From the recursive definition, the next term of a sequence is the previous term multiplied by 3, hence it is a geometric sequence with a common ratio of 3.
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
The recursive definition of a geometric sequence is:
[tex]a_{n+1} = qa_n[/tex]
In this problem, the sequence is given by:
[tex]u_{n+1} = 3u_n[/tex]
With first term [tex]u_1 = \frac{4}{27}[/tex].
Hence it is a geometric sequence with a common ratio of 3.
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Provide three additional commonly used statistical measures for the characterization of data dispersion.
The three additional commonly used statistical measures for the characterization of data dispersion are: Standard Deviation, Interquartile Range and Range.
What is dispersion in statistics?Dispersion in statistics refers to how far the data deviates from the mean.When measures of central tendency are insufficient to explain the data, it is highly helpful. Consider the case where the mean is the same across two completely different datasets. Then, in order to explain the variation in the datasets, we employ metrics of dispersion.Now,
The most common examples of statistical metrics of dispersion include:
Standard Deviation: A measurement of how widely apart data are from the mean is the standard deviation. It is the most typical method of measuring dispersion.Interquartile Range: The middle 50% of observations are described by the interquartile range (IQR). The middle 50% of observations are widely separated if the interquartile range is big. Extreme values have no impact on it. Consequently, is helpful when the extreme values are not precisely recorded.Range: The range of data is the distance between the largest and smallest observation. It does not use all of the observations in a data collection and is particularly sensitive to outliers. Therefore, giving the minimum and maximum values rather than the range is more instructive.Hence, The three additional commonly used statistical measures for the characterization of data dispersion are: Standard Deviation, Interquartile Range and Range.
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8x10+
4x1+ 6x (1/100)
Answer:
8x¹⁰+203x/50
Step-by-step explanation:
Answer: 4203/50
Step-by-step explanation:
8 x 10 + 4 x 1 + 6 x (1/100)=
80 + 4 + 6/100=
84 + 6/100=
84 + 3/50=
(84 + 3/50)*50/50= ==> multiply by 50 to remove denominators
(84 * 50 + 3 * 50/50)/50=
(84 * 50 + 150/50)/50=
(4200 + 3)/50=4203/50
If f (x) = (x^2 − 3)^4, then f '(1) =
Answer:
f'(1) = -64
Step-by-step explanation:
To find f'(1), we will be finding the f'(x) first which means the first derivative of f(x), we can find the derivative by using chain rule to this function.
The formula of chain rule is:
[tex]\displaystyle f(u) = u^n \to f'(u) = nu^{n-1}\cdot u'[/tex]
In simple explanation, we derive normally (power rule) then multiply by the derivative of inside (u).
Applying the formula, we will have:
[tex]\displaystyle{f'(x)=4(x^2-3)^{4-1}\cdot (x^2-3)'}\\\\\displaystyle{f'(x)=4(x^2-3)^{3}\cdot 2x}\\\\\displaystyle{f'(x)=8x(x^2-3)^{3}}[/tex]
Substitute x = 1 in the f'(x):
[tex]\displaystyle{f'(1)=8(1)(1^2-3)^3}\\\\\displaystyle{f'(1)=8(1-3)^3}\\\\\displaystyle{f'(1)=8(-2)^3}\\\\\displaystyle{f'(1)=8(-8)}\\\\\displaystyle{f'(1)=-64}[/tex]
Kenny and Tara are both members of a population, and a simple random
sample is being conducted. If the chance of Kenny being selected is, what
is the chance of Tara being selected?
The probability or chance of Tara being selected is 1/29.
What is probability?Probability is the chance of happening something or the occurrence of something . We can also define the probability as the chance of occurring or the chance of selecting something from the total set of value. It is always ranges from 0 to 1 where 0 is minimum value and 1 is maximum value of probability.
Formula for probability is :
[tex]P(Event) =\frac{ Chance \ of \ occurring \ that \ event}{total \ occurance}[/tex]
where, the total occurrence is the sample space of our given data or we can say the total number of values in the sample space.
In the given question,
Chance of selecting Kenny = 1 / 29
=> P(Kenny is selected) = 1/29
That means sample space consist of 29 values.
Now, P(Tara is selected) = 1 / sample space
=> P(Tara is selected) = 1/29.
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The complete question is :
Kenny and Tara are both members of a population, and a simple random sample is being conducted. If the chance of Kenny being selected is 1/29, what is the chance of Tara being selected?
Which statement is true about the function f(x)=8^3
The function f(x) = 8 is even because f(x)= f(-x).
Given the function is f(x) = 8
Key to find if a function f(x) is even or odd is to replace the x with -x.
if the results comes out to be f(x) then it is even function.
if the results comes out to be -f(x) then it is odd function.
where as graphically even f(x) will be symmetric around the y-axis and odd f(x) will be symmetric around the origin.
In given case f(x)= 8
if we replace x with -x in above equation then results is 7
f(-x)= 8
hence f(x)= f(-x) = 8
Therefore, f(x) = 8, is an even function.
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Your question is incomplete. Please find the missing content here.
Which statement is true about the function f(x) = 8
question 4(multiple choice worth 5 points) (04.02 lc) two functions, a and b, are described as follows: function a y
The rate of change of function A is 3 times the rate of change of function B.
What is rate of change of a function?To determine the slope of a graphed function, we use the average rate of change formula: Divide the change in y-values by the change in x-values to determine the average rate of change. Identifying changes in measurable parameters like average speed or average velocity calls for the knowledge of the average rate of change.Now,
Given:
For Function A, y = 9x + 4For Function B, rate of change = 4 and y intercept = 4To find: The number of times the rate of change of function A is, as compared to the rate of change of function B.
Finding:
According to the information given,
Rate of change = 3, i.e., b = 3 for function By- intercept = 4, i.e., c = 4Thus, by the slope-intercept form, given by: y = bx + c, the rate of change for function B is given by:
y = 3x + 4
Now, on comparison with function A, we can see that the rate of change of the function A is exactly thrice of that of function B.
Hence, The rate of change of function A is 3 times the rate of change of function B.
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(COMPLETE QUESTION)
(04.02 LC) Two functions, A and B, are described as follows: Function A y = 9x + 4 Function B The rate of change is 3 and the y-intercept is 4. How much more is the rate of change of function A than the rate of change of function B? 2 3 6 9
Look at this incomplete multiplication problem.
154 times 63 = 462. 462 + question mark = blank
The missing value is
A. 904
B.9040
C.9240
Answer:
The answer is C
Step-by-step explanation:
The first step is to multiply 154 and 63 to find the product. The product of those two numbers is 9702.
So the the equation looks like...
462+ Blank = 9702
The easiest thing to do here is subtract 462 from both sides. So 9702-462 which would equal 9240.
So we'll say that the blank is x so now the equation says...
x = 9240
andres gasta 345$ mensuales.cuanto gasta en 1 Año 7 meses
Answer:
$6555
Step-by-step explanation:
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day :)
helppp meee 40points
Answer:
1) 4a x 4b when a is 2 and b is 2
2) 2a + 4x when a is 2 and x is 8
Step-by-step explanation:
then he spent $34 on lunches the next week.how much was in his account then?
In linear equations, -6 was in his account then .
What are instances of linear equations?
Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y).Kiran had $24 in her account
24-16=8
28-8=20 he deposited $20
he spent $34 on lunches in the next week.
28-34= -6 his account balance was -6
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The complete question is -
At the Beginning of the month Kiran had $24 in his school cafeteria account. Then he spent $34 on lunches in the next week. How much was in his account then?
Mentally estimate the product of 313 and 489
Answer:
remember: we are rounding!
313 × 489
Where 313 ≈ 300
Where 489 ≈ 500
Step-by-step explanation:
300 × 500 = 150,000 because 3 × 5 = 15
Hope this helps!
please help I've been trying to solve this for 30-35 minutes
Answers: middle box: 1.32
middle right box: -3.3
bottom left: -0.5
bottom middle: 0.6
Step-by-step explanation:
[Find out the middle box]
[tex]-1.2[/tex] x [tex]-1.1[/tex][tex]=1.32[/tex]
[Find out the box in the middle right]
[tex]3[/tex] x [tex]-1.1 = -3.3[/tex]
[To Find out the bottom left box - divide each side by three]
[tex]x[/tex] x [tex]3 = -1.5[/tex]
[tex]x = -0.5[/tex]
[Bottom middle box]
[tex]-0.5[/tex] x [tex]-1.2 = 0.6[/tex]
General Rule:
[tex]negative[/tex] x [tex]negative = positive[/tex]
[tex]negative[/tex] x [tex]positive = negative[/tex]
Hope this helps :)
the age distribution of a population (relative proportions of people of different ages) is not important when considering the growth rate of that population.
It is False to state that the age distribution of a population is not important when considering the growth rate of that population.
What is the growth rate of a population?Population growth is the rise in the number of inhabitants in a population or scattered group and it is usually stated in percentage.
Researchers often focus on four primary elements when forecasting changes in population size:
Birth rates,Death rates (life expectancy),The beginning age profile of the population (i.e. elderly or relatively young individuals), and Migration.Other factors include:
Economic development Social and cultural factorsEducation, etcAge distribution and statistics allow the pace of population growth to rise or decline as it is linked to the level of economic development of a population. a fast-expanding country's population has a pyramid-shaped age structure, with a higher share of younger people of reproductive age.
Therefore, we can conclude that it is False to state that the age distribution of a population is not important when considering the growth rate of that population.
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1 ÷ 200= 0.005
true or false?
Answer:
True
Step-by-step explanation:
1/200=0.005
Hope It Helps
Sorry If I'm Wrong
HELP ME OUT QUICK THANK YOU !What is -78.6 (-2.4)?
A. -188.64
B. -32.75
C. 32.75
D. 188.64
Answer:
d) 188.64
Step-by-step explanation:
Let's solve the problem,
→ -78.6(-2.4)
→ -78.6 × -2.4
→ 188.64
Thus, option (d) is correct.
Answer:
D. 188.64 is the correct answer!
Step-by-step explanation:
As captain of the cheer team Lily is choreographing a routine for a competition. The minimum allowable length for a routine is 3 minutes and the maximum allowable length for a routine is 5 minutes. Write an absolute value for which the two solutions are the minimum and maximum allowable lengths.
Lily, the cheer team's captain, is putting together a performance for a tournament. A routine may be no less than 3 minutes in length and no more than 5 minutes in total. For which the two solutions are the shortest and longest permitted lengths, write an absolute value.
The absolute value for 3 is 3 .
The absolute value for 5 is 5.
The two solutions are the shortest and longest permitted lengths, The absolute value |2x−5|+|2x−3|=2
Absolute value is the non-negative value of a real number x, independent of its sign, is its absolute value (or modulus), | x |.
For example, 5 has an absolute value of 5, and -5 has a value of 5. Another way to think about a number's absolute value is as its distance from zero on the real number line. In addition, the distance between two real numbers is the absolute value of their difference.
Given that,
A routine may be no less than 3 minutes in length and no more than 5 minutes in total.
By absolute value equation
we can get 2x−5|+|2x−3|=m
By solving we get 2 m values they are,
m={-8,2}
Here, -8 we can take but the answer will be in decimal soo we take 2.
|2x−5|+|2x−3|=2
We get
[tex]|4x-8|=2\\|x-2|=1\\|x|=3\\[/tex]
If we take 2x =y
|y−5|+|y−3|=2
[tex]|2y-8|=2\\|y-4|=1\\|y|=5[/tex]
Therefore,
The absolute value for 3 is 3 .
The absolute value for 5 is 5.
The two solutions are the shortest and longest permitted lengths, The absolute value |2x−5|+|2x−3|=2.
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can please answer this question
Answer: about 7300 thousand per month
about 1700 per week
10 an hour? it doesn't sound right but it doesn't go into detail about how many hours he works so i don't know but i hope it helps.
Step-by-step explanation:
Kiara has $520 in her bank account. each week she deposits $80 and withdraws $35. gael has $310 in his account. each week he deposits $95 and withdraws $20. write and solve an equation to determine the week w when gael and kiara have the same amounts of money in their accounts.
The answer is D and the written answer is 7
Simplify.
√{24 x²y³)
Answer:
2xy√6y
Step-by-step explanation:
let a be the event that the sum of the faces showing is 6 and let b be the event that the face showing on one die is twice the face showing on the other die.
PABc = 3/36
PABc = 1/12.
Two dice are tossed.
Assume that each possible outcome has 1/36.
Let A be the event the probability of getting some of the faces showing is 6.
A = 1,5,5,12,44,23,3
Let B be the event that the face showing one die is twice on the other.
That is,
B =1,22,12,44,23,66,3
There are 36-6=30 events in Bc
However, A and Bc will only be having 3 pairs together = 1,55,13,3
Therefore,
PABc = 3/36
PABc = 1/12.
How many outcomes are possible for the sum of the faces showing?
There are countless outcomes that could occur. The sum of the faces shown has an endless number of outcomes. This is due to the fact that there are an endless number of ways to flip a coin, which will produce various combinations on the faces that are displayed. The sum of the faces and the tails has an endless number of outcomes. There are only two outcomes that can occur while tossing a coin because the total number of outcomes is always even.
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Find all values of x in the interval [0, 2] that satisfy the equation. (enter your answers as a comma-separated list.) 5 sin(2x) = 5 cos(x)
All values of x in the interval [0, 2] that satisfy the equation are [tex]\frac{\pi }{2} ,3\frac{\pi }{2}[/tex].
What is an equation?A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions and express their equality. A well-formed formula consisting of two expressions linked by an equals sign is considered to be an equation in English, but the word's cognates in other languages may have slightly different definitions. For instance, an équation is defined as having one or more variables in French.
The first step in resolving a variable equation is to identify the values of the variables that lead to the equality being true. The variables that must be changed in order to solve the equation are referred to as the unknowns, and the values of the unknowns that satisfy the equality are referred to as the equation's solutions.
Calculations:
16cos(x +8sin(2x)=0
Divide by 8
2cos(x)+sin(2x)=0
Identity:
sin(2x)=2sin(x)cos(x)
2cos(x)+2sin(x)cos(x)=0
Factor:
2cos(x)(1+sin(x))=0
2cos(x)=0
cos(x)=0=x=[tex]\frac{\pi }{2}[/tex],3[tex]\frac{\pi }{2}[/tex]
(1+sin(x))=0
sin(x)=−1=x=3[tex]\frac{\pi }{2}[/tex]
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Please help me on this
Answer:
second left
Step-by-step explanation:
Isabel’s competition,who sells books and no other products, charges a shipping fee of $1.99 per book plus a fixed fee of $3 for each order. Let x be the number of books purchased and f(x) be the price of shipping one order of books. Write a function that expresses f(x) and explain the value of f(x) for x = 0. (5 points)
Answer:
Step-by-step explanation:
for the function i get f(x)=1.99x+3
f(x) = 1.99x + 3 for x>0
x≥1
X cannot get to zero it is no allowed by the function I defined
i tried my best
Find three consecutive numbers whose sum is 84
Answer:
27 28 29
Step-by-step explanation:
Let the first be n , and if they are consecutive then the next two numbers are n+1 and n+2.
n+(n+1)+(n+2)=84.
3n+3=84.
⇒3n=81.
⇒n=27.
Hence numbers are n,n+1,n+2→27,28 and 29
What are the ordered pairs of the solutions for this system of equations? y=x^2-2x+3
y=-5x + 1
The ordered pairs of the solutions for this system of equations is (-2,11) and (-1,6)
Two integers written in a certain order make up an ordered pair. As a result, we may define an ordered pair as a pair of components that appear in brackets and in a specific order.
These equations are composed of a line and a parabola. The intersection points between them must be located:
[tex]y=x^2-2x+3[/tex]
y=-5x+1
Thus,
[tex]x^2-2x+3=-5x+1[/tex]
[tex]x^2-2x+5x+3-1=0[/tex]
[tex]x^2+3x+2=0[/tex]
[tex]x^2+x+2x+2=0[/tex]
[tex]x(x+1)+2(x+1)=0[/tex]
x+2=0, x=-2
x+1=0, x=-1
Since the quadratic expression may be factored out, the following x-values represent the system's solution:
x=-2 and x=-1
Now, we may obtain the corresponding y values using either of the system's original equations. We decide to use a linear equation as an illustration:
When x =-2,
y=11
x=-1,
y=6
Thus the two points solution us (-2,11) and (-1,6)
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A car speeds down the interstate at 85
miles per hour. What is this speed in feet per
second? (1 mile
= 5280 feet)
Answer:
124.67 feet per second
Step-by-step explanation:
First: multiply the feet per mile by the amount of miles that the car is going in order to get the feet per hour
5280 x 85 = 448,800
Second: divide the answer from the first step by 60 in order to get the number of feet per minute
448,800 ÷ 60 = 7480
Third: divide the answer from the second step by 60 in order to get the number of feet per second
7480 ÷ 60 = 124.67
Dodi has 2 cups of liquid starch and will use the entire amount. She plans to store the slime in containers that each hold a maximum of 6 fluid ounces how many containers will she need (hint 2 cups = 16 fluid ounces
The maximum containers Dodi will use will be 3
She plans to store the slime in containers that each hold a maximum of 6 fluid ounces how many containers will she need
number of containers is 3
Dodi has 2 cups of liquid starch each containers hold a maximum of 6 fluid ounces 2 cups = 16 fluid ouncesif containers hold maximum fluid ounceslet number of containers is x6x=16x=16/6but x is a number so x=3So minimum number of containers is 3The time period "equal" in math refers to two meanings, numbers, or quantities which can be the same. The equivalence of two such portions shall be denoted by a bar over an equivalent symbol or equivalent sign. It also means a logical equivalence among values or a fixed of quantities.
what is a equivalent instance?
The definition of equal is something that is essentially the same or identical to some thing else. An instance of equivalent is (2+2) and the wide variety four. due to the fact that 2+2= 4, these matters are equal.
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19. A carpenter cut the top section of a window frame with a 40º angle on each end. The side pieces each have a 50º angle cut at their top ends, as shown.
Will the side pieces of the frame be parallel?_____________________
How do you know?
If a carpenter cut the top section of a window frame with a 40º angle on each end. The side pieces each have a 50º angle cut at their top ends, as shown. Yes the side pieces of the frame will be parallel. How i know is that both side are equal or parallel.
ParallelThe interior angles are the same in measure and the sum of the interior angles have to be 180°.
The two side pieces on both the right and left hand side are equal in measure. The sides can be parallel only if the sum of both side angles is equal to 180°
Hence,
One side of the interior angle=40º+50º
One side of the interior angle=90°
Both side of the interior angle=90°+90°
Both side of the interior angle=180°
Hence,
180°=180°, the sides are parallel
Therefore Yes the side pieces of the frame will be parallel. How i know is that both side are equal or parallel.
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Darlene received $18.70 for 22 pounds of aluminum cans. How much did she receive per pound?
Answer:
$0.85/lb
Step-by-step explanation:
unit rate = dollar amount / pounds
unit rate = ($18.70)/(22 lb)
unit rate = $0.85/lb
Answer:
.85 per pound
Step-by-step explanation:
Explaining How to Use Linear Palls and
Imagine two lines intersect. How can the properties of
linear pairs and vertical angles help to determine the
angle measures created by the intersecting lines?
Explain.
Angles that are vertical are opposite ones that only have one common vertex.
Two sets of vertical angles result from the intersection of two lines.
When two lines intersect, we obtain two linear pairs, which are two angles that make a straight line.
Knowing one of the angles formed when two lines intersect enables us to determine that the vertical angle, which is the angle directly across from it, has the same measurement.
Additionally, we know that the angle next to it, which creates a linear pair, will be added to it (add to 180), allowing us to discover its measure by subtracting it from 180.
Since they are both vertical angles, the remaining missing angle will be the same as this supplementary angle.
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