The sequences below are either arithmetic sequences or geometric sequences. For each sequence, determine whether it is arithmeticthor geometric, and write the formula for the nterm a, of that sequence.SequenceTypethnterm formula2 8 08
Answers
A geometric sequence is one where each term is the previous one by a constant term we call the common ratio. The quotient between consecutive numbers is the common ratio.
An arithmetic sequence is one where each term is at the same distance from the next. The difference between consecutive numbers is constant, we call that constant common difference.
The first sequence given is:
6, 12, 24
The first term, 6, is at a distance of 6 from the next term, 12. The term 12 is at a distance of 12 from the next one. Since the distance between two consecutive terms is not constant, the sequence is not arithmetic.
Let's see if its a geometric sequence:
\(\begin{gathered} \frac{12}{6}=2 \\ . \\ \frac{24}{12}=2 \end{gathered}\)The quotient is constant, thus this is a geometric sequence.
The formula for the nth term of a geometric sequence is:
\(a_n=a_1r^{n-1}\)Where:
a_1 is the first term
r is the constant ratio
n is the term we want to find.
In this case:
a_1 = 6
r = 2
Thus, the nth term equation of this sequence is:
\(a_n=6\cdot2^{n-1}\)The second sequence is:
9, 11, 13...
We can see that the first term is at a distance of 2 from the second term. The second term is at a distance of 2 from the third term.
Since the distance between two consecutive terms is constant, This is an arithmetic sequence.
The formula for the nth term of an arithmetic sequence is:
\(a_n=a_1+d(n-1)\)Where d is the common difference.
In this case:
a_1 = 9
d = 2
Thus, the nth term equation of this sequence is:
\(a_n=9+2(n-1)\)Related Questions
Boris started on the treadmill after setting timer for 99 minutes. The display says he have finished 43% of his run. How many minutes have gone by. Round to the nearest tenth
Answers
99 minutes * 0.43 = 42.57 minutes
Rounding to the nearest tenth, we can say that approximately 42.6 minutes have gone by.
A square plywood platform has a perimeter which is 11 times the length of a side,
decreased by 42. Find the length of a side. (P = 4L)
Answers
Answer:
Step-by-step explanation:
Question Below.
Answers: 250|253|254|255|307|433|434|435|507|.
First to answer this question the quickest is rewarded branliest + 100 points
Answers
Answer:
Minimum--> 250
Q1--> 255
Q2--> (Median): 307
Q3--> 433
Maximum-->507
Step-by-step explanation:
To find the five-number summary of this data set, we need to determine the minimum value, maximum value, and three quartiles (Q1, Q2, Q3) which divide the data into four equal parts.
First, we need to sort the data set in ascending order:
{ 250, 253, 255, 267, 307, 425, 433, 435, 507 }
Minimum: 250
Maximum: 507
To find the quartiles, we need to find the median of the entire data set (Q2) and then the medians of the two halves of the data set, which will give us Q1 and Q3.
Q2 (Median): The median of the entire data set can be found by averaging the two middle numbers.
Q1: The median of the lower half of the data set is 255, which is the middle value of { 250, 253, 255, 267, 307 }. Therefore, Q1 = 255.
Q3: The median of the upper half of the data set is 433, which is the middle value of { 425, 433, 435, 507 }. Therefore, Q3 = 433.
Which expression is equivalent to 3(8 + 7)
Answers
Answer:
24+21
Step-by-step explanation:
24+21
Hope you got your answer
I need help with homework D) y ≤ 1∕4x – 4
Answers
Explanation
Step 1
let's find the equation of the line
a)slope
the slope of a line is given by:
\(\begin{gathered} \text{slope}=\frac{chang\text{e in y}}{\text{change in x}}=\frac{y_2-y_{1|}}{x_2-x_1} \\ \text{where} \\ P1(x_1,y_1) \\ \text{and } \\ \text{P2(x}_2,y_2) \\ \text{are 2 points from the line} \end{gathered}\)so
pick up 2 points from the line
let
P1=(0,-4)
P2=(4,-3)
now, replace in the equation to find the slope
\(\begin{gathered} \text{slope}=\frac{y_2-y_{1|}}{x_2-x_1} \\ \text{slope}=\frac{-3-(-4)}{4-0}=\frac{-3+4}{4}=\frac{1}{4} \end{gathered}\)Step 2
b) the equation of the line, it can be found by using the poitn slope formula
\(\begin{gathered} y-y_1=m(x-x_1) \\ \text{where m is the slope and } \\ P1(x_1,y_1) \end{gathered}\)then, let
P1=(0,-4)
slope=1/4
replace and isolate y
\(\begin{gathered} y-y_1=m(x-x_1) \\ y-(-4)=\frac{1}{4}(x-0) \\ y+4=\frac{1}{4}x \\ \text{subtract 4 in both sides} \\ y+4-4=\frac{1}{4}x-4 \\ y=\frac{1}{4}x-4 \end{gathered}\)Step 3
finally, we need the shaded region, it means all the values over the line, in other words, the values greater than the function, so
\(\begin{gathered} y=\frac{1}{4}x-4\Rightarrow shaded\text{ region }\Rightarrow y\ge\frac{1}{4}x-4 \\ \text{the line is continous so}\Rightarrow\ge \end{gathered}\)therfore, the answer is
\(c)y\ge\frac{1}{4}x-4\)I hope this helps you
what is the simplified form of 4 log3x+6 log3y-7 log3z
Answers
Answer:
A
Step-by-step explanation:
Using the properties of logarithms, we can simplify the expression:
4 log3x + 6 log3y - 7 log3z = log3x^4 + log3y^6 - log3z^7
Now, we can use another property of logarithms, which states that:
loga (mn) = loga m + loga n
Using this property, we can combine the logarithms with addition or subtraction:
log3x^4 + log3y^6 - log3z^7 = log3(x^4 * y^6 / z^7)
Therefore, the simplified form of 4 log3x + 6 log3y - 7 log3z is log3(x^4 * y^6 / z^7).
PLZZZZZ ILL MARK BRAINLY
Answers
Answer:
the answer is b
Step-by-step explanation:
I hope this helps
A simple random sample from a population with a normal distribution of 98 body temperatures has x=98.20°F and s=0.61°F. Construct a 99% confidence interval estimate of the standard deviation of body temperature of all healthy humans. Click the icon to view the table of Chi-Square critical values. °F
Answers
from the question;
we are to construct 99% confidence interval. this can be done using
\(\bar{}x\text{ }\pm\text{ z}(\frac{s}{\sqrt[]{n}})\)where,
\(\bar{x}\text{ = }98.20,\text{ s = 0.61, n = 98 z= 2.576}\)inserting values
\(\begin{gathered} 98.20\text{ }\pm2.576\text{ }\frac{0.61}{\sqrt[]{98}} \\ 98.20\text{ }\pm\text{ 2.576}\times0.0616 \\ =\text{ 98.20 }\pm\text{ }0.159 \\ =98.20\text{ + }0.159\text{ or 98.20 - 0.159} \\ =\text{ 98.359 0r 98.041} \end{gathered}\)therefore the 99% confident inter vale is between 98.041 to 98.359
Simplify the equation.
Answers
Answer:
The answer is 3x+5/7
Step-by-step explanation:
Hope this helps
Mark brainliest please :)
Find the surface area of a rectangular solid with the given dimensions length 7 feet, width 5 feet and height 8 feet give your answer without units
Answers
262
Explanations:The formula for finding the surface area of a rectangular solid is expressed as:
\(SA=2(lw+wh+lh)\)where:
• l is the ,length, of the solid
,• w is the ,width ,of the solid
,• h is the ,height, of the solid
Given the following parameters:
\(\begin{gathered} l=7\text{feet} \\ w=5\text{feet} \\ h=8\text{feet} \end{gathered}\)Substitute the given parameters into the formula:
\(\begin{gathered} SA=2\lbrack(7\times5)+(5\times8)+(7\times8)\rbrack \\ SA=2(35+40+56) \\ SA=2(131) \\ SA=262 \end{gathered}\)Therefore the surface area of the rectangular solid is 262.
What is a tessellation, how are tessellations used, and what must happen at vertices in order for polygons to tessellate?
Answers
A tessellation is a pattern made by repeating geometric shapes without any gaps or overlaps. These shapes, called tiles or polygons, fit together perfectly to cover a plane or a surface. Tessellations can be found in various forms of art, architecture, and design. They are used to create visually appealing patterns and decorations, as well as to explore mathematical concepts.
Tessellations are utilized in various practical applications, such as tiling floors, walls, and pavements, designing mosaics and quilts, and creating computer graphics and textile patterns. They are also studied in mathematics to understand concepts like symmetry, geometry, and transformations.
For polygons to tessellate, certain conditions must be met at their vertices. At each vertex, the angles formed by the polygons must add up to a whole number of degrees, typically 360 degrees. In other words, the sum of the interior angles of each polygon meeting at a vertex must be a multiple of 360 degrees.
This ensures that the polygons can fit together seamlessly without leaving any gaps or overlaps. Examples of polygons that tessellate include equilateral triangles, squares, and hexagons, as their angles add up to 360 degrees at each vertex.
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Kacie just bought a new house and needs to buy new sod for her backyard, if the dimensisons of her yard are 33.5 feet by 13.6 feet, what s the area if her yard
Answers
SHE shortens the leash by 6 feet. What is the length of the shorten leash.
Answers
Answer:
6 feet is the answer
Step-by-step explanation:
3^4=12-6=6
Jada has 12 library books checked out and Han has 1/4 less than that. How many books does
Han have checked out?
Answers
12-3=9
han has 9 books checked out
A family of four went to dinner at a local restaurant. Three of the family members ordered the special dinner that costs $12.88 each and the fourth family member ordered the hamburger and fries combo that costs $6.78. If they want to leave a 15% tip, which of the following expressions represents the amount of tip they should leave?
A. (12.88+6.78)×0.15
B. (3×12.88+6.78)×0.15
C. 3×12.88+6.78
D. [3×(12.88+6.78)]×0.15
Answers
What three consecutive integers have a sum of 12?; What is the sum of 3 consecutive integers?; What is the formula for 3 consecutive integers?; What are the consecutive numbers of 12?
Answers
The three consecutive numbers that have a sum of 12 is 3, 4 and 5. The formula for calculation is x + x + 1 + x + 2 = 12.
Let the first number in three consecutive numbers be x. So, the next two numbers will be (x+1) and (x+2). Now, their sum wil be represented as mathematical equation -
x + x + 1 + x + 2 = 12
Performing addition on Left Hand Side of the equation
3x + 3 = 12
Rewriting the equation
3x = 12 - 3
Performing subtraction on Right Hand Side of the equation
3x = 9
x = 9/3
Performing division on Right Hand Side of the equation
x = 3
So, next number = x+1
Second number = 3+1
Second number = 4
Third number = x+2
Third number = 3+2
Third number = 5
Hence, the three consecutive numbers are 3, 4 and 5.
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Find the error in the multiplication
Answers
Answer:
the answer is 9688
Step-by-step explanation:
this is because 346 × 28 is 9688
HELP ASAP AGAIN!!
It rained 10% of the 30 days last month. On how many days did it rain.
Answers
3
10
15
27
Answers
Answer:
10 days
Step-by-step explanation:
10 is 10% of 30
Julian belongs to a club that is marching in a parade. Each member of the club needs to wear one of the hats listed in the table below.
PARADE HATS
Straw Hat
25 red
20 white
40 blue
Cowboy Hat
30 red
25 white
10 blue
Julian chooses the first hat at random from all the hats. What is the probability the hat Julian chooses is blue? Show your work or explain your answer.
Answers
The probability Julian chooses a blue hat is 1/3.
What is the probability Julian chooses a blue hat?Probability refers to the branch of math which deals with finding out the likelihood of the occurrence of an event.
Total hat is:
= 25+20+40+30+25+1
= 150.
There are a total of 150 hats to choose from.
The number of blue hats to choose from is:
= 40 + 10
= 50.
The probability that Julian chooses a blue hat is:
= 50/150
= 1/3
= 0.33 or 33.33%.
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The Directed Disjoint Paths Problem is defined as follows. We are given a directed graph G
and k pairs of nodes (s1, t1), (s2, t2), . . . , (sk, tk). The problem is to decide whether there exist node
disjoint paths P1, P2, . . . , Pk so that Pi goes from si to ti.
Show that Directed Disjoint Paths is NP-complete.
Answers
To show that the Directed Disjoint Paths Problem is NP-complete, we can use a reduction from the well-known NP-complete problem of Hamiltonian Path, which is defined as follows: given a graph G and a starting node s, does G contain a simple path that visits every node exactly once and ends at s?
We can reduce the Hamiltonian Path problem to the Directed Disjoint Paths Problem as follows. Given a graph G and a starting node s for the Hamiltonian Path problem, we can construct a new graph G' as follows:
For each node v in G, create two new nodes v1 and v2 in G'.For each edge (u,v) in G, create an edge (u2,v1) in G'.For each node v in G, create an edge (v1,v2) in G'.For each node v in G, create an edge (v2,s1) in G' if v is not the starting node s, or an edge (v2,s2) in G' if v is the starting node s.Now, consider the k pairs of nodes (s1,t1), (s2,t2), ..., (sk,tk) in G', where si and ti are the corresponding nodes in G' for the ith node in G. We can see that G contains a Hamiltonian path from s to s if and only if G' contains k node-disjoint paths from si to ti for all i.
Since the Hamiltonian Path problem is NP-complete, and we have shown that it can be reduced to the Directed Disjoint Paths Problem in polynomial time, it follows that the Directed Disjoint Paths Problem is also NP-complete.
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I require assistance
Answers
Answer: 50°
Step-by-step explanation:
Hi ! As you can see, the whole angle on which there are the three angles is plane, so it is 180°.
And with this information, you can guess that : C = 180 - ( 65 + 65)
C = 180 - 130
C = 50°
You verify : 65 + 65 + 50 = 180, which means it should be correct, and there you go, hope it helped !
can someone please help me
Answers
9514 1404 393
Answer:
central: XWR, VWUinscribed: VSTStep-by-step explanation:
Point W is the center of the circle. Any angle with W as its vertex is a central angle:
angles XWR and VWU are central angles
Any angle with its vertex on the circle and rays that intersect the circle is an inscribed angle.
angle VST is an inscribed angle
Find the measure of angle AEB
Answers
Answer:
∠ AEB = 114°
Step-by-step explanation:
the chord- chord angle AEB is half the sum of the measures of the arcs intercepted by the angle and its vertical angle , that is
∠ AEB = \(\frac{1}{2}\) (AB + CD) = \(\frac{1}{2}\) (140 + 88)° = \(\frac{1}{2}\) × 228° = 114°
Convert (87.1352) 10 to base 8
Answers
Answer:
It comes out to around 127
Step-by-step explanation:
What are the features of the quadratic function graphed in the figure?
A) Vertex = (–3,4), y-intercept = (0,–5), x-intercepts = (1,0) and (5,0), axis of symmetry is x = –3
B) Vertex = (–4,3), y-intercept = (5,0), x-intercepts = (0,1) and (0,5), axis of symmetry is x = –4
C) Vertex = (–3,4), y-intercept = (0,–5), x-intercepts = (–5,0) and (–1,0), axis of symmetry is x = –3
D) Vertex = (3,–4), y-intercepts = (–1,0) and (–5,0), x-intercept = (0,5), axis of symmetry is x = 3
Answers
The correct option is A) Vertex = (–3,4), y-intercept = (0,–5), x-intercepts = (1,0) and (5,0), axis of symmetry is x = –3.
What is quadratic function ?A quadratic function is a type of polynomial function with a degree of two, represented by a parabolic curve when graphed, and can have a maximum or minimum point known as the vertex.
To determine the correct option, we need to compare each feature given in the options with the graph. Here are the steps:
Step 1: Identify the vertex of the graph.
From the graph, we can see that the vertex is located at (–3,4).
Step 2: Identify the y-intercept.
From the graph, we can see that the y-intercept is located at (0,–5).
Step 3: Identify the x-intercepts.
From the graph, we can see that there are two x-intercepts located at (1,0) and (5,0).
Step 4: Identify the axis of symmetry.
The axis of symmetry is the vertical line that passes through the vertex and divides the parabola into two symmetric halves. From the graph, we can see that the axis of symmetry is the vertical line x = –3.
Comparing the features given in the options with the graph, we can see that option A matches all the features correctly.
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I NEED HELP ON THIS
Answers
The expression that correctly name the angle below is ∠K, So correct option is C.
Describe Angles?In geometry, an angle is a figure formed by two rays, or half-lines, that originate from a common endpoint, which is called the vertex. The rays can be thought of as emanating from the vertex and extending infinitely in opposite directions.
The measure of an angle is typically given in degrees, where a full circle is 360 degrees. Angles can be classified according to their size:
An acute angle is less than 90 degrees.
A right angle measures exactly 90 degrees.
An obtuse angle is greater than 90 degrees but less than 180 degrees.
A straight angle measures exactly 180 degrees.
A reflex angle is greater than 180 degrees but less than 360 degrees.
A full angle measures exactly 360 degrees.
Angles can also be classified based on their position relative to other angles or lines:
Adjacent angles share a common vertex and one common side.
Complementary angles add up to 90 degrees.
Supplementary angles add up to 180 degrees.
Vertical angles are formed by two intersecting lines and are opposite each other.
The expression that correctly name the angle below is ∠K.
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The answer C is accurate since the formula that correctly identifies the angle below is ∠K.
Describe Angles?An angle is a figure in geometry made up of two rays, or half-lines, that start from a single endpoint known as the vertex. You can imagine the rays coming from the vertex and continuing in opposing directions indefinitely.
A whole circle has 360 degrees, hence an angle is commonly measured in degrees. Angles can be grouped based on their size:
Any angle that is below ninety degrees is considered acute.
Obtuse angles are those that are greater than 90 degrees but below 180 degrees.
The length of a straight angle is 180 degrees.
A reflex angle is one that is above 180 degrees and less than 360 degrees.
Angles can also be categorised according on where they are situated in relation to other angles or lines:
Adjacent angles have one shared side as well as a common vertex.
Complementary angles add up to 90 degrees.
The sum of all supplementary angles is 180 degrees.
Two intersecting lines that are opposite one another form vertical angles.
The formula K accurately identifies the angle below.
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2. A linear model for the data in the table is shown in the scatter plot. X 1 2 5 6 7 9 y 2 6 9 9 13 Variable y 14 10 8 LT 5 4 321 0 1 2 3 4 5 6 7 8 9 10 11 Variable x (a) Which two points should you use to find the equation of the model? 6,9 and 10,13. (b) What is the slope of the linear model? 1 (c) What is the equation of the linear model in point-slope form? Y-9 =(x-6) (d) What is the slope-intercept form of the equation you wrote in Part (c)? y=x+3 (e) What is the equation for the least squares regression line? y = bx + a (f) decimal places. Answer: Y= 1.028x + 2.271
pls check my answers
correct any mistakes pls
thanks!
Answers
You answered 6,9 and 10,13. The correct answer is 6,9 and 7,13 to find the equation of the linear model.
(a) The two points you selected are (6,9) and (10,13). This is correct.
(b) To find the slope of the linear model, we can use the formula: slope = (change in y) / (change in x). By using the points (6,9) and (10,13), we have (13-9) / (10-6) = 4/4 = 1. So, the slope is indeed 1. This is correct.
(c) The equation of the linear model in point-slope form is given as: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Plugging in the values (6,9) as the point and 1 as the slope, we get y - 9 = 1(x - 6). This simplifies to y - 9 = x - 6. This is not the same as the equation you provided. It seems you made a mistake here.
(d) The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. To convert the equation y - 9 = x - 6 to slope-intercept form, we can add 9 to both sides: y = x - 6 + 9, which simplifies to y = x + 3. This matches the equation you provided. So, this is correct.
(e) The equation for the least squares regression line is in the form y = bx + a, where b is the slope and a is the y-intercept. In this case, the slope is 1, and we need to find the y-intercept.
We can use the point (6,9) and the slope-intercept form equation y = x + 3 to find the y-intercept: 9 = 6 + 3. Solving this equation, we find that the y-intercept is 3.
Therefore, the equation for the least squares regression line is y = x + 3. This does not match the equation you provided. It seems you made a mistake here.
(f) Based on the correct equation from part (d) (y = x + 3), the correct equation for the least squares regression line is y = 1x + 3. When rounded to three decimal places, this would be y = 1.000x + 3.000.
The equation you provided (Y = 1.028x + 2.271) is slightly different, so it appears you made a mistake in the calculations or rounding.
To summarize, your answers in parts (a) and (b) are correct. However, there are mistakes in parts (c), (e), and (f). The corrected answers are:
(c) The equation of the linear model in point-slope form: y - 9 = x - 6.
(d) The slope-intercept form of the equation: y = x + 3.
(e) The equation for the least squares regression line: y = 1x + 3.
(f) When rounded to three decimal places, the equation is: y = 1.000x + 3.000.
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Slope 3/5 yintercept2 write an equation slope-intercept form
Answers
The equation of the line in slope-intercept form is y = (3/5)x + 2. This form allows us to easily identify the slope and y-intercept of the line and to graph it on a coordinate plane.
To write the equation of a line in slope-intercept form, we use the formula:y = mx + b
where:
- y represents the dependent variable (the vertical axis)
- x represents the independent variable (the horizontal axis)
- m represents the slope of the line
- b represents the y-intercept, the point where the line intersects the y-axis.
In this case, we are given the slope as 3/5 and the y-intercept as 2. Plugging these values into the formula, we get:
y = (3/5)x + 2
This equation represents a line with a slope of 3/5, indicating that for every 5 units we move horizontally (along the x-axis), the line moves 3 units vertically (along the y-axis). The y-intercept of 2 tells us that the line intersects the y-axis at the point (0, 2).
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Susan can solve 8 math problems in 20 minutes while Betsy can solve the same 8 math problems at a rate of 1 problem per 5 minutes. Who works faster? Show your work.
Answers
if you solve 8 problems in 20 minutes, that is faster than 1 problem per minute because even once you do 5 problems you are at 25 minutes and that is longer than the 20 minutes
A rectangular room is
1.5
times as long as it is wide, and its perimeter is
35
meters. Find the dimension of the room.
The length is :
meters and the width is
meters.
Answers
The dimensions of the room are approximately 7 meters by 10.5 meters.
The length is 10.5 meters and the width is 7 meters.What are dimensions?In Mathematics, dimensions are referred to as measures of size such as length, width, and height of an object or a shape. A rectangle has length and width as its dimensions that define the area of a rectangle.
Let's start by using algebra to represent the information given in the problem. Let x be the width of the rectangular room, then the length is 1.5 times the width or 1.5x.
The perimeter of a rectangle is the sum of the lengths of all its sides, which can be expressed as:
\(\text{Perimeter} = 2(\text{length} + \text{width})\)
Substituting the values we have for length and width, we get:
\(\rightarrow35 = 2(1.5\text{x} + \text{x})\)
Simplifying the equation, we get:
\(\rightarrow35 = 2(2.5\text{x})\)
\(\rightarrow35 = 5\text{x}\)
\(\rightarrow\text{x}=\dfrac{35}{5}\)
\(\rightarrow\bold{x\thickapprox7}\)
So the width of the room is 7 meters.
To find the length, we can substitute x into the expression we have for the length:
\(\rightarrow\text{Length} = 1.5\text{x}\)
\(\rightarrow\text{Length} = 1.5(7)\)
\(\rightarrow\bold{Length=10.5}\)
So the length of the room is 10.5 meters.
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