Answers
The solution to the geometric sequence in the question are;
First part;
r = 3
\(a_{8} = 8748 \)
Second part;
r = 4
\(a_{6} = 9216 \)
Practice:
r = 8
\(a_{7} = 0.3125 \)
Third part;
Please see the detailed reasons in following section
Fourth part;
\( {a}_{n} = 4 × {a}_{n-1}\)
\( {a}_{n} = 0.2 × {a}_{n-1}\)
How can the geometric sequence be evaluated?First part;
The formula for geometric progression can be presented as follows;
\( a_{n} = a_{1} \times {r}^{n - 1} \)
\(a_{4} =108 = a_{1} \times {r}^{4 - 1} \)
Where;
\(a_{1} = 4 \: and \: a_{4} = 108\)
We have;
\(a_{4} =108 = 4 \times {r}^{4 - 1} = 4 \cdot {r}^{3} \)
Which gives;
\( {r}^{3} = \frac{108}{4} = 27\)
\(r = \sqrt[3]{27} = 3\)
r = 3
Therefore;
\(a_{8} = 4 \times {3}^{7} = 8748 \)
Second part;
Where;
\(a_{1} = 9 \: and \: a_{3} = 144\)
Therefore;
\( {r}^{2} = \frac{144}{9} = 16\)
\(r = \sqrt{16} = 4\)
r = 4
Which gives;
\(a_{6} = 9 \times {4}^{5} = 9216 \)
Practice;
\(a_{1} = 3 \: and \: a_{4} = 1536\)
Therefore;
\( {r}^{3} = \frac{1536}{3} = 512\)
\(r = \sqrt[3]{512} = 8\)
r = 8
\(a_{1} = 20 \: and \: a_{3} = 5\)
Therefore;
\( {r}^{2} = \frac{5}{20} = 0.25\)
\(r = \sqrt{0.25} = 0.5\)
Which gives;
\(a_{7} = 20 \times {0.5}^{6} = 0.3125 \)
Third part
Recursively means expression in terms of previous terms
The meaning of the equation is that each term of a geometric sequence is given by the product of the common ratio and the previous term
Fourth part;
The recursive formula for the sequence, {2, 8, 32, 128...} is found as follows;
r = 8/2 = 4
Therefore;
\( {a}_{n} = 4 × {a}_{n-1}\)
Part;
The sequence is {200, 40, 8, 1.6...}
The common ratio is; 40/200 = 0.2
The recursive formula is therefore;
\( {a}_{n} = 0.2 × {a}_{n-1}\)
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Related Questions
Find the equation of the parabola with focus (5,0) and directrix x =5
Answers
Answer:
y²=20x
Step-by-step explanation:
Note: I'm assuming you mean x=-5 for the directrix because what you're asking isn't possible
Since we are given a horizontal directrix, the parabola must also be horizontal.
Horizontal Parabola:
(y-k)² = 4p(x-h)
Vertex: (h, k)
Focus: (h+p, k)
Directrix: x = h - p
Since the focus of the parabola is (5,0), then k=0 and h+p=5. We also know that since the directrix is x=-5, then -5=h-p. If we set these equations equal to each other, we can solve for h and p:
h+p=5
h-p=-5
2p=10
p=5
Since p=5, then h=0. Therefore, we have for our equation of the parabola:
(y-k)² = 4p(x-0)
(y-0)² = 4(5)(x-0)
y²=20x
Find the value of the indicated length(s) in ⨀C. A and B are points of tangency. Simplify all radicals.
Answers
The length of the arc is 7 units, or (7/360) × (180 - 0) = 7.
What is Length?Length is a measure of distance from one end to the other. It is commonly used to quantify the size of objects, the extent of space, and the magnitude of a certain phenomenon. Length can be measured in a variety of ways, such as feet, meters, miles, and kilometers, as well as by other units of measurement, like inches and centimeters. It is also used to measure the duration of time, such as seconds, minutes, and hours. Length is a fundamental concept in mathematics and physics, as it is an important part of measurements and calculations.
The length of ⨀C is 7 units. To find the length of the arc between A and B, we use the formula for the length of an arc:
L = (⨀C/360) × (θB - θA)
where θA and θB are the angles formed by the two points of tangency. Since the points of tangency lie on the x-axis, θA = 0 and θB = 180. Therefore, the length of the arc is 7 units, or (7/360) × (180 - 0) = 7.
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No LINK Easy math please help is this liner y=2\x +1 explain please too
Answers
Answer:
It is not linear
Step-by-step explanation:
If you plug that function into Desmos graphing Calculator, you can see there are two leparate lines and they are not straight.
Use a geometric tool to draw a circle. Draw and measure a radius and a diameter of the circle .
Answers
Answer:
Attached is an example of a circle with a radius of 5 and a diameter of 10.
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Read the following prompt and type your response in the space provided.
Describe the relationship between the probability of an event and its complement.
If the probability of an event is 0.95, what is the probability of its complement?
Answers
The probability of the complement of the event is 0.05.
The complement of an event is the probability of that event not occurring. The relationship between the probability of an event and its complement is that they always add up to 1.
Therefore, if the probability of an event occurring is p, then the probability of its complement not occurring is 1-p.
In the case where the probability of an event is 0.95, the probability of its complement not occurring would be 1-0.95 = 0.05. This means that the probability of the complement of the event is 0.05.
This concept is important in probability theory and is used to calculate the probabilities of events and their complements. It allows us to consider all possible outcomes of a given situation and calculate the likelihood of each of them.
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Complete the table below to solve the equation 2.5x − 10.5 = 64(0.5x)
Answers
| x | 2.5x - 10.5 | 64(0.5x) |
|-------|-----------------|--------------|
| 0 | -10.5 | 0 |
| 2 | 2 | 64 |
| 4 | 7 | 128 |
| 6 | 11 | 192 |
By substituting different values of x into the equation, we can see that there is no single value of x that satisfies the equation for both sides. Therefore, there is no solution to the given equation.
Please do this carefully as i can't afford to get this wrong
Answers
The solutions to x = 4 are: (4, 1). The other ordered pairs are not solutions to the equation.
What is Set theory ?
Set theory is a branch of mathematical logic that deals with the study of sets, which are collections of objects. The objects in a set are called elements or members of the set.
The basic idea of set theory is to study the properties of sets and their relationships with other sets. Set theory provides a foundation for most of modern mathematics, as it provides a way to define mathematical objects in terms of sets and to reason about them using set-theoretic operations.
In set theory, the most basic concepts are sets, elements, and subsets. A set is a collection of distinct objects, which can be anything from numbers to colors to people. An element is a member of a set, and a subset is a set whose elements are all contained in another set.
To determine whether each ordered pair is a solution to x = 4, we need to check whether the value of x in each pair is equal to 4.
For the pair (4, 1), the value of x is 4, so it is a solution to x = 4.For the pair (-6, 0), the value of x is not 4, so it is not a solution to x = 4.For the pair (-3, 4), the value of x is not 4, so it is not a solution to x = 4.For the pair (5, -7), the value of x is not 4, so it is not a solution to x = 4.Therefore, the solutions to x = 4 are: (4, 1). The other ordered pairs are not solutions to the equation.
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the product of 9 and sum of a number x and 12
Answers
Answer:
9(x + 19)
Step-by-step explanation:
Product is a multiplication key word where you'll usually always put parenthesis when multiplying, and where the keyword sum comes you'd add x and 12 for your equation :)
A. (0,60)
B. (80,80)
C. (7,70)
D. (8,90)
Answers
Answer:
Most likely C
Step-by-step explanation:
where's is the other info. If no there info is provided then its most likely c because there's an obvious relationship. If I didn't help delete my answer thx.
Lesson 17: Use the Four Operations to Solve Problems Cool Down: Andre's Balloons Andre has 125 balloons. He and 4 friends hung up some balloons for a party at school and now there are 80 balloons left. If each person hung up the same number of balloons, how many balloons did each person hang up? 1. Write an equation with a letter for the unknown quantity to represent the situation. 2. Solve the problem. Explain or show your reasoning.
Answers
a) Using the four basic mathematical operations, the number of balloons that each person hang up is 9.
b) An equation representing the situation is x = (125 - 80)/5.
What are the mathematical operations?The four basic mathematical operations include addition, subtraction, division, and multiplication.
The mathematical operations provide solutions to mathematical problems using operands.
What is an equation?An equation is a mathematical statement showing that two or more mathematical expressions are equal or equivalent.
The total number of balloons that Andre has = 125
The number of balloons remaining after hanging some for the school party = 80
The difference (number of balloons used) = 45 (125 - 80)
The number of friends who hang the balloons = 5
The number of balloons hung by each friend of Andre = 9 (45/5)
Thus, we can conclude that each of the 4 friend and Andre hung 9 balloons, with 80 remaining.
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I need some help with this math problem. I really appreciate it. thank you very much!
Margaret's savings account had $500 in it last month. This month it has $545.
Answers
Answer:
9% increase
Step-by-step explanation:
you have $8 and a $5 off coupon to buy snacks at a concession stand. Write and solve an inequality to represent the regular price of snacks. you can buy if you use the coupon
Answers
An inequality to represent the regular price of snacks, if i can buy using the coupon, x ≤ $13
What are inequalities?Inequalities are the comparison of mathematical expressions, whether one quantity is greater or smaller in comparison to another quantity.
We use these symbols to represent inequalities, '>' , '<', '≥', '≤'
Given that,
There are two coupons available, $8 and a $5 off on buying snacks
Let's call the regular price of the snacks "x".
Since you have a $5 off coupon,
the price you would actually pay would be x - $5.
And since you only have $8, the price you pay for the snacks cannot be greater than $8:
x - $5 ≤ $8
Adding $5 to both sides:
x ≤ $13
So, the regular price of the snacks must be less than or equal to $13 if you want to use the coupon and still have enough money to pay for them.
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Your challenge is to create a cylindrical can that minimizes the cost of materials but must hold 100 cubic inches. The top and bottom of the can cost $0.014 per square inch, while the sides cost only $0.007 per square inch. Show how you did it too?
Answers
Answer:
\(Radius = 1.997\ in\) and \(Height = 7.987\ in\)
\(Cost = \$1.05\)
Step-by-step explanation:
Given
\(Volume = 100in^3\)
\(Cost =\$0.014\) -- Top and Bottom
\(Cost =\$0.007\) --- Sides
Required
What dimension of the cylinder minimizes the cost
The volume (V) of a cylinder is:
\(V = \pi r^2h\)
Substitute 100 for V
\(100 = \pi r^2h\)
Make h the subject
\(h = \frac{100 }{\pi r^2}\)
The surface area (A) of a cylinder is:
\(A = 2\pi r^2 + 2\pi rh\)
Where
\(Top\ and\ bottom = 2\pi r^2\)
\(Sides = 2\pi rh\)
So, the cost of the surface area is:
\(C = 2\pi r^2 * 0.014+ 2\pi rh * 0.007\)
\(C = 2\pi r(r * 0.014+ h * 0.007)\)
\(C = 2\pi r(0.014r+ 0.007h)\)
Substitute \(h = \frac{100 }{\pi r^2}\)
\(C = 2\pi r(0.014r+ 0.007*\frac{100 }{\pi r^2})\)
\(C = 2\pi r(0.014r+ \frac{0.007*100 }{\pi r^2})\)
\(C = 2\pi r(0.014r+ \frac{0.7}{\pi r^2})\)
\(C = 2\pi (0.014r^2+ \frac{0.7}{\pi r})\)
Open bracket
\(C = 2\pi *0.014r^2+ 2\pi *\frac{0.7}{\pi r}\)
\(C = 0.028\pi *r^2+ \frac{2\pi *0.7}{\pi r}\)
\(C = 0.028\pi *r^2+ \frac{2 *0.7}{r}\)
\(C = 0.028\pi *r^2+ \frac{1.4}{r}\)
\(C = 0.028\pi r^2+ \frac{1.4}{r}\)
To minimize, we differentiate C w.r.t r and set the result to 0
\(C' = 0.056\pi r - \frac{1.4}{r^2}\)
Set to 0
\(0 = 0.056\pi r - \frac{1.4}{r^2}\)
Collect Like Terms
\(0.056\pi r = \frac{1.4}{r^2}\)
Cross Multiply
\(0.056\pi r *r^2= 1.4\)
\(0.056\pi r^3= 1.4\)
Make \(r^3\) the subject
\(r^3= \frac{1.4}{0.056\pi }\)
\(r^3= \frac{1.4}{0.056 * 3.14}\)
\(r^3= \frac{1.4}{0.17584}\)
\(r^3= 7.96178343949\)
Take cube roots of both sides
\(r= \sqrt[3]{7.96178343949}\)
\(r= 1.997\)
Recall that:
\(h = \frac{100 }{\pi r^2}\)
\(h = \frac{100 }{3.14 * 1.997^2}\)
\(h = \frac{100 }{12.52}\)
\(h = 7.987\)
Hence, the dimensions that minimizes the cost are:
\(Radius = 1.997\ in\) and \(Height = 7.987\ in\)
To calculate the cost, we have:
\(C = 2\pi r(0.014r+ 0.007h)\)
\(C = 2* 3.14 * 1.997 * (0.014*1.997+ 0.007*7.987)\)
\(Cost = \$1.05\)
Help pls part b is how many batches of jam can the farmer make
Answers
The equation we need to find will relate the amount of remaining berries to the number of batches of jam the farmer can make is 16 = 2 1/2 + 2 1/4b (option b)
To start with, we know that the farmer picks 16 quarts of berries. Out of those, 2 1/2 quarts cannot be used, which means the farmer has 16 - 2 1/2 quarts of berries that can be used to make jam.
Now, the recipe requires 2 1/4 quarts of berries to make one batch of jam. Let's represent the number of batches of jam the farmer can make with the remaining berries as "b".
Therefore, the equation we need to find will relate the amount of remaining berries to the number of batches of jam the farmer can make is written as,
=> 16 = 2 1/2 + 2 1/4b
Hence the correct option is (b).
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
The scaled triangle will be larger than the initial size by a factor 2.
The scaled square will be smaller than the initial side by a factor 4.
What is dilation?Dilation refers to a transformation that changes the size of a geometric figure without altering its shape.
Dilation involves scaling an object by a certain factor, that might result in enlarging or reducing its dimensions uniformly in all directions.
Based on the given diagram, the new length and size of the object is calculated as follows;
For the triangle, (measure the length with ruler)
new lengths = 2 times the original lengthoriginal length = 2 cm, new length = 4 cmthe new size of the triangle will increase by a factor 2For the square; (measure the length with ruler)
new lengths = 0.25 times the original lengthoriginal length = 4 cm, new length = 2 cmthe new size of the square will decrease by a factor 4Learn more about dilation here: brainly.com/question/20482938
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The formula for an account that earns
compound interest is Pt = P0 ⋅ (1 + r)
t
,
where Pt
represents the balance in the
account after t years, P0 represents the
initial amount of the deposit, and r
represents the interest rate.
Carrie is considering depositing $1480 into
an account that pays compound interest.
How much will be in her account if she
receives 1.9% compound interest for
10 years? Round to the nearest cent.
Answers
After 10 years with a Compound interest rate of 1.9%, the amount in Carrie's account will be approximately $1777.87.
The amount that will be in Carrie's account after 10 years with compound interest, we can use the formula Pt = P0 ⋅ (1 + r)^t.
Given:
P0 = $1480 (initial deposit)
r = 1.9% = 0.019 (interest rate as a decimal)
t = 10 (number of years)
Substituting these values into the formula, we get:
Pt = $1480 ⋅ (1 + 0.019)^10
Using a calculator, we can evaluate the expression inside the parentheses:
(1 + 0.019)^10 ≈ 1.201223
Now we can calculate the final amount in Carrie's account:
Pt ≈ $1480 ⋅ 1.201223
Pt ≈ $1777.87
Therefore, after 10 years with a compound interest rate of 1.9%, the amount in Carrie's account will be approximately $1777.87.
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Complete the following statement of congruence:
ANMO
Answers
Answer:
SRT IS your answer.hope this help
Answer:
STR
Step-by-step explanation:
a p ec
HELP ME!
A standard I.Q. test produces normally distributed results with a mean of 104 and a standard deviation of 16 for 52,000 students in grade 12 in the state. Approximately how many of these students would have I.Q.s above 140?
Answers
Answer: approx 1196 students.
Step-by-step explanation:
As known for normal distribution 95.4% of all results are situating at +-2*s distance from the mean. (s is the standard deviation)
2s=16*2=32 . The mean +2s= 104+32=136 = approx 140.
95.4% from 52000 = 49608 students. The residual amont ( which is out of the border mean+-2s)= 52000-49608=2392
Because of the normal distribution simmetry the number of the students which has IQ 140 and more is twice less than 2392.
N=2392:2=1196
What is the explicit formula for this sequence?
-7, -3, 1, 5,
Answers
Step-by-step explanation:
-7, -3, 1, 5, ...
To get to -3 you must add 4.
To get to 1 you must add 4.
To get to 5 you must add 4.
The formula/rule is to add 4.
The list of accounts of Guardian Company contained the following information:
Accounts Amount $
Sales 750,000
Sales Returns and Allowances 20,000
Rent Expense 5,000
Purchases 600,000
Sales Discounts 7,000
Purchase Returns and Allowances 25,000
Cost of Goods Sold ?
Interest Revenue 15,000
Sales commission 15,000
Purchase Discounts 11,000
Interest Expense 10,000
Freight-out 2,000
Store Salaries Expense 50,000
Freight-in 19,000
Utilities Expense 28,000
Depreciation Expense 7,000
Dividend revenue 5,000
Beginning inventory 45,000
Rent Revenue 10,000
Ending inventory 55,000
Lawsuit defrayal expense 8000
Accumulated depreciation 15000
Instruction:
Use the above information to prepare a multiple-step income statement for the year ended
December 31, 2019. (Show the calculation of COGS)
Answers
Answer:
sorry I don't know the answer ,but I want to ask u something ,r u a accounting student if yes please comment.i am also a accounting student but on learning stage so I don't know the answer,
Whats 5-5-5-5-5-5x5757575
Answers
Answer:
-28787890
Step-by-step explanation:
What’s the difference between solving a whole number and a fraction?
There’s these two methods I saw but not sure when I should use them when I do stumble on a problem.
1 method: start by multiply the numerator towards the whole number and once u do then divide the numerator and denominator separately.
2 method: start by giving the whole number a 1 of the denominator and find the lCD of the fraction and start finishing the problem from either adding or subtracting.
Answers
Answer:
hey
Step-by-step explanation:
Select the correct answer.
Which statement correctly compares the graph of function g with the graph of function ??
FE) = e²-
g(x) = ² - 4
O A.
OB.
O C.
O D.
The graph of function g is a horizontal shift of the graph of function to the right.
The graph of function g is a vertical stretch of the graph of function f.
The graph of function g is a vertical compression of the graph of function f.
The graph of function g is a horizontal shift of the graph of function f to the left.
Reset
Next
Answers
A statement that correctly compares the graph of function g with the graph of function f include the following: C. The graph of function g is a vertical compression of the graph of function f.
What is a dilation?In Mathematics and Geometry, a dilation is a type of transformation which typically transforms the dimension (size) or side lengths of a geometric object, without affecting its shape.
Therefore, the dimension or side lengths of the dilated geometric object would be stretched or compressed (shrunk) depending on the scale factor that is applied.
When the parent function \(f(x) = e^x -4\) is vertically compressed by a scale factor of 1/2, the transformed function g(x) is given by the following equation;
g(x) = kf(x)
g(x) = 1/2f(x)
\(g(x) = \frac{1}{2} e^x -4\)
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Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to $\frac{21}{4}$ times the largest of the seven integers. What is the smallest integer that Pearl wrote down?
Answers
The smallest integer that Pearl wrote down is -12.Let's assume the smallest integer that Pearl wrote down is represented by the variable "x."
According to the given information, the sum of the seven consecutive integers is equal to $\frac{21}{4}$ times the largest integer.
The sum of consecutive integers can be expressed as the sum of an arithmetic series. The sum of an arithmetic series can be calculated using the formula:
Sum = (n/2)(first term + last term)
In this case, the first term is x and the last term is x + 6 (since there are seven consecutive integers). Therefore, the sum of the integers can be written as:
Sum = (7/2)(x + (x + 6))
Simplifying the equation:
(7/2)(2x + 6) = (21/4)(x + 6)
Multiplying both sides by 4 to eliminate the fractions:
14x + 42 = 21x + 126
Subtracting 14x from both sides:
42 = 7x + 126
Subtracting 126 from both sides:
-84 = 7x
Dividing both sides by 7:
-12 = x.
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change the following percentages to fractions 92%, 63%
Answers
To change the following percentages to fractions, we just have to divide them by 100:
\(\frac{92}{100}\)If the question says you have to simplify, then you simplify:
\(\frac{92}{100}=\frac{23}{25}\)\(\frac{63}{100}\)63/100 can't be more simplified.
answer?? please i need this
Answers
Answer:
1+78=133
1=133-78
1=55
Find the perimeter of a parallelogram whose base is 8cm and another side is 12cm
Answers
A parallelogram
P=2(a+b)
The answer is 64
P=2(a+b)=2·(24+8)=64
A jar of peanut butter contains 50 tablespoons of peanut butter.
How many sandwiches can you make from the jar of peanut butter, assuming you have plenty of bread and jelly?
A. 25 sandwiches
B. 9 sandwiches
C. 10 sandwiches
D. 50 sandwiches
Answers
Answer:
the correct answer is A. 25 sandwiches.
Step-by-step explanation:
Assuming you have plenty of bread and jelly, you can make 25 sandwiches from the jar of peanut butter.
Each sandwich typically requires 2 tablespoons of peanut butter, one slice of bread with peanut butter and one slice of bread with jelly.
So, if you have 50 tablespoons of peanut butter, you can make 25 sandwiches with it, because 50 / 2 = 25.
Therefore, the correct answer is A. 25 sandwiches.
Answer: 25
Step-by-step explanation:
We have 50 tablespoons of peanut butter and we know that it requires 2 tablespoons to make a single sandwich. In order to find how many sandwiches we can make with our 50 tablespoons, we would have to do 50 divided by 2.
2+2...=50
Which job would you rather work at and why?
Job A: 40 hours a week at an hourly rate of $12.75
Job B: 43 hours a week at a rate of $12.00 an hour?
Answers
Answer:
Job A, less hours and only a difference of money in Job B is 6 dollars.
Step-by-step explanation:
Job A: I multiplied 40 x 12.75 = $510
Job B: Multiple 43 x 12.00 = $516
Job A: Work less, money difference to Job B is 6 dollars
Job B: Work longer, 6 dollar gain difference from job A
Select the correct answer.
Which is the best objective summary of this passage?
A. A boy is so drawn to the music that he drops the bundle with all his possessions to the ground to listen better. He sees a girl and watches her dance. Some men attempt to frighten him, but they lose him in the woods.
B. A boy who enjoys adventure is traveling through some woods when he sees a girl singing and dancing. He is too afraid to approach her, so he finds a place to sleep. He encounters some men who attack him, but he is able to escape. The girl finds him in the morning.
C. A boy is traveling alone and encounters interesting musical tones and a girl dancing. He hears some strange voices before falling asleep. When he awakens the next morning, he is wondering if the events were real or just in his dreams. The girl appears at the end.
D. A boy is traveling alone when he stops at a ragged cabin, drawn in by the music and warmth of the fire,and it is there that he meets the girl who likes to dance. He is unable to stay because he is afraid of the dark. He meets up with the girl later.
Answers
The best objective summary is that D. A boy is traveling alone when he stops at a ragged cabin, drawn in by the music and warmth of the fire,and it is there that he meets the girl who likes to dance. He is unable to stay because he is afraid of the dark. He meets up with the girl later.
What is objective summary?It should be noted that an objective summary simply means the summary that doesn't include the opinions or judgement about what is written in the text.
It should be noted that the story was about a boy who was travelling and was drawn by a music. He met a girl at the place and eventually saw her later.
In conclusion, the correct option is D.
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