + 49 = 0
x² - 7x - 7x + 49 = 0
x(x - 7) -7(x - 7) = 0
(x - 7)(x - 7) = 0
Therefore,
x = 7 and x = 7
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a. How did you identify and name the semicircles?
Answer:
___And Its Name Is Half Circle
Tyrell is exploring a cave. Every hour, he makes 4 vertical descents of 3.5 meters. The expression 3(4)(-3.5) represents his change in elevation in meters after 3 hours. What is his change in elevation?
The value of the change in elevation is -42 meters
How to determine the change in elevation?From the question, we have the following parameters that can be used in our computation:
Expression = 3(4)(-3.5)
The above expression represents his change in elevation in meters after 3 hours
So, we have the following representation
Change in elevation = 3(4)(-3.5)
Remove the brackets and express them as products
So, we have the following representation
Change in elevation = 3 * 4 * -3.5
Evaluate the products
So, we have the following representation
Change in elevation = 12 * -3.5
Evaluate the products
So, we have the following representation
Change in elevation = -42
This represents the change in elevation
Hence, the change in elevation is -42 meters
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Evaluate 11.5x + 10.9y when x = 6 and y =7
The value of the algebraic expression 11.5x + 10.9y at x = 6 and y = 7 is 145.3
What is an algebraic expression?
Algebraic expression consists of variables and numbers connected with addition, subtraction, multiplication and division
The given algebraic expression is 11.5x + 10.9y
We have to find the value of the algebraic expression at x = 6 and y = 7
Putting x = 6 and y = 7 in the algebraic expression,
[tex]11.5 \times 6 + 10.9 \times 7[/tex]
69 + 76.3
145.3
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Please help will mark brainliest
The value of a is 5 on x- axis.
What are Coordinates?The pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x,y).
Given:
From the Graph we can mark the Coordinates.
One which the marked coordinates is (a, b) where is located at x- axis and y is located at y- axis.
Then, From the Figure we can see that a lies in between Coordinates (3, 3) and (6, 0) and close to a.
Hence, the value of a is 5 on x- axis.
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The hardware store sells orange buckets, which hold 10 liters of water, and teal buckets, which hold 3 liters. Alec bought 14 buckets. His buckets will hold 70 liters in total. How many of each type of bucket did Alec buy?
Alec buy 4 units of orange bucket and 10 units of teal bucket.
What is system of equations?
A set of one or more equations involving numerous variables is referred to as a system of equations. The variable mappings that satisfy all component equations are the solutions to systems of equations, or the points where the components of these equations intersect.
According to the given information, let us denote the quantity of orange bucket be x and teal bucket by y.
Therefore, budget constraints would be:
10x + 3y = 70 ..(1)
It is also given that total number of bucket is 14, such that:
x + y = 14 ..(2)
From equation (2),
x = 14 - y
Plug x = 14 - y in equation (1)
10(14 - y) + 3y = 70
140 - 10y + 3y = 70
140 - 7y = 70
7y = 140 - 70
7y = 70
y = 10
Plug y = 10 in x = 14 - y
⇒ x = 14 - 10
x = 4
Hence, Alec buy 4 units of orange bucket and 10 units of teal bucket.
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What is the meaning of ASA SAS and SSS postulate?
The aforementioned postulates - ASA, SAS, SSS - are defined and explained below.
The given theorems are used in order to prove the congruency of triangles. If we are presented with a problem in which we are required to prove the congruency of two triangles, we can use these three postulates to prove it.
The three postulates are as thus -
SSS postulate: if 3 sides of the given triangles are equal, then the triangles are congruent.
SAS postulate: If 2 sides and an angle of the given triangles are equal, then the triangles are congruent.
ASA postulate: If 2 angles and a side (in the middle of the angles)of the given triangles are equal, then the triangles are congruent.
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