Answer:
3/2Step-by-step explanation:
Given the limit of a function expressed as [tex]\lim_{x \to 1} (\dfrac{3x}{x-1} - \dfrac{3}{lnx})[/tex], we are to evaluate it. To evaluate it, we will simply substitute x = 1 into the function since the variable x tends to 1.
[tex]\lim_{x \to 1} (\dfrac{3x}{x-1} - \dfrac{3}{lnx})\\\\= (\dfrac{3(1)}{1-1} - \dfrac{3}{ln1})\\\\= \dfrac{3}{0} - \dfrac{3}{0}\\\\= \infty - \infty (ind)[/tex]
Since we got an indeterminate function, we will find the LCM of the function and solve again.
[tex]= \lim_{x \to 1} (\dfrac{3x}{x-1} - \dfrac{3}{lnx})\\\\= \lim_{x \to 1} \dfrac{3xlnx-3(x-1)}{(x-1)lnx}\\\\\\= \dfrac{3(1)ln(1)-3(1-1)}{(1-1)ln1}\\\\= \frac{3(0)-3(0)}{0(0)} \\\\= \frac{0}{0} (ind)[/tex]
Applying L'hospital rule;
[tex]\frac{x}{y} = \lim_{x \to 1} \dfrac{d/dx(3xlnx-3(x-1))}{d/dx((x-1)lnx)}\\\\= \lim_{x \to 1} \dfrac{3x(\frac{1}{x})+ 3lnx-3)}{(x-1)\frac{1}{x} +lnx}\\\\= \lim_{x \to 1} \dfrac{3 + 3lnx-3}{(x-1)\frac{1}{x} +lnx}\\\\= \frac{3ln1}{(1-1)\frac{1}{1} +ln1}\\\\= \frac{0}{0} (ind)[/tex]
Applying L'hospital rule again;
[tex]= \lim_{x \to 1} \dfrac{\frac{d}{dx} (3lnx)}{\frac{d}{dx} ((x-1)\frac{1}{x} +lnx)}\\\\= \lim_{x \to 1} \dfrac{\frac{3}{x} }{(x-1)\frac{-1}{x^2} + \frac{1}{x} +\frac{1}{x} }\\\\= \dfrac{\frac{3}{1} }{(1-1)\frac{-1}{1^2} + \frac{1}{1} +\frac{1}{1} }\\\\= \frac{3}{0(-1)+2}\\ \\= \frac{3}{2-0}\\ \\= 3/2[/tex]
Hence the limit of the function is 3/2.
A disinfectant spray bottle say it eliminates 90% of bacteria with each application. You apply the disinfectant once to a countertop in the shipping department and then apply the disinfectant again to the same countertop. If the bottle is correct what percentage of the bacteria originally on the table top have been eliminated
Answer:
%180?
Step-by-step explanation:
90+90 is 180
Easy Algebra Question! Solve for x [tex]b+3/x=f/2[/tex]
Answer:
Step-by-step explanation:
There are two denominators here: x and 2. The LCD is 2x.
Remove the fractions by multiplying all three terms by 2x:
2x(b) + 2x*3/x = 2x*f/2
Reducing these terms, we get:
2xb + 6 = x*f
Grouping the x terms together: 2xb - xf = -6
-6
Solving for x: x = ------------------
2b - f
Which of the following domains represent where the function f(x) = 2(2 - 5)2 + 3 is invertible?
А.
225
B.
IS 3
035
D
2 3
Answer:
a
Step-by-step explanation:
When 12 is divided by 3/4
which statement about the quotient is true? It is equal to 12 3/4, it is greater than 12, is greater than 3/4 but less than 12, it is less than 3/4 
Answer: 2 Answers By Expert Tutors
The rule for division by a fraction is "change to multiplication by the reciprocal." So you want(4/3)(12) which is 4(4) = 16
Step-by-step explanation:
A Queensland toad travels 10 m/day. How far will it travel in 5 hours?
Answer:
2.08
Step-by-step explanation:
10/x = 24/5
50 = 24 x
x = 50 / 24
x = 2.08 m
This answer is rounded to the nearest hundredth.
Answer:
2.083 meters
Step-by-step explanation:
10/24 = 0.416
if the toad travels 10 meters in a day then in order to get how many meters the toad travels in an hour you have to divide that number (10) by 24 which is the number of hours in a day
0.416 × 5 = 2.083
After that you just have to multiply the number of meter that the toad travels in an hour by 5 hours which will get you 2.083 meters
What is the expression for the calculation double 2 and then add 5? Then use x as the variable
Answer:
2x+5
Step-by-step explanation:
RES
Find (fºg)(1)
Ax) = x2 - 1
g(x)= v
a 0
c. 4.
b.
d. 18
Help pls
Answer:
A
Step-by-step explanation:
So we have the two functions:
[tex]f(x)=x^2-1\\g(x)=\sqrt x[/tex]
And we want to find:
[tex](f\circ g)(1)[/tex]
This is the same as:
[tex]f(g(1))[/tex]
So, to find the answer, find g(1) first:
[tex]g(x)=\sqrt x\\g(1)=\sqrt1\\g(1)=1[/tex]
Now, substitute this value for g(1):
[tex]f(g(1))\\=f(1)[/tex]
And plug this into f(x):
[tex]f(x)=x^2-1\\f(1)=(1)^2-1\\f(1)=1-1=0[/tex]
Therefore:
[tex]f(1)=f(g(1))=(f\circ g)(1)=0[/tex]
Our answer is A
The city planning committee wants one tree planted every 20 ft along Dayton Ave. if the perimeter of the plot of land is 234 ft about how many trees will be planted. explain. 12 is an incorrect answer.
Answer:
2 trees
Step-by-step explanation:
Since the city is planting a tree every 20 feet across Dayton Avenue, then we need to find the length of the side that is on Dayton Avenue.
We are missing 3 sides to this. But it's extremely important to note that the side adjacent to Dayton Avenue is the same length as the other missing two sides combined. This is because both of these lengths contain the 1 feather and 2 feather mark - these signify congruence.
This means that the side lengths of both of them combined will be [tex]234-52-68=114[/tex]
This means the side adjacent to Dayton Avenue is
[tex]114\div2=57[/tex] feet long.
Now that we know that the side is 57 feet long, we have to divide this by 20, as a tree is being placed every 20 feet. If we get a decimal, we will have to round down because it gets planted only, and only if, 20 more feet has been accomplished. If we are a fraction of the way there, a tree doesn't get planted.
[tex]57\div20=2.85[/tex]
Rounding down gets us 2.
Hope this helped!
The number of trees to be planted is 2 trees
The process of arriving at the above number of trees is as follows;
The given parameter are;
The perimeter of the plot of land adjacent to Dayton Avenue = 234 ft.
The perimeter has two pair of unknown lengths sides marked with equal lengths symbols
One length each of the two congruent pairs form a linear pair adjacent to the road
The length of one of the other side = 52 feet
The length of the fifth side of the perimeter = 68 ft.
Method;
Let, x, and y represent the lengths of the congruent pairs, we have;
52 ft. + 68 ft. + 2·x + 2·y = 234 ft.
2·x + 2·y = 234 ft. - (52 ft. + 68 ft.) = 114 ft.
The length of the linear pair forming the side of the perimeter adjacent to the road, x + y = 114 ft./2 = 57 ft.
The number of trees planted every 20 ft. = 1 tree
The number of trees, n, that can be planted along the perimeter of the plot of land adjacent to Dayton Avenue which is 57 ft. long is therefore;
n = 57 ft./(20 ft./Tree)
∴ n = 57/20 Trees = 2.85 trees
The number of trees that can actually be planted by the owners of the plot
of land is given by rounding down to the next whole number, given that the
the information is statistical analysis which gives;
n ≈ 2 Trees
The number of trees to be planted = 2 trees
Learn more about statistical analysis here;
https://brainly.com/question/3014289
"Scenario: You have to pay your share of the rent today. The total rent for your apartment is $1762.50. You have two roommates that you share the costs. You owe 1/3 of the rent. You checked your account balance online and your current balance is $668.72"
Answer:
You would be required to pay $587.50
Step-by-step explanation:
Divide $1762.50 by three:
You get $587.50
To find how much you have left:
Subtract 587.50 from 668.72:
You'd be left with
$81.22
Answer:
If you are asking if you can afford to pay rent, then yes you can. Your share of rent would be 1762.50 divided by 3, which equals 587.50. Therefore since 587.50 is less than 668.72, you can afford to pay your rent. Hope this helps!
Step-by-step explanation:
5. (5 points, bonus). Find the Singular Value Decomposition of the matrix A from problem 4. Verify your answer.
Answer:
The question is not complete.
I will explain the concept of Singular Value Decomposition
Step-by-step explanation:
The singular value decomposition (SVD) of a matrix A is the process of factorizing A into the product of three matrices A = [tex]U DV^{T}[/tex] where the columns of U and V are orthonormal and the matrix D is diagonal with positive real entries.
This process is used to carry out many tasks.
Data matrix A is useful to find a low rank matrix which is a good approximation to the data matrix.
The columns of V is called the right singular vectors of A and it normally form an orthogonal set with no assumptions on A. The columns of U is reffered to as the left singular vectors and it also forms an orthogonal set. The orthogonality forms the inverse of A for a square and invertible matrix A which is [tex]V D^{-1}[/tex][tex]U^{T}[/tex].
If we want gain better insight of the process, we will need to treat the rows of an n × d matrix A as n points in a d-dimensional space and find the best k-dimensional subspace with respect to the set of points. This means that we will minimize the sum of the squares of the perpendicular distances of the points to the subspace.
To find the best fitting line through the origin with respect to a set of points {xi |1 ≤ i ≤ n} will mean that we will minimize the sum of the squared distances of the points to the line.
Simplify the expression: 4(5 - n) + 10n
Answer: [tex]6n+20[/tex]
Distribute
[tex](4)(5)+(4)(-n)+10n\\20+-4n+10n[/tex]
Combine Like Terms
[tex]20+-4n+10n\\(-4n+10n)+(20)\\6n+20[/tex]
6 13 51
4 7 29
19 11 ?
What the missing number?
Answer:
I think the answer is 3 ( Maybe)
Whats $61.00 with 7% sales tax?
Answer:
$65.27
Step-by-step explanation:
Multiply $61.00*0.07=65.27
Answer:
$65.27
Step-by-step explanation:
61x.07=4.27
61+4.27=65.27
A student looking at global population figures remarks that between the years 1950 and 2010 the global population can be modelled by the equation 300y = 23t − 44 180 (1950 ≤ t ≤ 2010) Using algebra, calculate the year in which the population passed 6 billion
Answer:
The year in which the population passed 6 billion is 2000.
Step-by-step explanation:
We are given that a student looking at global population figures remarks that between the years 1950 and 2010 the global population can be modeled by the equation 300y = 23t − 44180; where (1950 ≤ t ≤ 2010).
And we have to calculate the year in which the population passed 6 billion.
The given expression is;
[tex]300y=23t-44180[/tex]
Firstly, put t = 1960 {as t lies between 1950 and 2010}
[tex]300y=(23\times 1960)-44180[/tex]
[tex]300y=45080-44180[/tex]
[tex]300y=900[/tex]
[tex]y = \frac{900}{300}[/tex] = 3 billion
But we have to cross the population by 6 billion.
Now, put t = 1999 in the expression;
[tex]300y=(23\times 1999)-44180[/tex]
[tex]300y=45977-44180[/tex]
[tex]300y=1797[/tex]
[tex]y = \frac{1797}{300}[/tex] = 5.99 billion
Still, it's not passed 6 billion, so finally put t = 2000;
[tex]300y=(23\times 2000)-44180[/tex]
[tex]300y=46000-44180[/tex]
[tex]300y=1820[/tex]
[tex]y = \frac{1820}{300}[/tex] = 6.1 billion
Now, the global population has crossed 6 billion.
Hence, the year in which the population passed 6 billion is 2000.
will mark BRANLIEST and give you ALL MY POINTS, and answer ANY QUESTIONS U MAY HAVE!!!! pls help! tysm <3
Answer:
[tex]\huge \boxed{1+(-3)=-2}[/tex]
Step-by-step explanation:
An arrow goes from 0 to 1.
So 0 + 1 or just 1.
An arrow goes from 1 to -2.
So 1 - 3 = -2.
1 moves 3 units to the left to -2.
[tex]1+(-3)=-2[/tex]
When a number is increased by 9.5%, the result is 58. What is the original number to the nearest tenth?
Answer:
50
Step-by-step explanation:
58 - 9.5
Answer:
Your correct answer is 52.49
Step-by-step explanation:
Subtract.
58 - 9.5% = 52.49
What is the equation, in slope-intercept form, of the line that passes through (0, 3) and has a slope of −6?
Answer:
The answer is
[tex]y = - 6x - 3[/tex]Step-by-step explanation:
To find the equation of the line given a point and slope we use the formula
[tex]y - y_{1} = m(x - x _{1})[/tex]where
m is the slope
( x1 , y1) is the point
From the question the point is (0 , 3) and slope is - 6
Substitute the values into the above formula and solve
That's
[tex]y - 3 = - 6(x - 0) \\ y - 3 = - 6x[/tex]We have the final answer as
[tex]y = - 6x - 3[/tex]Hope this helps you
Which of the following correctly describes the product below?
5.15 x 6V7
Answer:
Step-by-step explanation:
78
Answer:
50
Step-by-step explanation:
Which expression is equivalent to the algebraic expression below? Show your work. 3(-2x - 1) A. x + 2 B. x - 1 C. -6x - 3 D. -6x - 1
Answer:
C
Step-by-step explanation:
Multiply 3 and -2x and that's -6x Multiply 3 and -1 and that's -3Find the dot product of vectors a and b and the angle between them. a = (9,0) b = (5,8)
Answer:
57.99 degrees
Step-by-step explanation:
a = <9, 0> and b = <5, 8>.
Then the dot product is (9)(5) + (0)(8) = 45 (a scalar)
The cosine of the angle between these two vectors is
a · b 45 45 5
cos Ф = --------- = ------------------------ = ------------- = -------- = 0.53
|a||b| (9)( √[25 + 64] ) 9(√89) √89
The angle between the vectors is arccos 0.53, which comes out to 1.01 radian or 57.99 degrees.
A random sample of 20 purchases showed the sample mean of $48.77 and the sample standard deviation s is $17.58. How large is the margin of error for a 80 % confidence interval for the mean purchases of all customers
Answer:
$5.03Step-by-step explanation:
Given data
Sample Mean (M): $48.77
Sample Size (n): 20
Standard Deviation (σ) : $17.58
Confidence Level: 80%
we know that z*-Values for 80% Confidence Levels is 1.28
the expression for margin of error is given bellow\
MOE= z*σ/√n
We can now substitute into the expression and solve for the MOE as
MOE= 1.28*17.58/√20
MOE= 22.502/4.47
MOE= 22.502/4.47
MOE= 5.03
The margin of error for a 80 % confidence interval is $5.03
Solving these quadratics for x using complete the square 3x^2-4x-1=0. Show your work.
Which of the following expressions are equivalent to this expression:
-1(0) = ?
-14 + (-4)]
-1[4 + (4)]
1+ [4 +(-4)]
-11-4 + (-4)]
Answer:-1[4+(-4)]
Step-by-step explanation:
4 and -4 are equaled to 0. So it is -1(0)
Answer:
A
Step-by-step explanation:
Simplify the expressions. Type in your answer with no spaces.)
3(x + 1) - 2(x-4)
Simplify the expression.
x+11
Hope this helps (❁´◡`❁)
Answer:x+11
Step-by-step explanation:distribute the combine like terms
4. What is the correct simplified form? See picture
Answer:
option 3
Step-by-step explanation:
What is the ones digit in the number 3^20997
Answer:
7
Step-by-step explanation:
3^0 = 1
3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81
3^5 = 243
3^6 = 729
3^7 = 2187
3^8 = 6581
===========
You can see that the pattern is beginning to repeat itself.
===================
So all you need do is take 2099 and divide by 3. You must pay attention to the remainder.
2099 / 4 = 524.75
The answer means that you go through the cycle 524 times getting 1,3,9,7,1 as the units digit.
In this case the remainder is 0.75 which is the same as 3/4. The remainder then is 3
If there is no remainder, the ending is a one.
if there is a remainder of 1 the answer is 3
If there is a 2 remainder, the number ends in 9
If there is a 3 remainder, the number ends in 7
And that's your answer.
50% of 80 solve pls show working
pls I know it just try working it
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{40}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{50 \: \% \: of \: 80}[/tex]
To convert the percent into a fraction , divide it by 190 and remove the % symbol. Then , Simplify the fraction to its lowest term.
⇒[tex] \sf{ \frac{50}{100} \times 80}[/tex]
⇒[tex] \sf{ \frac{1}{2} \times 80}[/tex]
Divide 80 by 2
⇒[tex] \sf{40}[/tex]
Hope I helped!
Best regards!!
Answer:
40
Step-by-step explanation:
50% of 80 is just 0.5 x 80 = 40
Order Greatest to Least -22.52,-22.5, -22 1/4, -2223%
Answer:
-22.23 -22.25 -22.5 -22.52
Step-by-step explanation:
-22.52,-22.5, -22 1/4, -2223%
-22 1/4 = -89/4 = -22,25
-2223% / 100%= -22.23
-22.23 -22.25 -22.5 -22.52
Evaluate the expression below for s=4 and t=7. 3st^2 - s^2
Answer:
572
Step-by-step explanation:
3(4)*(7)^2-4^2
How many adults who have been told that they have hypertension would you expect to find in a sample of 20
Answer: 24
Step-by-step explanation: