The derivative of logₐ x (log x with base a) is 1/(x ln a).
Here, the interesting thing is that we have "ln" in the derivative of "log x". Note that "ln" is called the natural logarithm (or) it is a logarithm with base "e". i.e., ln = logₑ.
Further, the derivative of log x is 1/(x ln 10) because the default base of log is 10 if there is no base written.
The derivative of log x (base 10) with respect to x is denoted by d/dx (log x) or (log x)'. Thus,
d/dx(logₐ x) (or) (logₐ x)' = 1/(x ln a)
d/dx(log x) (or) (log x)' = 1/(x ln 10)
d/dx (logₐ x) = 1 / (x ln a)
Substitute a = e on both sides. Then we get:
d/dx (loge x) = 1 / (x ln e)
By the properties of natural logarithms, ln e = 1. So
d/dx (loge x) = 1 / (x · 1)
Thus, d/dx (loge x) = 1.
Replacing loge x with ln x back, we get d/dx (ln x) = 1/x.
Hence, the derivatives of logs are:
d/dx (logₐ x) = 1 / (x ln a) (this is the derivative of common logarithm)
d/dx (ln x) = 1/x (this is the derivative of natural logarithm)
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Pls someone help me on this
On solving the provided question we can say that from the graph, we can say as both sides are similar angle D is congruent to angle D'
What is graphs?Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle
from the graph, we can say as both sides are similar
Angle D is congruent to angle D'
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Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Answer:
x = 1 , x = 13
Step-by-step explanation:
(x - 7)² = 36 ( take square root of both sides )
x - 7 = ± [tex]\sqrt{36}[/tex] = ± 6 ( add 7 to both sides )
x = 7 ± 6 , then
x = 7 - 6 = 1
x = 7 + 6 = 13
For what value of k does the pair of linear equations has an infinite many solution KX 4y 3 6x 12y 9?
The required value of k will the system of linear equations has infinite number of solutions is 2.
What is Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
According to question:We know that
KX + 4y - 3 = 0 . ..........(1)
6x + 12y - 9=0 ..........(2)
Because there are infinity many solutions to linear equations.
[tex]\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}[/tex]
⇒ k/6 = 4/12 = -3/-9
k/6 = 1/3
k = 2
Thus,required value of k is 2.
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Sadie got food and drinks if it cost $22.50 and there is a 9% meals tax, how much is the bill
Answer:
Step-by-step explanation:
Tax would be about 2 dollars
how many ways are there to arrange $6$ beads of distinct colors in a $2 \times 3$ grid if reflections and rotations are considered the same? (in other words, two arrangements are considered the same if i can rotate and/or reflect one arrangement to get the other. assume that each square gets exactly one bead.)
There are 9 or 10 distinct ways to arrange 6 beads of distinct colors in a 2x3 grid if reflections and rotations are considered the same. We can solve this problem using Burnside's Lemma.
Burnside's Lemma states that for a group action on a set, the number of fixed points is given by the average over the group of the number of fixed points under a particular group element, where the average is taken over all group elements.
In this case, the group action is the action of rotating and reflecting the grid, and the set is the set of all possible bead arrangements in the grid. To use Burnside's Lemma, we need to find the number of fixed points (i.e., bead arrangements that are unchanged) under each group element, and then take the average over all group elements.
There are a total of $4$ rotations and $2$ reflections possible for a 2x3 grid.
The identity transformation keeps the grid in its original position, and thus there are
6!/(2!3!) = 60
The $90 rotation keeps $3 beads in the same place and switches the other $3, and similarly $180 and $270 rotation also keeps $3 beads in the same place and switches the other $3$, thus there are
3! = 6
The reflection on the horizontal axis keeps $3 beads in the same place and switches the other $3, and similarly the reflection on the vertical axis also keeps $3 beads in the same place and switches the other $3, thus there are
3! = 6
So the average number of fixed points is $(6+6+6+60)/8 = [tex]\frac{78}{8}[/tex] = 9.75$
So, there are 9 or 10 distinct ways to arrange 6 beads of distinct colors in a 2x3 grid if reflections and rotations are considered the same.
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what is the measure (in degrees) of the smallest interior angle of a triangle in which the exterior angle measures have the ratio $4:5:6?$
The measure (in degrees) of the smallest interior angle of a triangle in which the exterior angle measures have the ratio 4:5:6 is 36°.
The exterior angles of a triangle measure the angle between one side of a triangle and the extension of an adjacent side. The sum of the exterior angles of a triangle is always equal to 360 degrees.
In a triangle in which the exterior angle measures have the ratio 4:5:6, we can express the measures of the exterior angles as 4x, 5x, and 6x.
360 = 4x + 5x + 6x
360 = 15x
Solve for x by dividing both sides by 15:
x = 360/15 = 24
Knowing that the measures of the exterior angles are 4x, 5x, and 6x, we can find the measure of the smallest interior angle by subtracting the biggest exterior angle from 180 degrees:
biggest exterior angle = 6x = 6(24) = 144°
smallest interior angle = 180° - 144° = 36°
Therefore, the measure of the smallest interior angle of a triangle in which the exterior angle measures have the ratio 4:5:6 is 36°
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18 is 90% of what number?
Answer:
multiply the percentage by the number and then divide by 100
Step-by-step explanation:
What is 90% of something? To calculate, multiply the percentage by the number and then divide by 100. For example, 90 percent of 82 = 73.8.
bye noe
im tyler
Answer: 20
Step-by-step explanation:
If you take 90 percent of a number and get 18, then what is that number? In other words, you know that 90 percent of a number is 18 and you want to know what that initial number is.
To solve this problem you multiply 18 by 100 and then divide the total by 90 as follows: (18 x 100) / 90
G = the square root of m/t^2.
m = 6. 1 x 10^-5
t = 1. 7 x 10^-6
What is the value of G? wrote your answer in standard form correct to 3 s. F.
m is increased by 8%
t is increased by 5%
What is the new value of G?
Give your answer in standard form correct to 3 s. F.
Any help with these 2 questions would be extremely appreciated :)
The required required value of G is 1) 2.11 × 10^7 2) 2.06 × 10^7.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
According to question:We have,
1) m = 6. 1 x 10^-5, t = 1. 7 x 10^-6
G = m/t^2
G =6. 1 x 10^-5/(1. 7 x 10^-6)^2
G = 2.11 × 10^7
2)m is increased by 8%
New m = 6.59 x 10^-5,
t is increased by 5%
New t = 1.79 x 10^-6
So
G = m/t^2
G = 6.59 x 10^-5/(1.79 x 10^-6)^2
G = 2.06 × 10^7.
Thus, required value of G is 1) 2.11 × 10^7 2) 2.06 × 10^7.
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Measures of ___ describe the spread of the data.
A. Center
B. Frequency
C. Statistic
D. Variability
Answer: The Answer is D. Variability
Answer: D: Variability
Hope this helped!
A certain virus infects one in every 400 people. A test used to detect the virus in a person is positive 80% of the time if the person has the virus and 10% of the time if the person does not have the virus. (This 10% result is called a false positive.) Let A be the event "the person is infected" and B be the event "the person tests positive".
a) Find the probability that a person has the virus given that they have tested positive, i.e. find P(A|B). Round your answer to the nearest tenth of a percent and do not include a percent sign.
P(A|B)=
%
b) Find the probability that a person does not have the virus given that they test negative, i.e. find P(A'|B'). Round your answer to the nearest tenth of a percent and do not include a percent sign.
P(A'|B') =
%
a) The probability that a person has the virus given that they have tested positive is 0.5.
b) The probability that a person does not have the virus given that they test negative is 0.9.
What is probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.
Virus infects one in every 400 people.
Let A = be the event of being infected.
Let A' = be the event of not being infected.
Let B = be the event of being tested positive.
Let B' = be the event of being tested negative.
Let the population = 1,00,000
So, now the number of infected people are -
Infected people = (1/400) 100000
Infected people = 250
The number of non-infected people are -
Non-Infected people (T') = 100000 - 250
Non-Infected people (T') = 99750
The test is 80% positive when the person has the virus -
N(A|B) = 0.80 × 250
N(A|B) = 200
So, the probability value for N(A|B) -
P(A|B) = 200/400 = 0.5
The test is 10% positive when the person does not have the virus -
N(A'|B) = 0.10 × 99750
N(A'|B) = 9975
Number of people who test negative when they don't have the virus -
N(A'|B') = (T') - N(A'|B)
N(A'|B') = 99750 - 9975
N(A'|B') = 89775
So, the probability value for N(A'|B') -
P(A'|B') = 89775/99750 = 0.9
Therefore, the probabilities are 0.5 and 0.9.
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I want to delete this question. How do I do it?
To delete a question from the system you must complete a four-step procedure.
How to remove a question from the system?To delete a question from the system we must perform the following procedure:
First of all we must go to the home page.Once we are on the home page, we must click on the "Questions" tab.When you are in the "Questions tab", you have to find the question you want to deleteOnce you find it, you must click on the delete option.The previous procedure will help you to delete all the questions you want at any time you want.
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show the equation of V²=U²+2as
Answer: V² = U² + 2as
This equation is known as the equation of motion, and it relates the final velocity (V) of an object to its initial velocity (U), acceleration (a), and displacement (s).
The equation states that the square of the final velocity is equal to the square of the initial velocity plus twice the product of acceleration and displacement.
The equation can be used to calculate the final velocity of an object if the initial velocity, acceleration, and displacement are known, or it can be used to calculate the displacement of an object if the initial velocity, final velocity, and acceleration are known.
This equation is based on the concepts of physics and it's used to calculate the velocity of an object under constant acceleration.
Step-by-step explanation:
a family of four averages 4 showers a day for a month. the showers last on average of 10 minuetes each. calculate how much water the family would use each month just on showering if they only had standard floe shower heads in their house that delivered 5 gal/min. a
The family would use: 6000 gallons of water per month on showering.
In each day, the family would use;
4 showers/day * 10 minutes/shower
= 40 minutes of shower time per day.
In a month with 30 days, the family would use
40 minutes/day * 30 days
= 1200 minutes of shower time per month.
If each shower head delivers 5 gallons/minute, then the family would use 1200 minutes * 5 gallons/minute = 6000 gallons of water per month on showering.
The amount of water used by this family just on showering is more than half of the total amount of water used by the average family in a month.
Additionally, using standard flow shower heads can help to reduce water usage. Many cities have adopted regulations that require new shower heads to have a maximum flow rate of 2.5 gallons per minute or less. By using low-flow shower heads, this family could potentially reduce their water usage by half.
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2. Ana hace recuerdos para bodas con velas en forma de pirámide cua- drangular decoradas con semillas. a) Si un lado de la base mide 7 cm y la altura de la pirámide es de 15 cm, ¿qué volumen de cera ocupará para hacer 40 velas?
It will take 87.5 cm³ × 40 = 3500 cm³ volume of wax will it take to make 40 candles
How do you calculate a quadrangular pyramid's volume?The volume of a pyramid with a square base can be calculated using the formula V=13s2h, where s is the length of the base's sides. A polygonal base and an apex come together to form a polyhedron known as a pyramid. Volume = (1/3) base area height, where height is the height from the base to the apex, is the basic formula for a pyramid's volume.
Given,
side = 7cm
height = 15cm
Volume = 1/3 × h × 5/2 × s
⇒ volume = 15×7 ×5/6
⇒ volume = 87.5 cm³
It will take 87.5 cm³ × 40 = 3500 cm³ volume of wax will it take to make 40 candles
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Complete Question -
Ana makes wedding favors with candles in the shape of a quadrangular pyramid decorated with seeds. a) If one side of the base measures 7 cm and the height of the pyramid is 15 cm, what volume of wax will it take to make 40 candles?
Write 7/4 as a mixed fraction.
I need an answer fast!
it's inverted but still this is answer
Seven girls and three boys are waiting to audition for a school play. To be fair the staff is
choosing candidates at random for the auditions. If the first two selections were boys, how
does that affect the probability of the third candidate being a girl?
The first two selections do not affect the probability of the third candidate.
It increases the probability of a girl being the third candidate.
It decreases the probability of a girl being the third candidate
Since there is only one boy left, a girl will definitely be the third candidate.
If the first two selections were boys, the way that it affects the probability of the third candidate being a girl is; It increases the probability of a girl being the third candidate.
How to solve conditional probability?Conditional probability in mathematics is defined as the type of probability that depends on the occurrence or outcome of another event.
Now, we are told that in the school;
Number of Girls = 7
Number of boys = 3
Since the staff is choosing the candidates at random, then it means everyone has an equal chance to be picked.
Now, since we are told that 2 boys are selected first, it means that there would be only 1 boy left and as such the probability of selecting a girl will increase because there would now be seven girls out of 8 people.
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solve the inequality
Answer:
D.
Step-by-step explanation:
x + 6 ≤ 8
subtract 6 on both sides.
x ≤ 2
Option D is the correct answer.
The polynomial 2x³+x²-3x+ p has a remainder 20 when divided by (x - 2). Find the value of constant p.
The value of constant p is 6. Polynomials are algebraic formulas with variables and coefficients. Variables are also known as indeterminates.
How to get the value?Remainder for f(2) = 20.
F(2)=2(23)+22−3(2)+p=20
16+4−6+p=20
14+p=20
P=6
To divide polynomials, divide each term independently by the monomial (as mentioned above), and sum the quotients of each division to get the result. Polynomial long division is a procedure in algebra for dividing a polynomial by another polynomial of the same or lower degree, which is an extended version of the well-known arithmetic approach known as long division. It is simple to accomplish by hand because it divides an otherwise difficult division problem into smaller ones.
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how many quarters are in thirty dollars
Answer: 120 quarters
Step-by-step explanation:
There are 4 quarters in a dollar.
For 30 dollars, there are 3 * 40 = 120 quarters
120 quarters are in thirty dollars
What is substitute and example?
A substitute is a good or service that buyers can quickly swap out for another. For instance, a one-dollar bill can be used in place of another dollar bill.
In business and economics, a replacement, or substitutable good, is a good or service that consumers perceive as just being substantially the same as or reasonably similar to some other good. Consumers are given options and alternatives through substitutes, which also spur competition and lower prices in the market.
Here are a few examples of replacement goods:
1. A $1 bill can be exchanged for four quarters.
2. Coke against Pepsi
3. Regular vs. premium gas
4. Butter and lard
5. Tea and coffee
6. Apples and oranges
7. Comparing driving a car to riding a bike
8. Books in general and e-books
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What does K mean in linear functions?
K Representations of transformations to represent a constant value the parent.
What is linear functions?When the independent variable (often 'x') varies by a constant amount and the dependent variable (typically expressed by 'y') changes by a constant amount, the function is said to be linear. A linear function is, for instance, the progression in the number of ticks of a clock's second hand through time. A straight line makes up the graph of a linear function. Both the independent and dependent variables of a linear function are one. X is an independent variable, whereas Y is a dependent variable. A formula must take the form y=mx+b to be considered a linear function (in which m is the slope and b is the y-intercept).To learn more about linear functions refer to:
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Kiki painted 15 of her bookshelf on Monday and 56 of her bookshelf on Tuesday. She says she has painted 611 of her bookshelf.
Which statement is most accurate?
Responses
A. 6/11 is a reasonable answer for the fraction of her bookshelf Kiki has painted.
B. 6/11 is not a reasonable answer for the fraction of her bookshelf Kiki has painted. The fraction should be closer to 1/2.
C. 6/11 is not a reasonable answer for the fraction of her bookshelf Kiki has painted. The fraction should be closer to 1.
The solution is Option B.
The fraction of bookshelf Kiki painted is closer to 1/2
What is a Fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Given data ,
Let the total fraction of bookshelf painted be A
Now , the value of A is
The fraction of bookshelf painted on Monday = 1/5 of total
The fraction of bookshelf painted on Tuesday = 5/6 of total
Now , the total bookshelf painted A = ( 1/5 ) + ( 5/6 )
The total bookshelf painted A = ( 6 + 5 ) / 30
On simplifying the equation , we get
The total bookshelf painted A = 11/30
The total bookshelf painted A = 0.36667
So , the value of A is closer to 1/2
Hence , the fraction is 11/30
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Is the expression a polynomial? If so, is it a monomial, binomial or trinomial? 5x
Please help
The expression is a monomial.
The expression 5x is a monomial. A monomial is an algebraic expression that consists of one term and is not the sum or difference of other terms. It can be a constant number, a variable, or a product of a constant and one or more variables. In this case, the expression has only one term, which is the product of the constant 5 and the variable x. Therefore, it is a monomial.
A monomial is an algebraic expression that consists of one term and is not the sum or difference of other terms. It can be a constant number, a variable, or a product of a constant and one or more variables. For example, 5, x, and 3x^2 are all monomials.
A binomial is an algebraic expression that consists of two terms and is the sum or difference of those terms. The two terms can be monomials, for example, 3x+2 and 5x^2-7 are binomials.
A trinomial is an algebraic expression that consists of three terms and is the sum or difference of those terms. Like binomials, the terms can be monomials, for example, 2x^2 + 5x +7 or 3x^2 -2x -5 are trinomials.
Therefore, The expression is a monomial.
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Graphing equations for algebra
The solution for the inequality -4x-3>-5x+8 is x>11.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
1) -11+x≥-3
Move all terms not containing x to the right side of the inequality.
x≥8
2) -x/4 <7
Move all terms not containing x to the right side of the inequality.
-x<28
x>-28
3) The highest waterfall in the world is Angel falls in Venezuela at 1000 meters.
So, the inequality represent the height of waterfall is h≤1000.
4) -4x-3>-5x+8
Add 5x on both the sides of an inequality, we get
x-3>8
Add 3 on both the sides of an inequality, we get
x>11
5) Given that, Area≤48
Here, 1/2 ×8×x≤48
4x≤48
x≤12
6) -2x-9<-x-4
Add x on both the sides of an inequality, we get
-x-9<-4
Add 9 on both the sides of an inequality, we get
-x<5
x>-5
7) 1/2 x-8>-3
Move all terms not containing x to the right side of the inequality.
Here x>10
Therefore, the solution for the inequality -4x-3>-5x+8 is x>11.
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trigonometric ratios find a side length calculator
There are a few online calculators available that allow you to find the side length of a triangle using trigonometric ratios.
One example is The Calculator Site, which provides step-by-step instructions on how to use the calculator. By providing the known values of two angles and one side, the calculator can determine the length of the remaining side.
The Calculator Site provides a calculator which can be used to find the side length of a triangle using trigonometric ratios. The calculator requires the user to provide the known values of two angles and one side, after which it will calculate the length of the remaining side.
There are a few online calculators available that allow you to find the side length of a triangle using trigonometric ratios.
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What is log 2 called?
The binary logarithm, sometimes referred to as log base 2, is the inverse function of the power of two functions.
According to the generic logarithm, can be represented in exponential form as for every real number n.
n = [tex]a^x[/tex]
The logarithm form is expressed as Log base 2 is the power to which the number 2 must be raised to acquire the value of n.
[tex]log_a n[/tex] = x
In this case, "a" is a positive real integer that is used as a base and "x" is an exponent. The formulas for log base 2 functions are given for any real value x as
x = [tex]log_{2}n[/tex]
Which is equal to
[tex]2^x[/tex] = n
The real number system does not specify the logarithm of base 0 or logarithms of negative values.
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Parallelogram ABCD is given. Draw line EF such that it goes through vertex C, point E lies on side AD, and point F lies on the extension of BA.
Prove that AECD ~ ACFB.
Solving the provided question, we can say that area of parallelograms = 1/2[( a +b)/ 2 ] = 1/2[( AB+EF)/ 2 ]
What is parallelograms?A parallelogram is a straightforward quadrilateral in Euclidean geometry that has two sets of parallel sides. In a particular kind of quadrilateral known as a parallelogram, both sets of opposite sides are parallel and equal. There are four different kinds of parallelograms, including three unique kinds. Parallelograms, squares, rectangles, and rhombuses are the four different shapes. Having two sets of parallel sides makes a quadrilateral a parallelogram. In a parallelogram, the opposing sides and angles are both the same length. On the same side of the horizontal line, the interior angles are additional angles as well. 360 degrees is the total number of interior angles.
we have
area of parallelograms = 1/2[( a +b)/ 2 ]
a = AB and b = EF
area of parallelograms = 1/2[( AB+EF)/ 2 ]
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o is the centre of the circle and abc and edc are tangents to the circle what is bcd if o is 152
The requried measure of the angle m∠BCD is 28°.
What is the angle?Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
Here,
From the figure,
m∠BOD = 2m∠BFD
= 2 × 76°
= 152°
OD perpendicular to CE simultaneously OB perpendicular to CA
m∠ODC = m∠OBC = 90°
m∠ODC + m∠OBC + m∠BOD + m∠BCD = 360
90 + 90 + 152 + m∠BCD = 360
m∠BCD = 28°
Thus, the requried measure of the angle m∠BCD is 28°.
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Cruises are expensive. You can take steps that will help you save money and get the most out of every dollar you spend.
Make sure you understand exactly what the fare covers. On some lines, food, beverages, and tips are all included. On some ships, they cost extra.
Invest in travel insurance. Many things can interfere with your travel plans. Illness, flight delays, or bad weather happens.
rcruise in the spring or fall. The weather is just as good, crowds are fewer, and rates are lower.
Take your
Answer: I don’t get this question
Step-by-step explanation:
Answer: Answer Is D:
Cruises are expensive, meaning you should take steps that will help you save money and get the most out of every dollar you spend.
Make sure you understand exactly what the fare covers. On some lines, food, beverages, and tips are all included. On some ships, they cost extra.
Invest in travel insurance, on account of the many things that can interfere with your travel plans. Illness, flight delays, or bad weather happens.
Take your cruise in the spring or fall, since compared with the peak season, the weather is just as good, crowds are fewer, and rates are lower.
Step-by-step explanation: Just took the test and it sound correct
What is the product of AXB?
The product of AXB is the matrix C, where Cij = Σk=1nAikBkj, where n is the number of columns in A.
The product of two matrices A and B is a new matrix C, which is obtained by multiplying each of the elements of A with the corresponding elements of B. The size of the resultant matrix C will be the same as that of A and B. For example, if A is m×n and B is n×p, then the product AXB will be an m×p matrix. The value of each element of C is determined by multiplying the elements of corresponding rows of A with those of corresponding columns of B, and then summing up the products. Mathematically, the value of Cij (the element in the ith row and jth column of C) is given by the equation
Cij = Σk=1nAikBkj,
where n is the number of columns in A.
The product of AXB is the matrix C, where Cij = Σk=1nAikBkj, where n is the number of columns in A.
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