The inverse of the logarithmic function f(x) = [tex]\log_{e}x[/tex] is [tex]e^{x}[/tex].
In the given question, we have to find the inverse of the logarithmic function f(x) = [tex]\log_{e}x[/tex].
The given function is f(x) = [tex]\log_{e}x[/tex].
The features of logarithms will simply follow from our understanding of exponents if the logarithm is viewed as the inverse of the exponential function.
Now let, y = [tex]\log_{e}x[/tex]
Now x = log y
Then, y = [tex]e^{x}[/tex]
So, f(x) = [tex]e^{x}[/tex]
As a result, [tex]e^{x}[/tex] is the logarithmic function's inverse, where f(x) = [tex]\log_{e}x[/tex].
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The complete question is:
What is the inverse of the logarithmic function f(x) = [tex]\log_{e}x[/tex]?
A small company has one manager and 5 other employees. The manager’s salary is 25% of the company’s salary budget. If the company’s salary budget is x dollars, which expressions represent the amount of money, in dollars, from the salary budget that is left for the 5 other employees?
The amount of money left for the 5 other employees is 0.75x dollars.
How to determine the amount of moneyFrom the question, we have the following parameters that can be used in our computation:
Employees = 5
Salary = 25%
If the manager's salary is 25% of the company's salary budget, and the company's salary budget is x dollars, we can represent the manager's salary as 0.25x.
To find the amount of money left for the 5 other employees, we need to subtract the manager's salary from the total salary budget.
We can represent this using the following expression: x - 0.25x
Simplifying this further, we get
x(1-0.25) = 0.75x dollars
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Which of these expressions represents the sum of an irrational number and a rational number being irrational
The sum of an irrational number and a rational number can either be rational or irrational.
Depending on the specific numbers involved. There is no general expression for the sum of an irrational number and a rational number being irrational. If the sum of two numbers is irrational, it means that the result cannot be expressed as a simple fraction, and its decimal representation either goes on forever without repeating or repeats after a certain number of digits.
One example of the sum of an irrational number and a rational number being irrational is:
√2 + 1/2 = 1.732 + 0.5 = 2.232 (irrational)
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If 13 is added to a number and the sum is multiplied by 3, the result is 7 times the number decreased by 9. Find the number
Answer: 47/4
Step-by-step explanation:
Convert the words into math:
The number = x
( 13 + x ) * 3 = 7 * x - 9
Expand:
39 + 3x = 7x - 9
Subtract 3x from both sides:
38 = 4x - 9
Add 9 to both sides:
47 = 4x
x = 47/4
hi may you help if you can thanks
Answer: A 4 91/100
Step-by-step explanation: its 491/100 because the 100 is 1 and 4 is the number 4 and 91/100 is .91
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25-
Which ordered pair is a solution of the equation?
y + 5 = 2(x+1)
Choose 1 answer:
Only (5, 10)
B Only (-1,-5)
Both (5, 10) and (-1,-5)
Neither
Answer:
i tried to solve it and the solution is : x=3/2 or 1.5 so ig its neither
No need to explain. check picture.
Answer: What you chose was correct :>
What is the inverse of a convex function?.
The concept is Inverse function. The answer is, the inverse of a convex differentiable function with a non-zero derivative is strictly concave.
In mathematics, an inverse function is a function used to "cancel" another function. In other words, if f(x) yields y, then setting y to be the inverse of f yields x.
A convex function is a continuous function whose value at the middle of each interval of its domain does not exceed the arithmetic mean of its values at the ends of the interval.
The convex function has an increasing first derivative, making it appear curved upwards. Conversely, the concave function has a decreasing first derivative, so it curves down.
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Select the best Measures of Center for the data set:
4, 6, 9, 10, 6, 7
Question 3 options:
Either the Mean or the Median
The Median Only
The Mode Only
Answer:
either the mean or the median
The correct answer will get brainliest!!
Classify this triangle by its sides and angles.
A.) acute and isosceles, but not equilateral
B.) obtuse and isosceles, but not equilateral
C.) obtuse and equilateral
D.) acute and equilateral
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
[tex] \textsf{As per the given figure, observations can be made} [/tex] [tex] \textsf{that : } [/tex]
[tex] \textbf{1.) Two sides of the given triangle are equal.} [/tex]
Conclusion : [tex] \textsf{It's an } [/tex][tex] \textbf{Isosceles} [/tex][tex] \textsf{triangle} [/tex][tex] \textbf{2.) All the three angles are less than 90° } [/tex]
Conclusion : [tex] \textsf{ it's an} [/tex][tex] \textbf{ acute } [/tex][tex] \textsf{angled triangle } [/tex][tex] \textsf{So, to sum it up, it can be said that the } [/tex][tex] \textsf{triangle is both Isosceles and acute } [/tex][tex] \textsf{angled triangle.} [/tex]
Answer : A.) acute and isosceles, but not equilateral
Answer:
Acute and Isosceles, but not equilateral.
Step-by-step explanation:
First, let us address equilateral. Equilateral triangles assumes by definition that all triangle sides are symmetrical (60° in measurement), and that all side lengths are congruent (the same length). As shown in the picture, it is not a equilateral triangle, as there is only a pair of congruent sides.
Therefore, the given triangle is a isosceles triangle, which by definition calls for having two sides of equal length, and two equal angles.
Next, we are solving for whether or not the triangle angles are obtuse or acute. Acute angles measure less than 90° (The measurement of a right angle). Obtuse angles, on the other hand, measure more than 90°. In this case, all sides are less than 90°, per definition of isosceles triangle.
Therefore, the given triangle is acute.
Your answer is Acute and isosceles, but not equilateral.
A bag of Skittles has 3
green, 2 purple, 4 yellow, 6 red, and 5 orange candies.
If you pick one candy 10 times and replace it after each draw, how many times would you expect to get a candy that isn't green or purple?
Therefore , the solution of the given problem of probability comes out be probability of don't get green or purple candy = 0.75 .
What exactly does the probability process entail?Calculating the likelihood that a statement is true or that an event will occur is the focus of the branch of mathematics known as probability theory. Any number from range 0 to 1, where 1 represents certainty and 0 normally represents possibility, may be used to represent chance. The likelihood that a particular event will occur is depicted in a probability diagram.
Here,
Given :
there are 3 green, 2 purple, 4 yellow, 6 red, and 5 orange candies in the skittles.
total candies = 3 + 2 + 4 + 6 +5 =20
To find the probability that you don't get green or purple candy :
So , the probability of green candies is = 3/20 = 0.15
and the probability of purple candies is = 2/20 = 1/10 = 0.1
The probability of don't get green or purple candy
=> 0.15 + 0.1
=> 0.25
and 1 - 0.25 = 0.75
Therefore , the solution of the given problem of probability comes out be probability of don't get green or purple candy = 0.75 .
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Why doesn’t 100% of the data fall within 3 standard deviations of the mean?
As per the Empirical Rule and the properties of a Normal distribution , 99.7% of the data lies within three standard deviation not 100%.
What is Empirical Rule?
According to the empirical rule, also known as the three-sigma rule or 68-95-99.7 rule, practically all observed data for a normal distribution will lie within three standard deviations of the mean or average.
In specifically, the empirical rule predicts that 68 percent of observations will fall within the first standard deviation, 95 percent will fall within the first two standard deviations, and 99.7 percent will fall within the first three standard deviations.
Hence, as per the Empirical Rule and the properties of a Normal distribution , 99.7% of the data lies within three standard deviation not 100%.
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Find the length of the arc on a circle of radius r intercepted by a central angle θ?
A circle's arc length can be determined from its radius and central angle using the formula Length of an Arc = r, where is in radians.
How to Find Arc Length With the Radius and Central Angle?Length of an Arc = r, where is in radians, is a formula that may be used to calculate the arc length of a circle given its radius and central angle. A circle's length is equal to (r/180)r, where r is the radius and is the angle. The length of the arc on a circle of radius r intercepted by a central angle is S = r.
Multiply the radius (6 in) by the central angle's measurement in radians to determine the length of the arc. Remember that the angle must be expressed in radians in order to employ the calculation s = r.
Assuming that is measured in radians, the formula for the length s of the arc that is intercepted on a circle with radius r by a central angle is: s = r.
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Topic 6 Performance Task
Tomas and Emilio have a budget of $200 to plan their party at a movie theater. The party room at the theater costs $45.99 to rent and includes a free cake. Movie tickets cost $12.50
each, and a small bag of popcorn costs $4.50.
Seven friends accept the invitation to the twins' birthday party. At the last minute, Tomas and Emilio learn that their neighbor also wants to attend. The twins realize that they can stay
within their budget by buying different amounts of popcorn.
Small Popcorn
(serves 1)
$4.50
Medium Popcorn
(serves 2)
$5.75
Large Popcorn
(serves 2-3)
$6.50
Describe a different popcorn scenario that will allow the twins to bring 8 friends, including their neighbor, and still stay within their budget.
Small popcorn Scenario=Emilio is right.
Medium Popcorn Scenario=Tomas is right.
Large Popcorn Scenario=Tomas is right.
What is budget?A budget is a spending plan based on income and expenses. In other words, it’s an estimate of how much money you’ll make and spend over a certain period of time, such as a month or year.
1. Small popcorn Scenario.
Rent cost=46
Movie ticket cost + popcorn cost=17
For Tomas : 46+ (17*7)=46+119=$165
For Emilio : 46+(17*9)=46+153=$199
2.Medium Popcorn Scenario
Rent cost=46
Movie ticket cost + popcorn cost=?
For Tomas :46+ (18*7)=46+126=$172
For Emilio : 46+(18*9)=46+162=$208
3. Large Popcorn Scenario
Rent cost=46
Movie ticket cost + popcorn cost=?
For Tomas :46+ (19*7)=46+133=$179
For Emilio : 46+(19*9)=46+171=$217.
Small popcorn Scenario=Emilio is right.
Medium Popcorn Scenario=Tomas is right.
Large Popcorn Scenario=Tomas is right.
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Which equation matches the graph? f( x) = ( x + 4) 2 – 2 f( x) = ( x – 2) 2 + 4 f( x) = ( x + 2) 2 + 4 f( x) = ( x – 4) 2 + 2 f( x) = ( x + 2) 2 – 4
The quadratic equation that matches the graph is f(x) = (x - 2)² + 4.
The correct option is B.
What is a quadratic equation?For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.
Given:
The graph shows the function.
The graph is given in the attached image.
In the interval, [x = 0, x = 2],
we have a line that passes through the points (0, 8) and (2, 4).
That means, the points satisfies then function.
Let the f(x) = (x - 2)² + 4.
That means,
f(0) = 8
And f(2) = 4
Therefore, the quadratic function is f(x) = (x - 2)² + 4.
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if micheal's pool hold 21,000 gallons of water and it is 90 percent full, how many gallons of water are there?
The number of gallons of water that Michael's pool holds for the given condition will be 18,900 gallons.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
If Michael's pool holds 21,000 gallons of water and it is 90 percent full.
The number of gallons of water that Michael's pool holds will be given as,
⇒ 90% of 21,000
⇒ 0.90 x 21,000
⇒ 18,900 gallons
The number of gallons of water that Michael's pool holds for the given condition will be 18,900 gallons.
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explain how the probability associated with the roll of each individual die in the pair explains the higher variability in the total outcome of the roll of each pair. how do the concepts of permutations and combinations apply to this example? discuss how the notion of degree of freedom can be used to illustrate the accumulating results of a set of dice rolls.
The probability of each individual dying in the pair explains the higher variability in the total outcome of the roll of each pair because there are more possible combinations of outcomes.
The concepts of permutations and combinations apply to this example by showing the different ways the dice can be rolled to achieve a specific total outcome. Each die in a pair of dice has a probability of 1/6 of rolling any number between 1 and 6.
When rolling two dice, there are 36 different possible outcomes (6x6) and each one has a different probability of happening. This is where the concepts of permutations and combinations apply, as each possible combination of dice rolls will result in a different total outcome.
The notion of degree of freedom can be used to illustrate the accumulating results of a set of dice rolls by showing how the total outcome is affected by the roll of each individual die.
For example, if the first die rolls a 4, the second die has 5 degrees of freedom as it can roll any number between 1 and 6 (except for 4) and still achieve a total outcome of 9. As the number of dice being rolled increases, the degree of freedom decreases, making the probability of rolling a specific total outcome less likely.
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lydia went on a trip with her family. for three hours they drove east and drove 40 miles per hour. then, they drove north for one hour and drove 50 miles. how far was lydia and her family from their home after 4 hours
Answer:
170 miles
Step-by-step explanation:
first, for 3 hours they drove 40 mph. this means you have to multiply 40 mph by the 3 hours.
40*3=120
then you have to add the extra 50 miles that they drive north because their speed changed.
120+50=170
The arrows represent the forces acting on the object. Use the highlighter and draw an arrow to represent the direction that the object would be accelerating. Put an "X" if it is not accelerating.
Answer:
see attached
Step-by-step explanation:
You want the given diagram annotated with an arrow to show the direction of acceleration.
AccelerationAcceleration is a result of a net force on an object. It is in the direction of that net force.
ApplicationHere, the forces to the left and right are equal and opposite, so have a sum of zero.
The forces up and down are opposite, but unequal. The downward force is larger, so the direction of the net force is downward. (+5 +(-10) = -5)
The object will be accelerated downward in the direction of the 10 N force.
What is the distance between the origin and − 3 − 4 )?.
The distance between the origin and the point (3, 4) is 5 units.
The distance between the origin (0,0) and a point (x,y) in a two-dimensional coordinate system can be found using the distance formula, which is given by:
distance = √((x₂ - x₁)² + (y₂ - y₁)²)
In this case, the point is (3, 4) and the origin is (0, 0)
So, the distance between the origin and the point (3, 4) is:
distance = √((3 - 0)² + (4 - 0)²)
distance = √(3² + 4²)
distance = √(9 + 16)
distance = √(25)
distance = 5
So the distance between the origin (0,0) and the point (3,4) is 5
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Is this question right I just want to check?
Not quite, but really close. All you need to do is switch -4/3 and -0.2, because -4/3 is about -1.3, and negative numbers get greater as they get closer to 0
For what values of k will the system of equations KX 2y 5 3x Y 1 have a no unique solution?.
For k=6 the system of equations have a no unique solution
So,we have given 2 equations from the question:
kx+2y=5…(1)
3x+y=1 …(2)
First multiply the second equation by 2
We get:
6x+2y=2
Now subtracting (2) from (1), we get:
kx+2y−6x−2y=5−2
(k−6)x=3
x= 3/K-6
So, here if we put any value in k, then we will get a corresponding value of x but if we put k=6, then we will not get any value of x.
So, for k=6 this equation has no unique solution.
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Given:
R is the midpoint of QS
Prove: PRQ = TRS
Answer:
Step-by-step explanation: Hello!
I don't remember all of the postulates to these, but I hope this will help you! Vertical angles are congruent, so both angles SRT and PRQ are congruent. This also means that line segments PQ and ST are congruent. You also know that angles Q and S are congruent which is given. By the ASA Theorem, when two angles and a side are congruent, then the triangles are congruent.
What does it mean when you substitute a value into an equation and the result is a true statement?.
When you substitute a value into an equation and the result is a true statement it means solution to an equation is a value of a variable.
The substitution method is a quick and easy way to algebraically solve a set of linear equations and determine the variables' solutions. According to what the name implies, this method entails determining the value of the x-variable in terms of the y-variable from the first equation and then substituting or replacing the value of the x-variable in the second equation.
We can solve and determine the value of the y-variable in this method. Finally, we may use any of the above equations to obtain x by substituting the value of y. This procedure can also be switched around so that we first solve for x before solving for y.
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A train travels at a constant speed during a portion of its cross county route the table shows the distance the train traveled over different intervals of time at this speed.
what is the Speed of the train in Miles per hour?
The Speed of the train in Miles per hour will be 105 miles per hour.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The slope of the line is given as,
m = (y₂ - y₁) / (x₂ - x₁)
A train travels at a constant speed during a portion of its cross-country route the table shows the distance the train traveled over different intervals of time at this speed.
The slope represents the speed of the train. Then we have
m = (157.5 - 131.25) / (1.50 - 1.25)
m = 26.25 / 0.25
m = 105 miles per hour
The Speed of the train in Miles per hour will be 105 miles per hour.
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How to solve 3 equations with 3 variables using scientific calculator?.
Solving a system of 3 equations with 3 variables using a scientific calculator can be done by using matrix operations. The method is called Gaussian elimination or Gauss-Jordan elimination. Here is an overview of the steps you can follow:
Write the system of equations in matrix form. For example, if the equations are
a₁x + b₁y + c₁z = d₁
a₂x + b₂y + c₂z = d₂
a₃x + b₃y + c₃z = d₃
the matrix form would be:
| a₁ b₁ c₁ | |x| |d₁|
| a₂ b₂ c₂ | |y| = |d₂|
| a₃ b₃ c₃ | |z| = |d₃|
Enter the matrix of coefficients (on the left side of the equations) into your calculator, usually by using the matrix function or the linear equation solver function.
Enter the constant terms of the equations (on the right side of the equations) into your calculator as a column matrix or vector.
Perform row operations to make the matrix of coefficients into an upper-triangular matrix.
Solve the system by back-substitution using the values of x, y, z in the matrix of coefficients and the matrix of constant terms.
The calculator will give you the solution of the system in terms of x, y, z.
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In 1992, Jason bought a gallon of gas for $1.20. Yesterday, he bought a gallon of gas for $2.17. What is the percentage increase of the price of a gallon of gas from 1992 to yesterday? If necessary, round to the nearest tenth of a percent.
The percentage increase in the price of a gallon of gas is 80.84 %.
Given,
Jason bought a gallon of gas in 1992 = $1.20
He bought a gallon of gas yesterday = $2.17
Using the formula for the percentage increase in the price,
= ( New Price - Old Price) / Old Price × 100
= ( 2.17 - 1.20) / 1.20 × 100
= 80.84%
Therefore, the percentage increase in the price of a gallon of gas from 1992 to yesterday is 80.84 %.
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Two of the ways that we can factor the cubes are the addition of cubes and subtraction of the cubes.
How do you factor expressions step by step?The steps below can be used to determine an expression's GCF.
If there are any variables, list them separately and write each term as the prime factorization of the coefficient or constant. As an illustration, write x. y. as x. y. and x. as x. x. The elements that each phrase has in common should be noted. Add together those typical elements.
The set containing all items found in both sets A and B, or both sets A and B taken together, is referred to as the union of two sets A and B. With the symbol "," you can represent the union of the set.
First, we change the equation's form to read as ax2+bx+c=0, where a, b, and c are the coefficients. As a result, we enter these coefficients into the formula: (-b(b2-4ac))/(2a).
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Determine whether the probability given is experimental or theoretical probability. There are 120 seniors out of a total school population of 400. Elizabeth says the probability of randomly choosing a senior from a list of all the students is 3/10.
Answer:
Theoretical.
Step-by-step explanation:
120/400 = 30/100 = 3/10
She is correct.
It is the theoretical probability since it is based on calculations alone.
Is an angle a defined term?.
The figure in which two rays intersect at a single location known as the vertex is referred to as an angle. The symbol "" is used to indicate an angle.
An angle is the figure formed when two rays cross at a common endpoint, according to the definition of angles. Simply put, an angle is a shape made up of two lines or rays that diverge from a central point (the vertex). The letter "a" stands for an angle.Vertex: The intersection of two angles is referred to as a vertex. It is the location where two rays converge. Arms: The two angle sides that are connected at a single endpoint. The initial side is also referred to as the reference line.
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What is the formula of product in math?.
The multiplication formula in maths is given as follows Multiplier × Multiplicand = Product.
The product meaning in maths is a number you get to by multiplying two or more other numbers. For example, if you multiply 3 and 5 together, you get a product of 15.
Multiplication is an important part of maths. Learning and understanding how to find the product in maths is an important basis for developing their skills in maths.
You can help children learn the maths definition of the product by reminding them that it is produced when two or more numbers are multiplied together.
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