The first 5 terms of some sequences are given. State a rule that each sequence could follow.
2, 4, 6, 8, 10
5, 7, 9, 11, 13
50, 25, 0, -25, -50
1/3, 1, 3, 9, 27
Answers
The first , second and third sequence is arithmetic and the fourth sequence is geometric.
A sequence is a series of numbers such that each number follows a very specific rule or explicit function which determines its value. There are numerous types of sequence and series . But for this particular question we will need to know :
Arithmetic sequence : Number in an arithmetic sequence or AP are at equal distance from each other if plotted on a number line. The difference between any two consecutive numbers is the same and it is called the common difference.Geometric sequence : a sequence of numbers is said to be in a GP such that the ratio of each number to the preceding and the succeeding numbers is same.Let us now take each series of numbers and find the type of sequence it is:
sequence 1: 2, 4, 6, 8, 10
Common difference = 10-8 = 6-4 =2
So the sequence is arithmetic.
sequence 2: 5, 7, 9, 11, 13
Common difference = 13-11 = 7-5 =2
So the sequence is arithmetic.
sequence 3: 50, 25, 0, -25, -50
Common difference = 50-25 = - 25 - ( - 50) = 25
So the sequence is arithmetic.
sequence 2: 5, 7, 9, 11, 13
Common difference = 13-11 = 7 - 5 =2
So the sequence is arithmetic.
sequence 2: 1/3, 1, 3, 9, 27
Common ratio = 3 ÷ 1 = 27 ÷ 9 = 3
So the sequence is geometric.
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Related Questions
From 2018 to 2010, the total number of passengers passing through Changi Airport increased by 4% In 2019, the total number was 68 280 000. Calculate the number of passengers passing through Changi Airport in 2018.
Leave your answer correct to the nearest whole number.
Answers
Step-by-step explanation:
I guess this means from 2018 to 2019 (and not to 2010).
so, compared to 2018 the numbers of 2019 were 104% (100% of 2018 plus 4% increase).
104% = 68,280,000
100% = 104%/1.04 = 68,280,000/1.04 =
= 65,653,846.15 ≈ 65,653,846
the number of passengers in 2018 were about
65,653,846
if h(t)=1/t divided by 1 what is h(1/2)
Answers
Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Given the function [tex]h(t)=\frac{1}{t+1}[/tex], we can find [tex]h(\frac{1}{2} )[/tex] by substituting [tex]\bf{t=\frac{1}{2}}[/tex].
When t= [tex]\frac{1}{2}[/tex],
[tex]h(\frac{1}{2})[/tex]
[tex]=\frac{1}{\frac{1}{2}+1 }[/tex]
[tex]=\frac{1}{(\frac{3}{2} )}[/tex]
[tex]=\bf{\frac{2}{3}}[/tex]
Additional:
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helpp- question linked below
Answers
Answer:
Ann = 67 stickers
Josh = 60 stickers
Claire = 30 sickers
Find the missing angles x and y vertical/adjacent angles
Answers
Answer: x = 49 degrees, y = 41 degrees
Step-by-step explanation:
Using supplementary angles, we know that x + y + 90 degrees = 180 degrees.
Using complimentary angles, we know that x + 41 degrees = 90 degrees, and x + y = 90 degrees.
Solving first for x,
x + 41 degrees = 90 degrees
x = 90 - 41 degrees
x = 49 degrees
Solving for y,
x + y = 90
Substituting 49 degrees in for x,
y + 49 degrees = 90 degrees
y = 90 - 49 degrees
y = 41 degrees
Solve the equation for x. Write your answers as fractions. x2 = 9 100
Answers
X=4550 (answer)
Hope it helps
I’m having trouble understanding this. So pls help me: 5 √(5)^2
Answers
Check out the attached photo
Answer:
5 √(5)^2 = 25
Step-by-step explanation:
The square root of 5^2 is 5. Then we will have to multiply by 5 to get our answer. So we'd do 5 x 5 and it'd equal 25. Therefore our final answer is 25.
I hope this helps, have a blessed day! :D
the average lifetime of a certain new cell phone is three years. the manufacturer will replace any cell phone failing within two years of the date of purchase. the lifetime of these cell phones is known to follow an exponential distribution. the decay rate is:
Answers
The decay rate of a certain new cell phone is 0.333
For given question,
The average lifetime of a certain new cell phone is three years.
The manufacturer will replace any cell phone failing within two years of the date of purchase.
Also, the lifetime of these cell phones is known to follow an exponential distribution.
We need to find the decay rate.
We know that an exponential decay is the process of reducing an amount by a consistent percentage rate over a period of time.
since the average lifetime of a certain new cell phone is three years, the decay rate would be 1/3 = 0.333
Therefore, the decay rate of a certain new cell phone is 0.333
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40 is 77% of what number?
Answers
Step by step
40 is (=) 77% (.77) of (multiply) what number (x)
So
40 = .77x
Divide both sides by .77 to solve for x
40/.77 = .77/.77 x
51.9 = x
Check your work, substitute 51.9 in for x
40 = .77 x 51.9
40 = 40
Problem solved
x = 100%
Cross multiplication = 77x = 4000
x = 4000/77
x = 51.95 (2dp)
The line y=kx+4 goes through the point (2,-2)
Sketch the graph the line
Please write it step by step
Answers
The line of the graph y= kx +4 goes through the point (2,-2) is given by
y = -3x +4.
As given in the question,
Equation of the line is given by y = kx + 4
Passing through the point (2, -2)
Substitute the value in equation we get,
-2= k(2) + 4
⇒2k = -2 -4
⇒k =-6 /2
⇒k =-3
Equation of the line y= -3x + 4 sketched on graph passing through (2,-2).
Therefore, the line of the graph y = kx +4 goes through the point (2,-2) is given by y = -3x +4.
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Lamar's office recycled a total of 6 kilograms of paper over 3 weeks. how many weeks will it take lamar's office to recycle a total of 24 kilograms of paper? solve using unit rates.
Answers
Lamar's office will take 12 weeks to recycle a total of 24 kilograms of paper
Information about the problem:
Kg recycled= 6 kgtime= 3 weeksWeeks= ?Total recycle = 24 KgTo solve this problem, we have to state the equation using the information of the problem:
Calculating the recycle rate of Lamar's office, we get:
Rate = Kg recycled / time
Rate = 6 kg/3 weeks
Rate = 2 kg/week
Calculating how many weeks Lamar's office will take to recycle 24 kilograms:
Weeks = Total recycle/ rate
Weeks = 24 kg / 2kg/week
Weeks = 12 weeks
What are algebraic operations?We can say that they are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
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Jill records the temperature outside every hour for 4 hours. She finds that the temperature dropped by the same amount each hour. After 4 hours, she finds that the temperature dropped a total of 20∘F. She writes this number sentence.
(−20)÷4=−5
What does the number sentence mean?
1. The total drop in temperature, −20∘F, divided by 4 hours equals −5∘F per hour. The temperature dropped 5∘F each hour.
2. The total number of drops, 20, divided by 4 hours equals 5 times per hour. The temperature dropped 5 times per hour.
3. The total drop in temperature, −20∘F, divided by 4∘F in the first hour, equals −5 drops. The temperature dropped 5 times.
4. The total number of hours, 20, divided by 4∘F equals 5 hours. The temperature dropped once every 5 hours.
Answers
The total drop in temperature, −20∘F, divided by 4 hours equals −5∘F per hour. The temperature dropped 5∘F each hour. (option 1)
What does the sentence mean?Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operation.
If the total drop in temperature over 4 hours is −20∘F, in order to determine the temperature drop each hour, divide −20∘F by 4.
Drop each hour = −20∘F / 4 = −5∘F
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Bob told Margaret that he ate half if the amount of cookies that Jeff ate. Margaret does not know how many cookies Jeff ate.
If bob actually ate one more than half of the amount Jeff ate, write an expression that represents the amount of cookies bob ate
Answers
The expression that represents the amount of cookies Bob ate is 1 + 0.5x.
How to illustrate the expression?From the information, Bob told Margaret that he ate half if the amount of cookies that Jeff ate. Bob actually ate one more than half of the amount Jeff ate.
Let the amount that Jeff are be represented as x.
Since Bob actually ate one more than half of the amount Jeff ate, this will be:
= (1/2 × x) + 1
= 0.5x +1
Therefore, the expression is 1 + 0.5x.
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mary robertson sells tires at a large car service center she earns 10 commission on the first $1000 15 on the next $2000 and 20 on sales of more than $3000 last
Answers
Her total commission was $560.
As 10% of the first $1,000, 15% of the next $2,000, and 20% of sales beyond $3,000 are commissions that she receives. She sold $3,400 worth of tires last week.
What does "total commission" mean?
The commission serves as a benefit or an inducement for the worker to close agreements so that the business can increase revenue and profits. The total commission is calculated by multiplying the total sales by the commission percentage.
After dividing the outcome by 100, multiply the sale price by the commission percentage. Perform the subsequent calculation: Each blue gadget costs $70. The salesman receives a 14% commission on each sale, or $9.80.
The percentage or fixed payment connected to a specific number of sales is referred to as a "commission rate." A commission, for instance, can be $30 or 6% of sales.
It is therefore $560.
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Find the measure of ∠b ?
Answers
Answer:
Below
Step-by-step explanation:
b = 180 - 81° (because of the Z angle law)
b = 99°
Answer:
Step-by-step explanation:
by inspection it is given that b and 81° are inside the parallel angles...they are sorted such that now we know they are co-inter.. anglesb+81°=180 since co-inter... angles are supplementaryb=180°-81°∴b=99°factorize 5y^2- 125z^2
Answers
Answer:
[tex]5\left(y+5z\right)\left(y-5z\right)[/tex]
Step-by-step explanation:
[tex]\mathrm{The \;given \;equation \;is \; 5y^2-125z^2}[/tex]
[tex]\mathrm{Factor\:out\:common\:term\:}5:\quad 5\left(y^2-25z^2\right)\\\\= 5\left(y^2-25z^2\right)[/tex]
[tex]\left y^2-25z^2\right[/tex]
[tex]25z^2 = \left(5z\right)^2[/tex]
==> [tex]\left y^2-25z^2\right = y^2-\left(5z\right)^2[/tex]
[tex]\mathrm{Apply\:Difference\:of\:Two\:Squares\:Formula:\:}x^2-y^2=\left(x+y\right)\left(x-y\right)[/tex]
[tex]y^2-\left(5z\right)^2=\left(y+5z\right)\left(y-5z\right)[/tex]
So the factored expression is
[tex]5\left(y+5z\right)\left(y-5z\right)[/tex]
Audrey misses 10% of the free throws she attempts in a season. How many total free throws did she attempt if she missed 52?
Answers
Answer:
520
Step-by-step explanation:
10 missed in 100 free throw ( because of 100%)
=> 1 missed in (100/10) free throw
=> 52 missed in (52*100/10) free throw
= 520 free throw
Hope it helps!
Brainliest?
The Galveston-Port Bolivar ferry take cars across Galveston Bay. One day, the ferry transported a total of 350 cars over a 5-hour period.the ferry took the same number of cars each hour. how many cars did it take each hour? complete the bar diagram to help
Answers
Answer:
70 cars
Step-by-step explanation:
if the ferry took the same number of cars each hour, then you would just do 350/5 = 70
The ideal height (in centimeters) of a mountain bike frame is about 10 centimeters less than two thirds of the bike riders leg length (in centimeters). Two riders leg length are 80 centimeters and 85 centimeters. To the nearest tenth of a centimeter, how much taller should the taller mountain bike frame be?
Answers
The taller mountain bike frame should be 3.4cm taller.
What should be the difference in the frames?The equation that can be used to determine the ideal height of the mountain bike frame is:
Mountain bike frame : (2/3 x length of the bike rider's leg) - 10
Mountain bike frame when leg length is 80cm: (2/3 x 80) - 10 =53.3 - 10 = 43.3 cm
Mountain bike frame when leg length is 85cm: (2/3 x 85) - 10 = 56.7 - 10 = 46.7cm
Difference in mountain bike frame :46.7 cm - 43.3 cm = 3.4cm
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I need help with this question so I came to Brantley
Answers
The value of the variable x is 5 and the lengths of PL and LQ are 9 and 48, respectively.
How to find the value of a variable and the length of the line segments behind that variable
In this problem we find a line segment generated by points P and Q and in which a point L divides the line segment PQ in two sections: PL and LQ. In accordance with the statement, we have the following equations describing the geometric system:
PQ = PL + LQ
PQ = PL + LQ
57 = (2 · x - 1) + (9 · x + 3)
Now we proceed to clear the variable x with the resulting equation:
57 = 11 · x + 2
55 = 11 · x
x = 5
And finally we find the length of each line segment:
PL = 2 · 5 - 1
PL = 9
LQ = 9 · 5 + 3
LQ = 48
The value of the variable x is 5 and the lengths of PL and LQ are 9 and 48, respectively.
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How many solutions does this question have?
17h - 7 = 10h - 2 + 7h
Answers
Our initial equation:
17h - 7 = 10h - 2 + 7h
I want to get variables ("h") on one side, and numbers on the other, hence I will add 2 to both sides to shift numbers to the left side.
17h - 5 = 10h + 7h
Now I want to simplify the "h" on the right side.
17h - 5 = 17h
Now I will move the variable from the left to the right.
-5 = 0
17h - 17h is zero, think of h being equal to 1 if you don't get it.
-5 = 0 is a false inequality, there are no solutions.
THERE ARE NO SOLUTIONS.
Jaime $8.00 of the $25.00 in his wallet. which decimal represents the fraction of the $25.00 Jaime spent
Answers
Decimal which represents the fraction of the $25.00 Jaime spent is equal to 0.32.
As given in the question,
Total amount in wallet = $25.00
Amount spent = $8.00
Decimal which represents the fraction of the $25.00 Jaime spent
Fraction spent by Jaime = (Amount spent by Jaime)/(Total amount in wallet)
⇒Fraction spent by Jaime = ($ 8.00 ) / ($ 25.00)
⇒Fraction spent by Jaime = 8/25
Convert it into decimal
Decimal represents the fraction spent by Jaime = 0.32
Therefore, decimal which represents the fraction of the $25.00 Jaime spent is equal to 0.32.
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the cities portland, oregon; tacoma, washington; and seattle, washington, in respective order, lie approximately in a straight line. the distane from portland to tacoma is 120 miles. the distance from portalnd to seattle is 145 miles. find the distance from tacoma to seattle.
Answers
The distance from Tacoma to Seattle is estimated as 25 miles.
What is distance?Distance is defined as an object's total movement without regard for direction. Distance can be defined as the amount of ground an object had also covered regardless of its beginning or ending point.
Distance is the total length of the path in between two points.Distance is a scalar quantity because it is determined solely by magnitude and not by direction.Only positive values can be assigned to distance.Now, as per the given question;
The following are the distances between cities:
120 miles from Portland to Tacoma
145 miles from Portland to Seattle
120+x = 145
x = 145 - 120
x = 25 miles
Therefore, the distance from Tacoma to Seattle is estimated as 25 miles (according to the given graph).
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The complete question is -
Item 17 The cities Portland, Oregon; Tacoma, Washington; and Seattle, Washington, in respective order, lie approximately in a straight line. The distance from Portland to Tacoma is 120 miles. The distance from Portland to Seattle is 145 miles. Find the distance from Tacoma to Seattle.
(see attached figure)
What is the maximum value for y in the following function?
Answers
Answer:
D. 8
Step-by-step explanation:
well, let's look at the different parts of the functional expression :
the maximum of 5 is 5, of course.
the maximum of 3 is 3.
the maximum of sin(2x) is the maximum of any sine = 1.
sin(2x) only changes the frequency of the sine wave (the max and min values appear twice as often than for sin(x)), but does not have an impact on the amplitude, which defines the max. and min. values.
sin(2x) is NOT the same as 2×sin(x).
sin(2x) still "waves" between +1 and -1.
so, the total maximum is
5 × 1 + 3 = 8
someone please help me with this question i really dont understand it
Answers
Answer:
d = 510 km
Step-by-step explanation:
She travelled the final 4 hours at a constant speed of 60 km/h.
distance = speed × time
distance = 60 km/h × 4 hours
distance = 240 km for the last 4 hours
She already had travelled 270 km in the first 3 hours.
d = total distance = 270 km + 240 km = 510 km
Answer: d = 510 km
The heights, in cm, of 32 female gymnasts were recorded:
148 152 147 149 150 147 151
142 156 148 148 149 150 152
155 154 151 154 148 150 149
145 147 148 161 152 162 149
146 151 150 157
a) Construct a grouped frequency table, using groups of 5 cm.
b) Draw a histogram to represent this data.
Answers
Step-by-step explanation:
142r4h+34-45=673cm2468228b288Answer the one you no please
Answers
Answer:
bro this is so easy it's letter d
Given y =
2x+1/4x-3
•Solve for x.
•evaluate x when y = 1
Answers
Answer:
Solve for x: [tex]x = \frac{3y+1}{4y-2}[/tex]
Evaluate x for y = 1: [tex]x = 2[/tex]
Step-by-step explanation:
[tex]Original:y=\frac{2x+1}{4x-3}\\Multiply\ out\ the\ denominator:(4x-3)*y = 2x+1\\Distribute: 4xy - 3y = 2x+1\\Group\ Like\ Terms:4xy-2x = 3y+1\\Factor\ Out\ x: x(4y-2) = 3y+1\\Divide\ to\ get\ x\ alone:x = \frac{3y+1}{4y-2}\\\\Plug\ in\ the\ value\ for\ y:x = \frac{3(1)+1}{4(1)-2}\\Multiply:x = \frac{3+1}{4-2}\\Add:x = \frac{4}{2}\\Simplify/Divide:x=2[/tex]
If the total price for two cars at a dealership is $98,000, where one car’s price is $13,000 less than twice the other, what is the price of the cheaper vehicle?
Answers
2x - y = 13000
3x = 111000
x= 37,000
y= 2(37,000) - 13,000 = 61,000
therefore x is the cheaper vehicle that costs 37,000$
No, by rounding the conversion ratio, the Ruiz family will not be getting the most accurate answer. Using the more accurate conversion ratio will give an answer with more than 2 decimal places so the answer can accurately be rounded after the conversion.
Answers
Using proportions, it is found that the Ruiz family is not getting the most accurate ratio and are losing money, thus the rounding should be realized after the conversion.
What is the missing information?The Ruiz family is exchanging Euros for USD dollars, considering the following currency rate:
1 euro = 1.35261 USD.
Considering that the amounts in USD are rounded to the nearest hundredth, the use the following rule
1 euro - 1.35 USD.
It asks if the Ruiz family will be getting the most accurate answer.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
For this problem, we suppose a 1000 euros amount, them:
1000 x 1.35261 = $1,352.61.1000 x 1.35 = $1,350.Hence the Ruiz family is not getting the most accurate ratio and are losing money, thus the rounding should be realized after the conversion.
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1. 48/8 + 44/8 = ?
2. 10/10 + 30/10 = ?
3. 6/4 + 2/3 = ?
4. 1/8 + 2/16 = ?
5. 4/4 + 14/16 = ?
6. 4/3 + 2/9 = ?
7. 2/4 + 4/8 = ?
8. 20/5 + 15/5 = ?
9. 2/4 + 4/6 = ?
10. 4/7 + 6/21 = ?
11. 4/2 + 16/18 = ?
i rlly need the answers rn bcs i have to pass it tom
Answers
Step-by-step explanation:
1. [tex] \frac{48}{8} +\frac{44}{8}= 11 \frac{1}{2} [/tex]
[tex]2.\frac{10}{10} + \frac{30}{10} = 4[/tex]
[tex]3.\frac{6}{4} + \frac{2}{3} = 2 \frac{1}{6}[/tex]
[tex]4.\frac{1}{8} + \frac{2}{16} = \frac{1}{4}[/tex]
[tex]5.\frac{4}{4} + \frac{14}{16} = 1 \frac{7}{8}[/tex]
[tex]6.\frac{4}{3} + \frac{2}{9} = 1 \frac{5}{9}[/tex]
[tex]7.\frac{2}{4} + \frac{4}{8} = 1[/tex]
[tex]8.\frac{20}{5} + \frac{15}{5} = 7[/tex]
[tex]9.\frac{2}{4} + \frac{4}{6} = 1 \frac{1}{6}[/tex]
[tex]10.\frac{4}{7} + \frac{6}{21} = \frac{6}{7}[/tex]
[tex]11.\frac{4}{2} + \frac{16}{18} = 2 \frac{8}{9}[/tex]