The value of a motorcycle each year follows the sequence $12,000 $9,600, $7,680, $6,144
Which formula represents the recursive definition of the sequence where n represents the number of years?
Answers
The recursive definition of the geometric sequence is given by:
A. [tex]a_n = (0.8)a_{n-1}[/tex]
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 basic recursive relation is given as follows:
[tex]a_n = qa_{n-1}[/tex]
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.
In this problem, considering the given sequence, the common ratio is given by:
[tex]q = \frac{6144}{7680} = \frac{7680}{9600} = \frac{9600}{12000} = 0.8[/tex]
Hence option A is correct.
More can be learned about geometric sequences at https://brainly.com/question/11847927
The values of the motorcycle follows a geometric sequence
The recursive definition of the sequence is (a) [tex]a_{n} = 0.8a_{n-1[/tex]
How to determine the recursive definition?The values are given as:
$12,000 $9,600, $7,680, $6,144
Calculate the common ratio using:
r = a2/a1
So, we have:
r = 9600/12000
Divide
r = 0.8
Recall that:
r = a2/a1
So, we have:
a2/a1 = 0.8
Multiply both sides by a1
a2 = 0.8a1
Rewrite as:
[tex]a_{2} = 0.8a_{2-1[/tex]
Substitute n for 2
[tex]a_{n} = 0.8a_{n-1[/tex]
Hence, the recursive definition of the sequence is (a) [tex]a_{n} = 0.8a_{n-1[/tex]
Read more about sequence at:
https://brainly.com/question/7882626
Related Questions
One of the roots of the quadratic equation 2x^2+10x+c=0 is equal to 2. Find the value of coefficient c.
Answers
Answer: c = -28
Step-by-step explanation:
substitue x for 2
2(2^2) + 10(2) + c = 0
8 + 20 + c = 0
28 + c = 0
c = -28
The value of coefficient c of the quadratic equation 2x^2+10x+c=0 is -28.
One of the roots of the quadratic equation 2x^2+10x+c=0 is equal to 2.
What is the root?The roots of a quadratic equation are the values of the variable that satisfy the equation.
They are also known as the solutions or zeros
The equation is 2x^2+10x+c=0.
a=2, b=10 and c=?
To substitute x for 2
2(2^2) + 10(2) + c = 0
8 + 20 + c = 0
28 + c = 0
c = -28
To learn more about the quadratic equation visit:
https://brainly.com/question/1214333
for a area and perimeter math question what is 2/3x2/3????????
Answers
Answer:
4/9
Step-by-step explanation:
2/3 × 2/3 is 4/9
2×2 is 4 and 3×3 is 9
The sum of two numbers is 5/9.if one of the numbers is 1/3 find the other
Answers
Answer:
2/9
Step-by-step explanation:
The sum of two numbers is 5/9 can be expressed as:
[tex]\displaystyle \large{x+y=\dfrac{5}{9}}[/tex]
One of the numbers is 1/3. Find the other - this means that either x or y is 1/3 but that doesn’t matter as we can either let x = 1/3 or y = 1/3 via property:
[tex]\displaystyle \large{x+y = y+x}[/tex]
Hence, let x = 1/3:
[tex]\displaystyle \large{\dfrac{1}{3}+y=\dfrac{5}{9}}[/tex]
Solve for y - subtract both sides by 1/3:
[tex]\displaystyle \large{\dfrac{1}{3}-\dfrac{1}{3}+y=\dfrac{5}{9}-\dfrac{1}{3}}\\\displaystyle \large{y=\dfrac{5}{9}-\dfrac{1}{3}}[/tex]
We know that we can only evaluate the fractions if both have same denominator so what we have to do is to multiply 1/3 by 3 for both top and bottom:
[tex]\displaystyle \large{y=\dfrac{5}{9}-\dfrac{1\cdot 3}{3\cdot 3}}\\\displaystyle \large{y=\dfrac{5}{9}-\dfrac{3}{9}}\\\displaystyle \large{y=\dfrac{2}{9}}[/tex]
Therefore, the other number is 2/9
Answer:
The other number is 2/9
Step-by-step explanation:
"a" is the other number
The equation:
[tex]a+\frac{1}{3} =\frac{5}{9}[/tex]
Then
[tex]a=\frac{5}{9} -\frac{1}{3} =\frac{15-9}{27} =\frac{6}{27}[/tex]
simplifying the fraction:
[tex]a = \frac{2}{9}[/tex]
Hope this helps
The solid below is made from cubes.
Find Its volume.
Answers
Answer:
20
Step-by-step explanation:
2x2x5
Help!! It’s urgent I need help
Answers
7cm²+5cm²=10cm²
14cm+25cm=100cm
39=100
John wants to purchase a new freezer chest to store food. The amount of space in the freezer chest is known as A. Volume B. Area C. Perimeter
Answers
Answer:
A. Volume
Step-by-step explanation:
Volume is how much space is in a substance so that means it is A
Answer:
Volume
Step-by-step explanation:
The amount of space that a substance or object occupies is called Volume.
5. Consider the system of equation:
x+4y=13
3x +2y =19
(a) Multiply both sides of the second equation (b) Add the equation from (a) to the first
hu -2. What equation results?
equation. What happens? What can you
now solve for?
(d) What could you have multiplied both sides of
the first equation by to eliminate the x
instead of the y?
Answers
Answer:
A
Step-by-step explanation:
what is the equation in slope-intercept form of the line that passes through the points (-26,-11) and (39,34)?
Answers
Answer:
y = [tex]\frac{9}{13}x + 7[/tex]
Step-by-step explanation:
Slope (m):
34 - (-11)/39 - (-26) = 45/65 = 9/13
y-intercept (b):
34 = (9/13)39 + b
7 = b
the equation is:
y = (9/13)x + 7
Find the perimeter of the composite figure
Answers
7+7+5+5=24
So therefore the permeter is 24
Which of the following equations is the result after the first step in solving 5x – 4 = 15?
A 5x = 19
B x = 2
C 5x = 11
D x – 4 = 3
Answers
Answer:
[A} 5x = 19
Step-by-step explanation:
Let's solve to see what the first step in solving the following equations:
5x - 4 = 15
Add 4 to both sides
5x - 4 + 4 = 15 + 4
5x = 19 {First step after solving}
Divide both sides by the same factor
5x/5 = 19/x
x = 3.8
Thus, the answer is [A] 5x = 19
Kavinsky
Answer:
[A] 5x = 19
Step-by-step explanation:
Solving to see first step:
5x - 4 = 15
+4 +4 {15 + 4 = 19}
-------------------------
5x = 19
Divide both sides by 5
5x/5 = 19/5
x = 19/5
x = 3.8
As you can see 5x = 19 is the first step result after solving.
~Lenvy~
What is the volume in cubic inches
Answers
Answer:
80 cubic inches
Step-by-step explanation:
Hey there!
In order to find the volume, you need to split this shape in two parts
We are going to take the big rectangle and the small rectangle as our two shapes
The bigger rectangle has dimensions 5.5 x 6 x 2 which is 66 cubic inches
So now we need to get the volume of the smaller rectangle which has the dimensions: 2x2x3.5 which is 14 cubic inches
Now we add both volumes
66+14 is 80
So the total volume is 80 cubic inches
Work-
7.5•3.5•2=52.5
5.5•2.5•2=27.5
52.5+27.5=80
Raquel has 4 brownies. She wants to give an equal share to each of her friends. How would Raquel share these brownies equally among herself and 5 friends? What is the estimate equation????????
please tell me the estimatie and eqaution asap!!!!
Answers
Answer:
4/5
Step-by-step explanation:
divide brownies by friends
Need help. I don't understand how I work out the points to solve the equation. Help please, thanks.
Answers
Answer:
First u get the Y by itself then you read the less than or equal to or greater than or equal to.
Step-by-step explanation:
hope it helps
Betty's bedroom is 18ft
long and 25 ft wide. She
wants to install the
hardwood flooring. The
cost is $6.00 per square
foot. How much is the
total cost for room
flooring?
Answers
Answer:
You'll need to find the area first.
18ft x 25ft= 450ft
Area is 450ft.
Area divided by $6.00 = 75
The total cost is $75 dollar for the whole room flooring.
Please Solve I will give brainliest.
each graph shows a relation. The first and second numbers of each ordered pair in the relation are members of the set of real numbers. find the range and domain of the relation.
Answers
Using the domain and range concepts, it is found that:
For the first relation, the domain is [tex]-1 \leq x < 1[/tex], and the range is [tex]-1 \leq y \leq 0[/tex].For the second relation, the domain is [tex]-1 \leq x \leq 1[/tex], and the range is [tex]-1 \leq y \leq 1[/tex].What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input.The range of a function is the set that contains all the values of the output.In a graph:
The domain is given by the x-values, the horizontal axis.The range is given by the y-values, the vertical axis.Hence:
For the first relation, the domain is [tex]-1 \leq x < 1[/tex], and the range is [tex]-1 \leq y \leq 0[/tex]. The open circle at x = 1 means that x = 1 is not part of the domain, hence we have an open interval.For the second relation, the domain is [tex]-1 \leq x \leq 1[/tex], and the range is [tex]-1 \leq y \leq 1[/tex].More can be learned about domain and range concepts at https://brainly.com/question/27566140
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As the number of trials increases, the __________ probability will approach the __________ probability.
Answers
Answer:
Empirical probability
And
Theoretical
hope this helps! :)
Solve the following system of equations using elimination.
X + 2y = 5
3x + 5y = 14
Answers
Answer:
x = 3
y = 1
Step-by-step explanation:
x + 2y = 5 ------------(1)
3x + 5y = 14 ---------(2)
(1) × 3 : 3x + 6y = 15 ------ (3)
(3) - (2) : y = 1
y = 1, x + 2(1) = 5
x = 3
In parallelogram crhs, the measure of angle c is 48.Find the measure of angle h?
Answers
Answer:
48°
Step-by-step explanation:
we know that opposite angle of parallelogram is equal
so,
angel C is equal to opposite angle H
H = 48
angle C = 48°
angle R = 132°
angle H = 48° (opposite of angle C)
angle S = 132°(opposite of angle R)
Mark me Brainiest please
A punch recipe calls for 4 1/3
cups of pineapple juice per serving. Julie is making 1 2/5
servings.
Which equation shows the amount of pineapple juice
Answers
Answer:
The equation is 4 1/3(2/5+1)
Step-by-step explanation:
So, it's 4 1/3+1 11/15=
65/15+26/15=91/15
6 1/15
2/5x4 1/3
Which is 2/5 x 13/3
Which is 26/15
Which is 1 11/5
Mrs. Mueller writes an inequality on the board. The table shows the responses of six students for possible values of x.
Which students have correct responses to Mrs. Mueller's inequality?
Select ALL that apply.
Answers
Answer:
Maya, Pablo
Step-by-step explanation:
We solve the inequality to find how big x must be to fit the inequality.
[tex]\frac{3}{5}x > 6\\ x > 10[/tex]
Since x has to be greater than 10, anyone with an answer above that is correct.
Maya and Pablo are the only two.
PLEASE HELP 20 POINTS!!
Which statements are true about the graphed function?
Answers
Step-by-step explanation:
The Amplitude is 4
The period is 2π
The midline is y=1.5
OPTION 1, 3,6
Answer:
See below ~
Step-by-step explanation:
The period of the function is 2π as it is the time taken to travel between successive troughs/crestsThe midline of the function is the mean of the highest y-value and lowest y-value ⇒ 4 - 1 / 2 = 3/2 ⇒ y = 1.5Similarly, amplitude is the distance between the top of the crest and axis ⇒ A = 4!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
A
Step-by-step explanation:
the volume of a sphere (= a ball) =
4/3 × pi × r³
r (radius) is half of the diameter = 8.8/2 = 4.4 in
so, one ball has a volume of
4/3 × pi × (4.4)³ = 4/3 × pi × 85,184 = 113.5786667...×pi
6 balls are 6 times
113.5786667... × pi × 6 = 681.472...×pi in³
Find measure of the angle UTW
Answers
Answer:
57°
Step-by-step explanation:
Using the Law of sines,
[tex]\frac{sin57}{WT} = \frac{sinx}{UT}[/tex]But, WT = UT [both are radii of the circle]⇒ sin 57° = sin x°⇒ x° = ∠UTW = 57°What is the probability that the spinner will land on the number 1?
Answers
Answer:
30% or 4/12
Step-by-step explanation:
Answer:
33.333...% (2/3)
Step-by-step explanation:
the number 1 makes up one third of the numbers on the spinner.
64.89% of 407.68cm
Give your answer rounded to 2dp
Answers
Answer: 264.54cm
Step-by-step explanation:
407.68x0.6489=264.543552264.543552 rounded to 2 decimal points is 264.54
Josh is cutting a 25-inch beard inte tinch sections How many whole sections will the end up with
Answers
The radius of a circle is 17 yards. What is the circle's circumference? Use 3.14 for .
Answers
Answer:
Circumference of circle is 106.76 yardsStep-by-step explanation:
Given that, radius of Circle is 17 yards. To find the circumference of the circle we will the formula of circumference of circle:
Circumference of circle = 2πr
2 × 3.14 × 17
6.28 × 17
106.76 yards
Hence,
Circumference of circle is 106.76 yards⠀
Step-by-step explanation :
⠀
As, it is given that, the radius of a circle is 17 yards and we are to find the circumference of the circle.
⠀
We know that,
[tex]{\longrightarrow {\qquad{\mathfrak {\pmb{ Circumference_{(circle)} = 2 \pi r }}}}}[/tex]
⠀
Here,
r is the radius of the circle.We'll take the value of π as 3.14⠀
Now, substituting the values :
⠀
[tex]{\longrightarrow {\qquad{\sf {{ Circumference_{(circle)} = 2 \times 3.14 \times 17 }}}}}[/tex]
⠀
[tex]{\longrightarrow {\qquad{\sf {{ Circumference_{(circle)} = 6.28 \times 17 }}}}}[/tex]
⠀
[tex]{\longrightarrow {\qquad{\mathfrak {\pmb{ Circumference_{(circle)} = 106.76}}}}}[/tex]
⠀
Therefore,
The circumference of the circle is 106.76 yardsA picture 8 3/4 feet long is to be centered on a wall that is 12 1/2 feet long. How much space is there from the edge of the wall to the picture?
Answers
Answer:
15/4
Step-by-step explanation:
Find a common denominator in this case 4.
Turn both mixed numbers to an improper fraction
12 1/2 = 25/2
8 3/4 = 35/4
multiply 2 to 25/2 = 50/4
50/4 - 35/4 = 15/4
Alaska, Hawaii and Washington have active volcanoes. Alaska has 43, Hawaii has 5 and Washington has v. If they have 52 active volcanoes in all, how many volcanoes does Washington have?
Answers
Answer:
five
Step-by-step explanation:
A company makes wax candles in the shape of a cylinder. Each candle has a diameter of 6 inches and a height of 4 inches. How much wax will the company need to make 140 candles?
Use 3.14 for [tex]\pi[/tex] , and do not round your answer.
Answers
Answer:
The company will need 3,360 inches of wax
Step-by-step explanation:
To find how much wax you need per one candle you would do 6in.X4in. which gives you 24in. of wax. Then to find the amount of was for 140 candles you would do 140X24in. to get 3,360 inches of wax.