The explicit rule for the nth term of the sequence is an = (an-1)*3 +2.
According to the given statement
we have to find the explicit rule for the nth term of the given sequence,.
So, For this purpose
The given sequence is :
2, 8, 26, 80, 242.
And according to the ap series formula
[tex]a_{n} = (a_{n-1} -1)*3 +2[/tex]
If we put the terms in it then we get the exact value as the value in the sequence.
So,
[tex]a_{n} = (a_{n-1} -1)*3 +2[/tex]
For [tex]a_{2}[/tex]
[tex]a_{2}[/tex] [tex]= a_{1} *3 +2[/tex]
[tex]a_{2}[/tex] [tex]= 2*3 + 2[/tex]
[tex]a_{2}[/tex] [tex]= 8[/tex]
and by this way we get all the values as same as the sequence.
So, The explicit rule for the nth term of the sequence is an = (an-1)*3 +2.
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Find a power series for the function, centered at c. g(x) = 4x x2 2x − 3 , c = 0
The power series for given function [tex]g(x)=\frac{4x}{(x-1)(x+3)}[/tex] is [tex]g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n)[/tex]
For given question,
We have been given a function g(x) = 4x / (x² + 2x - 3)
We need to find a power series for the function, centered at c, for c = 0.
First we factorize the denominator of function g(x), we have:
[tex]\Rightarrow g(x)=\frac{4x}{(x-1)(x+3)}[/tex]
We can write g(x) as,
[tex]\Rightarrow g(x)=\frac{1}{x-1}+\frac{3}{x+3}\\\\\Rightarrow g(x)=\frac{-1}{1-x}+\frac{1}{1+\frac{x}{3} }\\\\\Rightarrow g(x)=\frac{-1}{1-x}+\frac{1}{1-(-\frac{x}{3} )}\\[/tex]
We know that, [tex]\frac{1}{1-x}=\sum{_{n=0}^\infty}~{x^n}[/tex] if |x| < 1
and [tex]\frac{1}{1-(-\frac{x}{3} )}=\sum{_{n=0}^\infty}~x^n(-\frac{x}{3} )^n[/tex] if [tex]|\frac{x}{6}| < 1[/tex]
[tex]\Rightarrow g(x)=-\sum{_{n=0}^\infty}~x^n+\sum{_{n=0}^\infty}~x^n(-\frac{x}{3} )^n\\[/tex] if |x| < 1 and if [tex]|\frac{x}{6}| < 1[/tex]
[tex]\Rightarrow g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n)[/tex] if |x| < 1
Therefore, the power series for given function [tex]g(x)=\frac{4x}{(x-1)(x+3)}[/tex] is [tex]g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n)[/tex]
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QUICK HELP PLSSSS
Find the probabilities of the events described and arrange them in order from the event with the lowest probability of occurrence to the event with the highest probability of occurrence.
The probability of getting red balls is 0.25, probability of getting peaches from fruits is 0.7, probability of getting green tokens is 0.2, probability of getting golf balls is 0.867.
Given A)Number of green marbles=5,number of red marbles=3, number of blue marbles=4,
B) Number of peaches=7,number of apples=3,
C) Number of red token=10, number of blue token=6,green tokens=4,
D)Number of golf balls=13, number of tennis balls=2.
We are required to find the following probabilities:
A) Probability of getting red marble=Number of red marbles/ Total marbles.
=3/12
=1/4
=0.25
B) Probability of getting peaches=Number of peaches/Total fruits.
=7/10
=0.7
C) Probability of getting green tokens=Number of green tokens/Total tokens
=4/20
=1/5
=0.2
D)Probability of getting golf balls= Number of golf balls/ Total balls.
=13/15
=0.867
The sequence will be from C-A-B-D.
Hence the probability of getting red balls is 0.25, probability of getting peaches from fruits is 0.7, probability of getting green tokens is 0.2, probability of getting golf balls is 0.867.
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If ph term of A.P. is q and qth term is p, then (p+q) term is??
If the pth term of an arithmetic progression is q and qth term is p then the (p+q) th term is 0.
Given that the p th term of an A.P is q aand q th term is p.
We are required to find the (p+q) th term of that A.P.
Arithmetic progression is a sequence in which all the terms have common difference between them.
N th term of an A.P.=a+(n-1)d
p th term=a+(p-1)d
q=a+(p-1)d-------1
q th term=a+(q-1)d
p=a+(q-1)d---------2
Subtract equation 2 by 1.
q-p==a+(p-1)d-a-(q-1)d
q-p=pd-qd-d+d
q-p=d(p-q)
d=(p-q)/(q-p)
d=-(p-q)/(p-q)
d=-1
Put the value of d in 1.
q=a+(p-1)(-1)
q=a-p+1
a=q+p-1
(p+q) th term=a+(n-1)d
=q+p-1+(p+q-1)(-1)
=q+p-1-p-q+1
=0
Hence if the pth term of an A.P is q and qth term is p then the (p+q) th term is 0.
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Name a pair of vertical angles
Name a pit of adjacent angles
If m
Can someone help I’m confused I never learned this
Answer: Vertical: angles ABF and DBE. Adjacent: angles ABC and CBD
Step-by-step explanation:
vertical angles are angles that share a common point. they are right across from each other, and in this case, share point B. adjacent angles are angles that are directly next to each other, and share a line or segment. in this case, the two angles share the segment BC. hope this helps.
A 10-acre parcel was sold for $3.50 per square foot. What was the total selling price for the parcel
Answer:
The total selling price for the parcel is 1,524,600 dollars.
Step-by-step explanation:
We are given that 10 acre parcel was sold for $3.50.
First we need to figure out how many square foot is in 10 acres.
when we convert 10 acres we get 435600 square feet.
Since we know that parcel was sold for $3.50 per square foot we simply multiply 435600 by 3.5 = 1,524,600
One of the famous Grand Prix races takes place in Monaco, a small country south of France and West of Italy. Each Spring, racers from around the world come to this prestigious event. Currently, the race has 78 laps through the town of Monte Carlo (you may have seen this famous event in Iron Man 2). Each lap of the race has a distance of 3.34 km.
The computation shows that the total distance will be 260.52km.
How to compute the value?From the information given, it was stated that the race has 78 laps through the town of Monte Carlo and that each lap of the race has a distance of 3.34 km.
Therefore, the total distance will be:
= 78 × 3.34
= 260.52 km
Therefore, the distance is 260.52km.
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Pls help I keep getting this wrong
Answer:
x = 8
y = -3
Step-by-step explanation:
Multiply the first equation with (-2)
(-2) * (x - 4y) = 20
-2x + 8y = -40 now find the sum of it with second equation
2x + 5y - 2x + 8y = 1 - 40 add like terms (2x will eliminate -2x)
13y = -39 divide both sides by 13
y = -3
Now we can use this to find the value of x
x - 4y = 20 rewrite the equation using the value we found for y
x - 4(-3) = 20 multiply (-4) and (*3) (product will be positive because we are multiplying two negatives)
x + 12 = 20 subtract 12 from both sides
x = 8
how many days will he cut the last section?
Solving a linear equation, we will see that after 9 days he cuts the last section.
how many days will he cut the last section?We know that the initial length of the piece of cloth is 20m, and the taylor each day cuts a piece of 2 meters of it.
So, the length as a function on the number of days, is:
L(x) = 20m - 2m*x
Here we just need to solve:
L(x) = 2m
Because the last cut is when the long piece measures 4 meters (in that case he does one cut and has the two final pieces of 2 meters).
Solving that, we get:
20m - 2m*x = 2m
20m - 2m = 2m*x
18m/2m = x = 9
After 9 days he cuts the last section.
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14. The average age of 4 siblings is 12.5 years. If 3 of the siblings are 12-year-old triplets, how old is the fourth sibling? (A) 11.5 (B) 13 (C) 13.5 (D) 14
Answer:
D) 14
Step-by-step explanation:
12+12+12 is 36 we don't know hold old the fourth sibling is so they are X
to get the average of 12.5 you need to add all the siblings ages then divide it by 4
(36+X)/4=14 so the other sibling is 14
Answer:
B
Step-by-step explanation:
12.5x3=37.5
37.5 +11.5 =49
49÷4 =12.25
HELP WANTED!!!!! NEED HELP ASAP!!!!! (02.06; 02.07 MC)
Part A: Michael bought vegetables that weighs 4 and 1 over 8 pounds. How many ounces does the vegetables weigh? Show your work. (5 points)
[16 ounces = 1 pound]
Part B: A running tap dispenses 0.16 gallons of water every second. How many pints of water is dispensed after 25 seconds? Show your work. (5 points)
[1 gallon = 4 quarts, 1 quart = 2 pints]
if you are every so kind.. PLS SHOW ME HOW TO DO THIS PLS!!!!!!!
Using proportions, it is found that:
A. The vegetables weigh 66 pounds.
B. 0.5 pints are dispensed after 25 seconds.
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 or inverse proportional, can be built to find the desired measures in the problem.
4 and 1/8 pounds is equivalent to 4.125 pounds. Since each pound has 16 ounces, the weight of the vegetable is of:
W = 16 x 4.125 = 66 pounds.
Every second, 0.16 gallons are dispensed. Hence the amount dispensed in 25 seconds is:
A = 25 x 0.16 = 4 gallons.
Each gallon has 8 pints, hence the number of pints dispensed is:
4/8 = 0.5 pints.
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Write the given second order equation as its equivalent system of first order equations
The second-order equation as its equivalent system of first-order equations is
[tex]\left[\begin{array}{ccc}u(1)\\\\v(1)\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}7.5\\\\9\end{array}\right][/tex]
An equivalent system that has the identical answer is known as an equivalent structure. Given a gadget of two equations, we can produce an equal system by way of replacing one equation by means of the sum of the 2 equations, or by way of changing an equation by means of a couple of of itself.
Systems of linear equations are equivalent if and handiest in the event that they have an equal set of solutions. In other phrases, two systems are equal if and only if each answer of one in all of them is likewise a solution of the opposite.
In the structures sciences, a machine equivalent system is the conduct of a parameter or thing of a machine in a way just like a parameter or component of a distinctive system. Similarity means that mathematically the parameters and additives will be indistinguishable from each different.
Taking v = u, we have:
u" + 4u' + 6u = 4sin(3t)
--> v' + 4v + 6u = 4sin(3t)
So the system of equations is:
u' = 0u + 1v
v' = -6u - 4v + 4sin(3t)
So we can write it as:
u(1) = 7.5
v(1) = u'(1) = 9
So the initial condition matrix is:
[tex]\left[\begin{array}{ccc}u(1)\\\\v(1)\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}7.5\\\\9\end{array}\right][/tex]
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If ABC = 2x and BAC = 3x + 10 what is the value of x ?
The value of x from the given diagram is -10
Similar triangleTwo triangles are known to be similar if the ratio of their similar sides is equal. The diagram shown is similar to the required diagram.
Given the following parameters
<ABC = 2x
<BAC = 3x + 10
Equate the expression since both angles are equal. Substitute;
2x = 3x + 10
Subtract 3x from both sides
2x-3x = 3x-3x+10
-x = 10
x = -10
Hence the value of x from the given diagram is -10
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(Sequences and Summations) How would you solve this? Please give an explanation rather than just answering the question.
Step-by-step explanation:
To find the Tth term of an arithmetic progression, you should use the formula: Tn: a + (n-1)d, whereby 'a' is the first term, you have to find 'n' and 'd' is the difference between the first 2 numbers to find out by how much the arithmetic progression is increasing or decreasing. Hence, 29/30 minus 4/5 equals to 1/6. 'a' is 4/5 and 'd' is 1/6.
Use the above formula by replace a and d then you'll get the answer. Hope this helps.
a probability Qs, please help! thx!
Answer:
10/13
Step-by-step explanation:
There are 52 cards in a standard deck. There are 4 queens (queen of spades, clubs, hearts, diamonds) and 36 (2 - 10 of four suites) number cards. Therefore the probability of drawing a queen or a number card is (4 + 36)/52 = 40/52 = 10/13.
There are 360 girls and 135 boys in a school. What is the ratio of girls to boys expressed in the lowest terms?
Answer: 8:3
Step-by-step explanation:
360:135
We can simplify both, dividing both of them by a common divisor (45)
360/45= 8
135/45= 3
The ratio in lowest terms is 8:3
the ratio of girls to boys in the school, expressed in the lowest terms, is 8:3.
To find the ratio of girls to boys in the school, we divide the number of girls by the number of boys.
Ratio of girls to boys = Number of girls / Number of boys
Ratio of girls to boys = 360 / 135
To express the ratio in the lowest terms, we can simplify the fraction by finding the greatest common divisor (GCD) of 360 and 135 and then dividing both the numerator and denominator by the GCD.
The GCD of 360 and 135 is 45.
Ratio of girls to boys = (360 / 45) / (135 / 45)
Ratio of girls to boys = 8 / 3
So, the ratio of girls to boys in the school, expressed in the lowest terms, is 8:3. This means that there are 8 girls for every 3 boys in the school.
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35*71+71*65+51*23+23+49
Answer:
35x71+71x65+51x23+23+49=8,345
Step-by-step explanation:
Answer:
8345
Is the correct answer
Step-by-step explanation:
hope it will help you
An architectural drawing lists the scale as 1/4" = 1'. if a bedroom measures 312" by 514" on the drawing, how large is the bedroom?
The length of the bedroom exists at x = 9 and y = 6.
How to estimate the length of the bedroom?From the given information, we get
Then [tex]$\frac{(1/4)}{(9/4)} = \frac{1}{x}[/tex]
Solve this for x.
simplifying the value of x we get
Equate (1/9) to 1/x.
x = 9 (feet).
Convert 1.5 inches to feet using a proportion:
[tex]$\frac{(1/4)}{(1.5)} = \frac{1}{y}[/tex]
Solve this for y.
simplifying the value of y we get
(1/4)y = 3/2
Multiply both sides of the equation by 4.
y = 6
Therefore, the length of the bedroom exists at x = 9 and y = 6.
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An astronaut visited mars. his weight on earth was 180 pounds, and his weight on mars was only 72 pounds. he removed a rock with a weight of 16 pounds on mars. what is the weight of the rock on earth? a. 1.4 pounds c. 6.4 pounds b. 4 pounds d. 40 pounds
Answer: d. 40 pounds
Step-by-step explanation: let e equal the number of pounds weigh on Earth and m equal the number of pounds weighs on Mars.
so
72m=180e
1m= 72m/72
e= 180/72 = 2.5
1m=2.5e
16m=1 x16
e= 16 x 2.5
e= 40
so therefore, 16m=40e
I hope this helps
Six pyramids are shown inside of a cube. The height of the cube is h units. The lengths of the sides of the cube are b.
The area of the base of the cube, B, is
square units.
The volume of the cube is
cubic units.
The height of each pyramid, h, is
. Therefore,
b = 2h.
There are
square pyramids with the same base and height that exactly fill the given cube.
Therefore, the volume of one pyramid is
or One-thirdBh.
We are required to fill in the solution to the question that we have here.
this is done below
Six pyramids are shown inside of a cube. The height of the cube is h units. The lengths of the sides of the cube are b. The area of the base of the cube,
B, is (b)*(b) square units.
The volume of the cube is (b)*(b)*(b) cubic units.
The height of each pyramid, h, is b/2
b = 2h.
There are 6 square pyramids with the same base and height that exactly fill the given cube.
Therefore, the volume of one pyramid is (1/6)(b)(b)(2h)
or One-third Bh.
What is a pyramid?This is the term that is used to refer to the shape that is known to have a square base and the base could also be triangular. The parts of the base are known to have a connection at the top of the pyramid.
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answer is in the attachment below :)
goodluck!!
The amount of unexplained variance in a relationship between two variables is called?
Answer:
The amount of unexplained variance in a relationship between two variables is called: coefficient of alienation also called coefficient of nondetermination. A positive correlation between two variables would be represented in a scatterplot as. line sloping upwards. .
Step-by-step explanation:
im having trouble with this question! pls help
Using a proportional relationship, it is found that the unit rate of change is of 9.
The relation d = 9t is graphed at the end of the answer.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
In this problem, we have d as a function of t, hence the relationship is:
d = kt.
When t increases by 0.2, d increases by 1.8, hence the constant is given as follows:
k = d/t = 1.8/0.2 = 9
The relation d = 9t is graphed at the end of the answer.
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3. Use the image to answer the following questions.
will brainiest if correct. try ur best!
(a) The angle pitch of a roof is safest when measuring between 18° – 27°. According to these guidelines, is the roof pictured in the image safe? (Note:
(b) What is length of the roof line (segment PR)? Round answer to the nearest tenth of a foot and show all your work.
Answer:
Answer:
Step-by-step explanation:
For missing hypotenuse: [tex]\sqrt({a^{2} + b^{2})[/tex]
Plug in the side lengths that are known to find the hypotenuse.
1. No, the angle is less than 18 degrees (closer to 15), so it is not safe
2. The length rounded to the nearest tenth is approximately 15.5 feet.
The Fruit Juice Company sold 5,909,999,222 cans of juice last year. This
year the company sold 3,999,002,135 cans. Which is the best estimate of
how many more cans were sold last year than this year?
OA) 2,000,000,000
OB) 3,000,000,000
OC) 9,000,000,000
OD) 10,000,000,000
HELPPP SIMPLE QUESTION‼️‼️‼️‼️‼️
Four less than a number x is twice another number y.
write in an equation
Answer:
x - 4 = 2y
Step-by-step explanation:
"four less than a number x" therefore; x - 4
"is twice another number y" therefore; 2y
When a detailed scoring guide and rubric is used to score open-ended questions, the result is?
When a detailed scoring guide or rubric is used to score open-ended questions, the result is scored.
The scoring guide assign points to special degrees of student performance. Instructors use them when a scholar's response can earn a number of the full possible factors, commonly for built-reaction items and performance responsibilities.
Rubrics and scoring guides were implemented into cutting-edge classrooms to offer college students higher know-how of what's being assessed, what standards grades are primarily based upon, and what clean and compelling product standards are addressed.
Even as scoring guides illustrate how college students can earn a certain amount of points for precise questions and responses, rubrics assign ratings primarily based on how well a pupil's reaction meets a degree of overall performance.
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How many diagonals does a regular n-gon have? ( An n-gon is a regular polygon with n sides)
Answer:
Use this equation to find out!
Step-by-step explanation:
Since you didn't specify the n-gon, you have to use this equation to find out!
Number of Diagonals = n(n-3)/2
Hope this helps! :)
Find the area of the figure with the coordinates, S(-3, 5), A (1, 5), L(2, 1) and T(-6, 1).
Answer: a = 24 units²
Step-by-step explanation:
Let us graph the figure given. This shape appears to be a trapezoid. Now, we can solve for the area. This shape also has a height of 4, which I forgot to show in the picture.
In the formula, h is the height, a is a base, and b is the other base.
[tex]\displaystyle a=\frac{a+b}{2} h[/tex]
[tex]\displaystyle a=\frac{4+8}{2} 4[/tex]
[tex]\displaystyle a=\frac{12}{2} 4[/tex]
[tex]\displaystyle a=(6)4[/tex]
[tex]\displaystyle a=24\; \text{units}^{2}[/tex]
What is the value of y¹ when y = 5 and x - 10?
Answer:
5
Step-by-step explanation:
y^1 = 5^1 (y = 5)
Anything raised to the power of 1 is just itself.
So, 5^1 = 5
Determine whether the geometric series is convergent or divergent. if it is convergent, find the sum. (if the quantity diverges, enter diverges. ) 7 − 8 64 7 − 512 49
The sum of the given series is 49 and it converges to infinity.
According to the statement
we have given that a series which is 7, -8, 64/7, 512/49
And we have to find that the series is converges or diverges.
So, For this purpose,
The nth term in the series is 6 multiplied by the (n-1)th power of -8/7:
So,
[tex]a_{1} = 7(\frac{-8}{7} )^{1-1}[/tex]
[tex]a_{2} = -8(\frac{-8}{7} )^{2-1}[/tex]
[tex]a_{3} = \frac{64}{7} (\frac{-8}{7} )^{3-1}[/tex]
And so on then
Sum of the series become to the nth partial sum
[tex]S_{N} = 7(1 +\frac{-8}{7} + ......+ (\frac{-8^(n-2)}{7^(n-2)}) + (\frac{-8^(n-1)}{7^(n-1)}))[/tex]
Multiplying both sides by -8/7 gives
[tex]\frac{-8}{7} S_{N} = 7(\frac{-8}{7} +\frac{-8^{2} }{7^{2}} + ......+ (\frac{-8^(n-1)}{7^(n-1)}) + (\frac{-8^n}{7^n}))[/tex]
and subtracting this from [tex]S_{N}[/tex] gives
[tex]\frac{-1}{7} S_{N} = 7(1-\frac{-8^n}{7^n} )[/tex]
[tex]S_{N} = 49 (-1 + (8/7)^n)[/tex]
Now the sum of the series is 49 and the it converges to infinity.
So, The sum of the given series is 49 and it converges to infinity.
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What values of c and d make the equation true? rootindex 3 startroot 162 x superscript c baseline y superscript 5 baseline endroot = 3 x squared y (rootindex 3 startroot 6 y superscript d baseline endroot)
Values of c and d make the equation true are c=6, d=2
Equations
We must find the values of c and d that make the below equation be true[tex]\sqrt[3]{162x^{c}y^{5} } = 3x^{2} y^{3} \sqrt[3]{6y^{d} }[/tex]
cubing on both sides -[tex](\sqrt[3]{162x^{c}y^{5} })^{3} = (3x^{2} y^{3} \sqrt[3]{6y^{d} })^{3}[/tex]
The left side just simplifies the cubic root with the cube:[tex]{162x^{c}y^{5} } = (3x^{2} y^{3} \sqrt[3]{6y^{d} })^{3}[/tex]
On the right side, we'll simplify the cubic root where possible and power what's outside of the root:[tex]{162x^{c}y^{5} } = 27x^{6} y^{3} ({6y^{d})[/tex]
Simplifying[tex]{x^{c}y^{5} } = x^{6} y^{3} ({y^{d})[/tex]
[tex]{x^{c}y^{5} } = x^{6} y^{3+d}[/tex]
On equating,c = 6
d = 2
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