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
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Answer:
Step-by-step explanation:
-4(3x+2)-5x
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Step-by-step explanation:
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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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HELPP plz I need the answer with step by step don't send a file plz
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13
Step-by-step explanation:
5^2 + 12^2 = Y
Sqrt Y = X
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
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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Part 1: How many phone numbers can be made if all the digits (that is, 10 digits) need
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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.
Ms. Robinson has $75 in her bank account and is depositing $15
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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
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
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Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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From the table, it is given that:
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Answers
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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
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
(2 x 10^5) x (3 x 10^4)
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Answers
Answer:
6x10⁹
Step-by-step explanation:
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(2×3)×(10⁵×10⁴)
6×10⁵+⁴
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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.
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Answers
Answer:
l = 16 cm
Step-by-step explanation:
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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.
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x = 6
Step-by-step explanation:
In the picture :) Hope that helped!
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Answer:
Step-by-step explanation:
180
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.
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Answer:
A.
i believe you are right
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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.
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
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
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
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
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°.
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
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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)
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