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
In a country, 31 % of the people that voted for candidate AA are women. Moreover, 10% of the population are women and voted for A. What is the percentage of people that voted for candidate AA?
This question is incomplete, the complete question is;
In a country, 31 % of the people that voted for candidate AA are women. Moreover, 10% of the population are women and voted for AA. What is the percentage of people that voted for candidate AA?
Answer:
the percentage of people that voted for candidate AA is 32.3%
Step-by-step explanation:
Given that;
31 % of the people that voted for candidate A are women
P( women/Candidate AA) = 0.31
Moreover, 10% of the population are women and voted for AA
P( women & candidate AA) = 0.10
so
p( Candidate AA) = P( women & candidate AA) / P( women/Candidate AA)
p( Candidate AA) = 0.10 / 0.31
p( Candidate AA) = 0.323
p( Candidate AA) = 32.3%
Therefore the percentage of people that voted for candidate AA is 32.3%
How can a percent be used to describe a change in quantity?
Answer:
remember,a percent means "per 100".You can describe the change as a fraction comparing the amount of change to the original and then use a proportion to rewrite your problem as a percentage out of 100.
How many cups are in 3 gallons? 1 gallon = 16 cups
Label your answer in cups.
Answer:
There are 48 cups in 3 gallons!
Hope this helped! :)
where n 2 1
OS – On -3
1-
Mn
(
01'0
-
1
)
=
"
n
direction: simplify the following fractions
1.6/12
2.9/15
3.8/10
4.6/14
5.8/18
Answer:
1.9/63 is the answer!!!!!
Select the correct answer.
The number of days, d, it will take Manny to read a book varles inversely as the number of pages, p, he reads per day. If kis the constant of
variation, which equation represents this situation?
OA. d+p=k
OB. dp = k
OC. d= pk
OD. d=p+k
The equation represents this situation will be dp = k. Thus, option B is correct.
What is directly proportional?Let there are two variables p and q
Then, p and q are said to be directly proportional to each other if
p = kq
where k is some constant number called constant of proportionality.
The inversely proportional relationship is denoted by
[tex]m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}[/tex]
As visible, increasing one variable will decrease the other variable if both are inversely proportional.
The number of days, d, it will take Manny to read a book varies inversely as the number of pages, p, he reads per day.
If k is the constant of variation.
The equation represents this situation will be
dp = k
Thus, option B is correct.
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A business is owned by 3 people. Mrs. Applegate owns
3
19
of the business. Mrs. Brown owns 3 times as much as
Mrs. Charles. What fractional part of the business does Mrs. Brown own?
Given:
Mrs. Applegate owns [tex]\dfrac{3}{19}[/tex] of the business.
Mrs. Brown owns 3 times as much as Mrs. Charles.
To find:
The fractional part of the business that Mrs. Brown owns.
Solution:
Let Mrs. Charles owns x part of business.
Mrs. Brown owns 3 times as much as Mrs. Charles.
Mrs. Brown owns = 3x part of business.
Mrs. Applegate owns [tex]=\dfrac{3}{19}[/tex] of the business.
[tex]x+3x+\dfrac{3}{19}=1[/tex]
[tex]4x=1-\dfrac{3}{19}[/tex]
[tex]4x=\dfrac{19-3}{19}[/tex]
[tex]4x=\dfrac{16}{19}[/tex]
Divide both sides by 4.
[tex]x=\dfrac{16}{4\times 19}[/tex]
[tex]x=\dfrac{4}{19}[/tex]
Now,
Mrs. Brown owns [tex]=3\times x[/tex]
[tex]=3\times \dfrac{4}{19}[/tex]
[tex]=\dfrac{12}{19}[/tex]
Therefore, Mrs. Brown owns [tex]\dfrac{12}{19}[/tex] of the business.
Solve for: 22≥4m-2 or 5-3m≤-13
Answer:
22≥4m-2=6
5-3m<-13=6
Step-by-step explanation:
The inequalities 22 ≥ 4m - 2 or 5 - 3m ≤ - 13 is m ≤ 6 or m ≥ 6.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
22 ≥ 4m - 2.
4m ≤ 22 + 2.
4m ≤ 24.
m ≤ 24/4.
m ≤ 6.
5 - 3m ≤ - 13.
- 3m ≤ - 13 - 5.
- 3m ≤ - 18.
3m ≥ 18.
m ≥ 18/3.
m ≥ 6.
So, m ≤ 6 or m ≥ 6.
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PLEASE ANSWER ASAP!!!
A right triangle always has obtuse exterior angles at two verticies, True or False?
Answer:
false
Step-by-step explanation:
Order the numbers from least to greatest.
Answer: -11/2, -5/7, 0.1, 4/5, 1.3
Step-by-step explanation:
It might be easier to convert these fractions into decimals so let’s do that. -5/7 becomes about -0.7, 4/5 becomes 0.8, 1.3 is already a decimal, -11/2 becomes -5.5, and 0.1 is already a decimal. Negative numbers are less than positive numbers and -5.5 is a bigger negative number than -0.7, so -5.5 (-11/2) comes first and -0.7 (-5/7) comes second. 0.1 is less than 0.8 so 0.1 is third and 0.8 (4/5) is fourth. That leaves 1.3 as the greatest number. This gives us the list -11/2, -5/7, 0.1, 4/5, 1.3. Hope this helps!
What is the formula for finding distance?
Answer:Learn how to find the distance between two points by using the distance formula, which is an application of the Pythagorean theorem. We can rewrite the Pythagorean theorem as d=√((x_2-x_1)²+(y_2-y_1)²) to find the distance between any two points. Created by Sal Khan and CK-12 Foundation
Step-by-step explanation:
How do I solve for x 7x–1=125
Answer:
x=18
Step-by-step explanation:
You add 1 on each side so you have 7x=126. Then you divide each side by 7, so you get x=18! Hope this helps!
The line below has slope 4 and y-intercep
3. Write the equation of the line in slope
intercept form
5
Answer:
y=4x+3
y=-2x+3
Step-by-step explanation:
13.25 x 64 please awnser it's for a test and I have no idea what it is.
Answer :
13.25 x 64
=848
Answer:
453x ^64 /4
Step-by-step explanation:
The price of stock A at 9 a.m. was $15.75. Since then, the price has been increase at rate of $.05 per hour. At noon , the price of stock B was $16.53. It begin to decrease at the rate of $.13 per hour. If the stock continue to increase and decrease at the same rate, in how many hours will the price of the stocks be the same?
Answer:
Step-by-step explanation:
15.75 plus .05x = 16.53-.13x
.78=.18x
4.3 hours is your answer
Is 900% of 6 less than 10, greater than 10 but less than 100, or greater than 100?
Answer:
its greater than 10 but lesser than 100 because simplifying them in fractional form indeed informs u that its greater than 10
What are the solutions to the quadratic equation 4(x + 2)2 = 36 x = −11 and x = 7 x = −7 and x = 11 x = −5 and x = 1 x = −1 and x = 5
Answer:
c
Step-by-step explanation:
edge2020
The solutions to the quadratic equation 4(x + 2)² = 36 is x = -5 and x = 1.
Hence, option c) x = -5 and x = 1 is the correct answer.
What is a Quadratic Equation?
Quadratic equation is simply an algebraic expression of the second degree in x. Quadratic equation in its standard form is;
ax² + bx + c = 0
Where x is the unknown
To solve for x, we use the quadratic formula
x = (-b±√(b² - 4ac)) / (2a)
Given that;
4(x + 2)² = 36
4( x(x + 2) + 2(x+2) ) = 36
4( x² + 2x + 2x + 4 ) = 36
4( x² + 4x + 4 ) = 36
4x² + 16x + 16 = 36
4x² + 16x + 16 - 36 = 0
4x² + 16x - 20 = 0
We can further simply ( divide through by 4 )
x² + 4x - 5 = 0
Hence,
a = 1b = 4c = -5x = (-b±√(b² - 4ac)) / (2a)
x = (-4±√(4² - (4 × 1 × -5)) / (2×1)
x = (-4±√(16 - (-20)) / (2)
x = (-4±√(16 + 20)) / (2)
x = (-4±√(36)) / 2
x = (-4±6)) / 2
Hence
x = (-4-6)) / 2 and x = (-4+6)) / 2
x = -10/2 and x = 2/2
x = -5 and x = 1
The solutions to the quadratic equation 4(x + 2)² = 36 is x = -5 and x = 1.
Hence, option c) x = -5 and x = 1 is the correct answer.
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solve for x and why please using these!!!
Answer:
[tex]x = 40[/tex]
[tex]y = 5[/tex]
Step-by-step explanation:
[tex]4x = 2x+80\\2x = 80\\x = 40[/tex]
Edit: Solve for Y
A straight line is 180 degrees so one side (the x side) is 160°, The Y side is 20, and you can work backwards by -
[tex]8y - 20 = 20\\8y = 40\\y = 5[/tex]
Help! Please!!! I seriously need this!!!!!
Answer:
it's related by product of 5/3 and directly proportional
A goat is tied to the corner of a rectangular shed in a large field full of grass. The rope is 2 yards long and a plane view (from above) of the shed and field is shown below. Use this information for Parts A and B below.
Part A: Calculate the area of grass that the goat can eat.
Part B: What length of rope would enable the goat to eat 30 square yards of grass? Show all your reasoning.
Answer:
9.42 yd²3.57 ydStep-by-step explanation:
Part AThe area of circle with radius of 2 yd (the length of the rope) is:
A = π*r² = 3.14*2² = 12.56 yd²Since 1/4 of the circle is occupied by the shed, the area of the grass is:
12.56*3/4 = 9.42 yd²Part BLet the area be 30 yd², finding the r as per above formula:
3/4*3.14*r² = 30r² = 30*4/3*3.14r² = 12.74r = √12.74r = 3.57 ydSolve for x.
4x +4=12
Answer:
x = 2
Step-by-step explanation:
4x +4=12
-4. -4
4x.= 8
divide both saide by 4
x. = 2
Subtract 4 from both sides
4x + 4 - 4 = 12 -4
Simplify
4x = 8
Divide both sdes by 4
4x/4 = 8/4
Simplify
x = 2
Find the value of X, I need help solving this
Answer:
B) 13
Step-by-step explanation:
The given angles are vertical angles and has same measurement
4x = 52° divide both sides by 4
x = 13
A manufacturer produces bolts of a fabric with a fixed width. The cost of producing x yards of this fabric is C = f(x) dollars.
Required:
a. What is the meaning of the derivative fâ'(x)? What are its units?
b. In practical terms, what does it mean to say that fâ'(2,000) = 10?
c. Which do you think is greater, fâ'(200) or fâ'(600)? What about fâ'(4,000)?
Correct is;
A manufacturer produces bolts of a fabric with a fixed width. The cost of producing x yards of this fabric is C = f(x) dollars.
(a) What is the meaning of the derivative f '(x)?
What are its units?
(b) In practical terms, what does it mean to say that f '(2000) = 10?
(c) Which do you think is greater,
f '(200) or f '(600)? What about f '(4000)?
Answer:
A) f'(x) means the rate of change of the cost of production with respect to the number of yards that were produced.
It's unit is $/yard
B) f '(2000) = 10 means that after production of 2000 yards of fabrics, the cost of production will be increasing at a rate of $10 per yard.
C) f' (200) > f'(600)
f'(4000) > f'(600)
Step-by-step explanation:
A) Since the cost of producing x yards of this fabric is C = f(x) dollars. f'(x) simply means the rate of change of C with respect to x.
In clearer terms, the derivative f'(x) means the rate of change of the cost of production with respect to the number of yards that were produced.
It's unit is $/yard
B) To say f '(2000) = 10 means that after production of 2000 yards of fabrics, the cost of production will be increasing at a rate of $10 per yard.
C) f '(200) is greater than f'(600) because the cost of making the 600th yard will be less than the cost of the 200th yard. Reason for this is due to economics of scale as the manufacturer will certainly make more efficient use of fixed costs of production.
As more units are produced, there may likely be more overtime costs and thus the rate of increase cost of production will likely increase faster.
Thus;
f'(4000) > f'(600)
The senior class sells movie tickets to students and teachers. The student tickets cost $4 each and teacher tickets cost $8 each. If they earned only $44, how many possible combinations of student and teacher tickets could have been sold?
find the 8th term of the geometric sequence 4, -20, 100, ...
Answer:
312500
Step-by-step explanation:
I believe the pattern is x5 x-5 x5 x-5 and if you follow that pattern, you get 312500. im sorry if im wrong
THIS IS DUE IN 10 MINS
Answer:
D
Step-by-step explanation:
Help me answer the math
Answer: 1. 2
2. 5
3. 2
4. 2
5. 2
Step-by-step explanation:
E E E HEY PLEASE HELP. IM LITERALLY ABOUT TO END MYSELF.
Answer:
( 5 , - 2 )
Step-by-step explanation:
( 10 × [tex]\frac{1}{2}[/tex] , - 4 × [tex]\frac{1}{2}[/tex] ) = (5, - 2)
pog help pog pog pog pog pog pog pog pog pog
Answer:
POG
Step-by-step explanation:
poggers + poggers = POGCHAMP
Answer:
only the green and pink line repent a proportional relationship
Pleeeeeeeeeeeeeeeeaaaaaaaaaaaaaasssssssssssssseeeeeeee help ASAP and giving 33 points the ma is the -2 and the 5 and t is -4 and h is -8
Answer:
-320
Step-by-step explanation:
-2×5 (-4×-8)
-10(32)
-10×32
-320