. A sequence starts with 180, 120, …. If the sequence is arithmetic, create a recursive and explicit formula for the sequence. If the sequence is geometric, create a recursive and explicit formula for the sequence.
Answer:
Arithmetic Sequence
[tex]T_n = 240-60n[/tex] ---- Explicit
[tex]T_n = T_{n-1} - 60[/tex] --- Recursive
Geometric Sequence
[tex]T_n = 270* (\frac{2}{3})^n[/tex] ---- Explicit
[tex]T_n = T_{n-1} * \frac{2}{3}[/tex] ---- Recursive
Step-by-step explanation:
Given
[tex]180, 120,....[/tex]
(a) Assume it is an arithmetic sequence
The explicit formula is calculated using:
[tex]T_n = a + (n - 1)d[/tex]
Where
[tex]a = 180[/tex]
[tex]d = 120 - 180[/tex]
[tex]d = -60[/tex]
So, we have:
[tex]T_n = 180 + (n - 1)*-60[/tex]
[tex]T_n = 180 -60n + 60[/tex]
Rewrite
[tex]T_n = 180 + 60-60n[/tex]
[tex]T_n = 240-60n[/tex]
The recursive function is calculated using:
[tex]T_1 = 180[/tex]
[tex]T_2 = 120 = 180 - 60 = T_1 - 60[/tex]
[tex]T_3 = 60 = 120 - 60 = T_2 -60[/tex]
-
[tex]T_n = T_{n-1} - 60[/tex]
(b) Assume it is a geometric sequence
The explicit formula is calculated using:
[tex]T_n = ar^{n-1}[/tex]
Where
[tex]a = 180[/tex]
[tex]r = \frac{120}{180}[/tex]
[tex]r = \frac{2}{3}[/tex]
So, we have:
[tex]T_n = 180 * (\frac{2}{3})^{n-1}[/tex]
Split
[tex]T_n = 180 * (\frac{2}{3})^n \div (\frac{2}{3})^1[/tex]
[tex]T_n = 180 * (\frac{2}{3})^n \div (\frac{2}{3})[/tex]
Rewrite as:
[tex]T_n = 180 * (\frac{2}{3})^n * (\frac{3}{2})[/tex]
[tex]T_n = 180 * (\frac{3}{2})* (\frac{2}{3})^n[/tex]
[tex]T_n = 180 * \frac{3}{2}* (\frac{2}{3})^n[/tex]
[tex]T_n = 90 * 3* (\frac{2}{3})^n[/tex]
[tex]T_n = 270* (\frac{2}{3})^n[/tex]
The recursive function is calculated using:
[tex]T_1 = 180[/tex]
[tex]T_2 = 120 = 180 * \frac{2}{3} = T_1 * \frac{2}{3}[/tex]
[tex]T_3 = 80 = 120 * \frac{2}{3} = T_2 * \frac{2}{3}[/tex]
-
[tex]T_n = T_{n-1} * \frac{2}{3}[/tex]
Please help! I will give Brainliest!
Who is correct?
Answer:
Dylan Is Correct
Step-by-step explanation:
Answer:
Dylan is correct
Step-by-step explanation:
What is sec 0 when cot 0 = -4V2? 0 (1,0) [?] [ ] Rationalize the denominator if necessary. sec 0 =
Answer:
[tex]Sec~ 0=\frac{\sqrt{66} }{8}[/tex]
Step-by-step explanation:
[tex]Cot~0=-4\sqrt{2}[/tex]
[tex]Sec~0=\sqrt{33}/4\sqrt{2}[/tex]
[tex]=\sqrt{33}/4\sqrt{2} *4\sqrt{2} /4\sqrt{2}[/tex]
[tex]=4\sqrt{66} /32[/tex]
[tex]= \sqrt{66}/8[/tex]
᪥༄᪥༄᪥༄᪥༄᪥༄᪥༄
hope it helps...
have a great day!!!
4 x 3/4
SHeeeeeeeeeeeeesh
It takes Jada 20 minutes to walk to school. It takes Andre 80% as long to walk to
school.
How long does it take Andre to walk to school?
Answer:
16
Step-by-step explanation:
A right square pyramid has a slant height of 25 feet, and the length of a side of the base is 14 feet. What is the height of the pyramid?
Answer: [tex]24\ ft[/tex]
Step-by-step explanation:
Given
The slant height of the square pyramid is [tex]l=25\ ft[/tex]
The length of the side of the base is [tex]a=14\ ft[/tex]
for the square pyramid, height is given by
[tex]\Rightarrow h=\sqrt{l^2-r^2}\quad \quad [\text{where r=}\frac{a}{2}]\\\Rightarrow h=\sqrt{25^2-7^2}\\\Rightarrow h=\sqrt{625-49}\\\Rightarrow h=\sqrt{576}\\\Rightarrow h=24\ ft[/tex]
Thus, the height of the prism is [tex]24\ ft[/tex]
62X + 310 =
2542 Find X
Answer:
36
Step-by-step explanation:
62x + 310 = 2542
62x = 2232
x = 36
Answer:
36
Step-by-step explanation:
62x + 310 = 2542
Subtract 310 from both sides
62x = 2,232
Then Divide by 62
x = 36
Enjoy.
Find the area of a circle with diameter 8 in.
Use the value 3.14 for n, and do not round your answer.
Be sure to include the correct unit in your answer.
Answer:
Step-by-step explanation:
50.27 should be the area of a circle that has a radius of 4 in.
A king bed measures 76 inches wide by 80 inches long. How much does the length exceed the width?
A) 4 inches
B) 7 inches
C) 11 inches
D) 14 inches
Answer:
A) 4 inches
Step-by-step explanation:
The length is 80 inches and the width is 76 inches. To find the difference subtract 80 minus 76 and you get 4... the amount that is exceeding the width!
Have a wonderful day!
Answer:
A. 4 inches
Step-by-step explanation:
In order to find by how much the length exceeds the width we have to subtract width from the length in order to get the difference between the two lengths, and so we get...
80 - 76 = 4
Therefore the answer is A. 4 inches
which expression below has a value in between 0 and 1?
a) 5(^-2)*1
b) (3^2)^3
c) 1/2*2^3
3(^-2)*3^3
Find the interquartile range (IQR) of the data in the dot plot below. goals luis's lacrosse
Answer:
3.5
Step-by-step explanation:
The interquartile range is the difference between the third and first quartile
IQR = Q3 - Q1
From the dot plot given :
The data, X could be culled :
X = 43, 44, 44, 44, 45, 45, 47, 48, 48
n = 9
Q3 = 3/4(n + 1)th term
Q3 = 3/4(10) = 7.5th term = (47 + 48) / 2 = 47.5
Q1 = 1/4(n + 1)th term
Q1 = 1/4(10) = 2.5th term = (44 + 44) / 2 = 44
Q3 - Q1 = 47.5 - 44 = 3.5
Answer:
3.5
Step-by-step explanation:
smart
Find the area of this triangle
Answer:
6km² sounds like a reasonable answer
Giving brainlist to whoever answers
will reward the brainliest
Rosa says 4x and -6x are like terms, so they can be combined. Tiffany says 5a and 5b are like terms, so they can be combined. Is Rosa correct? Is Tiffany correct? Why or why not?
please help =)
Answer:
Rosa is correct, it's the variable that determines if something has like terms, not the coefficients.
Step-by-step explanation:
at a fall festival student council sold two types of drinks hot chocolate in apple cider how many cups of apples are sold
Answer:
add a picture so i can see and help
Step-by-step explanation:
Answer:
your questions is completing
HELPP
Simplify: (x^3y^-3/ x^2y) ^-3
Answer:
A i the answer
Step-by-step explanation:
PLease answer!!! 30 points!!!
Answer:
a
Step-by-step explanation:
They make a right angle. A right angle adds up to 90.
Answer:
C.Step-by-step explanation:
Hopes this helps. Mark as brainlest plz!A cylinder has a base radius of 3m and a height of 17m. What is its volume in cubic m, to the nearest tenths place?
Answer:
V= 480.7 m cubed
The volume of the cylinder nearest to tenths place is 480 m^3.
What is cylinder?A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface.
For the given situation,
The formula for volume of the cylinder is [tex]V=\pi r^{2} h[/tex]
Radius of the cylinder,r = 3 m
Height of the cylinder, h = 17 m
The value of π = 3.14
On substituting the above values,
[tex]V=(3.14) (3^{2})(17)[/tex]
⇒ [tex]V=480.42[/tex] ≈ 480
Hence we can conclude that the volume of the cylinder is 480 m^3.
Learn more about volume of cylinders here
https://brainly.com/question/15891031
#SPJ2
Calculate the population
data set;
mean for the following
40, 50, 55, 78,58,60,73, 35, 43, 48.
Answer:
I think it’s 11.8
Step-by-step explanation:
The only time the word 'incorrectly' isn't spelled incorrectly is when it's spelled incorrectly. (⊙_ ⊙)
ahaha good one
Step-by-step explanation:
...........
Two groups went bowling. Here are the scores from each group.
Group A: 80, 100, 190, 110, 70, 90, 130
Group B: 50, 110, 100, 120, 107, 140, 150
70
80
190
50 60
90 100 110 120 130 140 150 160 170 180
score in points
1. Construct two box plots, one for the data in each group.
2. Which group shows greater variability? Explain how you know.
Answer:
Group A has greater variability
Step-by-step explanation:
Group A: 80, 100, 190, 110, 70, 90, 130
The variability of group A data :
Taking the range :
Maximum = 190 ; Minimum = 70
Range = Maximum - Minimum ; 190 - 70 = 120
Group B : 50, 110, 100, 120, 107, 140, 150
The variability of group B data :
Taking the range :
Maximum = 150 ; Minimum = 50
Range = Maximum - Minimum ; 150 - 50 = 100
Hence, Group A has greater variability
A color wheel is divided into 6 equal pieces. Select all of the true statements about the pieces of the color wheelA color wheel is divided into 6 equal pieces. Select all of the true statements about the pieces of the color wheel
Answer:
sidekick egocentric Jayco
How to find the central angle
Answer:
x = 50
Step-by-step explanation:
Note that the 3 interior angles must sum up to 180 degrees:
50 + x + 80 =180, or
50 + x = 100, or
x = 50
Here is the histogram of a data distribution.
What is the shape of this distribution?
A. Bimodal symmetric
B. Uniform
c. Unimodal symmetric
D. Bimodal skewed
E. Unimodal skewed
Answer:
Uniform
Step-by-step explanation:
We don't have any peaks in the histogram, so its neither unimodal or bimodal leaving only uniform as the answer.
The shape of this distribution, histogram is Unimodal skewed type. The correct option is E.
What is histogram?A histogram represents the graphical representation of the distribution of data. The histogram is indicated by using a set of rectangles adjacent to each other where each bar represent a kind of data. The histogram doesn't involve any gaps between the two successive bars.
The histogram would be classified into different types based on the frequency distribution of the data.
Based on the direction of the tail, the skewed distribution may be either right-skewed or left skewed.
Since skewed distribution is asymmetrical as a limit which is natural resists end results on one side.
Threfore, the correct option is E.
To know more about histogram, visit;
brainly.com/question/16819077
#SPJ7
3.
PROBLEM: Vincent started his piano practice at 5:15 PM. He ended his practice when the
minute hand moved 90 in the clock circle. What time did he finish?
MAKE SENSE:
MODEL and SOLVE:
5:15 + 90
Answer:
6:45
Step-by-step explanation:
please and thank you , 10 points
What is the slope of a line parallel to the line whose equation is 15x+9y=-16215x+9y=−162. Fully simplify your answer.
Answer:
-5/3
Step-by-step explanation:
Any line parallel to the given line will have the same slope as the given equation;
Given the equation 15x+9y=-162
Rewrite in standard from y = mx+b
15x+9y=-162
9y = -15x - 162
y = -15/9 x - 162/9
y = -5/3 x - 18
This gives the required equation;
Since mx = -5/3 x
m = -5/3
Hence the slope of the line parallel to the given line is -5/3
50 PTS!!!!
PLEASE LOOK AT THE SCREENSHOT AND ANSWER:
Which kind of model best describes this set of data?
Answer:
that is the correct answer
RIGHT ANSWER WILL BE MARK BRAINLIEST