First use appropriate properties of logarithms to rewrite f(x) and then find f’(x)
Answers
Answer:
f(x) = 6ln(8) -6ln(x)f'(x) = -6/xStep-by-step explanation:
You want to rewrite f(x) and differentiate it for f(x) = 6·ln(8/x).
Rules of logarithmsThe log of a ratio is the difference of logs:
ln(a/b) = ln(a) -ln(b)
ApplicationUsing this to rewrite f(x), we have ...
f(x) = 6ln(8/x) = 6(ln(8) -ln(x))
f(x) = 6·ln(8) -6·ln(x)
DerivativeThe derivative of the constant is zero, so ...
f'(x) = -6/x
Related Questions
The water tank at the institution is
full. A water truck begin to full the tank with
water at a rate of 8 litres per minute. After 15 minutes the tank was 5/2 full. Calculate
the number of litres of water that the tank can hold
Answers
Answer:
t = 48 litres when full
Step-by-step explanation:
The water tank at the institution is full. A water truck begin to full the tank with water at a rate of 8 litres per minute. After 15 minutes the tank was 5/2 full. Calculate the number of litres of water that the tank can hold.
8(15) = 5/2t
120 = 5/2t
240 = 5t
t = 48 litres when full
the equation y = 1x/3 + 3 is shown graphed below. If the equation y = 2x - 4 was added to this one to form a system, what would be its solution?
Answers
The solution of the system of the equations, y = 1/3x + 3 and y = 2x - 4, as shown in the graph below is: (4.2, 4.4).
What is the Solution to a System of Equations?A system involving two equations has a solution, which are the coordinates of the point on a graph where the two equations intersect.
Given the equation, y = 1/3x + 3, which is represented by the red line in the graph below, when y = 2x - 4 (represented as the blue line) is added, a system is formed which will make both lines intersect at the point that has the coordinates (4.2, 4.4).
Therefore, the solution of the system y = 1/3x + 3 and y = 2x - 4 is (4.2, 4.4).
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write an indirect proof in paragraph form. given: triangle rvt and svt are equilateral. triangle rvs is not equilateral
Answers
The indirect proof that defines triangle RVS is not equilateral is explained below.
How triangle look like?
In math, A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices and also a polygon.
Here we need to find the indirect proof for the triangle RVS which is not equilateral.
Here we know that, We need to write an indirect proof in paragraph proof.
For, the given statement, △RVT and SVT are equilateral;
And △RVS is not equilateral.
Then the explanation for this one is written as,
Let us assume temporarily that △RST is equilateral.
And we have given that △RVT and SVT are equilateral, then the sides of △RVT, SVT, and RST are congruent.
Therefore, RV≅VSRS which follows that △RVS is equilateral.
In contradicts the given that △RVS is not equilateral, then the temporary assumption must be false. It follows that △RST is not equilateral.
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For a hypothesis test comparing two independent population means, the combined degrees of freedom are 56. Which of the following statements about the two sample sizes cannot be true? Assume the population standard deviations are unknown but equal Multiple Choice O m = 29, n2 - 29 O m-27; 12 - 29 O m = 26; * 32 28O n2 = 30
Answers
Option B [tex]n_{1} = 27 ,n_{2} = 29[/tex] are the two sample sizes cannot be true.
HYPOTHESIS TEST
Hypothesis testing in statistics is the process of putting a population parameter assumption to the test. The analyst will select a method based on the type of data used and the goal of the research. Hypothesis testing is a method used to determine whether a hypothesis is tenable by using sample data.Given that:
The degree of freedom for the test of two independent population means is 56.
Degrees of freedom for two independent populations are well known.
[tex]n_{1} + n_{2} - 2[/tex]
[tex]n_{1} + n_{2} - 2[/tex] = 56
[tex]n_{1} + n_{2}[/tex] = 54
Total sample sizes = 54
Option B ( [tex]n_{1} = 27 ,n_{2} = 29[/tex] ) cannot be true.
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Which set of ordered pairs represents a function? {(-1, 3), (2, 6), (3, 9), (4, 12), (5, 20)} {(-7, 3), (-7, 6), (-7, 12), (-7, 18)} {(9, -3), (4, -2), (1, -1), (0, 0), (1, -3)}
Answers
From the given pairs of ordered pairs {(-1, 3), (2, 6), (3, 9), (4, 12), (5, 20)} it is a function.
What is a Function?The core concept of mathematics calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x.
As per the set of ordered pairs given in the question,
1.
{(-1, 3), (2, 6), (3, 9), (4, 12), (5, 20)}
It is a function because every input has a single output.
2.
{(-7, 3), (-7, 6), (-7, 12), (-7, 18)}
It is not a function because 7 corresponds to two different images like 3, 6, 12, and 18.
3.
{(9, -3), (4, -2), (1, -1), (0, 0), (1, -3)}
It is not a function because 1 corresponds to two different images, like -1 and 3.
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How would you limit the domain to make this function one to one f(x)=3-x^2
Answers
Answer:
x ≥ 0
Step-by-step explanation:
You want to know an appropriate limit on the domain of f(x) = 3 -x² so the function is one-to-one.
One to OneA function is one-to-one if it passes the "horizontal line test." That is, a horizontal line can intersect its graph in at most one place.
The function f(x) = 3-x² has a turning point at x=0 and is symmetrical about that line. In order to make the function be one-to-one, the domain must be restricted to one of ...
x ≥ 0, orx ≤ 0or any subset of either of those domains.
the lucas primality test is based on one finding of this man who pioneered the method of infinite descent. that result is a specific case of a theorem that takes an element to the totient function of n-1, euler's theorem. numbers for which the converse of that theorem do not hold are called carmichael
Answers
The name of this man's "small" and "final" theorems are Pierre de Fermat
He was a French mathematician who is recognized for his work on inequality and other early advances that helped pave the way for infinitesimal calculus. He is praised in particular for his work on number theory and his original invention of a technique for determining the largest and smallest ordinates of curved lines that is comparable to differential calculus, which was previously unheard of. He made important advances in probability, optics, and analytical geometry.
The Taniyama-Shimura Conjecture, commonly known as the modularity conjecture, was employed in another theorem that bears this man's name.
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Given f(x) =2x2 + 1 and g g(x) = 3x-5 , find the following. f(g)(2))
Answers
The value of f(g(2)) from the given functions f(x) and g(x) is 3.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given functions are f(x)=2x²+1 and g(x)=3x-5.
We need to find f(g(2)).
Put x=2 in the function g(x)=3x-5, we get
g(2)=3×2-5
= 6-5
= 1
So, g(2)=1
Put x=1 in the function f(x)=2x²+1, we get
f(g(2))=2(1)²+1
= 2+1
=3
Therefore, the value of f(g(2)) is 3.
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I need help with this Question.
Six items purchased at a grocery store weigh 15 kilograms. One of the items is detergent weighing 872 grams. What is the total weight, in kilograms, of the other five items?
The total weight of the other 5 items is. kg.
Answers
Answer:
14.128
Step-by-step explanation:
you need to extract the 872g which is 0.872kg
from the 15 and that is 14.128kg
11) Solve for n in s=(n-2) 180
A) n=180 s+2
B) n=(s-2) . 180
C) n=s/180-2
D) n=s/180+2
Answers
For the given equation the value of n is equal to option D.
n = (s/180) + 2.
As given in the question,
Given equation is equal to :
s = (n-2)180
Now take all the terms on one side and term n on other side of the equation we have,
Divide both the side by 180 we get,
s/ 180 = [(n-2)180]/180
s/180 = n -2
Add 2 both the side of the equation we get,
(s/180 ) + 2 = n -2 + 2
(s/180 ) + 2 = n
so here the value is equal to
n = (s/180) +2.
Therefore, the value of n in the equation is equal to option D.
n = (s/180) + 2.
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PLEASE PLEASE PLEASE HELP
Answers
Given the input f(-5), we know that 5 is less than zero; therefore, it satisfies the first restriction. This means that f(-5)=14 because x=-5 is less than zero.
Answer: f(-5)=14
The number line above shows the solution graph of which inequality?
A) 2x+9 > 25
B) 2x+9 ≥ 25
C) 2x+9 < 25
D) 2x +9 ≤ 25
Answers
Answer:
2x+9<25 or u just can say c
Why is it said that the rural landscape has been replaced by the urban landscape?
Answers
It is said that the rural landscape has been replaced by the urban landscape because rural landscapes have been transformed into urban ones.
¿What are rural and urban landscapes?We have to:
Rural landscapes are those where rural elements predominate, for example, in the fields. Urban countries are those where urban elements predominate, for example, cities.At present, more and more rural spaces become urban, which is why it is indicated that the urban landscape is replacing the rural one.
¡Hope this helped!
would you expect the proportion of stay-at-home residents to be higher in virginia than in arkansas? support your conclusion with the results obtained in parts (b) and (c). from the results obtained in parts (b) and (c), we would expect the number of stay-at-home residents to be higher correct: your answer is correct. in arkansas than virginia. the sample results show that, rounded to two decimal places, the estimated percentage of arkansas residents who were born there is %. the sample results also show that, rounded to two decimal places, the estimated percentage of virginia residents who were born there is %.
Answers
As per the estimated percentage, the test statistic is 0.6167 or 61.67%
The term percentage is defined as the number or ratio that can be expressed as a fraction of 100.
Here we have given that in Arkansas than Virginia. the sample results show that, rounded to two decimal places, the estimated percentage of Arkansas residents who were born there is %. the sample results also show that, rounded to two decimal places, the estimated percentage of Virginia residents who were born there is %.
And we need to find the test statistics.
While we looking into the given situation we have identified the following values,
=> H0 : p = 0.577
=> Ha : p ≠ 0.577
Now, we have estimate the proportion of stay-at-home residents in Arkansas is calculated as,
Here the Proportion of stay-at-home residents in Arkansas is written as,
=> p = 74/120 = 0.6167
Therefore, the test statistics is 0.6167.
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Which BEST describes the decimal form of a rational number?
Responses
A either terminates in 0's or repeats.
B eventually repeats a non-zero digit
C neither terminates nor repeats
D always terminates in 0s
I WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST PLS HURRY
Answers
Answer:
C
Step-by-step explanation:
A rational number can be written as a ratio of two integers. In decimal form, a rational number will either terminate or repeat a pattern.
Solve the equation.
3^2x= 6,561
x=3
x=4
x=8
x= 16
Answers
Answer: 4
Step-by-step explanation
3^2×=6561
then think 3 raise to power what is 6561
the answer is 8
3^2×=3^8
three cancel three
2×=8
divide both sides by 2
then ×=4
Hello, I need help with this problem.
Fill out the Venn Diagram and answer the questions.
Thank you.
Answers
Answer:
see the attachment for the Venn diagram
17949173182153248Step-by-step explanation:
Given the numbers of students in various combinations of three courses, you want the associated Venn diagram and some numbers associated with additional combinations of courses.
Venn diagramIt is often easiest to populate the numbers in a Venn diagram by starting with the center one: 286 are taking all three courses. (V. = 286)
Working outwards from there, the numbers taking two courses can be filled in: (II. = History & Dance - V. = 343; IV. = History & Math - V. = 319; VI. = Dance & Math - V. = 318.)
Finally, the number taking a single course can be found. (I. = History -II. -IV. -V.; III. = Dance -II. -V. -VI.; VII. = Math -IV. -V. -VI.)
Adding all the numbers found so far gives the total in History, Dance, or Math (question 4). The difference between the number surveyed and the number in courses is VIII, the number taking none of the courses (question 5).
History or Not DanceThe least arithmetic may be involved if you rewrite this expression to ...
H ∪ D' = (H'∩D)' = 2401 -(III +VI) = 2401 -(289 +318) = 1794
(History or Math) and Not DanceThis will be the sum of numbers I, IV, VII.
226 +319 +372 = 917
Dance and Math and Not HistoryThis is VI alone: 318
History, Dance, or MathThis is all but VIIII: 2401 -248 = 2153
None of the CoursesThis is VIII alone: 248
URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
Answers
The solution is Option D.
The value of x from the triangle is x = 31
What are similar triangles?
If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.
Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides
Given data ,
Let the first triangle be ABC
The measure of side AB = 14.5
The measure of side BC = 15.5
Let the second triangle be XYZ
The measure of side XY = 29
The measure of side YZ = x
Now , if the triangle ABC is similar to triangle XYZ , then the corresponding sides of the triangles will be equal in ratio
So , the equation will be
XY / AB = YZ / BC
Substituting the values in the equation , we get
29 / 14.5 = x / 15.5
On simplifying the equation , we get
x/15.5 = 2
Multiply by 15.5 on both sides of the equation , we get
x = 2 x 15.5
x = 31
Therefore , the value of x is 31
Hence , the value of x of side YZ is 31
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Suppose that the population of a certain town is made of 45% men and 55% women. Of the men, 40% wear glasses, and of the women 20% wear glasses. Given that a person chosen at random from this town wears glasses, what is the probability that the person is a woman?
Answers
The probability that the person is a woman is 40%.
what is the probability that the person is a woman?P(woman | glasses) = (20% * 55%) / (40% * 45% + 20% * 55%) = 0.55There is a 50% probability that a sperm will fertilize a boy and a 50% chance that a sperm will fertilize a female ovum each time.The probability that a randomly chosen person in this town wears glasses is equal to the sum of the probability of a man wearing glasses and the probability of a woman wearing glasses.P(Glasses) = P(M ∩ G) + P(W ∩ G)
P(Glasses) = 0.45 × 0.40 + 0.55 × 0.20
P(Glasses) = 0.27
The probability that the randomly chosen person is a woman is equal to the probability of a woman wearing glasses divided by the probability of a person wearing glasses.P(Woman) = P(W ∩ G) / P(Glasses)
P(Woman) = 0.55 × 0.20 / 0.27
P(Woman) = 0.44
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Which expressions are equivalent
Answers
Answer:
b and c
Step-by-step explanation:
How do I get n(E)/n(S)= 7,650/341,055 simplified to 170/7579
Answers
Answer:
Divide the numerator and denominator by 45.
Step-by-step explanation:
7650/341055
Divide the numerator and denominator by 5.
1530/68211
Divide the numerator and denominator by 3.
510/22737
Divide the numerator and denominator by 3.
170/7579
What is the value of q?
O 4√5
O 2√14
O 20√5
O 64√5
Found the answer thought I would help
Answers
Answer:
18
Step-by-step explanation:
a ladder is 8 feet 3 inches tall. How tall is it in inches?
Answers
Answer:
99 inches
Step-by-step explanation:
1 foot=12 inches
8x12=96
96+3=99
Find the distance AB:
A = (-2, 1) and B=(5,-4)
Simplify.
d =
= √(5--2)² + (-4-1)²
Answers
Answer:
now
Step-by-step explanation:
d= √(X2 _ X1) +(Y2 - Y1). = (5 -2 )+ (-4- 1)=
The graph models the linear relationship between the number of monthly payments made on a loan and the remaining balance in dollars left to pay on the loan.
Which statement describes the x-intercept of the graph?
The x-intercept is 40 , which represents the initial balance in dollars of the loan.
The x-intercept is 30,000 , which represents the initial balance in dollars of the loan.
The x-intercept is 40 , which represents the number of monthly payments needed to repay the loan.
The x-intercept is 30,000 , which represents the number of monthly payments needed to repay the loan.
Answers
The x - intercept is 40 ,which represents the number of monthly payments needed to repay the loan .
Given :
The graph models the linear relationship between the number of monthly payments made on a loan and the remaining balance in dollars left to pay on the loan.
From the graph :
Two points are ( 6 , 25500 ) and ( 25 , 11250 )
x - intercept = 40
The x - intercept gives information about the variable represented on the x - axis of a graph which is the number of monthly repayments needed to cover the loan.
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Your
gross pay is $2,759.00. Your involuntary deductions are FICA (7.65%), federal
withholding (12%), and state withholding (7%). How much are you allowed for housing and
fixed expenses
Answers
The amount allowed for housing and expenses is $2023.73.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Gross pay = $2759
Deduction:
7.65%
= 7.65/100 x 2759
= $211.06
12%
= 12/100 x 2759
= $331.08
7%
= 7/100 x 2759
= $193.13
The remaining amount.
= 2759 - 211.06 - 331.08 - 193.13
= $2023.73
Thus,
The amount allowed is $2023.73.
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Consider two urns, Urn A and Urn B, where each urn initially contains 1 black ball and 2 white balls. In each round, a ball is randomly selected from each urn, and the two balls are changed place. Let X denote the number of black balls in Urn A after the nth round of exchange. Clearly, {Xn;n > 0} is a Markov chain. (a) State the transition probability matrix of {Xn;n > 0}. (b) What is the probability that after 3 exchanges, there are exactly 2 black balls in Urn A? (c) What is the probability that by the time we have done 3 exchanges, there has never been 2 black balls in Urn A? (d) Determine the long-run proportions that there are 0, 1, and 2 black balls in Urn A. (e) What is the long-run proportion that both balls that are selected from the urns are black?
Answers
a. P = [tex]\left[\begin{array}{ccc}\frac{2}{3} &\frac{1}{3} &0 \\\\\frac{2}{9} &\frac{5}{9} &\frac{2}{9}\\ \\0&\frac{2}{3} &\frac{1}{3} \end{array}\right][/tex]
b. P[[tex]x_{3} = 2[/tex]] = 0.18
c. p = 0.8353
d [tex]\pi _{1} = \frac{1}{2} \\\\\pi _{2} = \frac{1}{6} \\\\\pi _{0} = \frac{2}{6}[/tex]
Given that:
{[tex]x_{n}[/tex] ; n > 0} is a Markov chain
[tex]x_{n}[/tex] denotes no of black balls in Urn A after [tex]n^{th}[/tex] round of exchange.
Clearly know that no of black balls in Urn A cannot exceed.
Hence, state space is {0, 1,2}
Transition probabilities can be
(a) [tex]P_{00}[/tex] = P [white ball is selected from A & white ball is selected from B]
= P [white ball from A] × P [white ball from B]
= [tex]\frac{2}{3}[/tex]
[tex]P_{01}[/tex] = P [white ball from A & black ball from B ]
= [tex]\frac{1}{3}[/tex]
[tex]P_{10}[/tex] = P [black ball from A & white ball from B]
= [tex]\frac{2}{9}[/tex]
[tex]P_{11}[/tex] = P [black ball from A & black ball from B]
or P [white from A & white from B]
[tex]= \frac{1}{3} * \frac{1}{3} + \frac{2}{3} *\frac{2}{3}\\ \\ = \frac{1}{9} + \frac{4}{9}\\ \\= \frac{5}{9}[/tex]
[tex]P_{12}[/tex] = P [white from A & white from B]
= [tex]\frac{2}{9}[/tex]
[tex]P_{21}[/tex] = P [black ball from A & white ball from B]
= [tex]\frac{2}{3}[/tex]
[tex]P_{22}[/tex] = P [white from A & white from B]
= [tex]\frac{1}{3}[/tex]
Transition probability matrix P = [tex]\left[\begin{array}{ccc}\frac{2}{3} &\frac{1}{3} &0 \\\\\frac{2}{9} &\frac{5}{9} &\frac{2}{9}\\ \\0&\frac{2}{3} &\frac{1}{3} \end{array}\right][/tex]
(b) The probability that after 3 exchanges, there are exactly 2 black balls in Urn A.
P[[tex]x_{3} = 2[/tex]]
given initial distribution
[tex]p [x_{0} = 0] = 0 , p [x_{0} = 1] = 1 , p [x_{0} = 2] = 0[/tex]
p[tex][x_{3} = 2] =[/tex] ∑ i = 0 to 2 P [tex][x_{3} = 2 , x_{0} =i ][/tex]
= ∑ i = 0 to 2 P [tex][x_{3} = 2 , x_{0} =i ][/tex] . P[tex][ x_{0} = i][/tex]
= ∑ i = 0 to 2 P [tex]i^{2^3}[/tex] P[tex][ x_{0} = i][/tex]
Transition probability matrix can be calculated by increasing power of P matrix to 3 i.e [tex]P^{3}[/tex]
P[[tex]x_{3} = 2[/tex]] = 0.18
(c) The probability that by the time we have done 3 exchanges, there has never been 2 black balls in Urn A.
[tex]P[x_{3} \neq 2 , x_{2} \neq 2, x_{1} \neq 2 | x_{0} = 1 ][/tex]
p = 0.8353
(d) Long run proportions of state 0,1,2.
[tex]\pi _{0} = \frac{2}{3} \pi _{0} + \frac{2}{3} \pi _{1}[/tex]
[tex]\pi _{1} = \frac{1}{3} \pi _{0} + \frac{5}{9} \pi _{1} + \frac{2}{3} \pi _{2}[/tex]
[tex]\pi _{2} = \frac{2}{9} \pi _{1} + \frac{1}{3} \pi _{2}[/tex]
[tex]\pi _{0} + \pi _{1} + \pi _{2} = 1[/tex]
[tex]\pi _{0} = \frac{2}{3} \pi _{1} \\[/tex]
[tex]\pi _{2} = \frac{1}{3} \pi _{1}[/tex]
[tex]\pi _{1} [\frac{1}{3} + \frac{2}{3} + 1 ] = 1[/tex]
[tex]\pi _{1} = \frac{1}{2} \\\\\pi _{2} = \frac{1}{6} \\\\\pi _{0} = \frac{2}{6}[/tex]
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Find the vector v with an initial point at (5, 7) and a terminal point at (2, 10). write your answer in component form. then write the vector v as a linear combination of the unit vectors i and j. finally, find the length of the vector.
Answers
The length of the vector v is approximately 4.24. A vector is a mathematical object that has both magnitude and direction
Vectors are commonly used in physics, engineering, and other fields to represent quantities that have both magnitude and direction, such as velocity, acceleration, and force. They are also important in linear algebra, where they can be used to represent lines and planes in space, and to solve systems of linear equations.
The vector v can be expressed in component form as v = <2-5, 10-7> = <-3, 3>.
To express the vector v as a linear combination of the unit vectors i and j, we can write it as v = (-3)i + 3j.
To find the length of the vector, we can use the Pythagorean theorem:
length of v = sqrt((-3)^2 + 3^2) = sqrt(9 + 9) = sqrt(18) = 3*sqrt(2) = 4.24
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which of the following is a function that is passed as an argument to another function? question 40 options: anonymous value callback restricted
Answers
callback restricted is a function that is passed as an argument to another function
It tests whether the condition returned by the callback function holds for at least one item in array.
What is an array?
It should be noted that an array means a data structure that can store a fixed size collection of elements.
In this case, the true statement of the array is that it tests whether the condition returned by the callback function holds for at least one item in array.
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6. Writing When you add a
one-digit number to a
decade number, what do you
notice about the ones place
digit of the sum?
Answers
When you add one-digit number to a decade number, you will notice that the ones place digit sum is interchanged in their positions
How to add a one-digit number to a decade number?You should know the word decade means ten. so a decade number is a number with ten digits. The digits of the decade number are
1,2,3,4,5,6,7,8,9
So write the number as
12345679
A digit number is say 9
123456789+9
= 123456798
Therefore when a digit number is added to a decade number, the last digits interchange their positions
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