Answer:
Step-by-step explanation:
A bacteria culture contains 1500 bacteria initially and doubles every hour. Find a function N that models the number of bacteria after t hours. Write out how many bacteria there will be for t = 0, 1, 2, etc. and think about how you are getting those values.
Answer: N(t) = (2^t)*1500
Step-by-step explanation:
Let's define the hour "zero" as the initial population.
So if N(t) is the number of bacteria after t hours, then:
N(0) = 1500.
Now, we know that the population doubles every hour, so we will have that after one hour, at t = 1
N(1) = 2*1500 = 3000
after two hours, at t = 2.
N(2) = 2*(2*1500) = (2^2)*1500
After three hours, at t = 3
N(3) = 2*(2^2)*1500 = (2^3)*1500
So we already can see the pattern, the number of bacteria after t hours will be:
N(t) = (2^t)*1500
Find the solution of the second-order linear differential equation that satisfies the given initial conditions. y'' + 6y' + 9y = 0 y(0) = 0 y'(0) = 1
Answer:
The solution of this differential system is [tex]y(x) = x\cdot e^{3\cdot x}[/tex].
Step-by-step explanation:
This second-order differential equation is homogeneous and linear of the form:
[tex]y'' + p\cdot y' +q\cdot y = 0[/tex] (1)
Where:
[tex]p[/tex] - First-order constant coefficient, dimensionless.
[tex]q[/tex] - Zero-order constant coefficient, dimensionless.
Whose characteristic polynomial is:
[tex]\lambda^{2}+p\cdot \lambda + q = 0[/tex] (2)
Where [tex]\lambda[/tex] contains the roots associated with the solution of the differential equation.
If we know that [tex]p = 6[/tex] and [tex]q = 9[/tex], the roots of the characteristic equation are, respectively:
[tex]\lambda^{2}+6\cdot \lambda + 9 = 0[/tex]
[tex](\lambda +3)\cdot (\lambda + 3) = 0[/tex]
Which means that [tex]\lambda_{1} = \lambda_{2} = 3[/tex] and the solution of the differential equation is of the form:
[tex]y(x) = e^{3\cdot x}\cdot (c_{1}+c_{2}\cdot x)[/tex] (3)
Where [tex]c_{1}[/tex] and [tex]c_{2}[/tex] are integration constants.
The first derivative of the equation above is:
[tex]y'(x) = 3\cdot e^{3\cdot x}\cdot (c_{1}+c_{2}\cdot x)+c_{2}\cdot e^{3\cdot x}[/tex] (4)
Now, if we get that [tex]y(0) = 0[/tex] and [tex]y'(0) = 1[/tex], then the system of equations to the solved is:
[tex]c_{1} = 0[/tex] (3b)
[tex]c_{1}+c_{2} = 1[/tex] (4b)
The solution of this system is: [tex]c_{1} = 0[/tex], [tex]c_{2} = 1[/tex]. Therefore, the solution of this differential system is [tex]y(x) = x\cdot e^{3\cdot x}[/tex].
What is the result of 72 divided by 12? 6 8 9 12
Answer:
the answer is 6
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
Hope this helps!!!!!!
Suppose that you are asked to pick a card from a deck of 52 cards. Once you have selected a card, you place it face down on the table. You are then asked to selected another card from the deck. Is the event of you picking the first card going to affect the probability of the second card selected, why or why not? Are these events independent or dependent?
Answer:
Step-by-step explanation:
The second card is influenced by the first only in that you have not replaced the first card. That makes a difference.
1/52 is the probability for the first card.
1/51 is the probability for the second card.
They are independent events. Drawing the 7 of diamonds does not make the chances of drawing the Ace of Spades other than the 7 came first and the probability of getting the Ace is slightly larger.
Step-by-step explanation:
The only way the second card is influenced by the first is if you did not swap out the first card. That alters everything.
The likelihood of getting the first card is 1/52.
The odds of getting the second card are 1/51.
They happen separately. Other than the fact that the 7 came first and the odds of receiving the Ace is a little bit higher, drawing the 7 of diamonds does not increase the chances of drawing the Ace of Spades.
A monthly budget with expenses is shown.
MONTHLY BUDGET
for a family of three
in San Antonio, Texas
Rent
$870
Food
$550
PR Child care
$375
Transportation
$480
Utilities
$400
Insurance
$235
Savings
$400
Taxes
$290
Monthly total
Which equation can be used to determine y, the minimum amount of money a family must earn to meet the requirements of this budget for one year?
y = 3600 x 12
y = 3600 + 7
y = 3600 x 4
y = 360052
Answer:
[tex]y = 3600 * 12[/tex]
Step-by-step explanation:
Given: Breakdown of Monthly Budget
Required
Determine the equation that shows minimum earnings in a year
First, we need to get the sum of the given list of budgets:
[tex]Budget = 870 + 550 + 375 + 480 + 400+235+400 + 290[/tex]
[tex]Budget = 3600[/tex]
The are 12months in a a year; So, the yearly budget (y) is:
[tex]Yearly\ Budget = Monthly\ Budget * Duration[/tex]
[tex]Yearly\ Budget = 3600* 12[/tex]
i.e.
[tex]y = 3600 * 12[/tex]
Which of the following offers the least price per ounce of shampoo?
A) $6 for 8 ounces of shampoo
B) $4 for 5 ounces of shampoo
C) $8 for 12 ounces of shampoo
D) $12 for 16 ounces of shampoo
The required offer is the least price per ounce of shampoo is $8 for 12 ounces of shampoo. Option C is correct.
Given that,
To determine the offer the least price per ounce of shampoo.
The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
Here,
A) $6 for 8 ounces of shampoo
6 / 8 = $0.75 per ounces of shampoo
B) $4 for 5 ounces of shampoo
4/ 5 = $0.80 per ounces of shampoo
C) $8 for 12 ounces of shampoo
8/12 = $0.67 per ounce of shampoo
D) $12 for 16 ounces of shampoo
12/16 = $0.75 per ounce of shampoo
Thus, the required offer is the least price per ounce of shampoo is $8 for 12 ounces of shampoo. Option C is correct.
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jim koslo earns $156,200 annually as a plant manager. He is married and supports 3 children. The state tax rate in his state is 3.55% of taxable income. What ammount is withheld yearly for state income tax?
Answer:
44
Step-by-step explanation:It's 44 because 156,200 divided by 3.55=44.
If jim koslo earns $156,200 annually as a plant manager. The state tax rate in his state is 3.55% of taxable income. then 5545.1 is the amount is withheld yearly for state income tax
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
jim koslo earns $156,200 annually as a plant manager.
The state tax rate in his state is 3.55% of taxable income.
We need to find the amount is withheld yearly for state income tax
We need to find 3.55% of 156200
First we have to convert 3.55% to decimal by dividing with 100
3.55/100=0.0355
Now multiply 0.0355 with 156200
0.0355×156200
5545.1
Hence 5545.1 is the amount is withheld yearly for state income tax.
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The slope- intercept form of the equation of a line is y = mx + b. When the formula is solved for m, the result is
1. y-x/b
2. y - bx
3. y-b/x
4. x/y - b
(((click on the image to see it all))))
I need the answers to number 2 and 4 asap
Answer:
2.Matrices and Linear Algebra. 2.1 Basics. Definition 2.1.1. A matrix is an m × n array ... aij = 0 i = j. (1b) A diagonal matrix A may be denoted by diag(d1,d2,... ,dn) ... space of A. With r1 (A),...,rm (A) denoting the rows of A the row space
4.Introduces reflections in the x- and y-axes. Demonstrates the ... This leaves us with the transformation for doing a reflection in the y-axis. For this transformation, I'll switch ... Many textbooks don't get any further than this. If these are all the rules ...
Select all the statements that are true for the graph shown.
Submarines descent graph of a diagonal line on a coordinate plane going down and to the right with Time in seconds on the x-axis and Height above Sea Level in feet on the y-axis. The line begins at the origin and passes through point 4 comma negative 12.
The relationship is proportional.
The rate of change is −32
The rate of change is −83
The relationship is linear.
The equation of the line is y = –3x.
Answer:
The relationship is proportional.
The relationship is linear.
The equation of the line is y = –3x.
Step-by-step explanation:
The line in the question passes through origin and (4,-12).
The rate of change of the line is
[tex]m=\dfrac{-12-0}{4-0}\\\Rightarrow m=\dfrac{-12}{4}\\\Rightarrow m=-3[/tex]
The rate of change of the line or slope of the line is -3
Equation of the line is given by
[tex](y-0)=-3(x-0)\\\Rightarrow y=-3x[/tex]
This means that the relationship is linear.
If we take any value of x then there will be only one value of y this means that the relationship is proportional.
So the following statements are true
The relationship is proportional.
The relationship is linear.
The equation of the line is y = –3x.
Answer:
Step-by-step explanation:
Proportional
Linear
Equation of line is y=-3x
x/4-6=2 simplify the following two step equation
Answer:
First, collect the like terms by one side
x/4=2+6
x/4=8
Then, criss-cross it, which means multiply 4 with 8
x=4×8
x=32
Step-by-step explanation:
I hope this is the answer to your question, if it helped you, please give me brainliest
Please could you show the working out as well:)
Answer:
( [tex]\frac{6}{7}[/tex] - [tex]\frac{1}{3}[/tex] ) is closer to [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]\frac{2}{15}[/tex] + [tex]\frac{1}{3}[/tex] = [tex]\frac{2 + 5}{15}[/tex] = [tex]\frac{7}{15}[/tex]
[tex]\frac{6}{7}[/tex] - [tex]\frac{1}{3}[/tex] = [tex]\frac{18-7}{21}[/tex] = [tex]\frac{11}{21}[/tex]
[tex]\frac{7}{15}[/tex] , [tex]\frac{1}{2}[/tex] , [tex]\frac{11}{21}[/tex]
LCD (2, 15, 21) = 210
[tex]\frac{98}{210}[/tex] , [tex]\frac{105}{210}[/tex] , [tex]\frac{110}{210}[/tex]
105 - 98 = 7
110 - 105 = 5 ⇒ [tex]\frac{11}{21}[/tex] is closer to [tex]\frac{1}{2}[/tex] ⇒ ( [tex]\frac{6}{7}[/tex] - [tex]\frac{1}{3}[/tex] ) is closer to [tex]\frac{1}{2}[/tex]
Select the expression equivalent to (-133–15)-(-9x + 16).
А
4x - 31
B
--4x + 1
с
-4x - 31
D
-22x-31
Clara’s school awarded 1900 raffle tickets as incentives. The principal will draw one winning ticket. The winner will receive an iPad pro. Clara received 5 tickets for good attendance, 4 for making the honor roll, and 8 for tutoring other students.
What is the probability that one of Clara’s tickets will be selected by the principal? (write your answer as a %, once it is in % form round to the hundredths place)
Answer:
0.89%
Step-by-step explanation:
Given that :
Total number of raffle tickets = 1900
Total number of Clara's tickets (5 + 4 + 8) = 17
Probability that one of Clara's tickets will be picked :
Probability = (required outcome / Total possible outcomes)
Required outcome = total number of Clara's ticket
Total possible outcomes = total number of raffle tickets
Hence,
P(picking one of Clara's tickets) = 17 / 1900
17 / 1900 = 0.0089473
0.0089473 * 100%
= 0.8947%
= 0.89%
Please help me I don’t understand stand it
What is the estimate of the sum of 165, 123, 376 and 134 using front end estimation? A. 600 B. 700 C. 800 D. 900
Answer:
A.
Step-by-step explanation:
Sorry, just unexplainable thinking.
given that a=2 and b=3, what is (ab)^2
Answer:
(ab)² = 36
Step-by-step explanation:
Plug in 2 for a and 3 for b:
(2·3)²
Multiply 2 and 3:
6²
Square the number:
36
Y-p=m(x-8) solve for x
Answer:
x = Y /m − p /m +8
Step-by-step explanation:
At a university, Todd deposits $100 into his cafeteria account. He spends $5 on dinner every day. Seth deposits $140 into his account. He spends $5 on lunch and $5 on dinner every day. After how many days will Todd and Seth have the same amount of money in their accounts? 16 8 4 2
Answer:
The answer is 8 days.
Step-by-step explanation:
By applying the correct equations to Todd and Seth's balances for each day we end up with Todd and Seth having an equal balance in their accounts by day 8, alternatively, we can show that Todd and Seth have the same amount of money in their accounts by day 8 with this table
Day - Todd - Seth
1 - 95 - 130
2 - 90 - 120
3 - 85 - 110
4 - 80 - 100
5 - 75 - 90
6 - 70 - 80
7 - 65 - 70
8 - 60 - 60
What's 15/45 written as a fraction in simplest form
A. 3/15
B.13
C.53
D. 153
Answer:
None of the above
Step-by-step explanation:
15/45=1/3
Answer:
None of those options lol
Step-by-step explanation:
But the answer is 1/3
Suppose that a population of bacteria triples every hour and starts with 700 bacteria.
(a) Find an expression for the number n of bacteria after t hours.
(b) Estimate the rate of growth of the bacteria population after 1.5 hours.
Answer:
(a) An expression for the number n of bacteria after t hours is n(t)=700*[tex]3^{t}[/tex]
(b) The rate of growth of the bacteria population after 1.5 hours is 3,996 number of bacteria per hour.
Step-by-step explanation:
An exponential function is one in which the independent variable x appears in the exponent and has a constant a as its base. Its expression is:
f(x)=aˣ
being a real positive.
When 0 <a <1, then the exponential function is a decreasing function and when a> 1, it is an increasing function.
An exponential function allows us to refer to phenomena that grow faster and faster, such as population growth.
In that case, the formula used to model the growth of a population is given by:
P(t)=P0*[tex]a^{t}[/tex]
where the function P (t) grows exponentially and represents the quantity of the population at time t; a represents the constant of growth or decrease and P0 represents the initial population at time zero.
In this case:
P0=700a=3Replacing, you get:
P(t)=700*[tex]3^{t}[/tex]
An expression for the number n of bacteria after t hours is n(t)=700*[tex]3^{t}[/tex]
The derivative of this function P (t) is:
n'(t)=700*ln(3)*[tex]3^{t}[/tex]
and reflects the growth rate of the bacteria population.
So, the rate of growth of the bacteria population after 1.5 hours is:
n(1.5)=700*ln(3)*[tex]3^{1.5}[/tex]
Solving, you get:
n(1.5)≅ 3,996
The rate of growth of the bacteria population after 1.5 hours is 3,996 number of bacteria per hour.
i need help on this question
Please help with my homework
It's 65. Because you add the other angles and get 90+25 and get 115. 180 -115 = 65.
Answer:
c=65°
Step-by-step explanation:
180-90=90
90-25=65
hopefully this helps :)
a city depatment uses an average of 25 10cent,35 15 cent and 350 20 cent postage stamps each day.the total cost of stamps used by the department in a 5 day period is
At a carnival, Tammy bought 9 packs of 17 tickets each. She has used 36 of the tickets so far. How many tickets does she have left?
Answer: 117 tickets left
Step-by-step explanation:
evaluate the expression when x=4/5 and y=-2/9: 3y-x
Answer:
-2/15
Step-by-step explanation:
what is 25+30 pleas help me
The new Xbox series gaming console sells for 499 all units are sold out at stores but can be found online for 34% more than the original price how much would it cost to get it online at the marked up price
PLS HELP!!! Which statement about numbers is true?
All whole numbers are rational numbers
All rational numbers are integers
All rational numbers are whole numbers
All integers are whole numbers
First to answer will be voted brainliest!!
Answer:
all integers are whole numbers
PLZ HELP I BEG U!!!!!! ILL MARK U BRAINLIEST
Create a story using the inequality symbols , ≤,≥,≠ . the story must be creative, detailed, coherent, and written clearly. it does not have to be solely math related.
Answer:
T_T said to 个_个: Hallo, I am so happee!!!
Step-by-step explanation:
Plz mark as Brainliest!