A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 230. (a) Find an expression for the number of bacteria after t hours. (b) Find the number of bacteria after 2 hours. (Round your answer to the nearest whole number.) P(2) = ___bacteria (c) Find the rate of growth after 2 hours. (Round your answer to the nearest whole number.) P'(2) = ___bacteria per hour (d) When will the population reach 10,000? (Round your answer to one decimal place.) t = ___hr
Answers
Answer:
P(t) = 100·2.3^t529 after 2 hours441 per hour, rate of growth at 2 hours5.5 hours to reach 10,000Step-by-step explanation:
It often works well to write an exponential expression as ...
value = (initial value)×(growth factor)^(t/(growth period))
(a) Here, the growth factor for the bacteria is given as 230/100 = 2.3 in a period of 1 hour. The initial number is 100, so we can write the pupulation function as ...
P(t) = 100·2.3^t
__
(b) P(2) = 100·2.3^2 = 529 . . . number after 2 hours
__
(c) P'(t) = ln(2.3)P(t) ≈ 83.2909·2.3^t
P'(2) = 83.2909·2.3^2 ≈ 441 . . . bacteria per hour
__
(d) We want to find t such that ...
P(t) = 10000
100·2.3^t = 10000 . . . substitute for P(t)
2.3^t = 100 . . . . . . . . divide by 100
t·log(2.3) = log(100)
t = 2/log(2.3) ≈ 5.5 . . . hours until the population reaches 10,000
Related Questions
One advantage to using your debit card is: A:You don’t have to subtract it from your checking account balance B: It is convenient C:You can spend as much as you want D:You can give your friend the PIN number in case you forget it. Plz help me
Answers
Answer:
B.
Step-by-step explanation:
First, you never want to give out your banking information to anyone, so D is incorrect. A is incorrect because a debit card withdraws money from your checking account to pay for items you purchase. C is also incorrect because you can only spend the same amount of money in your checking account.
Most of the seniors at Roosevelt High School took a math class this year. The graph shows the breakdown: Find the number of degrees for each math class. State the class and the degrees. Show your work.
Answers
Answer:
Step-by-step explanation:
Since, sum of central angles of a circle = 360°
Therefore, sum of all central angles formed by each math class = 360°
And measure of angles formed by each class will be in the same proportion as the percentage of seniors in each class.
Geometry → 27% of 360° = 97.2°
Precalculus → 4% of 360° = 14.4°
Advanced algebra → 33% of 360° = 118.8°
Consumer math → 36% of 360° = 129.6°
Answer:
There are 360 degrees in a circle so I need to do the percentage of 360
Geometry: 27% of 360 = 97.2 °
Consumer Math: 36% of 360 = 129.6 °
Advanced Algebra: 33% of 360 = 118.8 °
Precalculus: 4% of 360 = 14.4 °
PLS HELP ME IVE BEEN TRYING
Answers
Answer:
try and let me know is it correct or not line A-4 lineB-8
Step-by-step explanation:
i also use mathswatch
The solution of the following System of linear equation 2x-3y=-11 is x+3y=8 a) (1,3) b) (-1,3) c) (1,-3) d) (-1,-3)
Answers
Answer:
(-1,3)
Step-by-step explanation:
Because bruh
If you were solving the system of linear equations below by using Elimination, choose the answer that would be the best first step of solving with Elimination.
Answers
Answer:
multiply the bottom equation by 3
Step-by-step explanation:
we multiply to make the values of x same
9x+5y=1
-3x+2y=10 after= -9x+6y=10 thus one can eliminate the x value 9x
y=-x^2-2x-5 whats the vertex of this parabola
Answers
Answer:
The vertex is (-1, -4)
Step-by-step explanation:
Let's find the vertex by completing the square of y= -x^2 - 2x - 5.
Isolate the first two terms inside parentheses: y= -(x^2 + 2x) - 5
Now complete the square of the expression inside these parentheses:
y = -(x^2 + 2x + 1 - 1) - 5
and rewrite this as
y = -(x + 1)^2 + 1 - 5, or
y = -(x + 1)^2 - 4
(x + 1) tells us that the x-coordinate of the vertex, h, is -1, and the -4 term tells us that the y-coordinate, k, is -4.
The vertex is (-1, -4)
14. What is the percent decrease on a DVD recorder that is marked down from $400 to $350?
1. 87.5%
2. 20%
3. 12.5%
5. 14.29%
Answers
Answer:
12.5%
Step-by-step explanation:
Percent decrease is calculated as
[tex]\frac{decrease}{original}[/tex] × 100%
Decrease = $400 - $350 = $50 , thus
percent decrease = [tex]\frac{50}{400}[/tex] × 100% = [tex]\frac{50(100)}{400}[/tex] = 12.5%
The percent decrease on a DVD recorder that is 12.5%. The correct option is 3
What is the percentage?A percentage is a minimum number or ratio that is measured by a fraction of 100.
let the value of which a thing is represented in percentage is "a'
let the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), therefore we will first divide the whole part in 100 parts and then we multiply it with b so that we can get b items per 100 items(that is exactly what b per cent means).
Hence, that thing in number is
(a/100)x b
Percent decrease is calculated as;
Decreased in price/original price × 100%
Decrease = $400 - $350 = $50 , thus
Therefore, percent decrease = 50/400 × 100%
= 12.5%
Learn more about percentages;
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Explain how to solve for the rate in a simple interest equation if you are given the interest amount, the principal, and the time.
Answers
Answer:
divide the interest amount by the product of the principal and time
Step-by-step explanation:
The simple interest formula is I = prt where I is the interest, p is the principal, r is the rate and t is the time (in years). Rewriting this formula so that r is the subject we get r = I / pt. Therefore the answer is divide the interest amount by the product of the principal and time.
Latisha worked for six hours and 45 minutes how should she write that on her time card
Answers
Answer:
Hey there!
6 hrs 45 mins = 405 mins, or 6.75 hours.
Hope this helps :)
Kendrick rolls a pair of standard six-sided dice. What is the probability that both faces show an odd number?
Answers
Answer:
1/4 , 25%
Step-by-step explanation:
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What are the zeros of f(x) = x2 - 8x+ 15?
Answers
Answer:
x=5 x=3
Step-by-step explanation:
f(x) = x^2 - 8x+ 15
Factor
What two numbers multiply to 15 and add to -8
-5*-3 = 15
-5+-3 = -8
f(x) = (x-5) (x-3)
Setting equal to 0
0= (x-5) (x-3)
Using the zero product property
x-5 =0 x-3=0
x=5 x=3
Sarah cannot completely remember her four-digit ATM pin number. She does remember the first two digits, and she knows that each of the last two digits is greater than 5. The ATM will allow her three tries before it blocks further access. If she randomly guesses the last two digits, what is the probability she will get access to her account
Answers
Answer:
3/16 or 0.1875
Step-by-step explanation:
Since she remembers the first two digits, she only has to guess the last two digits. If both digits are greater than 5, there are 4 possible alternatives for each digit (6, 7, 8 or 9).
In three tries, the probability that she will get it right is:
[tex]P=\frac{3}{4*4}\\P=\frac{3}{16}=0.1875[/tex]
The probability she will get access to her account is 3/16 or 0.1875.
what is an inequality that represents this sentence?
if seven times a number is decreased by three, the result is less than thirty.
Answers
Answer:
7x-3<30
Step-by-step explanation:
7 times a number = 7x
is decreased by 3 = -3
the result is less than 30 = <30
Answer:
7x - 3 < 30
Step-by-step explanation:
We can put "seven times a number" as 7x since a number is unknown -->
now decreased is subraction so we have 7x - 3 -->
the result is less than thirty is that the difference must be less then 30.
so, 7x - 3 < 30.
Hope this helps!
(not a joke question) 81 1/4 is equal to 2. true or false and please explain why!
Answers
Answer:
Fasle
Step-by-step explanation:
81 1/4s would be 81/4 which would be 20 and 1/4
Mariah is completing a language arts review sheet she estimates that it takes her one minute to complete each multiple-choice question and six minutes to complete each essay question this equation represents the total time it takes her to complete X multiple choice question and y essay question X plus 6Y equals 36 select the correct answer from each drop down menu
Answers
Answer:
The answer is below
Step-by-step explanation:
Given the time taken to answer each multiple choice question as one minute, the time taken to x multiple choice question = 1 minute/question × x questions = x minutes
Given the time taken to answer each essay question as six minute, the time taken to y essay question = 6 minute/question × y questions = 6y minutes
Therefore the total time taken to complete X multiple choice question and y essay questions = the time taken to x multiple choice question + the time taken to y essay question = x + 6y
Answer:
directly off of edmentum
can anyone help me to answer this question
Answers
Answer:
0 or 6
Step-by-step explanation:
2aa = 12a
2a² = 12a
Subtract 12a from both sides.
2a² - 12a = 0
Factor left side of equation.
2a(a - 6)=0
Set factors equal to 0.
2a = 0
a =
a - 6 = 0
a = 6
Explanation:
2A x A = 12A
2A=12A/A
2A=12
A=12/2=6
Now let’s take A = 6 and try it in the equation
2(6) x 6=12(6)
12 x 6= 12 x 6
72= 72
So A = 6 is the right answer
how can knowledge of circles apply to daily life??
Answers
Answer:
sdgsdgsdgsdgsdgsd
Step-by-step explanation:
gsdgsdgsdgsdgsd
What is the volume of the sphere shown below?
O A. 69127 units
O B. 23047 units
O C. 1927 units
O D. 57677 units
Answers
Answer:
Step-by-step explanation:
r = 12
V = 4*pi * r^3 / 3
V = 4 * 3.14 * 12^3 /3
V = 4 * 3.14 * 1728 / 3
V = 4 * 5425.92 /3
V = 21703.68/3
V = 7234.56
None of the answers look correct.
Help!!!!! please!!!!!
Answers
Answer: A
Step-by-step explanation:
In a cylinder A=2πrh+2πr^2. Plugging in the values of the problem gives you about 489.8
In the figure, angle A measures 45° and angle E measures 15°.
The measurement of angle C is___
The measurement of angle D is___
Answers
Answer:
m<C = 45
m<D = 30
Step-by-step explanation:
m<A + m<B + m<C = 180
45 + 90 + m<C = 180
m<C = 45
m<E + m<A = 60
60 + 90 + m<D = 180
m<D = 30
How did the temperature change if:
It increased by 50 % and
then decreased by
33 1
— %
3
Answers
Answer
it didnt change at all
Step-by-step explanation:
i gotcha help
The vertex of this parabola is at (-3,-2). Which of the following could be its
equation?
(-3,-2)
O A. y=-2(x-3)2 + 2
O B. y=-2(x+3)2 + 2
O C. y=-2(x-3)2-2
O D. y=-2(x+3)2 - 2
Answers
Answer:
y=-2(x+3)^2-2
Step-by-step explanation:
Answer:
D y= -2(x+3)2 - 2
Step-by-step explanation:
The vertex is (h,k )
h = -3
k= -2
These equations are in vertex form.
Vertex form: y= a(x-h)^2 + k
so,
y= a(x- (-3)) ^2 + (-2)
y= a (x+3) ^2 -2
What is the measure of ∠x angles are not necessarily drawn to scale.
Answers
Answer:
58 degrees
Step-by-step explanation:
The other two angles are 56 and 66 degrees and you know that all the angles add up to 180 degrees.
So just subtract:
180-56-66= 58 degrees
it works because the lines are parallel in the picture.
Identify the parts relating to CircleA. What is Line F G? Secant What is Line segment D B? Tangent What is Line segment D H? Secant What is AC? Radius
Answers
Answer:
Line FG secant
Line segment DH secant
Line segment DB tangent
Line segment AC radius
Step-by-step explanation:
A Secant is a line that passes through the two points on a circle.It cuts the circle on two points.
Line FG is a secant as it passes through two pints.
Line segment DH is also a secant as it passes through two points.
A tangent is a line that passes through only one point on a circle. It is outside the circle. It is perpendicular to the radius at the point where it touches the circle.
Line segment DB is a tangent as it passes through only one point.
Radius is the line segment joining the center of the circle and any point on the circumference of the circle. It is half of the diameter.
Line segment AC is a radius as it joins the center of the circle with the circumference.
Answer:
1) FG -- Secant
2) DB -- Tangent
3) DH -- Secant
4) AC -- Radius
Step-by-step explanation:
1 Negative numbers do not need the
negative sign (-) in front of them.
O True
O False
Answers
Answer:
The answer is False
Step-by-step explanation:
Answer:
FALSE ALL NEGATIVE NUMBERS NEED A NEGATIVE SIGHT(-)
Step-by-step explanation:
-1,-2,-3, PLEASE MARK BRAINLEST
A roof has a cross section that is a right triangle. The diagram shows the approximate dimensions of this cross section. Find the height h of the roof. Round your answer to the nearest tenth.
Answers
Answer:
The height of the roof is 25 ft.
Step-by-step explanation:
Consider the right angled triangle BCD.
Determine the measure of side BD using the Pythagoras theorem
[tex]BD^{2}=BC^{2}+CD^{2}\\\\BD=\sqrt{BC^{2}+CD^{2}}\\\\=\sqrt{10^{2}+5^{2}}\\\\=\sqrt{125}[/tex]
Compute the measure of angle x as follows:
[tex]tan\ x=\frac{BC}{CD}\\\\tan\ x=\frac{10}{5}\\\\tan\ x=2\\\\x=tan^{-1}2\\\\x=63.4[/tex]
Now consider the triangle ABD.
The hypotenuse AD is the height of the roof.
Determine the measure of side AD as follows:
[tex]cos\ x=\frac{BD}{AD}\\\\cos\ 63.4=\frac{\sqrt{125}}{AD}\\\\0.4478=\frac{\sqrt{125}}{AD}\\\\AD=\frac{\sqrt{125}}{0.4478}\\\\AD=24.967\\\\AD\approx 25[/tex]
Thus, the height of the roof is 25 ft.
Answer:
25ft :)
Step-by-step explanation:
Gracie has 1/2 of a cantaloupe that she wants to divide. How many 1/6s of a cantaloupe are there in 1/2 of a cantaloupe
Answers
Answer:
There are 6 1/6 slices in half a cantaloupe
Answer:
3
Step-by-step explanation:
(1/2)/(1/6)= 1/2*6/1=3 it has 3 (1/6)s
The diagram represents a difference of squares. A 2-column table with 2 rows. The labels for the columns and rows are blank. First column entries are m squared, 6 m. Second column entries are negative 6 m, negative 36. What are the factors of m2 – 6m + 6m – 36? (m – 2)(m + 18) (m – 3)(m + 3) (m – 4)(m + 9) (m – 6)(m + 6)
Answers
Answer:(m-6)(m+6)
the last one on edge
Step-by-step explanation:
math
An expression is a set of numbers, variables, and mathematical operations. The factors of the given expression m²–6m+6m–36 are (m+6)(m–6). The correct option is D.
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.
The factors of the given expression can be found as shown below.
m² – 6m + 6m – 36
Taking m as the common factor from the first two terms of the expression and 6 as the common factor from the last two terms,
= m(m–6) + 6(m–6)
Taking (m–6) as the common factor from the two terms,
= (m+6)(m–6)
Hence, the factors of the given expression m²–6m+6m–36 are (m+6)(m–6).
Learn more about Expression here:
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How can we find HCF of a number
Answers
Answer:
We can find the highest common factor of a number by listing down all the factors of that number. The greatest factor from that list is the highest common factor.
How to find HCF of two numbers
❒ Explanation -:We can find the HCF of any numbers using three methods -:
Common FactorPrime FactorisationDivision Method[tex] \small \underline {\underline{\bf Common \: Factor \: Method }}[/tex]
[tex] \small \orange{\bf{ Step \: 1 :}}[/tex]
Find all factors of the given number[tex] \small \blue{\bf{ Step \: 2 :}}[/tex]
Find the common factor[tex] \small \purple{\bf{ Step \: 3 :}}[/tex]
Find out the highest common factor from the common factor . The highest common factor is the HCF of the number.[tex] \small \underline{\underline{\bf{ Prime \: Factorisation }}}[/tex]
[tex] \small \orange{\bf{ Step \: 1 :}}[/tex]
Find the prime factor of the given number by division method.[tex] \small \blue{\bf{ Step \: 2 :}}[/tex]
Find out the common prime factor.[tex] \small \purple{\bf{ Step \: 3 :}}[/tex]
The product of the common prime factor gives the HCF of the number.[tex] \small \underline{ \underline{\bf{ Division \: Method}}}[/tex]
[tex] \small \orange{\bf{ Step \: 1 :}}[/tex]
Divide the greater number by the smaller number. By the remainder in step 1 divide the smaller number[tex] \small \blue{\bf{ Step \: 2 :}}[/tex]
By the remainder in Step 2 divide the remainder obtained in Step 1.[tex] \small \purple{\bf{ Step \: 3 :}}[/tex]
Complete in the same way till no remainder is left.[tex] \rule{91mm}{3pt}[/tex]
47:PLEASE HELP Find the y-intercept of -x +2y=20
Answers
Answer:
(0,10)
Step-by-step explanation:
-x + 2y = 20
2y = x +20
y = 1/2x + 10
This is slope-intercept form. The y-intercept is 10.
(0,10)
Answer:
(0, 10)
Step-by-step explanation:
Can be simplified to
2y = x+20 by adding x to both sides
then divide by 2 to get to slope intercept form: y = ax+b
b is the y-intercept
y = 1/2x + 10
so the answer is 10