[tex]P(t) = 3e^t - e^t + 3e - 2e^2[/tex]
The rate of growth of a population of bacteria is given by [tex]P'(t) = 3e^t - e^t.[/tex] To find the population P(t) at any time t, you need to integrate P'(t) with respect to t.
[tex]∫(3e^t - e^t) dt = 3∫e^t dt - ∫e^t dt = 3e^t - e^t + C[/tex], where C is the constant of integration.
Now, use the given information P(2) = 3e to find C:
[tex]3e = 3e^2 - e^2 + C => C = 3e - 2e^2[/tex]
So, the population P(t) at any time t is:
[tex]P(t) = 3e^t - e^t + 3e - 2e^2[/tex]
Unfortunately, none of the given options exactly match this answer. Please check the original question for any typos or errors.
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Help solve these (find the slope of each line) 8 problems don’t just give the answer show your work please
Answer:
Khan Academy.
Step-by-step explanation:
You can go on khan academy and search up "area and graphs." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.
Write an equation of a line in slope intercept form going through the points (1,6) and (3,0)
Answer:
y = -3x + 9
Step-by-step explanation:
The slope is
[tex] \frac{6 - 0}{1 - 3} = - 3[/tex]
Substituting into point-slope form, we get
y = -3(x-3)
y = -3x + 9
In the given circle the m∠DFB is 41°, mArc EF is 52° what is the m∠C ?
Check the picture below.
The requried measure of the angle m∠C in the given circle is 15°.
In the given circle the m∠DFB is 41°, mArc EF is 52°
To find out the measure of the angle m∠C.
Following the properties of arcs in the circle,
arc BD = 2m∠BFD
arc BD=2*41 = 82
Now we know that,
The angle subtended by two sectants drawn from the single point that lies outside the circle is given by the difference in larger and minor arcs divided by 2.
∠c= BD- EF / 2
∠c = 82°-52°/2
∠c = 15°
Thus, the requried measure of the angle m∠C in the given circle is 15°.
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. Distribute the among the atoms, giving ( for hydrogen) to as many atoms as possible. First get electrons atoms, then atoms.
Answer:
Bonding theories predict
Step-by-step explanation:
how atoms bond together to form compounds. They predict what combinations of atoms form compounds and what combinations do not. Bonding theories explain the shapes of molecules, which in turn determine many of their physical and chemical properties
Which of the following sets is equal to {1, 2, 3, ...}?
{x | x R, x ≥ 1}
{x | x R, x > 1}
{x | x N, x ≥ 1}
From the list of options, the set that is equal to the set {1, 2, 3, ...} is {x | x N, x ≥ 1}
How to determine the set?The set is given as:
{1, 2, 3, ...}
The three dots (...) after 3 implies that the elements of the set include other values such as 4, 5, 6 and so on
Using the above scenario, we can see that the set {1, 2, 3, ...} contains only positive integers.
All positive integers are natural numbers and they are denoted by N
From the list of options, we have:
{x | x R, x ≥ 1}
This represents the set of all real numbers greater than or equal to 1.
Note that this set includes decimal numbers i.e. 1, 1.5, 1.89 and so on
This does not represent the set {1, 2, 3, ...}
{x | x R, x > 1}
This represents the set of all real numbers greater than 1.
Note that this set includes decimal numbers i.e. 1.5, 1.89 and so on
This does not represent the set {1, 2, 3, ...}
{x | x N, x ≥ 1}
This represents the set of all natural numbers greater than or equal to 1.
Note that this set does not include decimal numbers i.e. 1, 2, 3, 4 and so on
This does represent the set {1, 2, 3, ...}
Hence, the set that is equal to the set {1, 2, 3, ...} is {x | x N, x ≥ 1}
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Write the quotient in scientific notation and in
standard form.
(3.64 x 10000000) (2.6 x 10000)
Answer:
3.64 × 10(raised to the power 7)
2.6 × 10⁴
M<2=7x+,m<3=4y,and m<4=122 , find the values of x and y.
The values of x and y in the equation are 15 and 28 respectively
How to find the variables in an equation?Let's find the x and y values in the equation,
m = 7x + 7
m = 4y
m = 112
Therefore,
4y = 7x + 7
4y - 7x = 7
4y = 112
y = 112 / 4
y = 28
Therefore,
4(28) - 7x = 7
112 - 7x = 7
112 - 7 = 7x
105 = 7x
x = 105 / 7
x = 15
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A lifeguard sitting in a tower 10ft off the ground spots swimmer in trouble at a 55 angle of depression. If the lifeguard tosses a ring in a 15ft rope to the swimmer, can the ring reach the swimmer? Finish solving the problem below to determine your answer
Based on the given parameters, the 15 ft rope will reach the swimmer
How to determine if the ring reach the swimmer?From the question, we have the following equation:
sin 55 = 10/x
Multiply both sides of the equation by x
x * sin 55 = 10/x * x
Evaluate the product
x * sin 55 = 10
Divide both sides by sin 55
x = 10/sin 55
Evaluate sin 55
x = 10/0.8192
Evaluate the quotient
x = 12.21
From the question, the lifeguard tosses a ring in a 15ft rope to the swimmer
15 is greater than 12.21
This means that the 15 ft rope will reach the swimmer
Hence, the 15 ft rope will reach the swimmer
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Can someone please help me
Answer:
Right option is B.
Step-by-step explanation:
[tex] \sf \longrightarrow \frac{ \sec x \sin( - x) + \tan( - x) }{1 + \sec( - x) } \\ \\ \sf \longrightarrow \frac{ \sec x( - \sin x) - \tan x}{1 + \sec x} \\ \\ \sf \longrightarrow \frac{ - \frac{1}{ \cos x } \times \sin x - \tan x }{1 + \sec x} \\ \\ \sf \longrightarrow \frac{ - \tan x - \tan x}{1 + \sec x} \\ \\ \sf \longrightarrow \frac{ - 2 \tan x}{1 + \sec x} \\ \\ \sf \longrightarrow \frac{ \frac{ - 2 \sin x}{ \cos x} }{1 + \frac{1}{ \cos x} } \\ \\ \sf \longrightarrow \frac{ \frac{ - 2 \sin x}{ \cos x} }{ \frac{ \cos x + 1}{ \cos x} } \\ \\ \boxed{ \sf{\longrightarrow \frac{ - 2 \sin x}{ \cos x + 1} }}[/tex]
What is the reason for statement 7 in the given proof?
A) definition of midpoint
B) definition of slope
C) parallel lines have equal slopes.
D) using point-slope formula
Answer: definition of slope
Step-by-step explanation:
The results in step 7 come from substituting the coordinates into the slope formula.
In your rectangular backyard, you know the width of the yard is three less than four times the length. If the perimeter of your yard is 24 yards, what is the width?
Answer: 9 yards
Step-by-step explanation:
Let's make equations to represent each situation.
The first equation says that the width is 3 less than 4 times the length, so let's put that into an equation:
[tex]w=4l-3[/tex]
Next, we can use the perimeter equation that [tex]P=2l+2w[/tex]. Since we know the perimeter is 24 yards, we can replace it for P.
[tex]24=2l+2w[/tex]
Now that we have two equations with two variables, we can use either elimination or substitution to solve them. Since w is already solved for in the first equation, let's plug it in the second equation.
[tex]24=2l+2(4l-3)\\ 12=l+4l-3\\ 12=5l-3\\ 15=5l\\ l=3[/tex]
Now, let's put l back into the first equation to solve for w.
[tex]w=4(3)-3\\ w=12-3\\ w=9[/tex]
The width is 9 yards
Seventy percent of kids who visit a doctor have a fever and 21% of kids have fever and sore throats . what is the probability that a kid who goes the doctor has a sore throat given that he has a fever? (when entering your answer remember that the probability is a number between 0 and 1)
The probability that a kid who goes to the doctor has a sore throat given that he has a fever is 0.30 or 30%. Computed using conditional probability.
The probability of any event A given that event B has already taken place is found using the formula P(A|B) = P(A ∩ B)/P(B). This is known as conditional probability, where P(A ∩ B) is the probability of events A and B, and P(B) is the probability of event B.
In the question, we are given that 70% of kids who visit a doctor have a fever and 21% of kids have a fever and sore throats.
We are asked to find the probability that a kid who goes to the doctor has a sore throat given that he has a fever.
We suppose the event of going to the doctor while having a fever to be B, and going to a doctor while having a sore throat to be A.
We are given that 70% of kids who visit a doctor have a fever, that is, the probability of event B, P(B) = 70% = 0.7.
We are given that 21% of kids who visit a doctor have a fever and sore throats, that is, the probability of event A and event B, P(A ∩ B) = 21% = 0.21.
We are asked to find the probability that a kid who goes to the doctor has a sore throat given that he has a fever, that is, we are asked to find the conditional probability of event A, when event B has already taken place, that is, P(A|B).
By formula, we know that:
P(A|B) = P(A ∩ B)/P(B) = 0.21/0.70 = 0.30.
Thus, the probability that a kid who goes to the doctor has a sore throat given that he has a fever is 0.30 or 30%.
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Given: AD BC and ZBCD ZADC
Prove: DE CE
D
Assemble the proof by dragging tiles to
the Statements and Reasons columns.
Intro
Angles Segments Triangles Statements Reasons
ZADC
ZDEA
Statements
ZECD
ZBCD
ZEDC
ZCBE
Reasons
ZCEB
ZDAE
The proofing of the triangle is illustrated below.
How to illustrate the triangle?Based on the information, the reflexive property of equality states that an angle or shape is always congruent to itself.
The alternate interior angle theorem is that when two parallel lines are cut by a transversal, then the alternate interior angles are the same.
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Answer:
answer in picture
Step-by-step explanation:
A fair die is tossed 5 times. Let $\dfrac{m}{n}$ be the probability that at least two consecutive tosses have the same number, where $m$ and $n$ are relatively prime positive integers. Find $m$.
The probability that no two consecutive heads will occur is 13/32.
What is probability?It should be noted that probability simply means the likelihood of the occurence of an event based on chance.
In this case, the fair coin is tossed 5 times and we simony want it find the probability that no two consecutive heads will occur.
This will be:
Let n be the number of strings of h
Let t be the length n with two adjacent H's.
Therefore, the probability will be:
= (8+5)/2^5
= 13/32
In conclusion, the probability that no two consecutive heads will occur is 13/32.
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i need help with this page
Step-by-step explanation:
what is not clear that you cannot answer this by yourself ?
please let me know what you need explained.
1. Rhombus
2. rectangle
3. square
4. rhombus
5. square
6. rectangle
7. rhombus
8. parallelogram
3. A train travels 20 km at a uniform speed of 60 km/h and the next 20 km at a uniform speed of 80km/h. Calculate its average speed.
Answer:
Given,
Distance traveled = 20 km
Speed = 60 km/h
So, timetaken=DistanceSpeed=2060=13h
For the next journey
Distance traveled = 20 km
Speed = 80 km/h
So, timetaken=DistanceSpeed=2080=14h
Now,
Total distance traveled = 20 + 20 = 40 km
Total time taken = 13+14=712
We know,
Averagespeed=TotaldistancetraveledTotaltimetaken=40712=68.5 km/h
Hence the average speed of the train is 68.5 km/h
X: -1/2
-6(x-2)
pls i need a result
Answer:
15
Step-by-step explanation:
First, we can plug -1/2 into the equation and get -6(-1/2 -2). Then, we can convert -2 into a fraction to get -4/2. If we subtract -4/2 from -1/2, we get -6(-5/2). We then multiply this and get 30/2 which simplifies to 15
Can someone help me
Answer: Choice B
All real numbers except 2 and 5
===========================================================
Explanation:
Factor the denominator. We need to find two numbers that multiply to 10 and add to -7.
Through trial and error, those two numbers are -2 and -5
-2 times -5 = 10
-2 plus -5 = -7
This means the denominator [tex]\text{x}^2 - 7\text{x} + 10[/tex] factors to [tex](\text{x}-2)(\text{x}-5)[/tex]. You can use the FOIL rule to confirm this.
Then each piece is set equal to zero to solve for x
x-2 = 0 leads to x = 2
x-5 = 0 leads to x = 5
------------
In short, if x = 2 or x = 5, then it causes the the denominator [tex]\text{x}^2 -7\text{x}+10[/tex] to turn into 0.
Dividing by 0 is not allowed; therefore, x = 2 nor x = 5 is allowed in the domain. Any other x value is valid.
If f(-1) for the polynomial….
Answer:
Yes ,because (x+1) is the factor of all degree 4 polynomial
What is the maximum number of consecutive odd positive integers that can be added together before the sum exceeds $401$
The maximum number of integers is 27 that can be added together before the summation of the A.P. Series exceeds 401.
According to the statement
We have a given that the maximum sum of the positive integers is 400.
And we have to find the value of n which is a maximum number of integers by which the value of sum become 400.
So, to find the value of the n we use the
A.P. Series'Summation formula
According to this,
S = n (n+1)/2
Here the value of s is 401
Then
S = n (n+1)/2
401 = n (n+1)/2
401*2 = n (n+1)
802 =n (n+1)
n (n+1) = 802
n^2 + n -802 =0
By the use of the Discriminant formula the
value of n becomes n = -28 and n = 27.
The negative value of n is neglected.
Therefore the value of n is 27.
So, The maximum number of integers is 27 that can be added together before the summation of the A.P. Series exceeds 401.
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WILL GIVE BRAINLIES!! How can one data display be used to create a data display of a different form?
The method whereby data display can be used to create a data display of a different form is as done below.
How to create a programming model?To answer this question means we are trying to create a view page where we need to display data as well as a form to insert data.
Now, for us to insert data we can use a bootstrap modal which is;
public ActionResult GetFirm()
{
return View(db.FirmModels.ToList());
}
The view page would be given and then the way to do it is;
Pass a list to the view and define your view model as:
model IEnumerable<models.FirmModel>
The IEnumerable interface is implementing the GetEnumerator() method used to iterate through the collection.
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Solve the following linear system algebraically. State why you chose the method you used.
x + 3y = 7
2x + 4y = 11
There are two methods of solving systems of equations:
substitutioneliminationSubstitution is where we substitute one equation into the other by isolating a certain variable, or a group of terms.
Elimination is where we subtract the two equations. Before doing this, we may have to multiply one equation by a certain number to make sure one variable cancels out.
Solving the QuestionWe're given the following equations:
[tex]x + 3y = 7[/tex][tex]2x + 4y = 11[/tex]Because they are organized in the same manner (i.e. x [operation] y [equals] number), it is easier for us to use elimination.
First, multiply the first equation by 2:
[tex]x + 3y = 7\\2(x + 3y) = 2(7)\\2x + 6y = 14[/tex]
Now, subtract the second equation from the one we just created:
[tex]\hspace{10}2x + 6y = 14\\-2x + 4y = 11\\\rule{67}{0.3}\\2y=3[/tex]
Solve for y:
[tex]y=\dfrac{3}{2}[/tex]
To solve for x, we can use substitution in the first equation:
[tex]x + 3y = 7\\\\x + 3(\dfrac{3}{2}) = 7\\\\x + \dfrac{9}{2} = 7\\\\x = 7- \dfrac{9}{2}\\\\x = 7- 4.5\\\\x = 2.5\\\\x=\dfrac{5}{2}[/tex]
Answer[tex]x=\dfrac{5}{2}[/tex]
[tex]y=\dfrac{3}{2}[/tex]
The elimination method is ideal for solving this system of equations. By which number must you multiply the second equation to eliminate the
y-varlable, and what is the solution for this system?
x+3y=42
2x-y=1
=======================================================
Explanation:
The 3y in the first equation must add to -3y so the y terms go away. We have -y in the second equation, which is why we triple everything in that equation
2x-y = 1 becomes 6x - 3y = 3 after tripling everything. This is the same as multiplying both sides by 3.
This is the updated equivalent system
[tex]\begin{cases}x+3y = 42\\6x-3y = 3\end{cases}[/tex]
Add the terms straight down
x+6x becomes 7x3y+(-3y) becomes 0y or 0. The y variables are eliminated.The right hand sides 42 and 3 add to 45We have the equation 7x = 45 which solves to x = 45/7.
Unfortunately it doesn't turn into a nice single whole number because 45 isn't a multiple of 7. So I would leave it as a fraction.
Optionally you could note that 45/7 = 6.42857 approximately. But I prefer the fraction form since it's most exact.
--------------
Use this x value to find y. Pick any equation involving x and y. Plug in that x value and solve for y.
x + 3y = 42
45/7 + 3y = 42
3y = 42 - 45/7
3y = 42*(7/7) - 45/7
3y = 294/7 - 45/7
3y = (294 - 45)/7
3y = 249/7
y = (249/7)*(1/3)
y = 83/7
Like with x, we also don't get a nice whole number.
I used WolframAlpha to confirm the solutions. GeoGebra is another tool you could use.
PLEASE HELP IM SERIOUSLY STUCK E
Answer: 2.12 × [tex]10^{-3}[/tex]
The coefficient (in green) will be 2.12
Step-by-step explanation:
Scientific notation is written by multiplying the number by a power of 10. This number is a number between 1 and 10.
Since this is a smaller number, we will be multiplying it by a power of 10 to a negative number.
To get this value to a number between 1 and 10, we must multiply it by 10 3 times (also shown as 10³) which gives us 2.12.
To get back to the original value, we multiply this by [tex]10^{-3}[/tex]. This gives us our answer.
Let your dependent variable in the function be y. Write the function that models the independent variable in terms of y, using logarithms.
Function: [tex]f(x)=2.56(1.04)^x[/tex]
The function that models the independent variable, x, in terms of y, is:
[tex]x = ln(\frac{y}{2.56})/ln(1.04)[/tex]
How to write the independent variable in terms of y?
Here we have the relation:
[tex]y = 2.56*(1.04)^x[/tex]
We want to write x in terms of y, so we just need to isolate x.
We have:
[tex]\frac{y}{2.56} = (1.04)^x[/tex]
Now we can apply the natural logarithm in both sides, so we get:
[tex]ln(\frac{y}{2.56}) = ln((1.04)^x)\\\\ln(\frac{y}{2.56}) = ln((1.04))*x[/tex]
Now we can just isolate x.
[tex]x = ln(\frac{y}{2.56})/ln(1.04)[/tex]
That is the function that models the independent variable, x, in terms of y.
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The volume of the cylindrical water tank shown below is 490π feet^3. If the tank is 10 feet high, what does its radius r equal?
The cylindrical water tank with a volume of 490π feet³, and a height of 10 feet, has a radius of 7 feet.
The volume of a cylinder having a radius of r units, and a height of h units, is given by the formula, V = πr²h.
In the question, we are asked to find the radius (r), of a cylindrical water tank, with a volume of 490π feet³, and a height of 10 feet.
Substituting the value of V = 490π feet³, and h = 10 feet, in the formula for the volume of a cylinder, V = πr²h, we get:
490π feet³ = π.(r²)(10 feet).
Rearranging this, we can write:
r² = (490π)/(10π) feet²,
or, r² = 49 feet²,
or, r = √49 feet,
or, r = 7 feet.
Thus, the cylindrical water tank with a volume of 490π feet³, and a height of 10 feet, has a radius of 7 feet.
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Every time I use a piece of scrap paper, I crumple it up and try to shoot it inside the recycling bin across the room. I'm pretty good at it: If I shoot $5$ pieces of paper at the recycling bin, at least one of them will make it inside the recycling bin with probability $\frac{211}{243}$. If I shoot $6$ pieces of paper at the recycling bin, what's the probability at least two of them make it inside the recycling bin
Using the binomial distribution, it is found that there is a 0.0012 = 0.12% probability at least two of them make it inside the recycling bin.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.With 5 shoots, the probability of making at least one is [tex]\frac{211}{243}[/tex], hence the probability of making none, P(X = 0), is [tex]\frac{232}{243}[/tex], hence:
[tex](1 - p)^5 = \frac{232}{243}[/tex]
[tex]\sqrt[5]{(1 - p)^5} = \sqrt[5]{\frac{232}{243}}[/tex]
1 - p = 0.9908
p = 0.0092
Then, with 6 shoots, the parameters are:
n = 6, p = 0.0092.
The probability that at least two of them make it inside the recycling bin is:
[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]
In which:
[P(X < 2) = P(X = 0) + P(X = 1)
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{6,0}.(0.0092)^{0}.(0.9908)^{6} = 0.9461[/tex]
[tex]P(X = 1) = C_{6,1}.(0.0092)^{1}.(0.9908)^{5} = 0.0527[/tex]
Then:
P(X < 2) = P(X = 0) + P(X = 1) = 0.9461 + 0.0527 = 0.9988
[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.9988 = 0.0012[/tex]
0.0012 = 0.12% probability at least two of them make it inside the recycling bin.
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The probability of an outcome being more than three standard deviations away from the mean in a normal distribution is approximately ___ percent.
The probability in a normal distribution is approximately 90% percent.
According to the statement
we have given that the
Probability of the more three standard deviations and we have to find the percentage in a normal distribution.
We know that the
A normal distribution is a type of continuous probability distribution for a real-valued random variable.
So, In the presence of a more than three standard deviations the normal distribution is about 95%.
Because in the normal distribution is 95% due to the empirical rule.
The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution.
So, The probability in a normal distribution is approximately 90% percent.
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Which graph is the sequence defined by the function f(x) = 3(2)x-1?
On a coordinate plane, 5 points are plotted. The points are (0, 2), (1, 6), (2, 18), (3, 54), (4, 162).
On a coordinate plane, 5 points are plotted. The points are (1, 2), (2, 6), (3, 18), (4, 54), (5, 162).
On a coordinate plane, 6 points are plotted. The points are (0, 3), (1, 6), (2, 12), (3, 24), (4, 48), (5, 96).
On a coordinate plane, 5 points are plotted. The points are (1, 3), (2, 6), (3, 12), (4, 24), (5, 48).
Answer: On a coordinate plane, 5 points are plotted. The points are (1, 3), (2, 6), (3, 12), (4, 24), (5, 48).
Step-by-step explanation:
When x=1, f(x)=3. So, it passes through (1,3).
So, everything is eliminated except for option (4).
Answer:
D!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
At a restaurant, Lana gets a bill that is $40 for the food plus a 5% sales tax. Lana decides to tip 20% on the total bill. How much will Lana pay in total?
Answer:
$50.40
Step-by-step explanation:
To find how much Lana will pay in total follow these steps.
First, multiply 40 by 1.05.
40×1.05=42.
This is how much she will pay for the food plus tax.
Now, multiply 42 by 1.2.
42×1.2=50.40
This is how much she will pay for the food, tax, and tip.
Lana will pay a total of $50.40.
Hope this helps!