a) The number of bacteria in the initial population is 34.
b) The exponential growth model is y = 34 * e^(kt)
Given data:
(a) To find the initial population, we can use the exponential growth formula:
y = A * e^(kt)
Where:
y = population at time t
A = initial population
k = growth rate
t = time
Given that there are 105 bacteria after 2 hours, so plug in these values into the formula:
105 = A * e^(k*2)
Similarly, given that there are 325 bacteria after 4 hours:
325 = A * e^(k*4)
We now have a system of equations:
105 = A * e^(2k)
325 = A * e^(4k)
To solve for A, divide the second equation by the first equation:
325/105 = e^(4k)/e^(2k)
Simplifying further:
325/105 = e^(2k)
Taking the natural logarithm of both sides:
ln(325/105) = ln(e^(2k))
ln(325/105) = 2k
Solving for k:
k = 0.56493
Substitute it back into one of the original equations to solve for A. Let's use the first equation:
105 = A * e^(2k)
Substituting k = ln(325/105) / 2:
105 = A * e^(2 * ln(325/105) / 2)
Simplifying:
105 = A * (325/105)
A = 105 * (105/325)
A ≈ 34 (rounded to the nearest whole number)
Hence, the initial population is approximately 34 bacteria.
(b) Now that we have the initial population, A, and the growth rate, k, we can write the exponential growth model for the bacteria population:
y = 34 * e^(kt)
where t represents the time in hours.
Hence, the exponential equations are solved.
To learn more about exponential growth factor, refer:
https://brainly.com/question/13674608
#SPJ4
The formula for the area of a triangle is A = 1/2bh, where b represents the length of the base and h represents the height. Part A; solve the formula for b.
Answer:
b = [tex]\frac{2A}{h}[/tex]
Step-by-step explanation:
Given
A = [tex]\frac{1}{2}[/tex] bh
Multiply both sides by 2 to clear the fraction
2A = bh ( divide both sides by h )
[tex]\frac{2A}{h}[/tex] = b
An old wheat-grinding wheel in a museum actually works. The sign on the wall says that the wheel has a rotational acceleration of 180 rad/s 2 as its spinning rotational speed increases from zero to 1700 rpm. How long does it take the wheel to attain this rotational speed?
Answer:
It will take 0.989 second to attain this speed
Step-by-step explanation:
In this question, we want to calculate the time it will take for the wheel of the machine to attain the given rotational speed
We proceed as follows;
From the question, we can identify the following parameters
Rotational acceleration of the wheel is, α = 180 rad/s^2
Initial spinning rotational speed of the wheel is, ω= 0 rpm
1 rpm = (1/60) revolution per second = 2π * (1/60) rad/s
Thus,
initial rotational speed ωi = 0 rad/s
Final spinning rotational speed ωf of the wheel is, = 1700 rpm =178.02 rad/s
Now, from the equations of motion (for rotational motions),
ωf = ωi + αt
where t is the time taken by the wheel to attain its final rotational speed.
178.02= 0 + 180 * t
t = 178.02/180
t = 0.989 second
Maya is on a game show. To win $1,000,000, she must answer this question: What key features are necessary-and how are the features used-to create the sketch of a polynomial function? What is Maya's winning answer? Explain in complete sentences
Answer:
To create the sketch of a polynomial function there are key features are necessary and these are the vertex, axis of symetry, x and y intercepts
Step-by-step explanation:
To create the sketch of a polynomial function there are key features are necessary and these are the vertex, axis of symetry, x and y intercepts
One of the key features arte the vertex and this shows where it changes concativity.
While the x and y intercepts give you a couple of points of reference.
Also, the axis of symetry is only applicable to even degree polynomials
Please answer it now in two minutes
Answer:
7.3 mi
Step-by-step explanation:
*Make sure your calculator is in degree mode*
Do this with the SOHCAHTOA method using angle V. Since we are trying to find the side that is the opposite of angle V (WY) and since the hypotenuse is already given, you would use SOH (sinΘ=[tex]\frac{opposite}{hypotenuse}[/tex])
sin(27)=[tex]\frac{x}{16}[/tex]
Multiply by 16 on both sides to cancel out the fraction:
16sin(27)=x
7.3=x
Julie will build a rectangular pen for her dog against a barn. A wall from the barn will form one side of the pen. She has 32 m of fencing to form the other three sides. She plans to build the pen so that it has its maximum possible area.
What will be the dimensions of Julie's pen?
Answer:
The width (side perpedicular to the barn): x = 8 m The lenght (side parallel to the barn): y = 16 mStep-by-step explanation:
x - the width of the barn
She has 32 m of fencing so for the lenght remain (32-2x) m of fencing:
y = 32 - 2x
Area of the fencing: A = x•y
A(x) = x•(32 - 2x)
A(x) = -2x² + 32x ← quadratic function
The maximum value of quadratic function occurs at: [tex]x=-\frac b{2a}[/tex]
a = -2, b = 32
[tex]x=-\frac b{2a}=-\frac{32}{2\cdot(-2)}=-(-8)=8[/tex]
32-2x = 32 - 2•8 = 16
o persoana depune la banca o suma de bani. banca ofera o dobanda anuala de 2%. dupa un an in cont se afla 8160 lei. Care a fost suma depuse la banca?
Answer:
8000 lei
Step-by-step explanation:
Ni se spune la întrebarea de mai sus să găsim suma depusă în bancă.
Ni se oferă următoarele valori
R = rata = 2% = 0.02
T = Timp = 1 an
Suma totală = A = 8160 lei
Trebuie să găsim principalul (suma depusă la bancă).
Formula de utilizat este dată ca:
P (Principal) = A / (1 + rt)
P = 8160 lei / 1 + 0.02 × 1
P = 8160 lei / 1.02
P = 8000 lei
Prin urmare, suma depusă în bancă este de 8000 de lei.
Answer:
the two percent of 8160 its 163.2 so its 7996.8
Step-by-step explanation:
Which linear function has the steepest slope? On a coordinate plane, a line goes through points (0, 1) and (1, negative 2). A 2-column table with 4 rows. Column 1 is labeled x with entries 3, 6, 9, 12. Column 2 is labeled y with entries 10, 13, 16, 19. On a coordinate plane, a line goes through points (0, negative 2) and (1, 0). A 2-column table with 4 rows. Column 1 is labeled x with entries 2, 4, 6, 8. Column 2 is labeled y with entries negative 4, negative 12, negative 20, negative 28.
Answer:
D
Step-by-step explanation:
Answer:d
Step-by-step explanation:
D
1
English
TIME REMAINING
58:10
The radius of the large sphere is double the radius of
the small sphere.
How many times is the volume of the large sphere than
the small sphere?
O 2
4
6
08
Answer
2
Step-by-step explanation
The radius of the large sphere is double the radius of the small sphere
PLEASE HELP
A hire purchase agreement offers gym equipment, with a marked price
$897, for $87 deposit and $46.80 a month payable over 2 years.
Calculate :
a) the total hire-purchase price
b) the amount of
amount of interest charged
Answer: a) $1,210.20 b) $313.20
Step-by-step explanation:
a) $87 down + $46.80(24 months) = $1,210.20 total paid
b) $1,210.20 - $897.00 = $313.20 interest paid
The cylinder shown has a lateral surface area of about 400 square inches. Which answer is closest to the measure of the cylinder's radius? Use 3.14 to approximate pi.
Answer:
r = 1.59inch
the radius of the cylinder is
1.59inch
Step by step Explanation
lateral surface of a cylinder can be calculated using the below formula
Surface Area= 2 πr h
We were given area as 400inch^2 and height as 40inch then substitute we have
400 = 2 ×π × r ×40
400= 2×22/7×40
Then do the calculation, where, π
=22/7
400 = r × 251.2
Make r subject of formula we have
r = 400 / 251.2
r = 1.59inch
Therefore, the radius of the cylinder is
1.59inch
CHECK THE ATTACHMENT FOR THE FIGURE
The speed(S) of a car varies partly directly as its mass(M) and partly directly as the quantity (Q) of fuel in it. When the speed is 80km/hr, the mass is 220kg and the quantity of fuel is 30litres, when the speed is 60km/hr, the mass is 300kg and the quantity of fuel is 40 litres. Find the volume of fuel if the speed is 100km/hr and the mass 250kg. DO NOT WRITE TRASH I WILL REPORT YOU
Answer:
Quantity of fuel is 24 L, based on the model S=2400/Q when S=100
Step-by-step explanation:
If the output power of the car remains constant, the speed would reduce as the masses increase, which is the shown in the observed data.
Hence S does NOT vary directly with the mass and quantity, but varies INVERSELY with the mass and fuel (which has a mass).
Many models are possible to fit the results. Product models with a single constant k
S(m,q) = kmq and S(m,q) = k/mq
do not fit both observation, hence rejected.
A possible model with two constants is shown below
S(m,q) = k1/m + k2/q..................(1)
1. m=220, q=30 => 80 = k1/220 + k2/30 ..........(2)
2. m=300, q=40 => 60 = k1/300 + k2/40 ..........(3)
Solve system (2) and (3) gives k1=0, k2 = 2400.
So it appears that the speed is independent of the mass (m) [unlikely], but inversely proportional to the quantity (q) of fuel, giving
S(q) = 2400/q
When speed = 100 km/h, and mass = 250 kg, substitute
100 = 2400/q => q=2400/100 = 24
Which expression can be used to find the surface area of the following square pyramid?A 16+16+55+55+8816+16+55+55+8816, plus, 16, plus, 55, plus, 55, plus, 88 (Choice B) B 10+10+55+55+8810+10+55+55+8810, plus, 10, plus, 55, plus, 55, plus, 88 (Choice C) C 8 +8+55+55+888+8+55+55+888, plus, 8, plus, 55, plus, 55, plus, 88 (Choice D) D 16+8816+8816, plus, 88
Answer:
4 + 3+3+3+3
Step-by-step explanation:
We add up all the areas to find the surface area
The bottom is
2*2 = 4
The sides are all the same
The area of one side is
A = 1/2 bh = 1/2 (2*3) = 3
There are 4 triangular side
SA = 4 + 3+3+3+3
Answer:
4 + 3 + 3 + 3 + 3
Step-by-step explanation:
The base is a square.
Find area of a square.
2² = 4
Find the area of one triangle.
2 × 3 × 1/2 = 3
There are 4 triangles.
3 + 3 + 3 + 3
Add all the areas:
4 + 3 + 3 + 3 + 3
Part B
Think about graphing the relationship between the length and the width of the TV screens. What do you predict the graph
would look like?
Answer:
They would be perpendicular to each other.
One would have a slope of 0 (horizontal line) and the other would have an undefined slope (vertical line)
Step-by-step explanation:
Can any kind soul help me
Answer:
a) 4.50m/s²
b) v= 21
c) 11.25m/s
Step-by-step explanation:
a) rate of change of speed in first 2 seconds
= gradient of graph from t=0s to t=2s
The two points are (0,0) and (2,9).
[tex]gradient = \frac{y1 - y2}{x1 - x2} [/tex]
Rate of change of speed
[tex] = \frac{9 - 0}{2 - 0} \\ = \frac{9}{2} \\ = 4.50m/ {s}^{2} [/tex]
Total distance= area under graph
Distance travelled for first 6s
= area of traingle +area of rectangle
= ½(2)(9) +(6-2)(9)
= 9 + 4(9)
= 9 +36
= 45m
Distance travelled from t=6s to t=12s
= 135 -45
= 90m
Area under graph from t=6s to t=12s =90
Area of trapezium= 90
½(A +B)(h)= 90
½(9+ v)(6)= 90
3(9 +v)= 90 (simplify)
9 +v= 30 (÷3 throughout)
v= 30 -9
v= 21
c) Average speed
= total distance ÷total time
= 135 ÷12
= 11.25 m/s
a car is driving at a speed of 40mi/h.what is the speed of the car in feet per minute
Answer:
[tex]\boxed{3520\ ft/min}[/tex]
Step-by-step explanation:
1 miles per hour = 88 feet per minute
Multiplying both sides by 40
40 miles per hour = 88*40 ft/min
40 mi./hr = 3520 ft/min
Answer:
3520 feet/min
Step-by-step explanation:
the speed of the car in feet per minute:
first convert miles to feet ( 1 mile =5280 feet) and hours to minutes(1hr=60min.)
(40*5280)/1*60=3520 feet/min
Please help me with this math problem
Answer:
E. y = 2/3x
Step-by-step explanation:
You need to make an equation in slope-intercept form.
First, you need to find the slope. You can do this by taking two points and dividing the difference of the y's by the difference of the x's. I will use the first two points, but you can pick whichever points you want and still get the right answer. Also, the values in the left column will be x's, and the values in the right column will be y's.
8 - 2 = 6
12 - 3 = 9
6/9 = 2/3
The slope is 2/3. The only equation with this value is E.
ZE is the angle bisector of AngleYEX and the perpendicular bisector of Line segment G F. Line segment G X is the angle bisector of AngleYGZ and the perpendicular bisector of Line segment E F. Line segment F Y is the angle bisector of AngleZFX and the perpendicular bisector of Line segment E G. Point A is the intersection of Line segment E Z, Line segment G X, and Line segment F Y.Which must be true? Point A is the center of the circle that passes through points E, F, and G but is not the center of the circle that passes through points X, Y, and Z. Point A is the center of the circle that passes through points X, Y, and Z but is not the center of the circle that passes through points E, F, and G. Point A is the center of the circle that passes through points E, F, and G and the center of the circle that passes through points X, Y, and Z. Point A is not necessarily the center of the circle that passes through points E, F, and G or the center of the circle that passes through points X, Y, and Z.
Answer:
Point A is the center of the circle that passes through points E, F, and G and the center of the circle that passes through points X, Y, and Z.
Step-by-step explanation:
A is the intersection of angle bisectors, so is the incenter of triangle EFG. It is also the intersection of the perpendicular bisectors of the sides of triangle EFG, so is the circumcenter.
The altitudes at X, Y, and Z are perpendicular to sides EF, EG, and FG, and pass through the incenter, so X, Y, Z are points on the incircle.
A is the center of circles through E, F, and G, and through X, Y, and Z.
Answer:
Point A is the center of the circle that passes through points E, F, and G and the center of the circle that passes through points X, Y, and Z.
C on edg2020
Given the function [tex]h:x=px-\frac{5}{2}[/tex] and the inverse function [tex]h^{-1} :x=q+2x[/tex], where p and q are constants, find a) the value of p and q c)[tex]h^{-1} h(-3)[/tex]
Answer:
[tex]p = \frac{1}{2}[/tex]
[tex]q = 5[/tex]
[tex]h^{-1}(h(3)) = 3[/tex]
Step-by-step explanation:
Given
[tex]h(x) = px - \frac{5}{2}[/tex]
[tex]h^{-1}(x) = q + 2x[/tex]
Solving for p and q
Replace h(x) with y in [tex]h(x) = px - \frac{5}{2}[/tex]
[tex]y = px - \frac{5}{2}[/tex]
Swap the position of y and d
[tex]x = py - \frac{5}{2}[/tex]
Make y the subject of formula
[tex]py = x + \frac{5}{2}[/tex]
Divide through by p
[tex]y = \frac{x}{p} + \frac{5}{2p}[/tex]
Now, we've solved for the inverse of h(x);
Replace y with [tex]h^{-1}(x)[/tex]
[tex]h^{-1}(x) = \frac{x}{p} + \frac{5}{2p}[/tex]
Compare this with [tex]h^{-1}(x) = q + 2x[/tex]
We have that
[tex]\frac{x}{p} + \frac{5}{2p} = q + 2x[/tex]
By direct comparison
[tex]\frac{x}{p} = 2x[/tex] --- Equation 1
[tex]\frac{5}{2p} = q[/tex] --- Equation 2
Solving equation 1
[tex]\frac{x}{p} = 2x[/tex]
Divide both sides by x
[tex]\frac{1}{p} = 2[/tex]
Take inverse of both sides
[tex]p = \frac{1}{2}[/tex]
Substitute [tex]p = \frac{1}{2}[/tex] in equation 2
[tex]\frac{5}{2 * \frac{1}{2}} = q[/tex]
[tex]\frac{5}{1} = q[/tex]
[tex]5 = q[/tex]
[tex]q = 5[/tex]
Hence, the values of p and q are:[tex]p = \frac{1}{2}[/tex]; [tex]q = 5[/tex]
Solving for [tex]h^{-1}(h(3))[/tex]
First, we'll solve for h(3) using [tex]h(x) = px - \frac{5}{2}[/tex]
Substitute [tex]p = \frac{1}{2}[/tex]; and [tex]x = 3[/tex]
[tex]h(3) = \frac{1}{2} * 3 - \frac{5}{2}[/tex]
[tex]h(3) = \frac{3}{2} - \frac{5}{2}[/tex]
[tex]h(3) = \frac{3 - 5}{2}[/tex]
[tex]h(3) = \frac{-2}{2}[/tex]
[tex]h(3) = -1[/tex]
So; [tex]h^{-1}(h(3))[/tex] becomes
[tex]h^{-1}(-1)[/tex]
Solving for [tex]h^{-1}(-1)[/tex] using [tex]h^{-1}(x) = q + 2x[/tex]
Substitute [tex]q = 5[/tex] and [tex]x = -1[/tex]
[tex]h^{-1}(x) = q + 2x[/tex] becomes
[tex]h^{-1}(-1) = 5 + 2 * -1[/tex]
[tex]h^{-1}(-1) = 5 - 2[/tex]
[tex]h^{-1}(-1) = 3[/tex]
Hence;
[tex]h^{-1}(h(3)) = 3[/tex]
You want to buy a new sweater. The regular price was
$48 dollars. The sale price was $34. What was the
percent of discount to the nearest percent?
Answer:
29%
Step-by-step explanation:
48-34 = 14 dollar saving
14/48 = 29.17 % = 29% saving
Answer:
29%
Step-by-step explanation:
48-34= 14 dollar saving
14/48 = 29.17% = 29% saving
Lily is using dark power crystals to raise an army of zombies. Each crystal can raise 999 zombies. How many crystals does Lily need to raise 6{,}1746,1746, comma, 174 zombies?
Answer:
X= 618079825.9
Y= 6.18 crystals
Step-by-step explanation:
It takes Lily a crystal to raise 999 zombies.
It will take her x crystals to Raise 617461746174 zombies
Mathematically
One crystal= 999 zombies
X = 617461746174
X=( 617461746174*1)/999
X= 617461746174/999
X= 618079825.9
Again
It took one crystal to raise 999 zombies
It will take y crystal to raise 6174 zombies
Mathematically
One = 999
Y =( 6174*1)/999
Y= 6.18 crystals
what is 10 times 2 divided by 5.
Answer:
4(four)
Step-by-step explanation:
You take the number 10×2=20
Then,20÷5=4
Four{4}is your answer
Answer:
4Step-by-step explanation:
[tex]10 \times 2 \div 5[/tex]
Multiply the numbers
[tex] = 20 \div 5[/tex]
Divide :
[tex] = 4[/tex]
Hope this helps..
Good luck on your assignment..
Justin weighed 8 lb 12 oz when he was born. At his two-week check-up, he had gained 8 ounces. What was his weight in pounds and ounces?
Answer:
9 lb 4 oz
Step-by-step explanation:
Justin weighed 8 lb 12 oz at birth. He gained 8 ounces by his two-week checkup. So,
8 lb 12 oz + 8 oz = 8 lb 20 oz
But, 16 oz equals one pound. So,
20 oz = 1 lb with 4 oz remaining
Now add them together.
8 lb + 1 lb 4 oz = 9 lb 4 oz
Justin's weight is 9 lb 4 oz.
Hope that helps.
Which statement about the function is true?
The function is positive for all real values of x where
x > –4.
The function is negative for all real values of x where
–6 < x < –2.
The function is positive for all real values of x where
x < –6 or x > –3.
The function is negative for all real values of x where
x < –2.
Answer:
b
Step-by-step explanation:
The function is positive for all real values of x where
x < –6 or x > –3.
The function is negative for all real values of x where
x < –2.
What system shows the correct numbers to multiply by the coefficients in order to eliminate y from the first two
equations when applying the linear combination method?
50+ 2 = 0
2x – 3y = -19
o
3 (5+2g = 0)
2 (2x – 3y = -19)
o
–3 (5x + 2y = 0)
12 (2x – 3y = –19)
-2 (5x + 2y = 0)
5 (2x – 3y = -19)
s -2(5x + 2y = 0)
1-5 (2x - 3y = -19)
Answer:
3 (5x+2y = 0)
2 (2x – 3y = -19)
Step-by-step explanation:
5x+2y=0 (1)
2x-3y=-19 (2)
To eliminate y from the first two equation when applying the linear combination method
We will multiply y Equation (1) and (2) with 3 and 2 respectively so that the coefficients of y in the two equations +6 and -6 respectively
3(5x+2y=0)
2(2x-3y=-19)
We have,
15x+6y=0 (3)
4x-6y= -38 (4)
Add Equation (3) and (4)
19x=-38
x= -2
Substitute x= -2 into (1)
5x+2y=0
5(-2)+2y=0
-10+2y=0
-10= -2y
y=-10/-2
=5
y=5, x=-2
..............................
Answer:
D y = 9/x
Step-by-step explanation:
An inverse variation is of the form
xy = k where k is a constant
We can write this as
y = k/x
The only equation that is of this form is
D y = 9/x
Answer:
[tex]\boxed{\mathrm{Option \: D}}[/tex]
Step-by-step explanation:
Inverse variation is written as:
[tex]y=\frac{k}{x}[/tex]
Where k is the constant of proportionality.
A ladder is placed against a tree. The bottom is located 5 feet from the base of the tree and the top of the ladder is 18 feet up the tree. What is the angle created between the ladder and tree? Include a sketch that shows all known information and clearly shows what you need to find. Show all work and give the answer rounded to the nearest tenth of a degree.
Answer:
The angle created between the ladder and tree is [tex]15.5^{0}[/tex].
Step-by-step explanation:
The required sketch is shown in the attachment to this answer.
Applying the appropriate trigonometric function to the question, we have;
Tan θ = [tex]\frac{Opposite side}{Adjacent side}[/tex]
= [tex]\frac{5}{18}[/tex]
= 0.2777777777
⇒ θ = [tex]Tan^{-1}[/tex] 0.2777777777
= 15.5241
= [tex]15.5^{0}[/tex]
Therefore, the angle created between the ladder and tree is [tex]15.5^{0}[/tex].
If Andrew has $72 in his wallet, what is the largest number of bags of sugar he can afford? (Each bag of sugar costs $6.33)
Answer:
11 bags
Step-by-step explanation:
$72/6.33=11.3744075829 or 11.4
11.4 estimate= 11
Answer:
11 bags of sugar
Step-by-step explanation:
In order to find the answer to this question simply divide the amount of money Andrew has by the amount of money it cost per bag of sugar.
[tex]S=6.33[/tex]
[tex]W=72[/tex]
[tex]72\div6.33=11.3744075829[/tex]
Round:
[tex]=11[/tex]
Hope this helps.
What is the solution set of |–x| = 3.5? {–3.5, 3.5} {–3.5} {3.5} {7}
Answer:
{-3.5, 3.5}
Step-by-step explanation:
Interpreting
|-x| = 3.5
gives
3.5 = +(-x) or 3.5 = -(-x)
or
x = + / - 3.5
so the answer is
{-3.5, 3.5}
Answer:
A
Step-by-step explanation:
Which equation is true for the value b = 10? A. 2(b + 4) = 16 B. 2(b + 2) = 40 C. 3(b – 2) = 24 D. 2(8 + b) = 42 E. 3(b – 4) = 20
Answer:
C is the correct answer
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
have a good day
Help please you need to find the rise in the blue triangle. Thank you!!
Answer:
12.65
Step-by-step explanation:
In the case of the blue triangle, to calculate the rise, which would be the increase, therefore it would be the hypotenuse formed by the arrow.
We have to Pythagoras is:
h ^ 2 = a ^ 2 + b ^ 2
In this case:
a (x-axis) = 4
b (y-axis) = 12
replacing:
h ^ 2 = 4 ^ 2 + 12 ^ 2
h ^ 2 = 160
h = 12.65
Which means that the rise in the blue triangle is 12.65 units