Which represent geometric sequences? A marathon runner runs half of a race, then runs half the distance left to the finish line, then runs half the distance that still remains, and so on. The first movie rental costs $2, and each additional rental costs $1. 10, 1, 0.1, 0.01, … –4, 20, –100, 500, … –1, 5, 11, 17, 23, …
Answers
Answer:
Step-by-step explanation:
1). Let the length of a marathon race = x miles
Marathon runner runs this race in the sequence formed as,
[tex]\frac{x}{2},\frac{x}{4},\frac{x}{8}.........[/tex]
Common ratio = [tex]\frac{\frac{x}{4}}{\frac{x}{2}}[/tex]
= [tex]\frac{x}{4}\times \frac{2}{x}[/tex]
= [tex]\frac{1}{2}[/tex]
Therefore, it's a geometric sequence.
2). First movie rental cost = $2
Followed by each additional movie rental cost = $1
Therefore, rental of movies will be in the form of a linear equation,
y = 2x + 1
where x = number of movies
And y = Rental of movies
It's not a geometric sequence.
3). 10, 1, 0.1, 0.01.......
Ratio in 2nd and 1st term = [tex]\frac{1}{10}=0.1[/tex]
Ratio in 3rd and 2nd term = [tex]\frac{0.1}{1}=0.1[/tex]
Therefore, ratio in each term is common.
Sequence formed will be a geometric sequence.
4). [tex]\sum_{k=1}^{7}4(0.2)^{k-1}[/tex]
Expression represents a common ratio of 0.2,
Therefore, expression given will represent a geometric sequence.
5). -4, 20, -100, 500, ...........
Ratio of 2nd and 1st term = [tex]\frac{20}{-4}[/tex] = -5
Ratio of 3rd and 2nd term = [tex]\frac{-100}{20}[/tex]
= -5
There is a common ratio = -5
Therefore, it's a geometric sequence.
6). -1, 5, 11, 17.........
Ratio of 2nd and 1st term = [tex]\frac{5}{-1}=-5[/tex]
Ratio of 3rd and 2nd term = [tex]\frac{11}{5}=2.2[/tex]
-5 ≠ 2.2
Therefore, sequence is not a geometric sequence.
7). -500, 100, -20, 4........
Ratio of 2nd and 1st term = [tex]\frac{100}{-500}=-\frac{1}{5}[/tex]
Ratio of 3rd and 2nd term = [tex]\frac{-20}{100}=-\frac{1}{5}[/tex]
Answer:
I agree with person above
Step-by-step explanation:
Related Questions
In its second year of operation, a local internet provider's profits were $171,500. If this amount was 666% of the company's first-year profits, find the first-years profits
Answers
The first year profit of the local internet provider was $ 22,389.04.
What was the profit of a company in its second year of operation?
According to the statement, we find that the profit of the company in its second year of operation is 666 % greater than its profit in its previous year, that is, the profit in its second year of operation is 7.66 times the profit in its first year of operation. Then, the missing profit is found by using the following arithmetic expression:
x = 171,500 / 7.66
x = 22,389.04
The first year profit of the local internet provider was $ 22,389.04.
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Please guys help me please with this question please please please please
Answers
Answer:
x = 18
Step-by-step explanation:
Given:
160 total learners34 play soccer and rugby40 play soccer and hockey42 play hockey and rugby36 play soccer only72 play hockey8 play rugby only28 play none of these sportsx play all three sportsAs "x" learners play all three sports, the Venn diagram should have three overlapping circles labelled soccer (S), rugby (R) and hockey (H).
x play all three sports: Label the area that's in S, R and H with x.
8 play rugby only: Label the area that is R only with 8.
36 play soccer only: Label the area that is S only with 36.
28 play none of these sports: Place 28 outside the three circles.
34 play soccer and rugby: Place "34 - x" in the area that's in S and R.
40 play soccer and hockey: Place "40 - x" in the area that's in S and H.
42 play hockey and rugby: Place "42 - x" in the area that's in H and R.
72 play hockey
72 is the total for all the sections of H.
⇒ H = 72 - x - (40 - x) - (42 - x)
⇒ H = 72 - x - 40 + x - 42 + x
⇒ H = x - 10
Place "x - 10" in the area that is H only.
The total number of learners is 160.
Therefore, to find x, sum the areas of the Venn diagram and equal to 160:
⇒ 36 + 8 + 28 + 34 - x + x + 40 - x + 42 - x + x - 10 = 160
⇒ 36 + 8 + 28 + 34 + 40 + 42 - 10 - x + x - x - x + x = 160
⇒ 178 - x = 160
⇒ x = 178 - 160
⇒ x = 18
Finally, substitute x = 18 into the Venn diagram.
David wants to pack 574 cereal bars into bags of 10 and bags of 8. The number of bags of 8 is 2 more than the number of bags of 10. How many bags of 10 and 8 can David pack all the cereal bars into?
Answers
574 cereal bars will be placed in bags of 10 and bags of 8 by David. The number of bags of 8 is 33 and number of bags of 10 is 31.
Given that,
574 cereal bars will be placed in bags of 10 and bags of 8 by David. Two more bags of eight than bags of ten make up the total.
We have to find how many 10 and 8-bag sets of cereal bars can David fit.
Let us take,
x be number of bags of 8 and y be number of bags of 10.
So, we can write as
8x+10y=574→equation(1)
x=y+2→equation(2)
Taking the x value form equation(2) and putting in equation (1).
We get,
8(y+2)+10y=574
8y+16+10y=574
18y+16=574
18y=574-16
18y=558
y=558/18
y=31
We got y=31 substitute y value in equation(2).
x=31+2
x=33
Therefore, the number of bags of 8 is 33 and number of bags of 10 is 31.
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What would happen to a cell if the transport of materials across its membrane could not take place
Answers
If our cells couldn't control what crossed their membranes, either no molecules would make it across, or they'd be travelling willy-nilly and the internal environment would always be in flux.
Combine like terms to simplify the expression:
12x-3(3x-5)+24
Answers
Answer:
3(x+13)
Step-by-step explanation:
use the distributive property to multiply -3 by
3x -5
12x -9x + 15 + 24
then
combine 12x and -9x to get 3
add 15 + 24 to get 39
if you add all the prime numbers between 2 and 33 and then multiply it by itself y
Answers
Answer:
24964
Step-by-step explanation:
hope this works - btw this is not including 2 and 33
Dinesh has a goal of keeping his administrative tasks below 10% of his weekly hours. In which week(s) did he meet this goal? Be sure to show your work, list the percentages in the chart below, and answer the question. Administrative Hrs Total Hours
Answers
Dinesh met his goal of keeping administrative tasks below 10% of his weekly hours in Weeks 2, 3, and 4.
How are the percentages determined?The percentages of administrative tasks are computed by dividing the administrative hours worked by the total hours worked each week.
Percentages are ratios or portions of a variable in the whole number.
Data and Calculations:Administrative Hrs Total Hours Worked Admin % Goal Met?
Week 1 4.25 40 hours 10.625% No
Week 2 2.57 40 hours 6.425% Yes
Week 3 3.83 40 hours 9.575% Yes
Week 4 3.40 40 hours 8.500% Yes
Thus, Dinesh met his goal of keeping administrative tasks below 10% of his weekly hours in Weeks 2, 3, and 4.
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Question Completion:Administrative Hrs Total Hours Worked Admin % Goal Met?
Week 1 4.25 10 hours
Week 2 2.57 8 hours
Week 3 3.83 8 hours
Week 4 3.40 8 hours
The following expression gives an approximate value of the total average credit card debt in a U.S. household (in dollars)
t
years after 1995.
417
t
+
5850
Use this expression to predict what the total average credit card debt was or will be in the year 2014.
Answer: In the year 2014, the total average credit card debt for a U.S. household will be (or was)
dollars.
Answers
In the year 2014, the total average credit card debt for a U.S. household was 13,773 dollars.
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
How to predict the total average credit card debt in 2014?In order to predict the total average credit card debt in 2014, we would determine the number of years (t) from 1995 to 2014 and then substitute the value into the given expression as follows:
Number of years, t = 2014 - 1995
Number of years, t = 19 years.
Substituting the years into the expression, we have;
Total average credit card debt = 417t + 5850
Total average credit card debt = 417(19) + 5850
Total average credit card debt = 7,923 + 5850
Total average credit card debt = $13,773.
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Explain how to do -12 - (-98) + 7 - 3
Answers
Step by step explanation:
Since we know a negative minus a negative equals a positive then
-12 - -98 = 86
Then 86 + 7 = 93
And finally 93 - 3 = 90
Hope this helps mate
Convert the following quantities to the indicated units.
24 grams per cubic centimeter to how many pounds per cubic inch?
Answers
24 grams per cubic centimeters equals 0.867 pounds per cubic inches
How to convert the quantities to the indicated units?The quantity (x) is given as:
x = 24 grams per cubic centimeters
1 gram equals 0.00220462 pounds
So, we have:
x = 24 * 0.00220462 pounds per cubic centimeters
Evaluate
x = 0.05291088 pounds per cubic centimeters
1 cubic centimeters equals 0.0610237 cubic inches
So, we have
x = 0.05291088 pounds per 0.0610237 cubic inches
Rewrite as
x = 0.05291088/0.0610237 pounds per cubic inches
Evaluate
x =0.867 pounds per cubic inches
Hence, 24 grams per cubic centimeters equals 0.867 pounds per cubic inches
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MAYA WALKED 34 1/2 MILES . KALEB WALKED 24 1/2 MILES. HOW MANY MILES WS WALKED IN TOTAL
Answers
Answer:
Two halves make a whole
34 + 24 + (1/2 + 1/2)
34 + 24 + 1
PLEASE HELPb) Darragh is inflating a balloon in the shape of a sphere. When fully inflated, the balloon has a radius of 15 cm. (i) Find the volume of Darragh's balloon when it is fully inflated. Give your answer in cm³, in terms of it.
solutions pls
Answers
We need to know the formula for volume of a sphere to solve this question.The volume of Darragh's balloon when it is fully inflated is 3532.5[tex]cm^{3}[/tex]
A sphere can be called a circle in 3D, for example a ball is a sphere. There can be solid spheres and hollow spheres, a balloon is a hollow sphere because it has air inside it. The volume of a sphere can be calculated irrespective of it being a solid or a hollow sphere. The volume of a sphere is the capacity the sphere has, incase of a balloon the volume of a balloon means it's capacity to hold air in it. The formula for volume of a sphere is
V=[tex]\frac{1}{3}[/tex]π[tex]r^{3}[/tex] where V is the volume, r is the radius of the sphere
In the question it is given that radius of the sphere when fully inflated is 15cm
V=[tex]\frac{1}{3}[/tex]×3.14×15×15×15=3532.5 [tex]cm^{3}[/tex]
Therefore we found the volume of the balloon when fully inflated to be 3532.5[tex]cm^{3}[/tex].
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find derivative from first principle:
x² tanx
Answers
Answer:
f'(x) = 2.x.tan(x) + x²/cos²(x)
Step-by-step explanation:
f(x) = x².tan(x)
=> f'(x) = (x²)' . tan(x) + x². (tan(x))'
= 2x.tan(x) + x² . 1/cos²(x)
=> f'(x) = 2.x.tan(x) + x²/cos²(x)
What is 8x99 in expression form
Answers
In expression form, 8(99) is 8 ( 100 - 1 ) = 792, by basic algebra.
What is basic algebra?Numbers, variables, constants, expressions, equations, linear equations, and quadratic equations are all part of the basics of algebra. Additionally, the algebraic expressions contain the basic arithmetic operations of addition, subtraction, multiplication, and division.
Now, Given:
8 x 99
We know 99 = 100 - 1.
Thus, by basic algebra, 8 ( 99) = 8 (100 - 1)
8 ( 100 - 1) = 8(100) - 8(1)
8( 100 - 1) = 800 - 8 = 792.
Hence, In expression form, 8(99) is 8 ( 100 - 1 ) = 792, by basic algebra.
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10. Over the summer, Maria read 2 books per week, and Janet read 4 books per week. Prior to the summer, Maria had read 28 books, and Janet had read 16 books. After w weeks, they had each read the same number of books. Write an equation to represent this situation. Then, solve the equation. Need a equation and solution.
Answers
6 WEEKS
2x + 28 = 4x + 16
x = 6
12. Ben and Jerry invest $50 000 and $75 000 respectively in the same bank.
If the rate is 8%, how many whole years will it take for Ben to cross the amount of money that Jerry would have in 2 years?
Answers
Ben: $50000 x 1.08 = $54000 x 1.08 = $58320 x 1.08 = $62.985.6 x 1.08 = $68024.45 x 1.08 = $73466.40 x 1.08 = $79343.72 x 1.08 = $85691.21 x 1.08 = $92546.51 after 8 years.
It would take 7 whole years to cross the amount that Jerry would have in 2 years.
Find the area of the shaded region. Help please!
Answers
Answer:
Around 73cm
Step-by-step explanation:
314.16 is the area of the whole circle
shaded is 85/365 (around 23 percent)
a map has a scale of 1:1000.
i)
What distance on the ground (in meters) is represented on the map as
(a) 2cm (b) 7.6cm?
ii)
What distance on the map represents
(a) 100m (b) 2.6km?
Answers
(a) The distance on the ground represented 2 cm on the map is 2000 cm.
(b) The distance on the ground represented 7.6 cm on the map is 7600 cm
It is a technique wherever we discover worth|the worth} of one unit from the worth of multiple units and also the value of multiple units from the worth of one unitIt is given that a map has a scale of 1:1000 which means that 1 cm of the map represents 1000 cm on the ground .
i) (a) Using unitary method , we get
1 cm on map is equivalent to = 1000 cm on the ground
2 cm on map is equivalent to = 2 × 1000
= 2000 cm on the ground
(b) Using unitary method , we get
1 cm on map is equivalent to = 1000 cm on the ground
7.6 cm on map is equivalent to = 7.6 × 1000
= 7600 cm on the ground
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In A PQR, QT is
an altitude...QT=
(1) 10
(3) 4
(2) 8
(4) 6
Answers
Answer:
20 psectacles and scranbled
convert into power notation (-2197)
Answers
The sum of
5
9
and six times a number is equal to
2
subtracted from seven times the number. Find the number.
Answers
ANSWER:
x=61
STEPS FOR SOLVING LINEAR EQUATION :
59+6x=7x−2Subtract 7x from both sides.
59+6x−7x=−2Combine 6x and −7x to get −x.
59−x=−2Subtract 59 from both sides.
−x=−2−59Subtract 59 from −2 to get −61.
−x=−61Multiply both sides by −1.
x=61Hope it helps!!!
;}
Answer:
answer to the question is x=61
4. Randall's monthly water bill from April to July is listed in the table below. What was the percent
increase in his bill from May to July?
Answers
The percent increase in his bill from May to July is 32.29%.
What is the percent increase in the bill?
Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred. Percentages are a measure of frequency. The sign used to represent percentages is %.
The percent increase in his bill from May to July = (bill in July / bill in May)^(1/number of months) - 1
(136.50 / 78)^(1/2) - 1 = 32.29%
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The study of Euclidean geometry has led to the development and acceptance
of other non-Euclidean types of geometry.
A. True
B. False
Answers
Answer:
True
Step-by-step explanation:
Identify whether the graph displays a linear or nonlinear function. Explain why. Graph B On a coordinate plane, Graph B curves up into quadrant 1. Graph B displays a
Answers
The attached graph displays a linear function
How to identify whether the graph displays a linear or nonlinear function?The graph that completes the question is added as an attachment
On the line of the graph, we have the following equation
y = 2x - 3
The above equation takes the form of a linear equation (i.e. y = mx + c)
This means that the graph displays a linear function
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Graph B displays a
✔ nonlinear function; the rate of change is not constant.
Step-by-step explanation:
(1.28 x 10^5) + (1.13 x 10^3) in scientific notation
Answers
Answer:
10 ( 12913 ) or 12913 * 10^1
Step-by-step explanation:
(1.28 x 10^5) + (1.13 x 10^3)
--------------------------------------------
1.28 = 128/100 = 128/10^2
1.13 = 113/100 = 113/10^2
-------------------------------------------
(128/10^2 * 10^5) + (113/10^2 * 10^3) <---- 10^5/10^2 = 10^3
(128 * 10^3) + (113 * 10^1)
10^1 ( 128 * 10^2 + 113)
10^1 ( 12800 + 113)
10 ( 12913 )
Amy paid $66.94 for a pair of running shoes during a 15%-off sale. What was the regular price?
...
Answers
$66.94/85 = $0.78752941 x 100 = $78.75
A cheetah can run 70 miles per hour. What is this speed in feet per hour?
Answers
the speed of the Cheetah in feet per hour will be 369600 feet per hour when the speed if 70 miles per hour.
Speed of the Cheetah = 70 miles / hour
1 mile = 5280 feet
Now, we will convert 70 miles into feet.
For this, we will use the operation of multiplication.
We will multiply 5280 to 70 to convert the miles into feet.
So, the speed of the Cheetah will become:
Speed of the Cheetah = 5280 × 70 / hour.
Speed of the Cheetah = 369600 feet / hour.
Therefore, we get that, the speed of the Cheetah in feet per hour will be 369600 feet per hour when the speed if 70 miles per hour.
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PLEASE HELP Line Segment AD=11x+10.6. Find the length of AB and CD. Show all work
Answers
Answer:
AB=11.4
CD=24.4
Step-by-step explanation:
Since AD=11x+10.6, then AB+BC+CD = AD.
Hence,
2x+3+21+7x-5=11x+10.6
Combine like terms:
9x+19 = 11x+10.6
Subtract 9x on both sides:
19 = 2x+10.6
Subtract 10.6 on both sides:
2x=8.4
Divide by 2 on both sides:
x=4.2
Since AB=2x+3, AB=11.4
Since CD=7x-5, CD=24.4
The speed of the wind, w, is at most 56 miles per hour. The translation is
Answers
Answer:
56mph
Step-by-step explanation:
i hope this is the answer you were looking for
6. What will be the speed of the train if it takes 10 hours to cover the 7. A bus travels at a speed of 40 km/h for 25 minutes and then at a speed of 60 km/h for next 25 minutes. Find out the total distance covered by the bus.
Answers
the total distance covered by the bus is 41.67 km in 50 minutes.
For first 25 minutes:
Speed of the bus = 40 km / hr.
Time = 25 minutes
Distance = Speed × Time
Distance = 40 km / hr. × 25 / 60 hr.
Distance = 16.67 km
For the next 25 minutes:
Speed of the bus = 60 km / hr.
Time = 25 minutes
Distance = Speed × Time
Distance = 60 km / hr. × 25 / 60 hr.
Distance = 25 km
Total distance covered = 16.67 km + 25 km
Total distance covered = 41.67 km.
Therefore, we get that, the total distance covered by the bus is 41.67 km in 50 minutes.
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