The number of bacteria in a culture is increasing according to the law of exponential growth. The initial population is 240 bacteria, and the population after 12 hours is double the population after 1 hour. How many bacteria will there be after 3 hours
Answer:
240
Step-by-step explanation:
According to law of exponential growth,
[tex]y=y_0e^{kt}[/tex]
Here, [tex]y_0[/tex] denotes the initial amount and k is the rate constant of the equation.
Now, the initial population is 240 bacteria.
Put [tex]y_0=240[/tex]
So,
[tex]y=240e^{kt}[/tex]
The population after 12 hours is double the population after 1 hour.
[tex]y(12)=2y(1)[/tex]
[tex]240e^{12k}=240e^{k} \\e^{12k}=e^{k} \\e^{12k-k}=1\\e^{11k}=1\\11k=log 1=0\\k=0[/tex]
(Formulae used: [tex]\frac{e^x}{e^y}=e^{x-y}\,,\,log 1=0[/tex])
So,
[tex]y=240e^{0}=240\\y=240[/tex]
Therefore,
Number of bacteria after 3 hours = 240
Solve the equation below. Show the steps that lead to your final solution.
5(2x+1)+6x-13=3(3x-2)
Answer:
this is how u would do it
5(2+1)+6−13=3(3−2)
10+5+6−13=3(3−2)
=2/7
there is only three options someone help
Answer:
Answer is Option 2
Step-by-step explanation:
Triangles equal to 180 degrees in total. So it is 55+54+x+74=180
The simplified version that I just wrote is Option 2
Ina crespo rowed 7.5 miles down the Hanbashabee river in 1.5 hours ,but the return trip took her 2.5 hours.find the rate ina rows in still water and the rate of the current.
Answer:
rate of current=1 mph
Step-by-step explanation:
-3.6 divided by 2 1/7? please help my assignment is due soon
Answer:
the answer is -9/35
Step-by-step explanation:
imjustgonnaeritedmrandomletterssinceotsajdit has to be 20 characters long but yea thee answer is -9/35
Answer:
Step-by-step explanation:
-1.68 is your answer
find the length of the missing sides round answers to the nearest tenth
Answer:
x= 9.37
y = 17.69
Step-by-step explanation:
in order to find the answer, use the trigonometries.
First finding x which is tan(32) = x/15
x = tan(32)15
and Y is cos(32) = 15/y
y = 15/cos(32)
I hope this helps
Question: Using only reciprocal, Pythagorean, sum/difference, and/or half angle identities, prove the equation below. You must use angles A and B, do not replace with actual vales. Only work with the right side of the equation. You should use TEN steps to accomplish this proof! cosA+cosB= 2cos(A+B/2)cos(A-B/2)
Answer:
See explanation below
Step-by-step explanation:
Recall the identity for the cosine of an addition of angles:
[tex]cos(\theta+\gamma)= cos(\theta)*cos(\gamma)- sin(\theta)*sin(\gamma)[/tex]
and that for a subtraction of angles:
[tex]cos(\theta-\gamma)= cos(\theta)*cos(\gamma)+sin(\theta)*sin(\gamma)[/tex]
Now, use the property of addition of angles above to write :
[tex]cos(\frac{A+B}{2} +\frac{A-B}{2} )=cos(\frac{A+B}{2} )*cos(\frac{A-B}{2} )-sin(\frac{A+B}{2} )*sin(\frac{A-B}{2} )[/tex]
but since : [tex]\frac{A+B}{2} +\frac{A-B}{2}= A[/tex]
Then the cosine of addition of angles above can be written as:
[tex]cos(\frac{A+B}{2} +\frac{A-B}{2} )=cos(\frac{A+B}{2} )*cos(\frac{A-B}{2} )-sin(\frac{A+B}{2} )*sin(\frac{A-B}{2} )\\cos(A)=cos(\frac{A+B}{2} )*cos(\frac{A-B}{2} )-sin(\frac{A+B}{2} )*sin(\frac{A-B}{2} )[/tex]
We do something similar now with the cosine of the subtraction of angles:
[tex]cos(\frac{A+B}{2} -\frac{A-B}{2} )=cos(\frac{A+B}{2} )*cos(\frac{A-B}{2} )+sin(\frac{A+B}{2} )*sin(\frac{A-B}{2} )[/tex]
and we notice that: [tex]\frac{A+B}{2} -\frac{A-B}{2}= B[/tex]
Then the cosine of subtraction of angles above can be written as:
[tex]cos(\frac{A+B}{2} -\frac{A-B}{2} )=cos(\frac{A+B}{2} )*cos(\frac{A-B}{2} )+sin(\frac{A+B}{2} )*sin(\frac{A-B}{2} )\\cos(B )=cos(\frac{A+B}{2} )*cos(\frac{A-B}{2} )+sin(\frac{A+B}{2} )*sin(\frac{A-B}{2} )[/tex]
and finally, we add term by term the expressions we got for cos (A) and for cos(B) and notice that the terms that contain the sine functions cancel each other because they have opposite signs, while the terms in cosine add up to double themselves:
[tex]cos(A )=cos(\frac{A+B}{2} )*cos(\frac{A-B}{2} )+sin(\frac{A+B}{2} )*sin(\frac{A-B}{2} )\\+\\cos(B )=cos(\frac{A+B}{2} )*cos(\frac{A-B}{2} )-sin(\frac{A+B}{2} )*sin(\frac{A-B}{2} )\\=\\cos(A) +cos(B)=2\,cos(\frac{A+B}{2} )*cos(\frac{A-B}{2} )[/tex]
which is what we wanted to prove.
any help will mark brainliest
Problem:
Craig earns extra money as a lifeguard. He earns $37 for 4 hours and $64.75 for 7 hours.
Answer:
The answer is: y = 9.25x
Step-by-step explanation:
Let the equation for the proportionality relation is y = mx .......... (1), where y represents the money that Craig earns for a duty of x hours.
Here, m is the constant of proportionality and we have to find its value.
Given that Craig earns $37 for 4 hours duty.
So, from equation (1), we have 37 = 4m, ⇒ m = 9.25
Therefore, the equation becomes y = 9.25x. (Answer)
Simplify the expression.
(6 + 5) x3
A. 16
B. 11
O
C. 33
D. 21
SUBA
Answer:
C. 33
Step-by-step explanation:
Solve 4-(-h)=12!!!can someone help meee
Answer:
The answer is 8
Step-by-step explanation:
Since there's already a negative sign right beside h and one outside of it, the answer has to be positive, and since 12-4=8, the answer is 8
finding integral from derivative graph
What is the probability that a student chosen at random has a GPA less than 3.00?
Answer:
1200/2000
Step-by-step explanation:
There are 1200 students total that have a GPA less than 3.00. That means that out of 2000 students, 1200 of them have a GPA less than 3.00, hence 1200/2000 chance that a student is picked at random with less than a 3.00.
100 plates served. The 1st waiter turnes every plate upside down. Then another waiter turned every other plate. Then the 3d waiter turned every 3d plate. The 4th turned every 4th plate, and so on, until the 100th waiter turned the 100th plate. At the end how many plates are placed normally?
Answer:
At the end of the 100th turn, you have 90 plates placed normally.
Step-by-step explanation:
Not sure if there is a formula to calculate this. I plugged the data into a spreadsheet and created formulas to turn every plate, every 2nd plate, every 3rd, .... to every 100th plate.
sergio must ride 7.5 miles in 1/4 hour to achieve this target speed, so he needs to ride an additional ____ mile per 1/4 hour
Answer: 7.0
Step-by-step explanation:
sergio must ride 7.5 miles in 1/4 hour to achieve this target speed so he needs to ride an addititonal 9.8 mile per1/4 hour
Answer:
30 mph
Step-by-step explanation:
since it is 1/4 you would multply 7.5 times 4, which adds up to 30.
87.039 as a mixed number
Answer:
87 39/1000
Step-by-step explanation:
what is equevelent to 5/7
Create a scenario (word problem) that goes with this equation.
100−3x=74.50 (best answer gets brainliest)
Answer:
I have $100 and I buy 3 lunches, after which I'm left with $74.50. How much does each lunch cost?
cooper's jump rope is for 4 2/5. luke's jump rope is 4 3/4 ft long. whose jump rope is longer? how much longer? show your work
Answer:
Juke's jump; by 0.35 feet
Step-by-step explanation:
Given that,
Cooper's jump rope is for [tex]4\dfrac{2}{5}[/tex] feet.
Juke's jump rope is [tex]4\dfrac{3}{4}[/tex] feet.
Cooper's jump is :
[tex]4\dfrac{2}{5}=\dfrac{22}{5}\ \text{feet}\\\\=4.4\ \text{feet}[/tex]
Juke's jump is
[tex]4\dfrac{3}{4}=\dfrac{19}{4}\\\\=4.75\ \text{feet}[/tex]
So, it is clear that Juke's jump is longer than Cooper's jump.
Juke's jump - Cooper's jump = 4.75 - 4.4
= 0.35 feet
or
So, Juke's jump is 375 feet longer.
f(x) = –2x2 + 8x – 10
Find f(-4)
Answer: x = -74
Step-by-step explanation:
What is the answer to this ?
Answer:
the missing angle is 5m
Step-by-step explanation:
Answer:
Ah yes, Pearson lol. It should be 4 or 5 m.
Step-by-step explanation:
Hope this helps :)
Last week Jane made deposits of $64,25,and$37 into her checking account.she then Wrote checks For $52 and $49. What is janes new account balance?
Answer:
$25.
Step-by-step explanation:
64+25+37=126
52+49=101.00
126-101=25
Answer:
$25
Step-by-step explanation:
Assuming her bank account was initially at $0 then:
$64+$25+$37 = $126
$126 - $52 - $49 = $25
A flying fish deep under the sea dreams to reach the clouds one day the fish is at a depth of 200 feet below sea level right under the clouds it has to fly 6700 feet to reach the clouds how many feet above sea level are the clouds
Answer:
6500
Step-by-step explanation:
6700-200= 6500
6500 ft above sea level
0.34 times 10 with an exponet 3
Answer: 340
Step-by-step explanation:
Because if you multiply 0.34x 10 to the 3rd power you get 340
Hope This helped :))
Answer:
340
Step-by-step explanation:
I think
The mean price of a gallon of milk at various stores is $2.60 with a standard deviation of $0.15. If the cost of milk at Target is 3 standard
deviations above the mean, how much does it cost?
Answer: The cost of milk at Target is 3 standard deviations above the mean = $3.05.
Step-by-step explanation:
Given: Mean price of a gallon of milk = $2.60
Standard deviation = $0.15
The cost of milk at Target is 3 standard deviations above the mean = Mean + Standard deviation
= $ (2.60+3(0.15))
=-$(2.60+0.45)
= $ 3.05
Hence, the cost of milk at Target is 3 standard deviations above the mean = $3.05.
is 3 months enough time to complete 300 assignments? my school is online and requires you to complete a certain amount of assignments each semester.
Answer:
ya if you do 3 a day
Step-by-step explanation:
Answer:
yes it is enough time you would have to do 25 assignments aweek
Step-by-step explanation:
a boat can travel 384 miles on 48 gallons of gasoline. how much gas does will it need to go 456 miles?
HELP!!!!! PLEASE! The length of 1 year on Uranus is a little more than 84 years on Earth. About how many Uranus years are equal to 175 Earth years?
Answer:
About 2.08 Uranus years is equal to 175 Earth years
Step-by-step explanation:
1 = ?
84 175
175/84 = 2.08
Number of Uranus years are equal to 175 Earth years is 2.08 years.
Given that, The length of 1 year on Uranus is a little more than 84 years on Earth.
What are proportions?Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.
Let the number of years be x
1 : 84 :: x : 175
⇒ 1/84 = x/175
⇒ 84x=175
⇒ x=175/84
⇒ x=2.08 years
Therefore, number of Uranus years are equal to 175 Earth years is 2.08 years.
To learn more about the proportions visit:
https://brainly.com/question/7096655.
#SPJ2
-6(x-3)+4x simplify the expression
Answer: -2x+18
Hope this will help :)
Answer:
-2x + 18
Step-by-step explanation:
Simplfy
-6 (x - 3) + 4x
-6x + 18 + 4x Combine liked terms
-2x + 18
Tim has a collection of model cars and boats.he has 3 cars for every 2 boat. He has a total of 12 boats.
Answer:
18 cars
Step-by-step explanation:
6 times 2= 12 boats
3 times 6= 18 cars
Hopefully this helps!
Answer:
He has 36 cars if there are 12 boats
Step-by-step explanation:
If he has 3 cars for every 2 boats he has then he would have 36 cars. You multiply 12 and 3 to get 36.