Write the explicit and recursive rules for a geometric sequence given a table of values.
Answers
(a) The Explicit Rule for f(n) is 0.1 × 3n The Recursive Rule for f(n) is f(n-1) × 3. (b) The Explicit Rule for f(n) is 100 × 0.1ⁿ The Recursive Rule for f(n) is f(n-1) × 0.1
What is Explicit rule ?The explicit rule states that the value of the sequence at each term is 0.1 multiplied by 3 raised to the power of n. The recursive rule states that the value of the sequence at each term is equal to the value of the preceding term multiplied by 3. This can be seen in the table of values where each value is 3 times the preceding value.
Given,
n = 0,1,2,3,4…
f(n) = 0.1,0.3, 0.9, 2.7, 8.1
(b) The Explicit Rule for f(n) is 100 × 0.1ⁿ, The Recursive Rule for f(n) is f(n-1) x 0.1
Given,
n= 0,1,2,3,4..
f(n) = 100, 10, 1,0.1, 0.01
The explicit formula is the formula to calculate the value of the sequence directly without using any previous terms. The recursive formula uses the previous term to calculate the value of the current term.
In this example, the explicit formula is 100 × 0.1ⁿ and the recursive formula is f(n) = f(n-1) × 0.1. This means that each term in the sequence is equal to the previous term multiplied by 0.1.
For example, the third term in the sequence is 1, so the fourth term is 1 × 0.1 = 0.1.
(c) The Explicit rule for f(n) is 1000 × 0.1⁽ⁿ ⁻ ¹⁾, The Recursive rule for f(n) is f(n-1) x 0.1
To solve,
f(5) = 1000 × 0.1⁽⁵ ⁻ ¹⁾(5-1)
= 1000 × 0.1⁴
= 1000 × 0.0001
= 0.1
Given,
n= 1,2,3,4,5…
f(n) = 1000, 100, 10, 1, 0.1
The explicit and recursive rules for this geometric sequence are both written as f(n) = 1000 × 0.1⁽ⁿ ⁻ ¹⁾. This means that the value of the sequence at any given point n will be equal to 1000 multiplied by 0.1 raised to the power of n-1. This means that the value of the sequence decreases by a factor of 0.1 for every increase in n.
In this case,
f(5) = 1000 x [tex]0.1^4[/tex]
= 0.1.
(d) The Explicit Rule for this geometric sequence is f(n) = 10⁽⁵⁰ ⁻ ³ⁿ⁾, where n is the term number of the sequence.
The Recursive Rule for this geometric sequence is f(n) = f(n-1) ÷ 10³, where f(n) is the value for the nth term of the sequence and f(n-1) is the value for the (n-1)th term of the sequence.
Given,
n= 1,2,3,4,5..
f(n) = 10⁵⁰,10⁴⁷, 10⁴⁴, 10⁴¹, 10³⁸….
The value for the 5th term of the sequence is f(5) = 10⁽⁵⁰ ⁻ ³⁽⁵⁾⁾ = 10³⁸. The explicit rule for this geometric sequence is f(n) = 10⁽⁵⁰ ⁻ ³ⁿ⁾, where n is the term number of the sequence. This means that the value of each term is determined by taking 10 to the power of 50 minus 3 multiplied by the term number.
The recursive rule for this geometric sequence is [tex]\frac{f(n-1)}{10^3}[/tex] which means that the value of each term can be calculated by dividing the previous term by 10 cubes. We can use
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Related Questions
PLEASE SOLVE FOR X I REALLY NEED HELP
Answers
Answer:
Below
Step-by-step explanation:
The bisector divides the base into lengths proportionate to the two sides (Angle Bisector theorem)
x+ 2 = 15/(15+20) * 14
x = 4 units
matie has 4 times as many stamps as arnav. if matie gives arnav 8 stamps, matie will have twice as many stamps as arnav. how many stamps does each boy have.
Answers
Answer: Mattie has 16 stamps and Arnav has 4 :)
Step-by-step explanation:
the system of equations used to solve it is
m=4a
m-8=2a
Martie have 48 stamps and Arnav have 12 stamps.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
Let Matie has x stamps and Arnav has y stamps.
Given that,
Matie has 4 times as stamps as Arnav
Implies that,
x = 4y (1)
Also, If Matie gives 8 stamps to Arnav will have twice stamps to Arnav.
Implies that,
x - 8 = 2(y+8)
x - 8 = 2y + 16
x = 2y + 24 (2)
From equation (1) and (2),
y = 12
and x = 48
Matie and Arnav each have 48 and 12 stamps respectively.
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Let f(x)= 4x2-3 and let g(x)= 2x+3. Find (fg)(3).
(f+g)(3)=
Answers
The value of (f . g) (3) is 594 and (f + g) (3) is 42 when function is f(x) = 4x² - 3 and g(x) = 2x + 3.
i) (f . g) (3)
(f . g) (x) = f(x) . g(x)
(f . g) (3) = f(3) . g(3)
= 4(3)² - 3 * 2(3) + 3
= 36 - 3 * 6 + 3
= 33 * 18
(f . g) (3) = 594
The value of (f . g) (3) is 594 when function is f(x) = 4x² - 3 and g(x) = 2x + 3
ii) ( f + g )( 3 )
( f + g )( x ) = f ( x ) + g ( x )
( f + g )( 3 ) = f (3 ) + g ( 3 )
= 4(3)² - 3 + 2(3) + 3
= 4(9) + 6
= 36 + 6
( f + g )( 3 ) = 42
The value of (f + g) (3) is 42 when function is f(x) = 4x² - 3 and g(x) = 2x + 3.
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What is the inverse of 12/(x-1)
100 points please I really want to figure this out
Answers
The inverse of the expression represented as 12/(x-1) is (12/x) + 1
How to determine the inverse of the expression?From the question, we have the following parameters that can be used in our computation:
12/(x - 1)
The given parameter is an expression
Also, we can see that the above expression is a quotient expression
So, we start by expressing it as an equation
This is represented as
y = 12/(x - 1)
Swap/Switch the positions of the variables x and y
So, we have the following representation
x = 12(y - 1)
This gives
y - 1 = 12/x
Make y the subject
y = (12/x) + 1
Hence, the inverse is (12/x) + 1
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If 20% of an income of a man is Rs 4,800, find his income
Answers
The income of the man is 24000.
Step-by-step explanation:
income of man =24000
Let the income of man be x
According to the question,
20%*x = 4800
0.2x=4800
As a result, x =24000
(4800*10= 48000/2= 24000)
So the income of a man is 24000.
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Man's income is, 24000 rupees.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given, 20% of an income of a man is Rs 4,800.
To find the income:
Use percentage formula,
let m be the man's income.
So, m x 20 / 100 = 4800
Rearranging,
m = 4800 x 100 / 20
m = 24000
Therefore, the income is, 24000 Rs.
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Graph the linear equation by solving for y first.
4x+5y=-2
Answers
Solving for y, the linear equation is: y = -4/5x - 2/5.
The table showing the corresponding y-value for each x-value is:
x | -8 -3 2 7
y | 6 2 -2 -6
The graph is in the attachment.
How to Graph a Linear Equation?To graph the linear equation of 4x + 5y = -2, rewrite in slope-intercept form by solving for y.
4x + 5y = -2
5y = -4x - 2
y = -4/5x - 2/5
Complete the table given by plugging each value of x into the linear equation, y = -4/5x - 2/5.
For x = -8:
y = -4/5(-8) - 2/5
y = 6
For x = -3:
y = -4/5(-3) - 2/5
y = 2
For x = 2:
y = -4/5(2) - 2/5
y = -2
For x = 7:
y = -4/5(7) - 2/5
y = -6
The complete table is:
x | -8 -3 2 7
y | 6 2 -2 -6
See the graph below.
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AolaksksmsmsmsmsO? A a a a a s sbhuaybua aybaybayabyaba
Answers
Answer: There are several statements that could be false if f(x) is continuous on [a, b] and differentiable on (a, b):
1 The function f(x) has a maximum or minimum value at some point in the interval [a, b].
2 The function f(x) is monotonic (either increasing or decreasing) on the interval [a, b].
3 The function f(x) has an inflection point (a point where the concavity of the function changes) in the interval [a, b].
4 The function f(x) has an asymptote (a line that the function approaches but never touches) in the interval [a, b].
5 Note that these statements are not necessarily false, but they could be false depending on the specific function f(x).
Decide where the first digit of the quotient should be placed. Do not complete the
division.
The first digit in the quotient of 1, 592 64 is in the
Choose...
place.
Answers
The first digit in the quotient of 1, 592 64 should be placed in the; Hundredths place.
How to find the quotient with Long division?
When we carry out long division, it is pertinent to note that the first digit of the quotient usually appears over the least significant digit of the very first portion of the dividend that is now greater than or equal to the divisor.
In this question, when we perform long division, we compare;
64 vs 1 . . . no quotient digit
64 vs 15 . . . no quotient digit
64 vs 159 . . . the first quotient digit appears with the same place value as the 9 in 1.59. That is, the first quotient digit will be 0.02, with 2 being in the hundredths place.
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I need help with this question.
Answers
Dude I am so sorry that I do not know this answer
One year, the population of a city was 102,000. Several years later it was 110,160. Find the percent increase.
Answers
Answer:
8% increase
Step-by-step explanation:
Difference between the two populations: 110160 - 102000 = 8160
Difference ÷ Initial population: 8160 ÷ 102000 = 0.08
which equation is in slope-intercept form?
Answers
Answer: y = 3/2x +-9
Step-by-step explanation:
The equation in slope-intercept form, y = mx + b, is the equation y = 3/2x +-9.
See attached for more information on slope-intercept form.
(4) The following question is from a New York State Algebra Common Core Exam.
Graph y=f(x) and y= g (x) the set of axes below.
f(x)=2 x²-8 x+3
g(x)=-2 x+3
State all paints that make both equations true.
Answers
The points that make both equations true are, (0,3) and (-3,3).
What is an equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.
A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
The graph of the equations is attached with the answer below. The points are (0,3) and (-3,3).
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What operation do you use when you distribute the number that is outside the
parenthesis to all of the numbers that are
inside the parenthesis?
Answers
Answer:
multiplication
Step-by-step explanation:
you multiply. I know this because I am in pre algebra right now and we learned about this again. If you are doing division then it’s the opposite same for subtraction as well as addition.
Are your finances, buying habits, medical records and phonecalls really private? A real concern for many adults is thatcomputers and the Internet are reducing privacy. A survey conductedby Peter D Hart Research Associates for the Shell Poll was reportedin USA Today. According to the survey, 37% of adults are concernedthat employers are monitoring phone calls. Use the binomialdistribution formula to calculate the probability that:
a. out of 5 adults, none is concerned that employers aremonitoring phone calls.
b. out of 5 adults, all are concerned that employers aremonitoring phone calls.
c. out of 5 adults, exactly 3 are concerned that employers aremonitoring phone calls.
Answers
As per binomial distribution the probability of the following conditions are as follow:
a. probability for out of 5 none is concerned is 0.09924.
b. probability for out of 5 all are concerned is 0.02825
c. probability for out of 5 three are concerned is 0.4669.
As given in the question,
Percent of adults are concerned = 37%
p = 0.37
Percent of adults are not concerned = (100 -37)%
= 63%
1 - p = 0.63
Total number of adults 'n' = 5
Probability using binomial distribution
= ⁿCₓ pˣ ( 1- p)ⁿ⁻ˣ
a. Out of 5 none is concerned
here x = 0
⁵C₀( 0.37)⁰(0.63)⁵⁻⁰
= 0.09924
b. Out of 5 all are concerned
here x = 5
⁵C₅( 0.37)⁵(0.63)⁵⁻⁵
= 0.02825
c. Out of 5 three are concerned
here x = 3
⁵C₃( 0.37)³(0.63)⁵⁻³
= 0.4669
Therefore , using binomial distribution the probability of the given percent of adult data is equal to as follow:
a. probability for out of 5 none is concerned is 0.09924.
b. probability for out of 5 all are concerned is 0.02825
c. probability for out of 5 three are concerned is 0.4669.
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WRITE THE EQUATION OF THE LINE IN SLOPE-INTERCEPT FORM.
Answers
The equation of the line that passes through the point ((0, 3) & (3, 0) is y = -1x - 3.
What is the system of linear equations?
A system of linear equations is a group of one or more linear equations that can be solved by using a simultaneous equation or elimination method. Therefore, by using the substitution method and writing the solution of the system in terms of coordinate point (x, y) = (-1, 1).
To write the equation of a line in slope-intercept form (y = mx + b), we need to find the slope of the line (m) and the y-intercept (b).
To find the slope of the line, we can use the slope formula:
m = (y2 - y1)/(x2 - x1)
We have given the line passes through the points(0, 3) & (3, 0),
so, m = (0-3)/(3-0)
= -3/3
m = -1
The y-intercept is the point where the line intersects the y-axis. This point is (0, b), where b is the y-intercept.
Since the given line passes through the point (3, 0), we can substitute these values into the slope-intercept form of the equation to find the y-intercept:
y = mx + b
0 = -1 * 3 + b
b = -3
Solving for b gives us:
b = -3
Therefore, the equation of the line that passes through the point ((0, 3) & (3, 0) is y = -1x - 3.
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an employer agrees to pay $5,000 for medical insurance and contribute an additional 5% of the employees'
Answers
Answer: $5,250
Step-by-step explanation:
1) Half of 5000 is 2500. But that's 50%.
2) Divide the remaining value by 10. You now have 250, which is 5%.
It's a given rule in math that if you're working with the Powers of 10, by either multiplying or dividing them, all you need to do is add or remove some zeros.
the chart shows the number of points different players scored during a game. what is the ratio of marcus's points to scott's points? responses
Answers
The ratio of Marcus's point to Scott's point will be = 1 : 2
According to the table given attached below,
We can find the ratio of the squares,
First, let us know about the definition of Ratio and Proportion.
The ratio is defined as the comparison between the two similar quantities
The fraction can also be represented as a ratio using the ' : ' sign
For example, let us consider two numbers a and b
In fraction, we could write it as = [tex]\frac{a}{b}[/tex]
Writing it as a ratio = a : b
According to the table given below,
Marcus's points = 7
Scott's points = 14
The ratio of Marcus's points to Scott's points = [tex]\frac{Marcus}{Scott}[/tex]
14 / 7
2 / 1
2 : 1
Therefore, The ratio of Marcus's point to Scott's point will be = 1 : 2
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A decade ago, the average class size at Newton Middle School was 30 students. Now it is 30% smaller. What is the average class size currently?
Answers
Answer: 21 students
Step-by-step explanation:
A number being 30% smaller means that it has reduced to 70% of its original size.
This means we can multiply the original value by its new percentage, 30x0.7=21 students.
5) A woman wants to borrow $12,000 to buy a car. She wants to repay the loan by monthly installments
for 4 years. If the interest in the loan is 10.5% per year, compounded monthly, what is the amount of
each payment?
Answers
Answer:
to much money to buy a car I try to work it down to 10k
Help i dont know how to do this problems.
Answers
The value of x = 9 (back)
The value of x = 12 (orange)
The value of x = 8 (purple)
The value of x = 12.75 (green).
What are corresponding angles?The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.
Corresponding angles are equal.
We have,
10 and 2x - 8 are parallel lines.
10 = 2x - 8
10 + 8 = 2x
18 = 2x
x = 9 (black)
7 and -17 + 2x are the two parts of a line separated by a midpoint.
7 = -17 + 2x
7 + 17 = 2x
2x = 24
x = 12 (orange)
7 and x + 15 are two parts of a line separated by a midpoint.
7 = x + 15
7 - 15 = x
x = 8 (purple)
m∠2 = 4x + 8
one angle = 45°
Other angle = 180 - 104 = 76°
The sum of the triangles is 180.
45 + 4x + 8 + 76 = 180
4x = 180 - 129
4x = 52
x = 12.75 (green)
Thus,
The value of x = 9 (back)
The value of x = 12 (orange)
The value of x = 8 (purple)
The value of x = 12.75 (green).
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What is equivalent to 2
Answers
Answer:
4 6 8 10
Are the ans
Step-by-step explanation:
Plus 2 each time
six pounds of potatoes cost 12.90 how much would 3.5 pounds cost
HELP
Answers
Answer:x=$7.31
Step-by-step explanation:6lbs
$12.90 x
6lbs x=($12.90 )(3.4 lbs)
6lbs x=43.86$lbs
6lbs x/6lbs=43.86$lbs/6lbs
Which of the following is an equivalent form of the compound inequality -33> -3x - 6 ≥
-36?
Answers
The equivalent form of the compound inequality is -9>-x≥-10.
What is a compound inequality?A sentence having two inequality statements connected by the words "or" or "and" is referred to as a compound inequality. The conjunction "and" denotes the simultaneous truth of both statements in the compound sentence. It is when the solution sets for the various statements cross over or intersect. The conjunction "or" means that the entire compound sentence is true as long as either of the two statements is true. It consists of the union or combination of the solution sets for the various statements. A conjunction is a compound inequality that contains the word "and." Even though "and" and "or" are considered to be conjunctions of speech, their meanings in mathematics are distinct from their grammatical counterparts. The conjunction (part of speech) "or"—when used to demonstrate this point—is whenever used in a compound inequality, it creates a disjunction, as the name suggests. Simply keep in mind that "con" stands for "with another" and "dis" for "one OR the other."
Calculation:Given -33>-3x-6≥-36.
Dividing everything by 3 we get -11>-x-2≥-12.
Now adding to every side we get compound inequality as -9>-x≥-10.
The equivalent form of the compound inequality is -9>-x≥-10.
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A train travels for 3.75 hours at 80 miles an hour. Use the formula d = r. t, where
d = distance, r = rate, and t = time, to find the distance the train traveled.
The distance traveled is
miles.
The solution is
Answers
The distance traveled by train would be 300 miles.
What is the relation between speed, distance, and time?
You can use the equivalent formula d = rt which means distance equals rate times time. To solve for speed or rate use the formula for speed, s = d/t which means speed equals distance divided by time. To solve for time use the formula for time, t = d/s which means time equals distance divided by speed.
A train travels for 3.75 hours at 80 miles per hour.
The distance traveled = speed * time
= 3.75 * 80
= 300 miles.
Hence, the distance traveled by train would be 300 miles.
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Learning geometry is tricky but test your knowledge for sure. Please help me. Thank you!!!
Answers
The area of the paper that remains is 375.04cm².
What is an area?
The measurement that expresses the size of a region on a plane or curved surface is called an area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
Here,
We take it that the semicircles cover the full width of the paper.
So the radius is 16/2 = 8 cm
Since there are two of them, the area is full circle.
First, we find the area of the rectangle before the cuts were made.
Area = L * W
L = 36
W = 16
Area = 36×16 = 576 cm²
Now, we find the area of the circle cutouts.
r = 8
Area = pi * r²
Area = 3.14 * 8²
Area = 3.14 * 64
Area = 200.96cm²
Now, we find the total area left
Total Area Left = rectangle - circle
Total Area Left = 576 - 200.96
Total Area left = 375.04cm².
Hence, the area of the paper that remains is 375.04cm².
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A hose fills a hot tub at a rate of 3.49 gallons per minute. How many hours will it take to fill a 343-gallon hot tub? Question content area bottom Part 1 It will take enter your response here hours to fill the hot tub. How many hours does it take to fill the hot tube?
Answers
If hose fills a hot tub at a rate of 3.49 gallons per minute. Then 1.64 hours will it take to fill a 343-gallon hot tub
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given,
A hose fills a hot tub at a rate of 3.49 gallons per minute.
We need to find how many hours will it take to fill a 343-gallon hot tub
3.49/1=343/x
Apply cross multiplication
x=343/3.49
x=98.28 minutes
1 hr=60 minutes
So divide 98.28/60
1.64
Hence, it takes 1.64 hours to fill the hot tub.
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Find the mean and standard deviation of the sample data in the table. (Round your answers to two decimal places.) x = [1, 2, 3, 4, 5]
f(x) = [2, 13, 15, 11, 13]
Answers
The mean and standard deviation of the sample data in the table is 182 and 508 respectively.
To calculate the mean and standard deviation,
mean= E(x)
= ∑x*f(x)
= 1(2) + 2(13) + 3(15)+4(11) + 5(13)
=2+26+45+44+65
=182
Standard deviation = E(x²)
= ∑x²*f(x)) - E(x)
=1(2) + 4(13) + 9(15)+16(11) +25(13) - E(x)
= 2 +52+135+176+325 - E(x)
=690 - 182 - E(x)
=508
The mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally.
The three most frequently employed measures of central tendency are the mean, median, and mode.
The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean.
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Find the value of B, Please.
[tex]\frac{-5x^3+2x+3}{x+2} = A+\frac{B}{x+2}[/tex]
A. -13
B. 39
C. -21
D. -33
Answers
Answer:
B) 39------------------------------
We need to find the remainder when -5x³ + 2x + 3 is divided by x + 2.
According to the remainder theorem, the remainder is the value of the polynomial when x = - 2:
-5(-2)³ + 2(-2) + 3 = - 5(-8) - 4 + 3 = 40 - 1 = 39The matching choice is B.
Answer:
B. 39
Step-by-step explanation:
Divide the polynomials using long division:
[tex]\large \begin{array}{r}-5x^2+10x-18\phantom{)}\\x+2{\overline{\smash{\big)}\,-5x^3\;\;\;\;\;\;\;\;\;\;\;+2x+3\phantom{)}}}\\{-~\phantom{(}\underline{(-5x^3-10x^2)\phantom{-b)))))))}}\\10x^2+2x+3\phantom{)}\\-~\phantom{()}\underline{(10x^2+20x)\phantom{)))}}\\-18x+3\phantom{)}\\-~\phantom{()}\underline{(-18x-36)\phantom{}}\\39\phantom{)}\\\end{array}[/tex]
The solution is the quotient plus the remainder divided by the divisor.
Solution
[tex]-5x^2+10x-18+\dfrac{39}{x+2}[/tex]
Assume that a sample is used to estimate a population mean
μ
. Find the 90% confidence interval for a sample of size 52 with a mean of 85.5 and a standard deviation of 12.3. Enter your answer as an open-interval (i.e., parentheses) accurate to 3 decimal places.
Answers
Confidence interval for given data is (82.156,88.843)
What is confidence interval?The confidence interval is the range of values that, if you repeated your experiment or resampled the population in the same manner, you would anticipate your estimate to fall within a specific proportion of the time.
The alpha value determines the confidence level, which is the proportion of times you anticipate being able to recreate an estimate between the top and lower boundaries of the confidence interval.
general form of a confidence interval is:
point estimate + Z SE (point estimate)
Formula for confidence interval is given by
[tex]X[/tex] ± [tex]Z\frac{s}{\sqrt{n} }[/tex]
Where:
X is the mean
Z is the chosen Z-value from the table above
s is the standard deviation
n is the number of observations
In given ques
X = 85.5, Z=1.960, s =+ 12.3, n= 52
confidence interval = 85.5± (1.960×12.3/√52)
(82.156,88.843)
Learn more about confidence interval here:
https://brainly.com/question/17212516
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List the elements of the following sets.
(a). {Vowels in the word "MATHEMATICS"}
(b). {The seven colours of the rainbow}
(c). {Multiples of 9 which are less than 50}
(d). {Even numbers which are between 10 and 23}
that's all pls I need it now asap
Answers
Answer:
a) {A,E,I}
b) {red, orange, yellow, green, blue, violet, indigo}
c) {9,18,27,36,45}
d) {12,14,16,18,20,22}
Lol I'm not sure if I did all of these correct :]
(Also what is this for? Like the coding class or something? (Just curious))