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
plz help will mark brainlist
Answer:
1. 1/7
2. 1/4
Step-by-step explanation:
maths
What is the equation of the line?
Answer:
y = 4
Step-by-step explanation:
find the coordinates of the point where y-4x=1 crosses the y-axis
Answer:
(0, 1)
Step-by-step explanation:
y - 4x = 1 crosses the y-axis at (0, 1)
Answer:
(0,1)
Step-by-step explanation:
PLEASE HELP! I WILL MARK BRAINLIEST AND IM GIVING OUT AS MANY POINTS AS I CAN!!
Answer: Answer to 13 is 16 as it is 81+ days. Answer 14 is 16/50 which is 32 percent The median on 15 is the 6th value and the minimum value is the smallest number in the sequence provided. The lower quartile is the 3rd number in the sequence but you need to put them from smallest to largest. The upper quartile is the 9th number in the sequence. The maximum value is the biggest number in the sequence
Step-by-step explanation:
If a1=4 and an =2an-1 – 1 then find the value of a4.
The value of [tex]a_{4} = 37[/tex].
Here,
The value of [tex]a_{1} = 4[/tex]
And, [tex]a_{n} = 2 a_{n-1} -1[/tex]
We have to find value of [tex]a_{4}[/tex].
What is Sequence?
A sequence is a collection of elements that are arranged according to a specific pattern.
Now,
The value of [tex]a_{1} = 4[/tex]
And, [tex]a_{n} = 2 a_{n-1} -1[/tex]
Then to find value of [tex]a_{4}[/tex], we can find [tex]a_{2} , a_{3}[/tex] as;
[tex]a_{2} = -2(a_{1} ) - 1\\a_{2} = -2(4) - 1\\a_{2} = -9[/tex]
And,
[tex]a_{3} = -2(a_{2} ) - 1\\a_{3} = -2(9) - 1\\a_{3} = -19[/tex]
Hence, the value of [tex]a_{4}[/tex] is;
[tex]a_{4} = -2(a_{3} ) - 1\\a_{4} = -2(-19) - 1\\a_{4} = 37[/tex]
Therefore, The value of [tex]a_{4} = 37[/tex].
Learn more about the sequence visit:
https://brainly.com/question/7882626
#SPJ2
please help! ASAP!!!!
Answer:
Part A) 2(n/6) - 9
Part B) the expression would change to 2(n/6) + 9 if it said 'more than'
Step-by-step explanation:
choose the number that is equal to: 2/3 divided by (-3) A.)-2 B.) -2/9 C.)2/9 D.) 2
Represent 0.533 (only the last 3 is bar number) into a rational number
Answer:
[tex]\frac{8}{15}[/tex]
Step-by-step explanation:
We require 2 equations with the repeating 3 placed after the decimal point.
let x = 0.5333.. ( multiply both sides by 10 and 100 )
10x = 5.333... → (1)
100x = 53.333... → (2)
Subtract (1) from (2) tus eliminating the repeating 3
90x = 48 ( divide both sides by 90 )
x = [tex]\frac{48}{90}[/tex] = [tex]\frac{8}{15}[/tex]
Answer:
IT IS 8/15
Step-by-step explanation: Divide and multiply the fraction from 100 to tens
Which statements are true for the functions g(x) = x2 and h(x) = –x2 ? Check all that apply.
For any value of x, g(x) will always be greater than h(x).
For any value of x, h(x) will always be greater than g(x).
g(x) > h(x) for x = -1.
g(x) < h(x) for x = 3.
For positive values of x, g(x) > h(x).
For negative values of x, g(x) > h(x).
Answer:
For any value of x, g(x) will always be greater than h(x)
g(x) > h(x) for x = -1
For positive values of x, g(x) > h(x).
For negative values of x, g(x) > h(x).
Answer:
Which statements are true for the functions g(x) = x2 and h(x) = –x2 ? Check all that apply.
g(x) > h(x) for x = -1.
For positive values of x, g(x) > h(x).
For negative values of x, g(x) > h(x).
Step-by-step explanation:
and for the lazy people its just C, E, F
Which measurements could not represent the side lengths of a right triangle?
F 25 feet, 60 feet , 65 feet
G 9 feet, 12 feet, 15 feet
H 20 feet, 25 feet, 30 feet
12 feet, 35 feet, 37 feet
There are 200 marbles in the bag. John picks 10 marbles out of
the bag and 6 of them are red. What would be an estimate for
the number of red marbles in the bag?
Answer:
120
Step-by-step explanation:
10 x 20 = 200
thus 6 x 20 is 120
Cómo trazar Polígonos regulares utilizando material geométrico como la regla, compas y el graduador porfa ayuda
Answer:
En matemática, un polígono construible es un polígono regular que puede ser construido con regla y compás. Por ejemplo, un pentágono regular es construible con regla y compás mientras que un heptágono regular no lo es.En matemática, un polígono construible es un polígono regular que puede ser construido con regla y compás. Por ejemplo, un pentágono regular es construible con regla y compás mientras que un heptágono regular no lo es.
solve for x. The segments labeled in the picture are the tangets.
determine the domain of the following graph
Answer:
[-5, 10) or you can write [tex]-5\le x < 10[/tex]
Step-by-step explanation:
The domain is the set of all values of x used in the function. Scan across the graph from left to right (much as you do when reading). The first point you find on the graph has an x-coordinate 5 (see the solid dot?). Then, as you continue reading across the graph, there are values of x used until you get to 10. The dot at x = 10 is open, not filled in. That indicates that the number x = 10 is NOT used by the function.
So the domain is all real numbers greater than or equal to -5 and less than 10.
[-5, 10) is called interval notation; a square bracket means the value next to it IS used by the function, a parenthesis means the value next to it is NOT used.
Find the measure of arc FV
Answer:
FV = 60
Step-by-step explanation:
VG => 65 × 2 = 130
FH major arc=> 119 × 2 = 238
FH major arc - GH = FG
FG => 238 - 168 = 70
VG - FG major arc = FV
FV => 130 - 70 = 60
Answer:
60 degrees
Step-by-step explanation:
The measure of an inscirbed angle is half the measure of the intercepted arc.
(The measure of the arc is twice the measure of the angle!)
The inscribed angle at V intercepts an arc of 2 x 119 = 238 degrees, so the measure of arc FGH is 238. Subtract arc GH from that, 238 - 168 = 70, so that is the measure of arc FG.
The angle at H intercepts an arc with measure 2 x 65 = 130. The measure of arc VFG is 130. But arc FG is part of that, so subtract its measure from 130. 130 - 70 = 60.
The measure of arc FV is 60 degrees.
Ms.Boyers is baking a cake for the holiday. She needs 3 cups of milk and 1 cup of corn syrup. How many ounces of milk and corn syrup does she need in all
Answer:
she will need 24 ounces of milk and 8 ounces of corn syrup
Step-by-step explanation:
let me know if im right good luck!
Answer:
[tex]48[/tex] oz of milk
[tex]16[/tex] oz of corn syrup
Step-by-step explanation:
[tex]3\times16=48\\1\times16=16[/tex]
Ill mark brainliest, question is attached
Answer:
-15u^2
Step-by-step explanation:
How do you do this pls I need help
Answer:
416 cm2
Step-by-step explanation:
The formula for surface area of prism.
2Ab+ Pb*h
2(1/2)(12)(8)+ 32*10
= 96+320
= 416 cm2
if my answer helps please mark as brainliest.
The zeros of a quadratic function are -7 and 3. Which of the following could be the function? Select all that apply.
A. F(x)=2x^2-8x-42
B. F(x)=5x^2+20x-105
C. F(x)=x^2+4x-21
D. F(x)=x^2-4x-21
The possible functions are
A. F(x)=2x^2-8x-42
B. F(x)=5x^2+20x-105
C. F(x)=x^2+4x-21
How to determine the possible equations?The zeros are given as:
x = -7 and x = 3
Rewrite as:
x +7 = 0 and x - 3 = 0
Multiply both zeros
(x + 7) * (x - 3) = 0 * 0
Evaluate the product
x^2 + 7x - 3x - 21 = 0
Evaluate the like terms
x^2 + 4x - 21 = 0
Express as a function
f(x) = a(x^2 + 4x - 21)
Where a is a constant
Let a = 1, 2 and 5 (according to the values in the options)
f(x) = 1 * (x^2 + 4x - 21) = x^2 + 4x - 21 --- option (c)
f(x) = 2 * (x^2 + 4x - 21) = 2x^2 + 8x - 42 --- option (a)
f(x) = 5 * (x^2 + 4x - 21) = 5x^2 + 20x - 105 --- option (b)
Hence, the possible functions are (a), (b) and (c)
Read more about quadratic functions at:
https://brainly.com/question/1214333
#SPJ1
find the volume of the figure. (3.14 as pi)
Answer:
84
Step-by-step explanation:
7x3x4
,,,,,,,,,,,,,,,,
Answer:
84 in^3
v=length x width x height
Why do u need pi in this, there are no circle or sphere or cone, or whatever
hope that answers your question
good luck and stay safe
Step-by-step explanation:
can someone please help me
Answer:
Step-by-step explanation:
whats bigger a street or a track
Answer:
Most likely a street
Step-by-step explanation:
depends on how big the track is
Solve for x.
One side = 10
Another side = 9
One side = x
(It's a right triangle.)
Answer:
x = 4.3588989435406
I hope it's helps you
I need an answer! NO LINKS! PLS ill give brainlist!
What is 165 rounded to the nearest ten?
Answer:
170
Step-by-step explanation:
5 and up you round up and 4 and below round down.
Look at the six then look at the number to the right, 5.
So, you round up to 170 instead of 160.
Find the area!
- please help!
Answer:
25 x 20 = 500
half of 25 = 12.5
12.5^2
156.25 x 3.14 = 490.625
490.625 divided by 2 = 245.3125
245.3125 + 500 = 745.3125 cm2 is your answer.
Which of the following relations is a function?
A. (0,4), (-3, 2), (5, 1), (-7, 2)
B. (0,0), (-3, 3), (5, 1), (-3, 5)
C. (5, 1), (-3, 4), (0, 1), (5,2)
D. (0,4), (-3, 6), (0, 3), (-7, 2)
Answer:
c is the one with function
Please check my answer !! thank you ⭐️
Which is a reasonable estimate for 7473 - 2875
Answer: the answer is 4,598.
Please help link=report it worth 15 points and you’ll get brainiest if it right
Answer:
d) none of these lines fit the data
Answer:
This has to be D - None of the lines fit the data
B > data at the end
A > data at the beginning
C doesn't really match at all.
[tex]\mathtt{: )}[/tex]