Answer:
They will have the same population after 6 hours
Step-by-step explanation:
The general exponential equation format for this is;
P = P_o(e^(kt))
For Culture A, we are told that it had an initial population of 200 and doubles every hour.
Thus;
After 1 hour, P = 400
After 2 hours, P = 800
After 3 hours, P = 1600
Thus;
At t = 1, we have;
400 = 200(e^(k × 1))
400/200 = e^(k)
e^(k) = 2 - - - (eq 1)
At t = 2, we have;
800 = 200(e^(k × 2))
800/200 = e^(2k)
e^(2k) = 4 - - - (eq 2)
To find k, let's divide eq 1 by eq 2.
(e^(2k))/e^(k) = 4/2
e^(2k - k) = 2
e^(k) = 2
k = In 2
k = 0.6931
Thus;
P = 200e^(0.6931t)
For Culture B, we are told that it had an initial population of 819200 but has been contaminated. Its population is now decreasing by half every hour.
Thus;
After 1 hour, P = 409600
After 2 hours, P = 204800
After 3 hours, P = 102400
Thus;
At t = 1, we have;
409600 = 819200(e^(k × 1))
409600/819200 = e^(k)
e^(k) = 0.5 - - - (eq 1)
At t = 2, we have;
204800 = 819200(e^(k × 2))
204800/819200 = e^(2k)
e^(2k) = 0.25 - - - (eq 2)
To find k, let's divide eq 1 by eq 2.
(e^(2k))/e^(k) = 0.25/0.5
e^(k) = 0.5
k = In 0.5
k = -0.6931
Thus;
P = 819200(e^(-0.6931t))
We want to find the time when the 2 cultures will have the same population. Thus;
200e^(0.6931t) = 819200(e^(-0.6931t))
Arranging, we have;
(e^(0.6931t))/(e^(-0.6931t)) = 819200/200
e^(0.6931t - (-0.6931t) = 4096
e^(1.3862t) = 4096
1.3862t = In 4096
1.3862t = 8.3178
t = 8.3178/1.3862
t ≈ 6 hours
HELP I DON’t know how to answer this!!
Answer:
35 ft
Step-by-step explanation:
Since E and F are both midpoints, you can create a midsegment between them. A midsegment is half the length of the line segment parallel to it (the 70 ft) So:
70/2=35
x/2+21=45
what is x in this equation?
Answer:
x = 48
Step-by-step explanation:
x/2+21=45
subtract 21 on both sides
x/2 + 21 - 21 = 45 - 21
x/2 = 24
Multiply by 2 on both sides
x/2 * 2 = 24 * 2
x = 48
Check
48/2 + 21 = 45
24 + 21 = 45
45 = 45 CORRECT
Hope this helped!
The line has been partitioned into three angles. Is there a triangle with these three angle measures?
Name the property. 7+(11+10)=(7+11)+10
Answer:
associative
Step-by-step explanation:
u switched parentheses
Help plz plz I would appreciate it
Answer:
14
Step-by-step explanation:
As we can see BD is the median of the Triangle ABC
So it breaks into two equal parts
AD = 7
And CD = 7
So
AC = AD + CD
= 7 + 7
= 14
Hope it will help :)
WILL mark brainliest
Answer:
do u have to find the pattern?
Step-by-step explanation:
what is the area of the shape
Answer:
A= 18
Step-by-step explanation:
To find the height, find the blocks inside the shape that is completely attached (they have to be in a straight vertical line). In this case, you can see that three vertical blocks in the middle of the shape is completely attached. That means your height is 3.
To find the width, look at the how many horizontal boxes make up the top. 6 block inside the shape corispond with 6 blocks on top of the shape, so the width is six.
Multiply 6 by 3 to get 18.
I don't understand how to find the negative. Some of these are wrong and just need help finding my errors
Answer:
-5pi/4
Step-by-step explanation:
someone help me with my math homework?
Answer:
c
Step-by-step explanation:
Which system of linear equations has the ordered pair (15, – 25) as its solution?
x - 2y = 35 and 2x + y = 55
x-2y = -35 and 2x - y = 55
2x+y=5 and 2x + y = 55
2x+y=5 and 2x – y=55
Answer:
The solution to the system of equations be:
(x, y) = (15, -25)
Therefore, the fourth system of equations i.e. 2x+y=5 and 2x – y=55 has the ordered pair (15, – 25) as its solution.
Step-by-step explanation:
Let us solve and check the 4th system of equations
2x+y=5
2x – y=55
solving the system of equations
[tex]\begin{bmatrix}2x+y=5\\ 2x-y=55\end{bmatrix}[/tex]
subtracting
[tex]2x-y=55[/tex]
[tex]-[/tex]
[tex]\underline{2x+y=5}[/tex]
[tex]-2y=50[/tex]
so the system of equations becomes
[tex]\begin{bmatrix}2x+y=5\\ -2y=50\end{bmatrix}[/tex]
solve -2y = 50
[tex]-2y=50[/tex]
Divide both sides by -2
[tex]\frac{-2y}{-2}=\frac{50}{-2}[/tex]
[tex]y=-25[/tex]
[tex]\mathrm{For\:}2x+y=5\mathrm{\:plug\:in\:}y=-25[/tex]
[tex]2x-25=5[/tex]
Add 25 to both sides
[tex]2x-25+25=5+25[/tex]
Simplify
[tex]2x=30[/tex]
Divide both sides by 2
[tex]\frac{2x}{2}=\frac{30}{2}[/tex]
simplify
[tex]x=15[/tex]
Thus, the solution to the system of equations be:
(x, y) = (15, -25)
Therefore, the fourth system of equations i.e. 2x+y=5 and 2x – y=55 has the ordered pair (15, – 25) as its solution.
Let n be the number of couples dancing in a competition. If there are 5 organizers, which expression represents the total number of people involved in the competition?
The expression representing the total number of people involved in the competition is 2n + 5.
What are Algebraic Expressions?Algebraic expressions are defined as the statements in mathematics which consist of constants, coefficients of the variables and variables connecting with basic operations like addition, multiplication, subtraction, etc.
Algebraic equations are something with an algebraic expression equal to something. But in algebraic expressions, there will be no equal to sign.
There are basically three classes of algebraic expressions, namely, monomial, binomial and polynomial expressions.
Number of couple dancing in a competition = n
Number of people involving in a couple dance is 2.
Total number of people dancing as couple = 2n
Number of organizers in the competition = 5
Total number of people involved = 2n + 5
Hence 2n + 5 number of people are involved in the competition program.
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1 one gets it right will get crown plz hurry!!!!!!!!!!!!!!!!
Thirty pounds of grass seed will cover One-third of an acre. Which unit rate describes this situation? 10 pounds per acre 40 pounds per acre 90 pounds per acre 120 pounds per acre
Step-by-step explanation:
As always, the "unit rate" can be written two ways. You have not specified which one you want.
.. (30 lb)/(1/3 ac) = 90 lb/ac
.. (1/3 ac)/(30 lb) = (1/90) ac/lb
Answer:
90 pounds per arce
Step-by-step explanation: cause he said
If I multiply a number L by another number M, I get 452,199. If I multiply L by the successor of M, I get 454,322. Find L x L.
plz tell the answer fast plz in is urgent :)
Step-by-step explanation:
L * M = 452,199
L * (M + 1) = 454,322
Therefore L * (M + 1) = L * M + L.
=> 454,322 = 452,199 + L, L = 2,123.
Hence L² = 2,123² = 4,507,129.
-3x + 4y = 24
4x - y = 7
Answer:
y=7-4x/-1
y=-7+4x
substituting y=-7+4x
-3x+4(-7+4x)=24
-3x-28+16x=24
-3x+16x-28-24=0
13x-52=0
13x=52
x=52/13
x=4
substituting x=4
-3x+4y=24
-3(4)+4y=24
-12-24+4y=0
-36+4y
4y=36
y=36/4
y=9
The product of 3.4×10 to the -14th power and 1.8×10 to the 28th power
Answer:
6.12x10¹⁴
Step-by-step explanation:
...........................
Answer:
A
Step-by-step explanation:
3.4x10^-14 x 1.8x10^28
3.4x1.8 x 10^-14+28
6.12 x 10^14
3x-10=8 i need help with this
Answer:
x=6
Step-by-step explanation:
3x=18
x=6
Answer:
x=6
Step-by-step explanation:
2 step equations
We want to factor the following expression:
4x² - 9y
MY
Which pattern can we use to factor the expression?
U and V are either constant integers or single-variable expressions.
Pro
Choose 1 answer:
Pro
Tea
(U + V)? or (U – V)
e-(U+V)(U-V)
We can't use any of the patterns.
Answer:
The answer is B :
Select the function that's represented in the graph.
options:
A)
ƒ(x) = (x + 3)2 – 5
B)
ƒ(x) = 3(x + 3)2 – 5
C)
ƒ(x) = (x – 3)2 – 5
D)
ƒ(x) = 3(x – 3)2 – 5
Answer:
the answer is c
Step-by-step explanation:
because it mets up
increase 19060 by 9%
Answer:
0.05
Step-by-step explanation:
brainliest plz
A miniature rocket is launched off a roof 20 feet above the ground with an initial velocity of 22 feet per second.
a) How high is the rocket after 3 seconds?
b) How long will it take before the rocket reaches the ground?
Answer:
B (had to be 20 leeters long ;-;;;;;;;;;;;;;;;;;;;;)
Step-by-step explanation:
The cost of polishing 35 identical wooden cubical boxes at the rate of rs. 20 per sq. cm is rs. 1,51,200. Find the edge of each cubical box
Answer: 6 cm
Step-by-step explanation:
Total surface area of cubical box = [tex]6a^2[/tex] , a= edge length of cube (i)
As per given ,
Total surface area of one box = [tex]\dfrac{\text{Cost of polishing}}{\text{Rate} \times\text{Number of boxes}}[/tex]
[tex]=\dfrac{151200}{20\times35}\\\\=\dfrac{151200}{700}\\\\= 216\ sq. cm[/tex] (ii)
Now from (i) and (ii) ,
[tex]6a^2 = 216\\\\\Rightarrow\ a^2= 36\\\\\Rightarrow\ a= 6 \text{ [By taking square root on both sides]}[/tex]
Hence, the edge of each cubical box = 6 cm.
I neeeeeedddddd helppppp
Answer:
yes
Step-by-step explanation:
They both have a 25 degree angle, and the second one is just the first one but put on the page at a different angle
Help me with this pls
Answer:
x=65
Step-by-step explanation:
90 degree angle
90-25= 65
It is a straight line with angle measures of 90°, x° and 25° opposite to the angle marked 180°.
Hence, their sum is 180°.
➛[tex]90 \degree + x + 25 \degree = 180 \degree[/tex]
➛[tex]115 \degree + x = 180 \degree[/tex]
Then,
➛[tex] x = 180 \degree - 115 \degree[/tex]
➛[tex]x = 65 \degree[/tex]
Hence:-The measure of the angle will be 65° (Ans)
~[tex] \large{ \blue{ \sf{FadedElla}}}[/tex]
Write an explicit formula for an, the nth term of the sequence 7, 12, 17,
Step-by-step explanation:
I can't really remember this but it should be
5n +2
Something like this, I am not sure but when you fix in the values you'll get the answer. Do you understand what I'm saying?
Need done quickly pls help
Write an equation of a line that passes through the point (4,3) and is perpendicular to the graph of the equation y=−13x+4.
Answer:
An equation of a line that passes through the point (4,3) and is perpendicular to the graph of the equation will be:
[tex]y=\frac{1}{13}x+\frac{35}{13}[/tex]Step-by-step explanation:
We know that the slope-intercept form of the line equation is
[tex]y=mx+b[/tex]
where
m is the slopeb is the y-interceptGiven the line
y = -13x+4
comparing with the slope-intercept form of the line equation
The slope of the line = m = -13
We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:
slope = m = -13
Thus, the slope of the the new perpendicular line = – 1/m = -1/-13 = 1/13
Using the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where
m is the slope of the line(x₁, y₁) is the pointsubstituting the values of the slope m = 1/13 and the point (4, 3)
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-3=\frac{1}{13}\left(x-4\right)[/tex]
Add 3 to both sides
[tex]y-3+3=\frac{1}{13}\left(x-4\right)+3[/tex]
[tex]y=\frac{1}{13}x-\frac{4}{13}+3[/tex]
[tex]y=\frac{1}{13}x+\frac{35}{13}[/tex]
Therefore, an equation of a line that passes through the point (4,3) and is perpendicular to the graph of the equation will be:
[tex]y=\frac{1}{13}x+\frac{35}{13}[/tex]y is inversely proportional to the square of x.
y = 8 when x = 3.5
8
Find the negative value of x when y= 8/9
Step-by-step explanation:
x²y = k, where k is a real constant.
When x = 3.5, y = 8.
=> (3.5)²(8) = k, k = 98.
When y = 8/9,
we have x²(8/9) = (98).
=> x² = 110.25
=> x = 10.5 or x = -10.5.
Since we want the negative value,
the answer is x = -10.5.
The required negative value of variable x when y = 8/9 is -10.5. To understand the calculations, check below.
Proportion:Important information:
y is inversely proportional to the square of x.y=8 when x=3.5.Using the given inverse proportional statement, we get
[tex]y\propto \dfrac{1}{x^2}[/tex]
[tex]y=\dfrac{k}{x^2}[/tex] ...(i)
Substitute [tex]x=3.5,y=8[/tex].
[tex]8=\dfrac{k}{3.5^2}[/tex]
[tex]8=\dfrac{k}{12.25}[/tex]
[tex]8\times 12.25=k[/tex]
[tex]98=k[/tex]
Substitute [tex]k=98[/tex] in (i).
[tex]y=\dfrac{98}{x^2}[/tex]
Substitute [tex]y=\dfrac{8}{9}[/tex].
[tex]\dfrac{8}{9}=\dfrac{98}{x^2}[/tex]
[tex]x^2=98\times \dfrac{9}{8}[/tex]
[tex]x^2=110.25[/tex]
[tex]x=\pm \sqrt{110.25}[/tex]
[tex]x=\pm 10.5[/tex]
We need only negative value.
[tex]x=-10.5[/tex]
Therefore, the required value of variable x is -10.5.
Find out more about 'Proportion' here:
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A bacteria sample can be modeled by the function f(x) - 350(1.20) which gives the number of bacteria in the sample at the end of x days. Which statement is the best interpretation of one of the values in this function? 11) A) The initial number of bacteria is 350. B) The number of bacteria at the end of one day is 350. 9 The initial number of bacteria decreases at a rate of 20% D) The number of bacteria increases at a rate of 120% each day.
Answer: A) The initial number of bacteria is 350.
Step-by-step explanation:
Exponential growth equation: [tex]f(x)=A(1+r)^x[/tex] , where A=Initial value, r= growth rate. (i)
Given: A bacteria sample can be modeled by the function [tex]f(x) = 350(1.20)[/tex]which gives the number of bacteria in the sample at the end of x days.
Here, [tex]f(x)=350(1+0.20)[/tex]
Compare this equation to (i) , we get A = 350 and r= 0.20 = 20% (growth rate)
So, the best interpretation of one of the values in this function are:
A) The initial number of bacteria is 350.
Answer:
A
Step-by-step explanation:
I did the prep
a number increased by eighteen
Answer:
can you explain a little bit more
Step-by-step explanation:
an alloy is made by mixing metals A and B in the ratio 3:5
metal a costs £42 per kg
metal b costs £20 per kg
how much would it cost to make 400g of the alloy?
Answer:
11.3
Step-by-step explanation:
First solve how many grams of each mineral you need.
To do this use this equation
[tex]\frac{3}{5} =\frac{x}{y} ; x+y=400[/tex]
Solve the system of equations to get
x=150, y=250
Since there are 1000 grams in 1 kg then the amount of kg of each material you need will be
[tex]x=\frac{150}{1000}; y=\frac{250}{1000}[/tex]
So you need to 0.15 of a kg of mineral a and 0.25 kg of mineral b.
Multiply 0.15 by 42 to get the amount of money needed to buy mineral a.
0.15*42=6.3
Multiply 0.25 by 20 get the amount of money needed to buy mineral b.
0.25*20= 5
Add them to get the final amount
6.3+5=11.3