Answers
a(n) = a1*r^(n-1)
Where
a(n) = nth term
a1 = first term
r = common ratio
n = 0,1,2,3,4,5, ... n
To establish which graphs agree with this formula, each graph should be tested separately as follows:
Graph A:
a2 = 9
Then
9 = a1*(1/3)^(2-1) =1/3a1 => a1 = 3*9 = 27
Sequence:
a1 = 27
a2 = 9
a3 = 27*(1/3)^(3-1) = 3
a4 = 27*(1/3)^(4-1) = 1
These are the same values shown and thus this graph corresponds to geometric sequence.
Graph B:
a1 = 12
a2 = 12*(1/3)^(2-1) = 4
a3 = 12*(1/3)(3-1) = 4/3
a4 = 12*(1/3)^(4-1) = 4/9
These are the values shown by the graph and thus it corresponds with geometric sequence.
Graph C:
a1 = 3+3/2 = 9/2
a2 = (9/2)*(1/3)^1 = 3/2
a3 = (9/2)*(1/3)^2 = 1/2
a4 = (9/2)*(1/3)^3 = 1/6
a0 = (9/2)*(1/3)^-1 = 13.5 (this is not the case as the graph shows a0 = 12)
Therefore, this graph does not correspond to geometric sequence.
Graph D:
a1 = 4
a2 = 4*(1/3)^1 = 4/3
a3 = 4*(1/3)^2 = 4/9
a4 = 4*(1/3)^3 = 4/27
a0 = 12
This graph seems to agree with values of geometric sequence and thus corresponds to geometric sequence.
Therefore, graphs A, B, and D corresponds with geometric sequence.
Related Questions
a $1600 principal earns 7% annual interest, compounded semiannually. What is the balance after 33 years?
Answers
FV = P(1 +r/n)^(nt)
FV = 1600*(1 +.07/2)^(2*33)
FV = 1600*1.035^66 ≈ 15,494.70
The balance after 33 years will be $15,494.70
The length of a rectangle is five times the width.
The area of the rectangle is 1620cm squared.
Work out the width of the rectangle
Answers
Let's use x for the width because we know the width is only 1. Next, we'll use 5x for the length because the length is 5 times the width. Now, we can set up an equation to solve for x.
WORK:
x * 5x = 1620
5x^2 = 1620
x^2 = 324
x = 18
ANSWER:
The width of the rectangle is 18 centimeters
Hope this helps!! :)
If there's anything else that I can help you with, please let me know!
Event A is a subset of event B. P(A)=.15 and P(B)=.53 Find P(A|B). Round the answer to the nearest hundredth.
Answers
[tex]\mathbb P(A\mid B)=\dfrac{\mathbb P(A\cap B)}{\mathbb P(B)}=\dfrac{\mathbb P(A)}{\mathbb P(B)}=\dfrac{0.15}{0.53}\approx0.28[/tex]
Answer:
C.
Step-by-step explanation:
An equilateral triangle's perimeter and a rectangle's perimeter have the same numerical value. The length of the rectangle is the same as the side of the triangle. The width of the rectangle is 12. What is the length of the rectangle?
Answers
Find the inverse of the function r(t) = 5^t. I WILL make you BRAINLIEST
Answers
hope it helps if not say something ill change it :P
Good Treads and Speed Tracks manufacture tires. Good Treads claims that their tires last longer than Speed Tracks tires. A car company decided to test Good Tread's claim. They purchased 20 sets of Good Tread's tires and 20 sets of Speed Track's tires. They tested the lifetime of each tire by simulating 1,000 miles of driving conditions for each set of tires each day. At the end of each day, they measured the tread on each of the tires. Once the tire tread drops below minimum safe tread depth, the tire is considered to have passed its lifetime.
After observing the lifetime of each tire, the car company reported that the average lifetime of a Good Treads tire is 55,000 miles and the average lifetime of a Speed Tracks tire is 65,000 miles.
Given the car company's report, what conclusion can be made regarding the average lifetime of Good Treads and Speed Tracks tires?
There is not enough information to make any conclusions from the car company's report.
Good Treads' claim is false; therefore, it can be concluded that Speed Tracks tires last longer than Good Treads tires.
Good Treads' claim is false; therefore, it can be concluded that Good Treads tires last longer than Speed Tracks tires.
Good Treads' claim is true; therefore, it can be concluded that Good Treads tires last longer than Speed Tracks tires.
Answers
Good Treads' claim is false; therefore, it can be concluded that Speed Tracks tires last longer than Good Treads tires.
D
The car company's report provides evidence that Speed Tracks tires have a longer average lifetime compared to Good Treads tires. Therefore, we can conclude that Good Treads' claim that their tires last longer is false.
Based on the car company's report, we can conclude that Good Treads' claim that their tires last longer than Speed Tracks' tires is false. The average lifetime of a Good Treads tire is reported to be 55,000 miles, while the average lifetime of a Speed Tracks tire is reported to be 65,000 miles.
To reach this conclusion, we compare the average lifetimes of the two tire brands. Since the car company tested 20 sets of each brand's tires and measured the tread on each tire after simulating 1,000 miles of driving conditions, we can assume that these results are representative.
By comparing the average lifetimes, we see that the average lifetime of Speed Tracks tires is greater than the average lifetime of Good Treads tires. Therefore, we can conclude that Speed Tracks tires last longer than Good Treads tires, contradicting Good Treads' claim.
In conclusion, the car company's report provides evidence that Speed Tracks tires have a longer average lifetime compared to Good Treads tires. Therefore, we can conclude that Good Treads' claim that their tires last longer is false.
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Because your friends stayed in bed instead of helping you with the breakfast, you agree to split the £248 hostel bill to the ratio of: 3:3:2 with you paying the least. How much will you have to pay?
Answers
The question posed is about the concept of ratio, you are required to divide £248 according to the ratio 3:3:2. Each part of the ratio is worth £31, thus you will have to pay for two parts, hence, your total responsibility is £62.
Explanation:The subject of this question is ratio. In the given problem, you need to distribute £248 hostel bill into the ratio of 3:3:2. Firstly, you add the three parts of the ratio which equals to 8 (3+3+2). Now, to find out how much each part is worth you need to divide the total sum, which is £248, by the total number of parts, which is 8. This gives you the value for one part, which is £31 (248 ÷ 8).
Given that you have to pay the least, which corresponds to 2 parts, you multiply £31 by 2, thus you have to pay £62 (31 * 2).
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Write the expression as a single natural logarithm.3 ln x – 5 ln c
Answers
[tex]\Longrightarrow \ln(\frac{a}{b})=\ln(a)-\ln(b)[/tex]
[tex]\Longrightarrow \ln(a^{b})=b\ln(a)[/tex]
Your expression makes use of both these rules.
[tex]3\ln(x)-5\ln(c)=\ln(x^{3})-\ln(c^{5})=\ln \left( \dfrac{x^{3}}{c^{5}} \right)[/tex]
Your single logarithm is ...
[tex]\ln \left( \dfrac{x^{3}}{c^{5}} \right)[/tex]
hey can you please help me posted picture of question
Answers
Following translations occur in F(x) to obtain G(x)
a) 2 units to Right
b) 4 units down
Translation towards right can be expressed as:
F(x - 2)
Vertically down translation can be expressed as:
F(x-2) - 4
So,
G(x) = (x-2)² - 4
Thus, option A is the correct answer.
Find the measure of each angle indicated.
Answers
(11). 110 degree (12).84 degree (13).80 degree (14).111 degree (15).125 degree (16).47 degree.
What is angle theorem?The relation between the angles which is formed by intersecting two lines , described by Geometry called angle theorem. Some common angle theorem are Alternate interior angle , Alternate exterior angle etc.
Given,
(11) One angle of 110 degree is given and other angle which is asked is
also 110 degree by alternate exterior angle theorem.
(12) One angle of 84 degree is given and other angle which is asked is
also 84 degree by alternate interior angle theorem.
(13) The angle formed by straight line is 180 degree .So one angle is
given which is 100 degree and other will be 80 degree. Now asked
also 80 degree by alternate interior angle theorem.
(14) One angle of 111 degree is given and other angle which is asked is
also 111 degree by alternate interior angle theorem.
(15) One angle of 125 degree is given and other angle which is asked is
also 125 degree by alternate interior angle theorem.
(16) One angle of 47 degree is given and other angle which is asked is
also 47 degree by alternate exterior angle theorem.
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Choose the single logarithmic expression that is equivalent to the one shown 5 log x + 3 log x^2
Answers
=log x^5+log x^(2×3)
=log x^5+ log x^6
=log (x^5×x^6)
=log x^(5+6)
=log x^11
Answer: log x^11
In 2012 the population of a city 6.16 was find the exponential growth function estimate the population
Answers
that would be your starting equation
The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is the _____.
Answers
In order to accumulate enough money for a down payment on a house, a couple deposits $300/month into an account paying 6% compounded monthly. If payments are made at the end of each period, how much money will be in the account in 5 years? What formula is required to complete this problem?
Answers
[tex]\bf \begin{cases} A= \begin{array}{llll} \textit{accumulated amount}\\ \end{array}\\ pymnt=\textit{periodic payments}\to &300\\ r=rate\to 6\%\to \frac{6}{100}\to &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\to &12\\ t=years\to &5 \end{cases}[/tex]
[tex]\bf A=300\left[ \cfrac{\left( 1+\frac{0.06}{12} \right)^{12\cdot 5}-1}{\frac{0.06}{12}} \right]\implies A=300\left[ \cfrac{(1.005)^{60}-1}{0.005} \right] \\\\\\ A=300(\stackrel{\approx}{69.770030509863214)}\implies A\approx 20931.009152958964[/tex]
Maggie ebought 52 ounces of swordfish selling for $6.92 per pund. What was the total cost?
Answers
The ratio of the lengths of corresponding sides of two similar octagons is 8:9. what is the ratio of their perimeters? *
Answers
_____
Any corresponding length measures of the similar figures will have the same ratio.
The ratio of the perimeters of the two similar octagons is the same as the ratio of the lengths of their corresponding sides, which is 8:9.
When dealing with similar polygons, such as octagons in this case, the ratio of the lengths of corresponding sides directly determines the ratio of their perimeters. Since the sides of the octagons are proportional, with a specific ratio of 8:9, we can infer that the perimeters of the octagons will also have the same ratio. This is due to the perimeter being the sum of the lengths of all sides of the polygon.
Therefore, if one side of the first octagon is scaled up by a factor of 8, the entire perimeter will be scaled by the same factor. Correspondingly, if one side of the second octagon is scaled up by a factor of 9, its entire perimeter will also reflect that scaling. Given that the ratio of the lengths of corresponding sides is 8:9, the ratio of their perimeters will also be 8:9.
Write the equation of the perpendicular bisector of CD.
A) y = -x + 6
B) y = x + 1 2
C) y = 1 2 x + 6
D) y = -x + 1 2
Answers
The general form of the linear equation is:
y = mx + c
where:
m is the slope and c is the y-intercept
1- getting the slope:
We will start by getting the slope of CD using the formula:
slope = (y2-y1) / (x2-x1)
We know that the line we are looking for is perpendicular to CD. This meas that the product of their slopes is -1. Knowing this, and having calculated the slope of CD, we can simply get the slope of our line
2- getting the y-intercept:
To get the y-intercept, we will need a point that belongs to the line.
We know that our line passes through the midpoint of CD.
Therefore, we will first need to get the midpoint:
midpoint = ([tex] \frac{x1+x2}{2} , \frac{y1+y2}{2} [/tex])
Now, we will use this point along with the slope we have to substitute in the general equation and solve for c.
By this, we would have our equation in the form of:
y = mx + c
Hope this helps :)
Answer:
The answer is A.) y= -x+6
Step-by-step explanation:
PLZ HELP ASAP CIRCLES
Answers
m(DKC) = 2(85°) = 170°
The total measure of the arc in a circle is equal to 360°. Hence,
m(DKC) + m(DUC) = 360°
Substituting the known value,
170° + m(DUC) = 360°
The value of m(DUC) is equal to 190°. The measure of the angle K is half this value.
m∠K = 190°/2 = 95°
Answer: 95°
Marty correctly answers 36 questions on his science test. There are 50 questions on the test. Find the percent of the questions Marty answers correctly.
Work Pls
Thx
Answers
Score = 36
Total = 50
36 ÷ 50 = 0.72
0.72 = 72%
Answer = 72%
Hope this helped :)
The percent of the questions Marty answers correctly is 72 percent.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Given that, Marty correctly answers 36 questions on his science test.
There are 50 questions on the test.
Percentage of correct answers = Number of correct answers/Total number of questions ×100
= 36/50 ×100
= 0.72×100
= 72%
Therefore, the percent of the questions Marty answers correctly is 72 percent.
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Which type of study contains a treatment?
Sample.
Experiment.
Survey.
Observational study.
Answers
So the answer is experiment.
An experimental set up usually involved random assignment of variables into different group and manipulation of a particular variable while others are controlled. This type of study is usually done to determine the effect of one variable on the outcome of another variable. The experimental set up is usually made up of control and treatment groups.
Find the value of x for which M//N. PLEASE EXPLAIN HOW TO SOLVE ALSO
A.
38
B.
62
C.
102
D.
150
Answers
The two angles are complementary so 3x-36+2x+26=180
Just simplify from there.
(3x-36)°+(2x+26)°=180°
(3x-36+2x+26)°=180°
3x-36+2x+26=180
5x-10=180
5x-10+10=180+10
5x=190
5x/5=190/5
x=38
Answer: Option A. 38
Indicate the general rule for this sequence. Find a 1 and the common difference. a 4 = 18 a 7 = 9
Answers
The general rule for the sequence is an = -9 + (n-1)(9). The first term (a1) is -9 and the common difference is 9.
Explanation:Sequence Analysis:
To find the general rule for a sequence, we need to determine the pattern or relationship between the terms. In this case, we are given a4 = 18 and a7 = 9. To find the common difference, we subtract the two terms: 18 - 9 = 9. So, the common difference is 9. To find a1, we can use the formula: an = a1 + (n-1)d, where n is the term number and d is the common difference. Substituting n = 4, a4 = 18, and d = 9, we can solve for a1. 18 = a1 + (4-1)(9), which gives us a1 = 18 - 3(9) = 18 - 27 = -9. Therefore, the general rule for this sequence is an = -9 + (n-1)(9). The first term (a1) is -9 and the common difference is 9.
a^1 = 27
d = -3
Step-by-step explanation:
A sales associate in a department store earns a commission on each suit and each pair of shoes sold. One week, she earned $47 in commission for selling 3 suits and a pair of shoes. The next week, she earned $107 in commission for selling 7 suits and 2 pairs of shoes. How much commission does she earn for selling each suit and each pair of shoes? Solve by substitution.
Answers
3s+h=47
7s+2h=107
substitution property:
3s=47-h
s=(47-h)/3
plug it into the other equation and solve for h:
7((47-h)/3)+2h=107
distribute 7 and multiply 3 on both sides:
329-7h+6h = 321
329-h=321
-h=-8
h=8 pair of shoes
s=(47-8)/3=13 suits
What's a parabola? What's a hyperbola?
Answers
Hyperbola:
In mathematics, a hyperbola (plural hyperbolas or hyperbolae) is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows
Hope this Helps
Given a slope of and the points left-parenthesis 220 comma 500 right-parenthesis and left-parenthesis 140 comma 350 right-parenthesis, which is the correct equation in point-slope form?
Answers
median mode mean and range on 84 45 10 28 75 63 16 55
Answers
10, 16, 28, 45, 55, 63, 75, 84
__________________
MEDIAN: Find the number in the middle of the set.
10, 16, 28, 45, 55, 63, 75, 84
There cannot be two medians, so you find the number between 45 & 55.
MEDIAN = 50
_________________
MEAN: Find the average by adding up all of the numbers and dividing them by how many numbers there are.
10 + 16 + 28 + 45 + 55 + 63 + 75 + 84 = 376
376/8 = 47
MEAN = 47
________________
MODE: The number that occurs most often. If no number repeats, there's no mode.
THERE IS NO MODE
________________
RANGE: The difference between the largest and smallest value in the set. Subtract the largest (84) and smallest (10) value.
84 - 10 = 74
RANGE = 74
Median: 50. Median is when you sort every number numerically and find which number is in the middle. Since there are 8 numbers, there are 2 numbers you'd find the number equally in between each of those 2 numbers. That number being 50.
Mode: There is no mode. Mode is the number that is "most frequent" or is repeated the most in the number sequence.
Range: 74. Range is when you subtract the smallest number of the sequence from the largest number.
I hope this helps!
Choose any numbers for he first column that will correctly complete the table.
Answers
2. Any number between 9,425 - 9,429
Number: 9,440
To finance her community college education, Sarah takes out a loan for $3700. After a year Sarah decides to pay off the interest, which is 5% of $3700. How much will she pay?
Answers
3700 + 0.05(3700)
But, if we want to make it shorter:
1.05(3700)
Now you just multiply(you may want to use a calculator)
1.05(3700) = 3885
She will pay $3885
A basket is filled with 8 white eggs and 10 brown eggs. Half of the white eggs are cracked. An egg is randomly selected from the basket. What is the probability that it is a cracked, white egg?Write the answer in a fraction in simplest form
Answers
Number of brown eggs = 10
Total sample = 8+10 = 18
Number of broken eggs = 4 white
P(broken egg) = 4/18 = 2/9
how long will it take to triple the amount of $500 if you invest it at a rate of 6% compound annually