A sequence can be both arithmetic and geometric, and this is illustrated where terms follow both an arithmetic and geometric progression.
Yes, a sequence can be both arithmetic and geometric. An example of such a sequence is when the terms of the sequence follow both an arithmetic progression, where the difference between consecutive terms is constant, and a geometric progression, where each term after the first is found by multiplying the previous term by a fixed, non-zero number.
3.4 divided by 0.16728
A stack of one hundred fifty cards is placed next to a ruler, and the height of the stack is measured to be
3/4 inches.
How thick is one card?
Answer: One card is 0.005 inches thick.
Step-by-step explanation:
Since we have given that
Number of cards in a stack = 150
Thickness of the stack = [tex]\dfrac{3}{4}\ inches[/tex]
So, Thickness of each card is calculated by "Unitary method":
Thickness of 150 cards = [tex]\dfrac{3}{4}\ inches[/tex]
Thickness of 1 card is given by
[tex]\dfrac{3}{4\times 150}\\\\=\dfrac{1}{4\times 50}\\\\=\dfrac{1}{200}\\\\=0.005\ inches[/tex]
Hence, One card is 0.005 inches thick.
Given the point and it''s image, determine the scale factor. A (3, 6) A'' (4.5, 9) G'' (3, 6) G (1.5, 3) B (2, 5) B'' (1, 2.5).
Final answer:
The scale factors for the points given are 1.5 for A to A', indicating an enlargement, and 0.5 for B to B', indicating a reduction. G to G' also indicates a reduction with a factor of 0.5.
Explanation:
To determine the scale factor given the point and its image, you can find the ratio between the coordinates of the image and the original coordinates. Let's analyze the pairs of points you've provided:
A (3, 6) and A' (4.5, 9)
G (1.5, 3) and G' (3, 6)
B (2, 5) and B' (1, 2.5)
We can find the scale factor by dividing the x-coordinates of the image by the original x-coordinate and doing the same for the y-coordinates. For point A:
Scale factor for x: 4.5 / 3 = 1.5
Scale factor for y: 9 / 6 = 1.5
For point G, we see that it's actually the reverse (original to image), but you can still calculate:
Scale factor for x: 3 / 1.5 = 2
Scale factor for y: 6 / 3 = 2
Lastly, for point B:
Scale factor for x: 1 / 2 = 0.5
Scale factor for y: 2.5 / 5 = 0.5
So, the scale factors for A to A' and for B to B' are 1.5 and 0.5, respectively, showing that A to A' is an enlargement while B to B' is a reduction. For G to G', the reverse is a reduction with a factor of 0.5.
calculate each of the following by using scientific notation and product rule. write the answer in scientific notation. 2.3 x 10^4 times 4.2 x 10^6
find the intercept of the line 15.579x +23.354y=13.997. please round your answer
You are given n = 5 measurements: 5, 3, 3, 8, 8. (a) calculate the sample mean, x. (enter your answer to one decimal place.)
the moon is 250,000 miles away. how many feet is it from earth
To convert the distance from the Earth to the Moon from miles to feet, multiply 250,000 miles by the number of feet in a mile, which is 5,280. This calculation yields a result of approximately 1.32 billion feet.
The distance from the Earth to the Moon is given as 250,000 miles. To convert this distance from miles to feet, we use the fact that there are 5,280 feet in a mile. Thus, we multiply the distance in miles by the number of feet per mile.
To find the distance in feet, perform the following calculation:
Multiply the distance in miles by the number of feet per mile: 250,000 miles × 5,280 feet/mile.
This equals 1,320,000,000 feet.
Therefore, the Moon is approximately 1.32 billion feet away from Earth.
What is the equivalent decimal for 67/100,1/100,81/1000,9 6/10, 3 21/100,5 3/100, 4 77/1000
Find, correct to the nearest degree, the three angles of the triangle with the vertices d(0,1,1), e( 2, 4,3) − , and f(1, 2, 1)
Sean lives about 15.5 miles from the airport. Which number rounds to 15.5 when rounded to the nearest tenth?
Your car gets about 30 miles per gallon. You are planning to drive to see your friends who live about 930 miles away. How many gallons of gas will you need to purchase to make the trip to see your friends and return home? State your anwser to the nearest gallon?
For the round trip of 930 miles each way, you will need to purchase about 62 gallons of gas, given a car's gas mileage of 30 miles per gallon.
To calculate the gallons of gas needed for the round trip, follow these steps:
Calculate the total distance for the round trip.
The round trip distance is twice the one-way distance.
Round trip distance = 2 * 930 miles = 1860 miles.
Find the number of gallons required for the round trip.
Divide the total distance by the car's gas mileage (miles per gallon).
Gallons required = Round trip distance / Gas mileage
Gallons required = 1860 miles / 30 miles per gallon
Perform the division.
Gallons required = 62 gallons.
Round the answer.
Since you cannot purchase a fraction of a gallon, round the answer to the nearest gallon.
You will need to purchase approximately 62 gallons of gas for the round trip.
So, to make the trip to see your friends and return home, you will need to purchase about 62 gallons of gas.
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Sue and jonah shose nummbers for a place value game.Sue chose the number one hundred.Jonah chose five million for his number.who chose the greater number
A PS4 uses 8.8 watts when on stand-by mode. How much carbon dioxide is emitted into the atmosphere by using this electricity?
In the citation, davis v. baugh industrial contractors, inc. 159 wash.2d 413, 150 p.3d 545 (2007) what does the "2d." represent
Multiplication Property of Inequality -1/2x<-12 simplify it all the way through
Nissan Appliances bought two dozen camcorders at a total cost of $3,864. The markup on the camcorders is 30% of the selling price. What was the original selling price of each camcorder?
what is a natural number
The set of counting numbers {1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ...} is called the set of natural numbers. The natural numbers begin at 1 and go on indefinitely.
Three examples of natural numbers are below.
642,000
440
81
Lee King Earns $5 per hour. Lee's brother, Nosmo, starts working three hours after Lee and earns $7 per hour. Write an equation that says each earned the same amount. Solve to find out how long each brother worked.
A car traveled 63 miles on 3 gallons of gas. What proportion can you set up to determine how many miles, m, the car can travel on 7 gallons of gas?
Frederick is working on a number puzzle and discovers that the product of the two base numbers is exactly twice as large as the sum of those same base numbers.
Help on this, please?
The two base numbers can be represented as x and y. Setting them equal in the equation x * y = 2(x + y) allows you to solve for them. One solution is x = 2 and y = 2.
Explanation:This problem can be solved using basic algebra. Let's assume the two base numbers be x and y. Since the product of the two base numbers (x * y) is twice as large as the sum of those numbers (x + y), we can create the following equation: x * y = 2(x + y).
To solve for x and y, you may set x and y to different numbers and check if they satisfy the equation. One solution is x = 2 and y = 2, since 2*2 = 2(2+2). Similarly, other pairs of numbers may also satisfy this equation based on the specific constraints of Frederick's number puzzle.
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To solve the number puzzle, we need to find two base numbers whose product is exactly twice as large as their sum. By rearranging the terms and factoring, we can find the base numbers that satisfy the equation. An example solution is provided with a = 3 and b = 6.
Explanation:To solve the number puzzle, we need to find two base numbers whose product is exactly twice as large as their sum. Let's represent the base numbers as 'a' and 'b'. According to the information given, we have the equation:
ab = 2(a + b).
We can simplify the equation by rearranging the terms and factoring: ab - 2a - 2b = 0. Using a technique called 'completing the square', we can rewrite the equation as (a - 2)(b - 2) = 4.
From here, we can choose different values for 'a' and 'b' that satisfy the equation, such as a = 3 and b = 6. Therefore, the base numbers for the number puzzle are 3 and 6.
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Answer:
-7(k+9)=9(k-5)-14k
A rectangular box has length 14 inches, width 11 inches, and a height of 16 inches. find the angle between the diagonal of the box and the diagonal of its base. the angle should be measured in radians.
During first semester, the ratio of the number of students in our class to the number of students in gym class was 2 to 7. However, the art classes were really small, and the gym classes with large, so the principal change the students classes for second semester. In second semester, the ratio of the number of students in our class to the number of students in gym class was 5 to 4. If 75 students were in our class second semester, how many were in our class in gym class first semester.
What is the common ratio for this geometric sequence?
Answer: The correct option is (C) [tex]\dfrac{1}{4}.[/tex]
Step-by-step explanation: We are given to find the common ratio for the following geometric sequence :
64, 16, 4, 1, . . .
We know that
if a(n) represents the n-th term of a geometric series, then the common ratio is given by
[tex]r=\dfrac{a(n+1)}{a(n)},~~~n=0,~1,~2,~~.~~.~~.[/tex]
For the given geometric sequence, we have
a(1) = 64, a(2) = 16, a(3) = 4, a(4) = 1, . . .
So, the common ratio r will be given by
[tex]r=\dfrac{a(2)}{a(1)}=\dfrac{a(3)}{a(2)}=\dfrac{a(4)}{a(3)}=~~.~~.~~.[/tex]
We have
[tex]\dfrac{a(2)}{a(1)}=\dfrac{16}{64}=\dfrac{1}{4},\\\\\\\dfrac{a(3)}{a(2)}=\dfrac{4}{16}=\dfrac{1}{4},\\\\\\\dfrac{a(4)}{a(3)}=\dfrac{1}{4},~~\cdots[/tex]
Thus, the required common ratio for the given geometric sequence is [tex]\dfrac{1}{4}.[/tex]
Option (C) is CORRECT.
you have a secret that you to one person every hour each of the people that know the secret tells one person. The number of people who know when is N and T is the number of hours since you told the first person. Is an a linear function s of t?
An equation that is not true for any values of the variable is called a(n
Answer:
I am pretty sure this is either a Linear Equation or called a Contradiction
An equation that is not true for any values of the variable is called a false or inconsistent equation.
Explanation:An equation that is not true for any values of the variable is called a false equation or an inconsistent equation. This means that the equation has no solution that satisfies the given equation. For example, if we have the equation x + 3 = x + 5, subtracting x from both sides gives us 3 = 5, which is not true for any value of x.
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HELP ME PLEASE!!
-1.3 ≥ 2.9 -0.6r
Graph the solution
The solution to the inequality -1.3 ≥ 2.9 -0.6r, is r ≤ 7. This is represented on a graph by placing a closed circle on 7 and drawing a line to the left, to represent all numbers less than 7.
Explanation:To solve this inequality, -1.3 ≥ 2.9 -0.6r, first, we isolate the variable r (which represents solving for 'r'). Start by subtracting 2.9 from both sides of the inequality.
This gives us -4.2 ≥ -0.6r. Then divide both sides by -0.6. However, remember when dividing or multiplying an inequality by a negative number, the direction of the inequality changes. So, it becomes r ≤ 7.
When graphing this inequality, you will place a closed circle at 7 (showing that point is included) and draw a line to the left from 7, extending to infinity (since all numbers less than 7 satisfy the inequality).
The graph represents the mathematical solution to the inequality.
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x/21 = 3/63 solve the proportion
The time to fly between new york city and chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. what is the probability that a flight is less than 135 minutes
Tiffany Baldwin earns $800 every week. Her federal income tax is $25. Her state tax is $11. Her FICA is 7.65% of his gross salary. She contributes 2% of her gross earnings to a 401K. She has $20 per paycheck deducted post-tax to pay for her gym membership. What are her pre-tax deductions?