The recursive sequence follow that rule a_n =- [3 ×a_(n-1)] -1.
What is the recursive sequence?
A recurrence relation is an equation that applies a rule to the previous phrase or terms in the series to generate the next term in the sequence. A recurrence relation is, in other words, an equation that is defined in terms of another equation.
Additionally, each and every recurrence relation must have an initial condition, which is a list of one or more terms in the sequence that arrive before the term where the recurrence relation begins.
Given sequence is 5,−16,47,...
Assume that a_1 = 5
a_2 = -16
a_3 = 47
Rewrite the second term of the sequence:
a_2 = - (3×a_1) - 1 = -(3 × 5) - 1 = -16
Rewrite the third term of the sequence:
a_3 = - (3×a_2) - 1 = -(3 × (-16)) - 1 = 47
The recursive rule is a_n =- [3 ×a_(n-1)] -1 where n is an integer.
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if rose and Carl share a 18 ounce bucket of clay. by the end of the week rose has used 1/6 of the Bucket and carl used 2/3 of the bucket How many ounces are left in the bucket
Answer:
3 ounces left
Step-by-step explanation:
We convert both 2/3 and 1/6 into a similar fraction. In this case, the simplest way to answer the problem is to convert them into eighteenths, as when we convert them to this, the numberator will show the amount of ounces used. SO, 2/3=12/18=12 ounces used and 1/6=3/18=3 ounces used. The total answer of ounces used is 15, so 18-15=3 ounces left
many of a bank's customers use its atms to transact business after normal banking hours. during the early evening hours customers arrive at a certain atm location at a rate of one every 7.2 minutes. on average 11.9 customers per hour can be served by the atm. what is the expected number of customers waiting for the atm?
The expected number of customers waiting for the ATM is approximately 0.78.
We can utilize the M/M/1 lining model to take care of this issue. Here, appearances follow a Poisson distribution and administration time follows a remarkable conveyance. The appearance rate is given as 1 client each 7.2 minutes or 60/7.2 clients each hour. This is equivalent to 8.33 clients each hour. The help rate is given as 11.9 clients each hour. Utilizing Little's regulation, the normal number of clients in the line (Lq) is equivalent to the appearance rate (λ) squared split by the contrast between the help rate (μ) and the appearance rate (λ):\(Lq = λ^2/(μ(μ-λ))\)Subbing the qualities, we get: Lq = \((8.33^2)/(11.9(11.9 - 8.33))\) Lq ≈ 0.78 Consequently, the normal number of clients hanging tight for the ATM is roughly 0.78.
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What does the "S" stand for? How do I find a1 and d?
Answer
a₁ = 4
d = -3
Explanation
a₇ = -14
S₇ = -35
using aₙ = a₁ + (n-1)d
a₇ = a₁ + (7 -1)d
a₇ = a₁ + 6d
substitute a₇ = -14, we have
-14 = a₁ + 6d
a₁ + 6d = -14 --------(i)
Sₙ = n/2[2a₁ + (n-1)d]
S₇ ⇒ n = 7
S₇ = 7/2[2a₁ + (7 - 1)d]
Substitute S₇ = -35, we have
-35 = 7/2[2a₁ + 6d]
Cross multiplying and opening the bracket yields
7(2a₁ + 6d) = -70
Divide both sides by 7
2a₁ + 6d = -70/7
2a₁ + 6d = -10 -------(ii)
Comparing equation (i) and (ii) and substract (i) from (ii)
a₁ + 6d = -14 --------(i)
2a₁ + 6d = -10 -------(ii)
2a₁ - a₁ = -10 - (-14)
a₁ = -10 + 14
a₁ = 4
To find d, substitute a₁ = 4 into equation (i)
Recall (i) a₁ + 6d = -14
4 + 6d = -14
6d = -14 - 4
6d = -18
d = -18/6
d = -3
on a circle of radius 4 and center (0, 0), find the x and y coordinates at angle 180 degrees (or π in radian measure).
On a circle with a radius of 4 and center at (0, 0), to find the x and y coordinates at an angle of 180 degrees (or π in radian measure), we can use the trigonometric functions.
At 180 degrees, the x-coordinate will be 0, as it lies on the y-axis. The y-coordinate can be found by using the sine function. Using the equation y = r * sin(θ), where r is the radius and θ is the angle in radians, we can substitute the values. In this case, r is 4 and θ is π (since 180 degrees equals π radians).
Therefore, the x-coordinate is 0 and the y-coordinate is 4 * sin(π) = 0. So, the x-coordinate is 0 and the y-coordinate is also 0.
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What is 108+259+301+405
Answer:
1073
Step-by-step explanation:
it's simple addition
c<(34.56-20.56) divided by 1 6/8
The value of c<(34.56-20.56) divided by \(1\frac{6}{8}\) is 8
First, we need to find the value inside the parentheses:
34.56 - 20.56 = 14
Next, we need to convert the mixed number \(1\frac{6}{8}\) into an improper fraction:
\(1\frac{6}{8}\) = (8 x 1 + 6) / 8 = 14/8
Now, we can substitute these values into the expression:
= 14 / (14/8)
To divide by a fraction, we can multiply by its reciprocal:
14 / (14/8) = 14 x (8/14)
We can simplify this by canceling out the common factor of 14:
14 x (8/14) = 8
Hence, the value of c<(34.56-20.56) divided by \(1\frac{6}{8}\) is 8
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Sandy’s 8th grade math class receives $13.50 for every 5 boxes of chocolates that they sell. Which graph shows this relationship with the same unit rate?
Answer:
See Explanation
Step-by-step explanation:
The graphs are not given; however, I'll answer with the graph equation and also attach the graph...
Represent the boxes with x and the cash received with y.
When x = 5
y = 13.50
When x = 10
y = 27
First, we need to get the slope of the graph.
m = (y2 - y1)/(x2 - x1).
m = (27 - 13.5)/(10 - 5)
m = 13.5/5
m = 2.7
Next, is to determine the graph equation using
y - y1 = m(x - x1)
y - 13.5 = 2.7(x - 5)
y - 13.5 = 2.7x - 13.5
y = 2.7x - 13.5 + 13.5
y = 2.7x..
See Attachment for graph
PLEASE HELP. FIRST (CORRECT) ANSWER GETS BRAINLIEST
Simplify the expression
12 - 4 x 3 / 7 + 13 x 15
Answer:
the answer is 240 multiply and divide
Answer:240
Step-by-step explanation:
Use the order of operations. (PEMDAS)
Parenthesis
Exponent
Multiply
Divide
Addition
Subtraction
Hope this helped dude
The Canton Grocery Store decides to give away 300 pounds
of vegetables as a part of a campaign to get people to eat more
vegetables. If 58 people get an equal amount of vegetables, how
many remaining pounds will Canton have to give away?
There are 10 remaining pounds will Canton have to give away.
Since, Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Here, We have to given that;
The Canton Grocery Store decides to give away 300 pounds of vegetables as a part of a campaign to get people to eat more vegetables.
Since, 58 people get an equal amount of vegetables.
Hence, the amount of remaining pounds will Canton have to give away is,
⇒ 300 / 58
After divide we get;
Remainder = 10
Thus, There are 10 remaining pounds will Canton have to give away.
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The sum of three consecutive odd integers is fifty-seven. Find the
three numbers.
Therefore, the three consecutive odd integers are 17, 19, and 21.
What is equation?An equation is a statement that shows the equality of two expressions, typically separated by an equal sign. An equation can contain variables, constants, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. The goal of solving an equation is to find the value(s) of the variable(s) that satisfy the equality.
Here,
Let x be the first odd integer, then the second and third odd integers are x+2 and x+4, respectively, since the difference between consecutive odd integers is 2.
The sum of the three consecutive odd integers is 57, so we can write:
x + (x+2) + (x+4) = 57
Simplifying and solving for x, we get:
3x + 6 = 57
3x = 51
x = 17
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What temperature do the thermometer show
Answer:
-12°F
Step-by-step explanation:
Answer:
-12
it should be this
solve the compound inequality-4x≤x-5<16
The solution to the compound inequality is 1 ≤ x < 21
Compound inequalityCompound inequality are type of inequality that has two or more parts.
In order to solve these simultaneous inequalities, we need to write them as two separate inequalities, and find the values of x that satisfy both of them
(-4x \(\leq\)x-5 -------------------------------Equation 1
(x-5< 16) --------------------------------Equation 2
Move all the term to the left side
(-4x +(-x+5) ≤ (x-5) +(-x+5) ---------Equation 3
(x-5) +(-16) < 16+(-16)------------------Equation 4
We need to get rid of expression interval. If there is a negative sign in front of it, each term within the expression changes sign
(-4x -x +5 ≤x-5-x+5)-------------------Equation 5
( X-5 -16 < 16 -16) ----------------------Equation 6
Rearrange and Simplify equation (5 & 6)
(-5x+5 ≤ ) ---------------------------------Equation 7
(x -21 < 0)----------------------------------Equation 8
We need to get rid of expression interval and subtract 5 from equation (7) and add 21 to equation (8)
(-5x ≤ -5) ---------------Equation (9)
(x < 21)------------------Equation (10)
Divide equation (9) by 5 on both sides and flip the sign because of the negative
5x/ 5 ≥ 5/ 5
( x ≥ 1 )
(x < 21 )
Therefore the solution to the compound inequality is 1 ≤ x < 21
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the region r is bounded by the x-axis, x = 0, ,x=2pi/3 and y=3sin(x/2). find the area of r
The region is bounded by the x-axis x=0, x=2pi*/3 and y= 3sin(x/2) is pi/3.
To find the area of region r, we first need to sketch the region on the x-y plane. From the given information, we know that the region is bounded by the x-axis, the line x=0, the line x=2pi/3, and the curve y=3sin(x/2). To sketch the curve, we can start by noting that sin(x/2) is a periodic function with period 2pi. This means that the curve will repeat itself every 2pi units on the x-axis. We can also note that sin(x/2) is non-negative for x in the interval [0, 2pi], which means that the curve will lie above the x-axis in this interval. To sketch the curve in the interval [0, 2pi/3], we can use the fact that sin(x/2) is increasing on this interval. This means that the curve will start at the point (0,0) and increase until it reaches its maximum value of 3sin(pi/6) = 3/2 at x=pi/3. The curve will then decrease until it reaches the x-axis at x=2pi/3.
Using this information, we can sketch the region r as a triangle with base 2pi/3 and height 3/2. The area of this triangle is given by:
area = 1/2 * base * height = 1/2 * (2pi/3) * (3/2) = pi/3
Therefore, the area of region r is pi/3.
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What number is the arrow point at?
Answer:
see below
Step-by-step explanation:
The lines in between 2 and 3 are splitting it up into 5ths and because the arrow is pointing to the fourth one the answer is \(2\frac{4}{5}\).
true or false The links in the blockchain that is created using an algorithm.
True, the links in the blockchain are created using an algorithm.
What is blockchain? Blockchain is a decentralized ledger technology that enables the secure exchange of digital assets across a network of participants without the need for a centralized authority or intermediary. The blockchain is created using an algorithm to secure the network and ensure that all transactions are transparent and verifiable.
In a blockchain, each block contains a cryptographic hash of the previous block, forming a chain of blocks (hence the name "blockchain"). The algorithm used to create the blockchain is a consensus algorithm, which ensures that all participants on the network agree on the same state of the ledger.
This consensus algorithm also ensures that no single participant can manipulate the ledger or change the contents of a block without being detected.
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10 points plz help!!
Answer:
38 is pounds, 84 is kilograms, 6 is ounces, 170 is grams, 180 is gallons, 680 is liters, 29 is cubic meters, 1024 cubic feet. If right plz give brainliest.
if the car has traveled 61.5 miles in 2 hours,how far will the car have traveled in 5 hours?
Answer:
in five hours you will travel 153.75 miles
Hello!
What does this problem want:
==> how far will the car have traveled in 5 hours
What we must find ==> how many miles does the car travel in an hour
\(\text{Rate}=\frac{61.5 \text{ miles}}{2 \text{ hours}} =30.75\text{ miles per hour}\)
Therefore: the car will travel in 5 hours
5 * 30.75 = 153.75 miles
Hope that helps!
The perimeter of a rectangular field is 318 yards. If the width of the field is 74 yards, what is its length?
Answer:
85 yards
Step-by-step explanation:
Perimeter= length+breadth+length+breadth
Length=(318-74-74)÷2
=170÷2
=85 yards
Answer:
length is 85
Step-by-step explanation:
l= p/2 - w=318/2 - 74 = 85
Marsha used a graphing calculator to graph an expense and a revenue function for her family’s printing business. The graph looked like the one below.
Answer:
a
Step-by-step explanation:
Upload answer sheets Consider the relation schema RAB.CDE) with the following functional dupandencies FAB-SC DE AB-SE ESC) Compute the candidate toy for the given relation . Compute the minimal cover of F.
The correct answer is the minimal cover of F is:F = {AB→C, AB→S, AB→E, ES→S}
Given, relation schema R(ABC,DE) with functional dependencies F:AB→SCDE→ABAB→SEES→C.
The candidate key of a relation R is a minimal set of attributes that can uniquely identify each tuple in R. To find the candidate key, we can compute the closure of each subset of attributes in R. Let's begin by finding the closure of AB, the subset of R. We can use the functional dependency AB→SC to compute the closure of AB as follows: AB+ = ABSC (by AB→SC)
Next, let's compute the closure of DE, the other subset of R. We can use the functional dependency DE→AB to compute the closure of DE as follows: DE+ = DEABSE (by DE→AB and AB→SE)
Now we have two potential candidate keys, AB and DEABSE. However, we need to check if they are minimal. To do this, we check if any subset of these candidate keys can also function as a candidate key. We can see that neither AB nor DEABSE has any proper subset that can function as a candidate key.
Therefore, both AB and DEABSE are candidate keys for the relation R. Next, let's compute the minimal cover of F. The minimal cover of a set of functional dependencies F is a minimal set of functional dependencies that is equivalent to F.
To find the minimal cover of F, we can use the following steps:
Step 1: Eliminate redundant dependencies. We can eliminate the dependency AB→SC since it is implied by AB→C.
Step 2: Decompose dependencies. We can decompose the dependency AB→SE into two dependencies, AB→S and AB→E, since S and E are not a subset of any other attribute set in F.
Step 3: Eliminate extraneous attributes. We can eliminate the attribute C from the dependency ES→C since C is already determined by AB→C.
Therefore, the minimal cover of F is:F = {AB→C, AB→S, AB→E, ES→S}
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Who ever gets it right first gets brainliest
Five sisters are busy. Ann is reading, Rose is cooking, Katie is playing chess, and Mary is doing laundry. What is the fifth sister doing?
Answer: Playing chess with Katie cause who'd play chess by themself right?
Step-by-step explanation:
If a police officer wants to find out whether the average speed of motorists on a highway with a speed limit of 55 mph is greater than 55 mph, then the null hypothesis is 55.
True or False?
The null hypothesis is that the average speed of motorists on a highway with a speed limit of 55 mph is equal to 55 mph.Given statement is false.
What is hypothesis test?A statistical hypothesis test is a technique for determining whether the available data are adequate to support a specific hypothesis. We can make probabilistic claims about demographic parameters through hypothesis testing.
According to question:The null hypothesis should be a statement of no difference or no effect. In this case, the null hypothesis would be that the average speed of motorists on the highway is equal to 55 mph.
So the correct statement would be:
The null hypothesis is that the average speed of motorists on a highway with a speed limit of 55 mph is equal to 55 mph.
Thus, Given statement is false.
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Okello who is x years old now, is 14years older than Nansubuga. In 5years time, he will be twice Nansubuga’s age. How old is Okello now?
Answer:
i think it is 28 i just think
Find the mean, median, mode, and range for the following values.
Option 1
Weekly earnings in dollars: 245, 250, 205, 240, 250, 275, 260, 295, 255, 225, 250
Option 1
Answer:
Mean - 250, Median - 250, Mode - 250, range - 90
Step-by-step explanation:
Answer:
mean: 250
mode: 250
median:250
range:90
Step-by-step explanation:
mean add everything and then divide
mode there are 3 250s making it the mode
median that is the middle
range 295-205=90
Write (5i)2 as either an integer
or an integer multiple of I
\((5i)^2\\\\=25\cdot i^2\\\\=25(-1)\\\\=-25\)
(5i)² can be written in integer form as as -25.
What is a Complex number?The numbers which can be expressed in the form of a + ib, where both 'a' and 'b' are real numbers and 'i' an imaginary number is called complex numbers.
So a complex number has a real part and an imaginary part.
The imaginary number 'i' is called iota and value of i is √-1.
We know the value of i.
i = √-1
i² = -1
(5i)² only has an imaginary part.
∴ (5i)² = 5² i²
= 25 × -1
= -25
Hence we can write (5i)² as -25 in the integer form.
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A particle is thrown vertically upwards with velocity 20 metre per second find a the distance travelled by the particle in first 3 second and displacement of the particle in 3 seconds
Step-by-step explanation:
\(\huge\underline\bold\blue{ƛƝƧƜЄƦ}\)
\(\huge\underline\bold\green{Gïvëñ}\)
[tex]\small\underline\bold\red{ v=0}\)
\(\small\underline\bold\blue{ v = u+gt}\)
\(\small\underline\bold\blue{0=20-10t}\)
\(\small\underline\bold\blue{t = 2 sec}\)
\(\huge\underline\bold\yellow{distance in first 2 second }\)
s = s(t=0 to 2 second) + s(2second to 3 second)
s = (ut+1\2(at)^2+ (ut+1\2at^2)
s = 20×2-1\2×10×4+1\2×10×1
s = 25
\(\huge\underline\bold\blue{Displacement}\)
s = 20 - 5 = 15
Hope it helps
solve for y: -72= -12y
Answer:
the value of y=6..................
Consider a Poisson distribution with μ=4. If needed, round your answer to four decimal digits. (a) Choose the appropriate Poisson probability mass function. (i) f(x)=
x!
4
x
e
4
(ii) f(x)=
x
4
x
e
−4
(iii) f(x)=
x!
x
4
e
−4
(iv) f(x)=
x!
4
x
e
−4
(b) Compute f(2). (c) Compute f(1). (d) Compute P(x≥2).
The value of f(1) is 0.0733. Compute P(x ≥ 2).P(x ≥ 2) = 1 - P(x < 2)= 1 - [P(0) + P(1)]= 1 - [1 + 4] * e-4 / 2!= 1 - [5/2.71828] * e-4= 1 - 0.0916= 0.9084 (rounded to 4 decimal places)∴ The value of P(x ≥ 2) is 0.9084.
(a) Choose the appropriate Poisson probability mass function.From the given data, the Poisson probability mass function can be given as, P(x; μ) = e-μ * μx / x!Where, P(x; μ) is the Poisson probability functionμ = 4f(x) can be given as,f(x) = P(x; μ) = e-μ * μx / x!From the given options,i) f(x) = x! 4x e-4(ii) f(x) = x4e-4(iii) f(x) = x! x 4 e-4(iv) f(x) = x! 4x e-4∴ The correct Poisson probability mass function is (i) f(x) = x! 4x e-4
(b) Compute f(2).f(2) = 24 * (1/2) * e-4= 0.1465 (rounded to 4 decimal places)∴ The value of f(2) is 0.1465.
(c) Compute f(1).f(1) = 14 * e-4= 0.0733 (rounded to 4 decimal places)∴ The value of f(1) is 0.0733.
(d) Compute P(x ≥ 2).P(x ≥ 2) = 1 - P(x < 2)= 1 - [P(0) + P(1)]= 1 - [1 + 4] * e-4 / 2!= 1 - [5/2.71828] * e-4= 1 - 0.0916= 0.9084 (rounded to 4 decimal places)∴ The value of P(x ≥ 2) is 0.9084.
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3. Maureen invested $5,000 in a 8-year CD
that eamed an annual interest rate of 4%. How
much money will he receive at the end of the 8
years if the interest was compounded monthly?
(black)
Answer:
6,881.9755
Step-by-step explanation:
A = P(1 + r/n)^nt
= 5000(1 + \(\frac{.04}{12}\))^12(8)
= 5000(1.00333)⁹⁶
= 5000(1.37639)
= 6,881.9755
Sutton takes 48 minutes to walk to work. after getting a new job, sutton takes 30.72 minutes to walk to work. what was the percent decrease in the travel time?
The percent decrease in the travel time after getting a new job is 36%.
Percentage is defined as part of a whole expressed in hundredths or out of 100. It is usually written with the symbol "%".
First, determine the decrease in travel time after getting a new job by subtracting the new travel time of 30.72 minutes from the initial travel time of 48 minutes.
decrease in time = 48 - 30.72
decrease in time = 17.28
Then, determine the percent decrease by dividing the decrease in time of 17.28 minutes by the initial travel time of 48 minutes and multiply by 100.
percent decrease = (17.28 / 48) x 100
percent decrease = 36%
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