What is the first derivative of the following function: f(x) = aexp(-bx)
Answer:
The first derivative of the given function
[tex]\frac{df(x)}{dx} = - ab e^{-b x}[/tex]
Step-by-step explanation:
Step(i):-
Given f(x) = ae⁻ᵇˣ ...( i )
we will use differentiation formula
[tex]\frac{d(e^{ax}) }{dx} = a e^{a x}[/tex]
Step(ii)
Differentiating equation (i) with respective to 'x', we get
[tex]\frac{df(x)}{dx} = a e^{-b x} \frac{d}{dx} (-b x )[/tex]
= -ab e⁻ᵇˣ
[tex]\frac{df(x)}{dx} = - ab e^{-b x}[/tex]
Final answer:-
The first derivative of the given function
[tex]\frac{df(x)}{dx} = - ab e^{-b x}[/tex]
please help, i will give brainliest
Answer:
24
Step-by-step explanation:
hope i helped
plsss help asap!!!! i need it i have a time limit
Answer:
32
Step-by-step explanation:
90 = 7y + 27
7y = 63
y = 9
180 = 58 + 7(9) + 27 + $
$ = 32
It might be wrong
A triangle drawn on a map has sides of lengths 9 cm, 12 cm, and 15 cm. The shortest of the
corresponding real-life distances is 122 km Find the longest of the real-life distances,
Answer:
26
Step-by-step explanation:
Please help me with some math im stuck
y = - 40
- 40 since theres no letters it gonna be -40.
The length of the carpet is 2a2 and width is 3a. Find the area of the carpet.
HELP ME PLEASE
Answer:
[tex]6a^{3}[/tex]
Step-by-step explanation:This is a very simple question.
We all know that the equation or formula for area is...
A= L*W
So multiply...
[tex]2a^{2} *3a[/tex]= [tex]6a^{3}[/tex]
Since 3a has an exponent power of 1 and you add the exponent power when multiplying...
The result would be... [tex]6a^{3}[/tex].
Hope this helps:)
please answer i need help quick
Answer:
(-2, 6)
Step-by-step explanation:
Since you want a 1 to 7 ratio, you want to divide the line into 2 parts, where one part has a length of 1 and the other has a length of 7. So the total length of the line is 8.
Start by looking at the difference in the X and Y coordinates.
X = | -4 - 12 | = | -16 | = 16
Y = | 7 - -1 | = | 8 | = 8
You could calculate the length of the line using pythagorian's theorem, but that's not needed. Simply use similar triangles. We have a right triangle with legs of length 16 and length 8. We want a similar triangle that is 1/8th as large (to get the desired 1 to 7 ratio). So divide both legs by 8, getting lengths of 16/8 = 2, and 8/8 = 1.
Now add those calculated offsets to point A.
A has an X coordinate of -4 and B has an X coordinate of 12 and the X coordinate for C must be between those limits. So calculate -4 + 2 = -2 to get the X coordinate for C.
The Y coordinate of A is 7 and the Y coordinate of B is -1. And since the Y coordinate must be between then, you have 7 - 1 = 6.
So the coordinates for C is (-2, 6)
How many tablets of 6 mg can be made from 0.6 kg of medicine?
Answer:
100 000 tablets
Step-by-step explanation:
1 mg = 0.001 g ⇒ 6 mg = 0.006 g
1 kg = 1000 g ⇒ 0.6 kg = 600 g
600 g / 0.006 g = 100 000 tablets
k=6
c=2
5 • k - 10c + 8
Answer:
22-10c
Step-by-step explanation:
The simplified value of the expression is 18
Given the expression :
5 * k - 10c + 8k = 6c = 2To solve , substitute the values of k and c into the equation
Now we have ;
5 * 6 - 10(2) + 8
5 * 6 - 20 + 8
30 - 20 + 8
30 - 12
= 18
Hence, the. simplified value of the expression is 18
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2635 divided by 17 in long form
Answer:
155
Step-by-step explanation:
17 can go into 26. 1 time then 26-17=9
bring down the 3 and it turns into 93
17 can go into 93 5 times. that equals 85
93-85=8 then add the 5 that make 85
85 divided by 17 =5
so the answer is 155
According to a family-oriented lobbying group, there is too much crude language and violence on television. Forty-two percent of the programs they screened had language they found offensive; 27% were too violent, and 10% were considered excessive in both language and violence. What percentage of programs did comply with the group's standards? Give your answer as a percentage and do not put the % sign in your answer.
Its C because its a loaded language
The sum of 18 and a number
Answer:
The expression you are looking for is: 18+x
Step-by-step explanation:
Select a counterexample for the conclusion.
The difference between two even numbers is positive.
A
9-13
B
13-9
C
10-2
D
2-10
Using every day knowledge which of the following statements is an if/then statement whose reverse is also correct.
A. if an ambulance has emergency lights on, then cars on the road pull over.
B. if the TV is unplugged, then the TV will not turn on.
C. if the wind is blowing, then the weather is chilly
D. if the light bulb was recently on, then the lightbulb is hot
B. if the TV is unplugged, then the TV will not turn on.
A conditional statement has two parts: hypothesis (if) and conclusion (then).
The converse is when we switch or interchange our hypothesis and conclusion.
So, we have given statements as:
A. if an ambulance has emergency lights on, then cars on the road pull over.
B. if the TV is unplugged, then the TV will not turn on.
C. if the wind is blowing, then the weather is chilly.
D. if the light bulb was recently on, then the lightbulb is hot.
If we see the converse statement of C.
If the tv does not turn on it’s unplugged.
So the statement is true in both the ways.
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True or False? The absolute value of any number the same as absolute value of its additive inverse
Answer:
true
Step-by-step explanation:
that is true i need twenty charcters
In the class election, the student who gets the highest number of votes will become the class president and the one who gets the second highest
number of votes will become the class vice president. Tabitha and four other students were candidates. Tabitha's teacher announces the election
results as percentages of the total number of votes. Two hundred votes were cast in the election. In this activity, you will relate the percentages of
the votes received to the actual numbers.
Question 1
The table gives the percentage of votes each candidate received. Use the information in the table to understand the results of the election
Candidate Percentage of Votes
Tabitha
30%
Vincent
12%
Esmeralda
22%
Nancy
5%
Tyler
31%
Part A
How many votes did Tabitha receive?
Answer:
Tabitha received 60 votes.
Step-by-step explanation:
200 votes × .30 = 60 votes
The given percentage of votes shows that Tyler win the class elections (has the highest percentage of votes - 31%), and Tabitha received 60 votes (30% of 200).
What are percentages?A percentage is a fraction of a whole number represented as a number out of 100.
How do we solve the given question?We are given the percentages of votes received by the candidates in a class election. We are also informed that a total of 200 votes were cast in the elections.
The percentages are as follows:
Tabitha = 30%
Vincent = 12%
Esmeralda = 22%
Nancy = 5%
Tyler = 31%.
We are asked to find the winner of the election and the number of votes Tabitha received.
As Tyler receives the highest percentage of votes (31%), he is the winner of the elections.
Tabitha received 30% of the votes, and the total number of votes = 200
∴ Number of votes Tabitha received = 30% of 200 = (30/100)*200 = 0.3*200 = 6.
∴ Tabitha received a total of 60 votes.
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Why isn't 0 at the far left of the scales?
Step-by-step explanation:
Why isn't "0" far left of the scales? It's not on the far left side because it wouldn't allow us to be much more precise if it was at the far end. Being where it is, it gives us a closer approximation to the actual distance in the real world.
A bag contains 8 green, 4 black and 6 yellow marbles. How could you use the complement to determine the probability of randomly selecting a green or black marble?
Answer:
12/18=2/3
Step-by-step explanation:
You should add up every marbles to find out how many marbles are in total. Then, you should add the green and black marbles. There are 4 black marbles, and 8 green marbles, which results 12 black+green marbles. Then you should make a fraction 12/18, because you are finding the probability of the green+black marbles out of the total marbles. If you simplify, you get 2/3.
The probability of randomly selecting a green or black marble is 12/18.
What is probability?Probability is the ratio that determines how likely an event is to occur from a set of possible events.
We can find the probability of randomly selecting a green or black marble as shown below:Total number of green marbles = 8
Total number of black marbles = 4
Total number of yellow marbles = 6
Total number of marbles = Total number of green marble + Total number of black marbles + Total number of yellow marbles = 18
P(selecting a green marble) = Total number of green marbles/Total number of marbles
= 8/18
P(selecting a black marble) = Total number of black marbles/Total number of marbles
= 4/18
P(selecting a green or black marble) = (Total number of green marbles + Total number of black marbles)/Total number of marbles
= (8 + 4)/18
= 12/18
Therefore, we have found the probability of randomly selecting a green or black marble to be 12/18.
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The cost of 1.00 Liters of gas is 26.9 cents. How many dollars will 12.0 gallons cost?
The cost of 12 gallons of gas will be 1221.80 cents.
It is given that 1 liter of gas cost 26.9 cents.
We have to calculate the cost of 12 gallons of gas.
What will be the cost of 10 pens if 1 pen costs 2 cent ?
The cost of 10 pens will be 10 × 2 = 20 cent.
As per the question ;
Cost of 1 liter of gas = 26.9 cent
∵ 1 gallon = 3.785 liters
So ,
The cost of 1 gallon of gas = 3.785 × 26.9
The cost of 12 gallons of gas will be ;
= 12 × 3.785 × 26.9
= 1221.80 cents
Thus , the cost of 12 gallons of gas will be 1221.80 cents.
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How many 1-1 functions from a set with five elements to a set with 4 elements?
Answer:
The number is zero
Step-by-step explanation:
From the question we are told to state the number of on-to-one that exist from the set of 5 element to the set 4 element
Generally there are no one-to-one function from a set with a higher number of elements to a set with the lower number of elements
So the correct answer to the question is there are no one-to-one function from the set of 5 elements to the set of 4 elements
1. Find the ratio of oranges to apples if there are 2 pineapples, 4 apples,
6 bananas, and 3 oranges in a fruit bowl.
a. 1 to 2
b. 2 to 4
c. 3 to 4
d. 3 to 2
Answer: the answer is C because there are 3 oranges and 4 apples
In the city of Lawrenceville, how many phone numbers are possible using the area code 678? The restrictions for the phone company are listed below. · The first digit of the phone number cannot be numbers 0-5. · The second number cannot be a zero. · The third and fourth numbers cannot be a zero or one · The fifth number cannot be a zero, one or two How many phone numbers are possible using the area code 678? a.2000 b.1,6128 c.1,612,800 d.300
Answer:
Hey there!
If there were no restrictions, there would be 10x10x10x10x10 phone numbers.
The first number can only be a 6-9, so that is four options.
The second number can have nine options.
The third and fourth numbers have eight options.
The fifth number has seven options
4x9x8x8x7=16128.
16128 numbers are possible.
Let me know if this helps :)
Valleywood Golf course offers classes Monday through Saturday. The Saturday classes last 75 minutes. If they offered 705-minutes of classes last week, what was the maximum number of weekday classes?
Answer:
Step-by-step explanation:
To make the problem easier to solve, we will set it up as the equation of the length of time of each class times the number of classes equals the total amount of minutes. However, since we don't know the number of classes, we'll symbolize our two unknowns with two variables.
75x + 45y = 705
(75x + 45y)/15 = 705/15
5x + 3y = 47
y = (47-5x)/3
It looks like we can't simplify the equation any more, so now it is a matter of trial and error. The minimum number of Saturday classes means the maximum number of weekday classes. We first will test for the maximum by assuming there are no Saturday classes, then will work our way up until x is an integer.
If x = 0
(47-5(0))/3 = 47/3 = 15.6666
If x = 1
(47-5(1))/3 = 42/3 = 14
This works. Therefore, the maximum number of weekday classes is 14, or choice b.
Help I’m dying I’m giving 20 points plz help
Answer:
20.25
Explanation:
We first need to find the length of one side of the square. We can do this by dividing the area by 4 (27/4), since a square has four sides. You should get 6.75. Now you can multiply 6.75 by three since one side of the square is the same as one side of the triangle. Also, it is an equilateral triangle and all sides are the same. If you multiply correctly, you should get 20.25. Hope this helped!
Answer:
9 sqrt(3)
Step-by-step explanation:
Since the area of the square is 27 cm^2
A = s^2
27 = s^2
Take the square root of each side
sqrt(27) = s
sqrt(9) sqrt(3) = s
3 sqrt(3) =s
We know the the side length of the triangle is s
The perimeter of the triangle is
P =3s = 3 ( 3 sqrt(3))
= 9 sqrt(3)
Please help me!!!!!!!!
Answer:
10) 1/11
11) 18/8 or 2 2/8 or 2 1/4
12) -8/5 or -1 3/5
Step-by-step explanation:
10) -6/11-(-5/11)=-6/11+(5/11)=1/11
11) 1 3/8-(-7/8)=11/8+7/8=18/8 or 2 2/8 or 2 1/4
12) -4/5-4/5=-8/5 or -1 3/5
x+3 divided by 5=30 i need help
Answer:
x = 147
147 + 3 = 150
150 ÷ 5 = 30
Answer:
See answer in the explanation below.
Step-by-step explanation:
x = 147
147 + 3 = 150
150 ÷ 5 = 30
The sum of three consecutive integers is 180. What is the largest integer?
Answer:
61
Step-by-step explanation:
Here's a neat trick when you have an odd number of consecutive numbers.
Call the middle number k
Then the smaller number is k-1
The larger number is k + 1
The two ones will cancel.
k-1 + k + k-1 = 180
3k = 180
k = 180/3
k = 60
Therefore the largest number is k + 1 = 60 + 1 =61
John has $90 in the bank. Every time herides the bus he spends
$2.50. Write an equation that John can use to see how many times
he can ride the bus. Let x = the number of times he can ride the bus.
Answer:90 divided by 2.50= X
36 = X
Step-by-step explanation:
|x+6|=|x−12| Graph the solution
Answer:
Step-by-step explanation:
[tex]\left|x+6\right|=\left|x-12\right|\\\\\mathrm{For\:each\:absolute\:find\:positive\:and\:negative\:intervals}\\ \\\mathrm{For\:}x<-6:\quad \mathrm{No\:Solution}\\\\\mathrm{For\:}-6\le \:x<12:\quad x=3\\\\\mathrm{For\:}x\ge \:12:\quad \mathrm{No\:Solution}\\\\\mathrm{Combine\:Solutions:}\\\\\mathrm{No\:Solution}\quad \mathrm{or}\quad \:x=3\\\\x=3[/tex]
The distribution of IQ (Intelligence Quotient) is approximately normal in shape with a mean of 100 and a standard deviation of 13. According to the standard deviation rule, only (what?) % of people have an IQ over 126.
Answer: 2.5% of people have an IQ over 126.
Step-by-step explanation:
Given: The distribution of IQ (Intelligence Quotient) is approximately normal in shape with a mean of 100 and a standard deviation of 13.
126 = 100 + 2(13) = Mean +2 ( standard deviation)
To find : % of people have an IQ over 126.
i.e. % of people have an IQ over Mean +2 ( standard deviation).
According to the standard deviation rule,
95% of data fall within two standard deviations.
Now, 100% - 95% = 5%
and Half of 5% is 2.5%.
So 2.5% of the data lies below 2 standard deviations of mean and 2.5% of the data lies above 2 standard deviations of mean .
i.e. 2.5% of people have an IQ over 126.