A) The equation for the growth of bacteria over time is : n(t) = 27( [tex]e^{25t}[/tex])
B) The number of bacteria the would be in 5 minutes 1 hour is :
n(5mins) = 215.055 , n(1) = 1944132282109.422
C) The time it will take for the bacteria to reach a population of 10,000 is : t = 0.237 hours
Determine the Equation, number of bacteria and time takenApplying the mathematical growth and decay modelling
a. n(t) = [tex]n_{0}[/tex] [tex]e^{rt}[/tex]
[tex]n_{0}[/tex] = initial amount of bacterial
[tex]e^{rt}[/tex] = exponent
r = rate
t = time
n(t) = 27( [tex]e^{25t}[/tex])
b. for 5 minutes
converting 5 minutes to hours; we divide by 60 minutes
[tex]\frac{5}{60}[/tex] = 0.083 hour
n(5 mins) = 27( [tex]e^{25t}[/tex])
n(5 mins) = 27( [tex]e^{25 * 0.083}[/tex])
n(5 mins) = 27( [tex]e^{2.075}[/tex])
n(5mins) = 27( 7.965)
n(5mins) = 215.055
For 1 hour we have
n(1) = 27( [tex]e^{25t}[/tex])
n(1) = 27( [tex]e^{25 * 1}[/tex])
n(1) = 27( [tex]e^{25}[/tex])
n(1) = 27 * (72004899337.386)
n(1) = 1944132282109.422
c. How long will it take for the bacteria to reach a population of 10,000?
10000 = 27( [tex]e^{25t}[/tex])
[tex]\frac{10000}{27}[/tex] = ( [tex]e^{25t}[/tex])
370.370 = ( [tex]e^{25t}[/tex])
㏑ (370.370 ) = ㏑ ( [tex]e^{25t}[/tex])
5.915 = 25t
[tex]\frac{5.915}{25}[/tex] = t
t = 0.237 hours
In conclusion this type of question can be done by mathematical modelling
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Your mom is building a garden around a fountain she has a space marked out but decides she wants to enlarge it without altering the center of it what type of transformation is this
Answer:
u didnt give out the choses but it might be a chance to be dilation
Step-by-step explanation:
"the action or condition of becoming or being made wider, larger, or more open."
since she enlarge it without altering the center of it
Find the surface area of a rectangular prism (like the rectangular prism below) that is 16 feet by 1.5 feet by 2 feet.
Solve and get 30pts!!
Answer:
Surface area of the rectangular prism=
Step-by-step explanation:
Given Dimensions of the rectangular prism are:
[tex]Length(L)=16yards[/tex]
[tex]Width(w)=2yards[/tex]
[tex]Height(H)=1.5yards[/tex]
Surface Area of a rectangular prism=
[tex]2(L*W+W*H+H*L)[/tex]
[tex]=2(16*2+2*6+6*16)[/tex]
[tex]=2(32+12+96)[/tex]
[tex]=2(140)[/tex]
[tex]=140yards^2[/tex]
The surface area of the rectangular prism is [tex]140yards^2[/tex]
pls need help in math<3
[tex]8 \times 60 = 480 \: \: min[/tex]
For 3 people
____________________________________________
Thus for each person it may take :
[tex]480 \div 3 = 160 \: \: min[/tex]
And for 5 people it will take :
[tex]160 \times 5 = 800 \: \: min[/tex]
Answer is 780 minutes
2.6 hours = 1 person
8/3 = 2.66 (continuing)
5 x 2.6 = 780 minutes (13 hours)
So, 5 people = 780 minutes
780, if rounded, = 800
The first sequence rule is subtract 10 starting from 55. The second sequence rule is add 3 starting from 6. What is the first number that appears in both sequences? 15
12
9
5
Answer:
15
Step-by-step explanation:
Trust me it 15.
Too long to explain...
It took a car 3 hours to travel from town a to town b the wheel of a car completes a rotation in one second how many degrees has it turned
The number of degrees that have been turned by the car when it travels from town a to town b will be 1080°.
How to calculate the number of degrees?From the information given, it was stated that it took a car 3 hours to travel from town a to town b and the wheel of a car completes a rotation.
In this case, a rotation is 360°, since there are 3 rotations, the degrees will be:
= 360 × 3
= 1080°
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The binomial (a 5) is a factor of a2 7a 10. what is the other factor? (a 2) (a 5) (a−2) (a−5)
An expression has numbers, variables, and mathematical operations. The other factor of the given binomial is a²+7a+10 except (a+5) is (a+2).
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
To find the other factor of the binomial a²+7a+10, we can write it as,
[tex]a^2+7a+10\\\\=a^2+5a+2a+10\\\\=a(a+5)+2(a+5)\\\\=(a+5)(a+2)[/tex]
Thus, the other factor of the given binomial is a²+7a+10 except (a+5) is (a+2).
Learn more about Expression:
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Answer:
(a + 2)
Step-by-step explanation:
Write in standard form
(4.6 x 10^6) x (5 x 10^-4)
uhh lol help?
'' The Jurassic period (199.6 million to 145.5 million years ago) was characterized by a warm, wet climate that gave rise to lush vegetation and abundant life. Many new dinosaurs emerged—in great numbers. Among them were stegosaurs, brachiosaurs, allosaurs, and many others. Combined these three dinosaurs measured over 749 feet tall. The brachiosaurs was four times larger than the allosaurs, the stegosaurs was twice the size of the allosaurs. How tall was the brachiosaurs? "
A. 107 feet
B. 214 feet
C. 321 feet
D. 428 feet
6 cm 4 cm 10 cm What is the surface area of the figure? square centimeters
Answer:
2 x 10 x 4 + (4 + 10) x 2 x 6 = 80 + 168 = 248
1.
Please show steps
Write the expression in simplest form.
( Sqrt x-sqrt3y) (sqrt x + sqrt3y)
[tex]\left(\sqrt x - \sqrt{3y} \right) \left(\sqrt x + \sqrt{3y} \right)\\\\=\left(\sqrt x\right)^2 - \left(\sqrt{3y} \right)^2\\\\=x -3y[/tex]
x - 3y
Solving Stepwise:
[tex]\hookrightarrow \sf \left(\sqrt{x}-\sqrt{3y}\right)\left(\sqrt{x}+\sqrt{3y}\right)[/tex]
[tex]\sf apply \ the \ rule : \bold{\left(a-b\right)\left(a+b\right)=a^2-b^2}[/tex][tex]\hookrightarrow \sf \left(\sqrt{x}\right)^2-\left(\sqrt{3y}\right)^2[/tex]
[tex]\hookrightarrow \sf x-3y[/tex]
Which of the following is equal to? ( in picture)
Answer:
2 option hope it helps
Hence, option D is correct.
Explanation:[tex]\dashrightarrow \sf \sqrt{\sqrt[3]{2}}[/tex]
apply radical rule
[tex]\dashrightarrow \sf \left(2^{\dfrac{1}{3}}\right)^{\dfrac{1}{2}}[/tex]
apply exponent rule
[tex]\dashrightarrow \ \sf 2^{\dfrac{1}{6}}[/tex]
A large aircraft is flying on a bearing of 310° (50° west of north) with an airspeed of 700 mph. It is being affected by a 100 mph wind
blowing towards the west, as shown in the diagram below.
The distance, R, as indicated in the diagram, that the plane has travelled after 1 hour is, to the nearest mile,
Answer:
779
Step-by-step explanation:
Aiming to get the value of formula
Given that
50° + 80² = 140°.
:: Cos140² = 100 + 700²³ - R²
kaw of ousines axivox. T
·· R² = 607246
R≈ 780 miles
• The result is T80 miles
Which expressions are perfect square trinomials? check all that apply. x2 16x 8 x2 14x 49 x2 – 5x 25 x2 – 24x 144 x2 9x – 81
The perfect square trinomial will be [tex]\rm x^2+14x+49[/tex] , [tex]x^2-24x+144[/tex]Expression 2 and 4 are correct.
What are trinomials?A mathematical expression with three terms or three monomials is called a trinomial. Polynomials having only three terms are known as trinomials.
The second and fourth expression seems to be the perfect square let's check it.
Expression 2;
[tex]x^2 + 14x+49 \\\\ x^2+7x+7x+49 \\\\ x(x+7)+7(x+7)\\\\ (x+7)(x+7) \\\\ (x+7)^2[/tex]
Expression 4;
[tex]x^2-24 x +144 \\\\ x^2-12x-12x+144 \\\\ x(x-12)-12(x-12) \\\\ (x-12)^2[/tex]
Hence the perfect square trinomial will be [tex]\rm x^2+14x+49[/tex] , [tex]x^2-24x+144[/tex] .Expressions 2 and 4 are correct.
To learn more about the trinomials refer to the link;
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Answer:
Options 2 and 4
Step-by-step explanation:
Gale the birthday clown is blowing up a fun spherical shaped balloon at a constant rate of 100 cubic inches per minute. How fast is the radius increasing when the sphere contains 50 cubic inches of clown breath
Answer:
Step-by-step explanatio the way the question is phrased Is confusing
An auditorium has 25 rows of seats and a total of 500 chairs.
How Many chairs in each row?
(21x⁵· y⁸)² divided by 3x²
show ur work
[tex]\cfrac{(21x^5y^8)^2}{3x^2}\implies \cfrac{((3)(7)x^5y^8)^2}{3x^2}\implies \cfrac{3^2\cdot 7^2x^{5\cdot 2}y^{8\cdot 2}}{3x^2}\implies \cfrac{3^2}{3}\cdot \cfrac{7^2 x^{10} y^{16}}{x^2} \\\\\\ 3\cdot 7^2 x^{10}\cdot x^{-2} y^{16}\implies 3\cdot 49x^{10-2}y^{16}\implies 147x^8y^{16}[/tex]
What’s the distance between -50 and 30
Answer:
80
Step-by-step explanation:
-50+x=30
x=80
Answer:
im pretty sure its 80
Step-by-step explanation:
how do you solve this
Answer: 254.5
Step-by-step explanation:
HELP ME PLEASE ILL MARK U THE BRAINLEST THING PLEASEE I BEG
Answer:
See below ~
Step-by-step explanation:
a)
The intersection of the points represents where they had travelled the same distance at that timeb)
Leslie passed Gale at approximately 2:00 PMc)
Leslie had travelled about 20 miles when they passed Galed)
Between 1:30 and 3:00, Gale had not moved any distance w.r.t time, meaning she had stopped, presumably to take a break, or to fix something that may have happened to her bikee
Rate of covering distance = 10 miles/1 hourTotal distance = 60 milesTotal time = 60/10 = 6 hoursNoon + 6 hours = 6:00 PMAgnes pays state income tax equal to 3.75% of her federal taxable income. she pays federal income tax equal to 28.4% of her federal taxable income. this year, she paid $15,449.60 in federal income tax. how much did agnes pay in state income tax? a. $573.36 b. $4,387.69 c. $1,170.04 d. $2,040.00 please select the best answer from the choices provided a b c d
Based on the information the amount that Agnes paid as state income tax is $2,040.
What is the federal income?Federal Income Tax is the tax system in the United States, levied and governed by Internal Revenue Services (IRS) which helps determine the tax that is charged on the income earned by individuals, corporates, and various other legal entities.
The first step is to calculate Agnes' federal taxable income.
Federal taxable income=$15449.60/0.284
Federal taxable income= $54,400
The second step is to calculate Agnes' state income tax.
State income tax=0.0375 ×$54,400
State income tax=$2,040
Hence, the amount that Agnes paid as state income tax is $2,040.
Learn more here federal income:
brainly.com/question/12600097
Answer:
its d
Step-by-step explanation:
y=2x^2-18x+40 solved in square root
Answer:
x=-4
or
x=-5
Step-by-step explanation:
STEP
1
:
Equation at the end of step 1
((0 - 2x2) - 18x) - 40 = 0
STEP
2
:
STEP
3
:
Pulling out like terms
3.1 Pull out like factors :
-2x2 - 18x - 40 = -2 • (x2 + 9x + 20)
Trying to factor by splitting the middle term
3.2 Factoring x2 + 9x + 20
The first term is, x2 its coefficient is 1 .
The middle term is, +9x its coefficient is 9 .
The last term, "the constant", is +20
Step-1 : Multiply the coefficient of the first term by the constant 1 • 20 = 20
Step-2 : Find two factors of 20 whose sum equals the coefficient of the middle term, which is 9 .
-20 + -1 = -21
-10 + -2 = -12
-5 + -4 = -9
-4 + -5 = -9
-2 + -10 = -12
-1 + -20 = -21
1 + 20 = 21
2 + 10 = 12
4 + 5 = 9 That's it
6. What is the area of the shared region to the nearest
tenth of square ft?
[tex]\textit{area of a circular ring}\\\\ A=\pi (R^2-r^2)~~ \begin{cases} R=\stackrel{larger}{radius}\\ r=\stackrel{smaller}{radius}\\[-0.5em] \hrulefill\\ R=50\\ r=36 \end{cases}\implies \begin{array}{llll} A=\pi (50-36)\implies A=14\pi \\\\\\ A\approx 44.0 \end{array}[/tex]
The radius of a circle is 3 ft. Find its area in terms of
π
π.
area of circle = πr² (where "r" is the radius)
===========
Here the radius: 3 ft
Area:
πr²π(3)²9πPlease help with 12. Simplify.
[tex]\dfrac 1{x+y} + \dfrac{3}{x-y} + \dfrac{2}{x^2-y^2} \\\\\\=\dfrac 1{x+y} + \dfrac{3}{x-y} + \dfrac{2}{(x+y)(x-y)}\\ \\\\=\dfrac{x-y+3(x+y)+2}{(x+y)(x-y)}\\\\\\=\dfrac{x-y+3x+3y+2}{(x+y)(x-y)}\\\\\\=\dfrac{4x+2y+2}{(x+y)(x-y)}\\\\\\=\dfrac{2(2x+y+1)}{(x+y)(x-y)}[/tex]
A container in the shape of a rectangular prism has a height of 2 feet. Its length is four
times its width. The volume of the container is 200 cubic feet. Find the length and width of
the container.
Answer:
length = 20 feet and width = 5 feet
Step-by-step explanation:
Volume is equal to volume = height * width * length. The questions tells us the total volume is 200 cubic feet and that the lenght is equal to length = 4w. Set up the equation 4w * w * 2 = 200 cubic feet. Multiply to get 8w^2 = 200 and solve for w.
Subtract and write your answer as mixed number. 5 3/4 - 1 2/3
Answer: 4 1/12
Step-by-step explanation:
What is the circumference (rounded to the nearest meter) of a circular swimming pool that has a radius of 10 meters?
A. 120
B. 63
C. 60
D. 31
E. 30
Please help with the answer and explain it to me.
Answer:
63
Step-by-step explanation:
You get the answer by multiplying the radius by 2 to get the diameter and then multiplying the result by pi or 3.14, which gives you 62.83 and then round it up which is 63
Tim bought 555 crayons that came in packs of of 15. There were 7 colors of crayons. How many crayons did Tim buy
Answer:
555
Step-by-step explanation:
The packs the colors came in and the colors do not matter. The initial value of crayons is 555.
For 5 points and brainliest to the best correct answer, find the missing measures.
Thank you
Answer:
x = 7y = 97°z = 19Step-by-step explanation:
The markings on the figure show this to be a parallelogram. That means opposite sides are congruent. Because the sides are parallel, "alternate interior" angles are also congruent.
__
Angle y forms a linear pair with the one marked 83°, so is supplementary to it:
y = 180°-83° = 97°
__
The angle marked y is an exterior angle to the triangle containing the angle marked (7x -5)°. As such, it is equal to the sum of the remote interior angles, the one marked (7x -5)° and the unmarked one that is congruent to (3x +32)°.
(7x -5) +(3x +32) = 97 . . . . . angle relations in the left-side triangle
10x +27 = 97 . . . . . . . collect terms
10x = 70 . . . . . . . . subtract 27
x = 7 . . . . . . . . divide by 10
__
The side marked Z is congruent to the opposite parallel side, so ...
z = 19
__
The missing measures are ...
x = 7y = 97°z = 19_____
Additional comment
You can also find the value of y by adding up the interior angles of the right-side triangle. The one not shown there is "alternate interior" to the one marked (7x -5)°, hence has the same measure. This gives ...
(7x -5) +(3x +32) +83 = 180
Subtracting 83° from both sides gives the equation we used above.
Suppose a car burns 1 gallon of gas in 25 miles. How much gas will be burned on a trip
of 400 miles?
Answer:
16
Step-by-step explanation:
400 miles / 1 gallon every 25 miles = 16 gallons total