The populations of two cultures of bacteria, A and B, after x hours are shown below. Which statement is a correct comparison of bacteria A and bacteria B?
Answers
Answer:
(c)
Step-by-step explanation:
Given
See attachment for A and B
Required
Compare A and B
First, we get the initial population of A and B.
The initial population is at when [tex]t =0[/tex]
From the table of bacteria A, we have:
[tex]Initial = 100[/tex] when [tex]t = 0[/tex]
From the graph of bacteria B, we have:
[tex]Initial = 75[/tex] when [tex]t = 0[/tex]
Since the initial of bacteria B is less than that of bacteria A, then (a) is incorrect.
Next, calculate the slope of A and B i.e. the rate
Slope (m) is calculated as:
[tex]m = \frac{y_2 - y_1}{t_2 - t_1}[/tex]
Where
y = Number of bacteria
t = time
For bacteria A:
[tex](t_1,y_1) = (0,100)[/tex]
[tex](t_2,y_2) = (2,140)[/tex]
So, the slope is:
[tex]m_A = \frac{140 - 100}{2 - 0}[/tex]
[tex]m_A = \frac{40}{2}[/tex]
[tex]m_A = 20[/tex]
For bacteria B:
[tex](t_1,y_1) = (0,75)[/tex]
[tex](t_2,y_2) = (1,100)[/tex]
So, the slope is:
[tex]m_B = \frac{100- 75}{1 - 0}[/tex]
[tex]m_B = \frac{25}{1 }[/tex]
[tex]m_B = 25[/tex]
Since [tex]m_B > m_A[/tex], then the rate of bacteria B is greater than that of bacteria A.
Hence, (d) cannot be true
Next, we determine the equation of both bacteria
This is calculated using:
[tex]y = m(t - t_1) + y_1[/tex]
For bacteria A, we have:
[tex]y = m_A(t - t_1) + y_1[/tex]
Where:
[tex](t_1,y_1) = (0,100)[/tex]
[tex]m_A = 20[/tex]
So:
[tex]y = 20(t - 0) +100[/tex]
[tex]y = 20(t) +100[/tex]
[tex]y = 20t +100[/tex]
For bacteria B, we have:
[tex]y = m_B(t - t_1) + y_1[/tex]
Where:
[tex](t_1,y_1) = (0,75)[/tex]
[tex]m_B = 25[/tex]
So:
[tex]y = 25(t - 0) + 75[/tex]
[tex]y = 25(t) + 75[/tex]
[tex]y = 25t + 75[/tex]
At 3 hours, the population of bacteria A is:
[tex]y = 20t +100[/tex]
[tex]y = 20* 3 + 100[/tex]
[tex]y = 60 + 100[/tex]
[tex]y = 160[/tex]
At 3 hours, the population of bacteria B is:
[tex]y = 25t + 75[/tex]
[tex]y=25 * 3 + 75[/tex]
[tex]y=75 + 75[/tex]
[tex]y=150[/tex]
After 3 hours, bacteria B is 150 while A is 160.
This implies that (c) is correct because the population of B is less than that of A, at 3 hour
Lastly, to check if they will ever have equal population or not, we simply equate both equations.
So, we have:
[tex]y = y[/tex]
[tex]25t + 75 =20t + 100[/tex]
Collect like terms
[tex]25t - 20t = 100 - 75[/tex]
[tex]5t = 25[/tex]
Solve for t
[tex]t = 25/5[/tex]
[tex]t = 5[/tex]
They will have equal population at 5 hours.
Hence, b is incorrect
From the above computation, only (c) is correct
Related Questions
Diego, Elena, and Andre participated in a walk-a-thon to raise money for cancer research. They each walked at a constant rate, but their rates were different. 3. a. How fast was Diego walking in miles per hour?
Answers
Answer:
3 miles per hour
Step-by-step explanation:
It is given that Diego and his friends took part in a walk a thon to raise money for cancer research.
From the table, it is given that:
Time took by Diego in hours = 2 hours
Miles walked by Diego in miles = 6 miles
Therefore, Diego is walking with a speed of = [tex]$\frac{6}{2}$[/tex]
= 3 miles per hour
can someone help please what is the answer?
Answers
[tex]\frac{1}{2}q = - 24\\q = - 24 * 2\\q = - 48[/tex]
Answer:
The answer is q= -48
Step-by-step explanation:
The steps to solve are:
Combine multiplied terms into a single fraction.
Next, multiply by one.
Then, eliminate common denominators.
After that, cancel multiplied terms that are in the denominator.
Finally multiply the numbers.
Write this number in standard form.
Seven hundred nine
thousand eight hundred
thirty-one
Answers
Answer:
709,831
Step-by-step explanation:
709,831
Answer:
709831
Explanation
Do the side lengths 9,12, and 17 form a right triangle?
Answers
Answer:
no
Step-by-step explanation:
Using the converse of Pythagoras' identity
If the square of the longest side is equal to the sum of the squares of the other 2 sides then the triangle is right.
longest side = 17 and 17² = 289
9² + 12² = 81 + 144 = 225 ≠ 289
Then the triangle is not right
Ms. Robinson has $75 in her bank account and is depositing $15
each week. Ms. LaSpina has $225 in her bank account and is
withdrawing $10 each week. How many weeks will it take for the
bank accounts to have the same amount? What will that amount
be?
Answers
Answer:
It will take 6 weeks
Step-by-step explanation:
Ms. Robinson: 75+15(6)=$160
Ms. LaSpina: 225-60 =$160
Therefore both will take 6 weeks
CAN SOMEONE PLZ HELP ME ON THIS ONE
Answers
Answer:
Both are true
Step-by-step explanation: When the letter has this (') that means it parallel
aka being mirrored
Can someone Help please
Answers
Answer:
Answer:17 (I think)
Because if you look at the problem below Y u can see the patter 5+3=8 8+3=11 contiously adding 3 you get 17
kelly buys a shirt for $14 dollars and pays the store clerk $20 how much change will kelly get back
Answers
Answer:
6
Step-by-step explanation:
6 maybe
-4(3x+2)-5x what is the answer to this question?
Answers
Answer:
Step-by-step explanation:
-4(3x+2)-5x
-12x - 8 - 5x
Solving like terms
-17x - 8
If you want to find the value of x then
-17x - 8 = 0
-17x = 8
x = 8/-17
Answer: -17x - 8
Step-by-step explanation:
First, we distribute the -4 into the parenthesis:
-4(3x + 2) - 5x
-12x - 8 - 5x
Now, we combine like terms:
-12x - 8 - 5x
-17x - 8
You can't simplify this expression any further because of the variable, so this is your final answer :)
What is the volume of this cylinder?
Use 3.14 and round your answer to the nearest hundredth.
14 mm
7 mm
Answers
4300( 4308.08)
Your welcome
So all you have to do is multiply the radius by itself. So in this case 14x14=196.
So then multiply that by pi aka 3.14. So 196x3.14=615.44 then multiply that by your height in this case its 7 So 615.44x7=4308.08
brilliance for the right answer
What does 1 cc mean?
1 cubic inch
1 cubic centimeter
1 cubic feet
1 cubic liter
Answers
1 cc (cubic centimeter) refers to a unit of volume in the metric system. It is equal to one cubic centimeter, which is equivalent to one milliliter (ml).
The abbreviation "cc" is commonly used in medical and scientific contexts to represent small volumes, especially when measuring liquids or medications.
A cubic centimeter (cc) is a unit of volume that is commonly used in the metric system. It is equivalent to a cube with edges measuring one centimeter each. The cubic centimeter is often used to measure the volume of small objects or quantities of liquids.
To better understand the size of a cubic centimeter, it can be visualized as the volume occupied by a sugar cube or a small dice. It is a relatively small unit of volume, and larger volumes are typically expressed in terms of liters or cubic meters.
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Convert 0.5 liters to milliliters.
Answers
Answer:
500 millilitres
Step-by-step explanation:
I hope it will help you
Answer:
Step-by-step explanation:
1 litre = 1000 millilitres
0.5 Litre = 500 milliliters
Pls solve this for 80 points
Answers
Answer and Step-by-step explanation:
For this problem, b is the y-intercept.
On the graph, the line intersects the y-axis at (0, 10).
That means b is 10.
For the slope, we need to find the rise over run of the line. We see that the line goes up 2 and over 4. This simplifies to [tex]\frac{1}{2}[/tex].
That means m is [tex]\frac{1}{2}[/tex].
#teamtrees #PAW (Plant And Water)
Step-by-step explanation:
b is the y intercept
the ordered pair is 0, 10
There are 5 blue
candies, 6 red
candies, and 9 yellow
candies. What is the
probability of
randomly picking a red
candy? Express your
answer as a percent.
Answers
Answer:
The probability of randomly picking a red candy is 1/20 and In percentage value 5%
Step-by-step explanation:
There are 5 blue candies, 6 red candies, and 9 yellow candies.
Now, Total
5 + 6 + 9 = 20 candies
Now, The probability of randomly picking a red candy is 1/20
Now, In percentage
1/20 × 100% = 5%
Thus, The probability of randomly picking a red candy is 1/20 and In percentage value 5%.
-TheUnknownScientist
PLEASE HELP! I don’t understand
Answers
Answer:
(-1,0) and (5,0)
Step-by-step explanation:
The roots are the points where the y-value is 0 and the point lies exactly on the x-axis.
(blank,0)
In this parabola, the points that are exactly on the x-axis is (-1,0) and (5,0)
Please help me
GEOMETRY
And please let me know how you solved it thank u!
Answers
Answer:
x = 6
Step-by-step explanation:
In the picture :) Hope that helped!
Given
BAI BD
mZCBD = 40 +52
m ABC = 82 - 10°
Find mZCBD:
B
D
Answers
Answer:
m∠CBD=68°
Step-by-step explanation:
BA is perpendicular to BD, meaning they form a right angle (90°)
This means m∠CBD + m∠ABC=90, or they are supplementary.
We have expressions given for these angles, so
4x+52+8x-10=90
12x+42=90
12x=48
x=4
Knowing x=4, we can substitute back into our expression for m∠CBD because that's what we're looking for.
4(4)+52=68
m∠CBD is 68°.
Find the factors of x3−7x−6
(x+3)(x+2)(x−1)
(x−3)(x+2)(x+1)
(x−4)(x−2)(x+1)
(x−6)(x−1)(x+1)
Answers
Answer:
B. (x−3)(x+2)(x+1)Step-by-step explanation:
Possible options are 1 or 2 as each has odd number of negative coefficients.
Open parenthesis and verify:
(x+3)(x+2)(x−1) = ³ + 4x² + x - 6, false(x−3)(x+2)(x+1) = x³ - 7x - 6, true
Joe bought two pizzas for 16.78 He wants to give the delivery person an 18% tip. How much money should should give the delivery person
Answers
Answer
23
Step-by-step explanation:
Answer:
$23.00
Step-by-step explanation:
The length of a rectangle is 9 centimeters more than half
the width. Find the length if the perimeter is 60 centimeters.
Answers
Answer:
l = 16 cm
Step-by-step explanation:
Let's set the width of the rectangle as "w" and the length of the rectangle as "w/2 + 9".
The perimeter of a rectangle is calculated by adding up the value of all of its side lengths. Therefore, we can find the perimeter using 2l + 2w = P.
We can substitute 60 for P and w/2 + 9 for l.
2(w/2 + 9) + 2w = 602w/2 + 18 + 2w = 60 w + 18 + 2w = 603w + 18 = 603w = 42w = 14Substitute w = 14 into the equation for length l.
l = w/2 + 9 l = 14/2 + 9 l = 16The length of the rectangle is 16 cm.
Part 1: How many phone numbers can be made if all the digits (that is, 10 digits) need
to be filled in and any single digit number (0-9) can be used for any digit?
Part 2: How many phone numbers can be made if the first digit must be 1, the second digit must be a number in the range 3-5, the third digit must be a number in the range
(6-9), and the last seven digits can be any single digit number 0-9?
PLZ HELP ASAP WOULD GREATLY APPRECIATE IF U R HERE TO NOT HELP DON'T BOTHER OR DON'T PUT A LINK THAT LEADS TO NOTHING THANK YOU!
Answers
Answer:
100
Step-by-step explanation:
Just do 10 times 10
Can you give the picture with the problem? Im confused on what the problem is because i dont see an equation set.
(2 x 10^5) x (3 x 10^4)
give your answer in standard form
(answer and you’ll get 20 points)
Answers
Answer:
6x10⁹
Step-by-step explanation:
so we regroup them
(2×3)×(10⁵×10⁴)
6×10⁵+⁴
=6×10⁹
Answer:
Below.
Step-by-step explanation:
(2 x 10^5) x (3 x 10^4)
= 2 x 3 x 10^5 x 10^4
= 6 x 10^(4+5)
= 6 x 10^9.
just a simple question, if you guys dont mind.
Answers
A bicyclist needs to pass two check points before completing a race. The matrix equation that represents the distance, in miles, from the starting point to checkpoint 1, y represents the distance from checkpoint 1 to checkpoint 2, and z represents the distance from checkpoint 2 to the finish line.
Answers
Answer:
A.
i believe you are right
The area of a rectangle if the length is 5 more than 4 times the width, what's the algebraic expression for this question
Answers
Please mark brainliest
The area of a rectangle if the length is 5 more than 4 times the width, the algebraic expression for this is, A = (4b + 5) × b
What is the area?An area is total space occupied by two-dimensional or flat surfaces. In other words we can say that it is a number of unit squares present in a closed figure. We use various units for measurement of area like, cm², m², ft², mm².
Given that,
The length is 5 units more than 4 times the width
Suppose,
length = l
width = b
So, according to given condition
l = 4b + 5
Now, the area for rectangle is
A = length × width
A = l × b
A = (4b + 5) × b
Hence, the algebraic expression is (4b + 5) × b
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HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
Answers
Answer:
D. (8,0), (4,0)
Step-by-step explanation:
they both on tha line
match the terms to the definition
Answers
Answer
1,3,4,2
Step-by-step explanation:
2. the distance around the outside of a circle
3. the ratio of the circumference of a circle to its diameter, approximately 3.14
4. the distance across a circle through the center
A 26 foot ladder is set against the side of a house so that it reaches up 24 feet. If Mila
grabs the ladder at its base and pulls it 12 feet farther from the house, how far up the side of the house will the ladder reach now?
Answers
Answer:
13.9
Step-by-step explanation:
13.85 feet far up the side of the house will the ladder reach now.
Given that, a 26 feet ladder is set against the side of a house so that it reaches up 24 feet.
What is heights and distances in trigonometry?In mathematics, you can calculate the height of an object using the distance and angles. Here distance is the horizontal distance between the object and the angle is the angle above the horizontal of the top of the object, which gives the height of the object.
Let the distance between base of house to foot of the ladder be x.
Using Pythagoras theorem 26²=24²+x²
⇒ 676 = 576 + x²
⇒ x² = 100
⇒ x =10 feet
Mila grabs the ladder at its base and pulls it 12 feet farther from the house.
Now, the distance between base of house to foot of the ladder = x+12
= 10+12 = 22 feet.
So, up the side of the house the ladder reach = 24-h
Then, 26² = (24-h)²+22²
⇒ 676 = (24-h)²+484
⇒ (24-h)² = 192
⇒ (24-h) = √192
⇒ (24-h) = 13.85
⇒ h = 24-13.85
⇒ h = 10.15 feet
Therefore, 13.85 feet far up the side of the house will the ladder reach now.
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I’m just confused help!
Answers
Answer:
Step-by-step explanation:
180
HELPP plz I need the answer with step by step don't send a file plz
Answers
Answer:
13
Step-by-step explanation:
5^2 + 12^2 = Y
Sqrt Y = X