Answer:
[tex]f^{-1}(x)=\dfrac{1}{3}(\ln x +1)[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=e^{3x-1}[/tex]
Replace f(x) with y:
[tex]\implies y=e^{3x-1}[/tex]
Take natural logs of both sides:
[tex]\implies \ln y = \ln e^{3x-1}[/tex]
Apply the Power Log Law [tex]\ln x^n=n\ln x[/tex] :
[tex]\implies \ln y = (3x-1)\ln e[/tex]
As [tex]\ln e=1[/tex] then:
[tex]\implies \ln y = 3x-1[/tex]
Rearrange to make x the subject:
[tex]\implies 3x=\ln y +1[/tex]
[tex]\implies x=\dfrac{1}{3}(\ln y +1)[/tex]
Swap x for [tex]f^{-1}(x)[/tex] and y for x:
[tex]\implies f^{-1}(x)=\dfrac{1}{3}(\ln x +1)[/tex]
the perimeter of a rectangle is 70 meters. the width of the rectangle is 10 meters. how long is the rectangle?
9 < 5+y
Solve the inequality
Answer:
4<y
Step-by-step explanation:
1st step:9=5+y
2nd step: 9-5=y
3rd step: 4=y
4th step: 4<y
Answer:
y > 4 or 4 < y
Step-by-step explanation:
In this inequality, the < sign, also known as the less than sign, means that 9 is less than the value of 5 + y. Solving inequalities can be simple to do - let's begin!
9 < 5 + y
We know that we must isolate y to determine its value. We can do this by subtracting 5 from both sides of the < sign.
9 - 5 < 5 + y - 5
Simplify!
4 < y → This means that 4 is less than y. Let's rewrite this.
y > 4 → Rewritten, your answer looks like this! This now states that y is greater than 4, which is the same as 4 being less than y.
For more information regarding inequalities, be sure to check out the following answers!
https://brainly.com/question/20085191https://brainly.com/question/12556359https://brainly.com/question/12526104The annual profits for a company are given in the following table, where x represents the number of years since 2014, and y represents the profit in thousands of dollars. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest tenth. Using this equation, estimate the calendar year in which the profits would reach 144 thousand dollars.
The linear regression equation that represents this data set is equal to y = 11.7x + 48.2 and an estimate of the calendar year is 2022.
How to write the linear regression equation?First of all, we would determine the slope of the given data set by using this formula:
[tex]Slope = \frac{\sum (x-\bar x)(y-\bar y)}{\sum (x-\bar x)^2}[/tex]
For the sample mean (years), we have:
∑x = 0 + 1 + 2 + 3
∑x = 6.
∑x² = 0² + 1² + 2² + 3²
∑x² = 14.
For the sample mean (profits), we have:
∑y = 46 + 57 + 84 + 76
∑y = 263.
∑xy = (0 × 46) + (1 × 57) + (2 × 84) + (3 × 76)
∑xy = 453.
Now, we can determine the slope:
[tex]Slope = \frac{4(453) - 6(263)}{4(14) - 6^2} \\\\Slope = \frac{234}{20}[/tex]
Slope, m = 11.7.
For the intercept, we have:
[tex]Intercept = \frac{14(263) - 6(453)}{4(14) - 6^2} \\\\Intercept = \frac{964}{20}[/tex]
Intercept, c = 48.2.
Therefore, the linear regression equation is given by:
y = 11.7x + 48.2.
Since the profit would reach 144,000 dollars, the calendar year would be calculated as follows:
144 = 11.7x + 48.2
11.7x = 144 - 48.2
11.7x = 95.8
x = 95.8/11.7
x = 8.2.
For the calendar year, we have:
Year = 2014 + 8.2
Year = 2022.2 ≈ 2022.
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(Image: Start Fraction x over 4 End Fraction) + 2 = –2
If the linear equation with one variable is x / 4 + 2 = –2. Then the value of x will be negative 16.
What is simplification?Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
The equation is given below.
x / 4 + 2 = –2
Solving for x, we have
x / 4 + 2 = –2
x / 4 = – 2 – 2
x / 4 = – 4
x = – 4 × 4
x = – 16
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question attached please help
Answer:
h(0.1) = 4.97
Step-by-step explanation:
See attached working :)
Remember that h(0.1) is the same as saying find what the equation is equal to when x = 0.1
How do you find the length of an unknown leg in a right triange
By using the pythagoras theorum you can find an unknown leg of right angled triangle.
Hypotenuse side is in the front of the 90 degree angle and other two sides can be taken as base and perpendicular, so formula goes as :-
(Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2
H^2 = B^2 + P^2
Step-by-step explanation:
Hope it helps you!!hi people ~
can you give me eassy on WORLD AGAINST CHILD LABOUR I need 80 word I already write this but I want 80 word more please give me your own choice on WORLD AGAINST CHILD LABOUR thnks
Child labor is a service rendered by children in any field during their childhood. This is done due to lack of resources for subsistence, irresponsibility of the parents or lack of resources by the owner to increase their returns on low investment.
This does not matter with the cause of child labor as all the reasons force children to live life without childhood. Childhood is the greatest and happiest period of everyone’s life, during which one learns about the basic strategy of life from parents, loved ones and nature. Child labor interferes with the proper growth and development of children in all aspects, mentally, physically, socially and intellectually.
☆...hope this helps...☆
_♡_mashi_♡_
PLEASE PLEASE PLEASE I HAVE 20 MINUNTES
Answer:
E. 38°
Explanation:
A rhombus has 360° interior angle.
Half of the other side has 180° angle.
Solve for x:
sum of interior angles = 180°
x + 14 + x + 14 + x + x = 180°
4x + 28° = 180°
4x = 180° - 28°
4x = 152°
x = 152°/4 = 38°
Sum of half interior angles=180°
So
x+x+14+x+x+14=1802x+2(x+14)=1802x+2x+28=1804x+28=1804x=152x=38°Option E
URGRENNTTT PLSS HELPP 50 POINTSS!!!!! Students were asked to simplify the expression cotangent theta plus tangent theta over cotangent theta. Two students' work is given.
Student A
Step 1: cotangent theta over cotangent theta plus tangent theta over cotangent theta
Step 2: 1 plus tangent theta over the quantity 1 over tangent theta end quantity
Step 3: 1 + tan2 θ
Step 4: sec2 θ Student B
Step 1: the quantity 1 over tangent theta end quantity plus tangent theta over the quantity cotangent theta
Step 2: the quantity 1 plus tangent squared theta end quantity over tangent theta all over cotangent theta
Step 3: secant squared theta over tangent squared theta
Step 4: csc2 θ
Part A: Which student simplified the expression incorrectly? Explain the errors that were made or the formulas that were misused. (5 points)
The student that simplified the expression incorrectly is student 2
How to determine the incorrect result?The steps are given as:
[tex]\frac{\cot(\theta) + \tan(\theta)}{\cot(\theta)}[/tex]
Student 1:
Step 1: [tex]\frac{\cot(\theta)}{\cot(\theta)} + \frac{\tan(\theta)}{\cot(\theta)}[/tex]Step 2: [tex]1 + \frac{\tan(\theta)}{\cot(\theta)}[/tex]Step 3: 1 + tan²(Ф)Step 4: sec²(Ф)Student 2:
Step 1: [tex]\frac{\cot(\theta)}{\cot(\theta)} + \frac{\tan(\theta)}{\cot(\theta)}[/tex]Step 2: [tex]\frac{1 + \tan^2(\theta)}{\cot(\theta)/\tan(\theta)}[/tex]Step 3: sec²(Ф)/tan²(Ф)Step 4: csc²(Ф)As a general trigonometry rule;
[tex]\frac{\cot(\theta) + \tan(\theta)}{\cot(\theta)} = \sec^2(\theta)[/tex]
This means that student 1 is correct, while student 2 is not
The first error in student 2's workings is in step 2, where we have:
[tex]\frac{\cot(\theta)}{\cot(\theta)} + \frac{\tan(\theta)}{\cot(\theta)} = \frac{1 + \tan^2(\theta)}{\cot(\theta)/\tan(\theta)}[/tex]
The above expression is not justified and cannot be proved by any trigonometry rule
Since the step 2 is incorrect, the other steps cannot be used.
Hence, the student that simplified the expression incorrectly is student 2
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Cost of Bikes ($) at Bike Shop
312, 352, 480, 392, 368, 352, 416, 640
Ic. mode
The mode is.
Answer:
352
Step-by-step explanation:
it repeated more than once
Ms. Lui earned an annual income of 775,000, what is the weekly salary?
Answer:
$14,903.85
Step-by-step explanation:
So, Ms. Lui earns $775,000 each year. To find the weekly salary, we have to divide the annual income by the amount of weeks in a year. There are about 52 weeks in one year. Let's find the weekly salary:
[tex]\frac{775000}{52} = 14,903.85[/tex]
Therefore, Ms. Lui earns $14,903.85 a week.
Hope this helps! If you have questions about my work, please leave them in the comments!
Which of the following produces an image that is not congruent to the pre-image?
A. translation
B. dilation
C. rotation
D. reflection
Answer:
Dilation
Step-by-step explanation:
it’s a dilation because the dilation changes how big the image is or what it looks like after the original image.
EASY POINTS Identify the type of function represented
Answer:
exponential growth
Step-by-step explanation:
f(x) = 4 * 2^x
This function is in the form
y = a * b^x where a is the initial value and b is the growth or decay rate
This is exponential form
if b > 1 then it is growth
0< b < 1 it is decay
b =2 so it is growth
The graph below represents which system of inequalities?
A) y > 2x − 3
y > −x − 3
b) y < 2x − 2
y < −x + 3
C) y ≤ 2x − 2
y > −x + 3
D) None of the above
The system of inequalities that represents the graph are y > -x + 3 and y ≤ 2x - 2
Equation of a lineA line is the shortest distance between two points. The equation of a line in slope-intercept form is y = mx + b
For the broken line, the coordinate points will be(0, 3) and (3, 0)
m = -3/3
m = -1
The equation of the line will be y > -x + 3
For the solid line, the coordinate points will be(0, -2) and (1, 0)
m = 2/1
m = 2
The equation of the line will be y ≤ 2x - 2
Hence the system of inequalities that represents the graph are y > -x + 3 and y ≤ 2x - 2
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help pleseeeeeeeeeeeeeeeeeeeeeeee
Complete the information as requested:
1.- Indicated dose: 300 mg of Ceftriaxone ampoules IV every 6 hours for 10 days.
Available: 1.2 g of Ceftriaxone vial. Reconstitute with 5ml of Sterile Water
a) Dose volume … Calculations
b) Number of doses per day to comply with the indication.
c) Number of ampoules needed for the entire treatment
2.- The patient has indicated:
Indicated quantity: 250 mg Tobramycin ampoule every 12 hours
Available Tobramycin 100 mg /ml vial
a) Dose volume for administration according to indication.
b) Number of ampoules needed for one day of treatment.
c) Amount of Tobramycin received per day - mg
3.- A doctor indicates 0.5 g PO c6h x 5 days
The drug available is 125 mg / 5 mL
a) What is the amount of drug administered per dose? in ml
b) how many total doses for the 5 days are required
c) how many 100 ml bottles do I need to deliver
If y = –0.96 when x = 2.4, what is y when x = 2.9?
Answer:
It should be -1.16
Step-by-step explanation:
Hope this helps :)
HELP ILL GIVE MONEY
Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 27 liters per minute. There are 700 liters in the pond to start.
Let W represent the total amount of water in the pond (in liters), and let I represent the total number of minutes that water has been added. Write an equation
relating W to T. Then use this equation to find the total amount of water after 17 minutes.
Equation:__
Total amount of water after 17 minutes: __liters
Answer: Equation: 27t +700 = w
Total amount of water after 17 minutes: 1159 L
Step-by-step explanation:
Equation: 27t +700 = w
let t = minutes
let w = total amount of water in pond (liters)
Total amount of water after 17 minutes: 1159 L
t = 17
therefore
27(17) +700 = 1159
Answer:
425 l
Step-by-step explanation:
please help! easy! it is due right now!!
Answer:
3 Cups of flour.
Step-by-step explanation:
interest on 2000 at 10% per 4years
Answer:
2,800
A = 2000(1 + (0.1 × 4)) = 2800
A = $2,800.00
156, 153, 150, ...
Find the 46th term.
The 46th term of the arithmetic progression is 288.
What is an arithmetic progression?An arithmetic progression is a series of numbers called a sequence and the difference from one interval to another is constant.
From the given information:
156, 153, 150, ...
The first term a = 156The common difference d = 3n = nth termThe 46th term will be:
[tex]\mathbf{a_{46} = a+ (n - 1) d}[/tex]
[tex]\mathbf{a_{46} = 153+ (46 - 1) 3}[/tex]
[tex]\mathbf{a_{46} = 153 + (45) 3}[/tex]
[tex]\mathbf{a_{46} =288}[/tex]
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Does the equation xy + 6y = 9 define y as a function of x?
O Yes
O No
Answer:
no. a function doesnt contain an = sign
Step-by-step explanation:
Answer:
Yes, it is a function.
Explanation:
xy + 6y = 9
y(x + 6) = 9
y = 9/(x + 6)
It is a inverse variation function.
Where equation: xy = k ["k" is constant]
Each value of x corresponds to a single value of y.A number is divided in the ratio 5:9. If the first part is 35, find the number.
A number is divided in the ratio of 5:9. If the first part is 35, the number will be 7.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
A number is divided in the ratio of 5:9. If the first part is 35, then we need to find the number.
By unitary method
5x = 35
x = 7
Then the other number will be
9x = 9(7)
= 63
Thus, A number is divided in the ratio of 5:9. If the first part is 35, the number will be 7.
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For each of the number lines, write an absolute value equation in the form |x - c |=d,
where c and d are some numbers, to satisfy the given solution set.
The absolute value equation that satisfy the solution set of -4 and -8 is |2 - x| = -6
How to determine the absolute value equation?The solution sets on the number line are given as:
x = {-8, -4}
Calculate the average of the solutions
Mean = (-8 - 4)/2
Mean = -6
Calculate the difference of the solutions divided by 2
Difference = (-4 + 8)/2
Difference = 2
The absolute value equation is the represented as:
|Difference - x | = Mean
Substitute known values
|2 - x| = -6
Hence, the absolute value equation is |2 - x| = -6
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Answer:
|b+6|=2
Step-by-step explanation:
what is the answer ???
Answer: Heyaa!~
- Write 63 as the product of prime factors -
Since, the prime factors of 63 are 3, 7. Therefore, the product of prime factors = 3 × 7 = 21.- Write the prime factors in ascending order -
I think it would be 3/7- what's the highest common factor of 63 and 105 -
21, divides both 63 and 105, i.e., 21.Hopefully this helps you! ^^^
Directions: In this last section, you will answer one problem. Be sure to read the
problem carefully and to answer the question completely. Show your work and circle
your answer. Use any method to solve this problem.
74. A restaurant has a total of 60 tables. Some of the tables can seat 4 people and some
seat 2 people. All of the seats are occupied when there are 160 people seated. How man
tables for 4 are there?
Answer:
40 tables
Step-by-step explanation:
I think lol I'm just guessing. Hope you get it right. If I'm right just remember me as legend or the chosen one.
Which clock shows 11:22?
A.
A clock shows the hour hand slightly past 11 and the minute hand at one mark past the 3.
B.
A clock shows the hour hand slightly past 11 and the minute hand at 6.
C.
A clock shows the hour hand slightly past 11 and the minute hand at two marks past the 4.
D.
A clock shows the hour hand slightly past 11 and the minute hand at one mark past the 2.
Answer:
Option C
Step-by-step explanation:
A clock shows the hour hand slightly past 11 and the minute hand at two marks past the 4.
Polygon G H I J K has 5 sides.
Which statements are true about the regular polygon? Select three options.
The sum of the measures of the interior angles is 900°.
Each interior angle measures 108°.
All of the angles are congruent.
The polygon is a regular hexagon.
The sum of the measures of the interior angles is 180(5 – 2)°.
Answer:
Each interior angle measures 108°.All of the angles are congruent.The sum of the measures of the interior angles is 180(5 – 2)°.Step-by-step explanation:
(1) The sum of the interior angles of a polygon is [tex]180(n-2)[/tex] degrees, where n is the number of sides. In this case, n=5, so the sum is 180(5-2)=540 degrees, meaning the first statement is false.
(2) Since the angles add to 540 degrees, dividing this amongst the five equal angles, we get that each angle measures 108 degrees, so this statement is true.
(3) By definition, all angles of a regular polygon are congruent.
(4) A hexagon has 6 sides, but this polygon has only 5 sides, so this statement is false.
(5) This is true. (See statement (1)).
Answer:
Options B, C, E
Step-by-step explanation:
alex has a box of 250 nails. he uses 80 nails. then he loses 35 nails. how many nails does alex have left? what is the hidden question
A spinner is spun `40` times for a game.
This graph shows the fraction of games that are wins.
Based on the graph, what is the probability of a spin winning this game?
(i) In decimals: 0.65
(ii) In percentage: 65%
The graph shows that after the spinner is spun after 40 times. The Fraction of wins is 0.65 out of 1. Look at the very end of the graph to look at the conclusion for probability. Similar cases when, after the spinner is spun after 20 times, the probability is 0.65.
Answer:
0.65 or 65%
Step-by-step explanation:
5 Keisha needs postage stamps to mail
invitations for her birthday party to
9 friends. If stamps cost 45¢ each, how
much will it cost Keisha to mail the
invitations?
LA
$
Answer:
$4.05
Step-by-step explanation:
45 x 9 = 4.05