Answer:
Please check the explanation.
Step-by-step explanation:
(a) What is the recursive rule for the sequence?
Given the sequence
6, 18, 54, 162,...
Please note that each successive term is 3 times the previous term.
i.e. 18 = 6×3, 54 = 18×3, 162 = 54×3
Here, r = 3 is the common multiplier
In other words, every next term can be obtained by multiplying the previous term by a number 'r', using the recursive formula
[tex]a_n=a_{n-1}\times r[/tex]
Here, aₙ is r times the previous term aₙ₋1.
For example, in order to determine the 2nd term a₂, just put n=2 in the recursive formula
[tex]a_n=a_{n-1}\times r[/tex]
so substituting r = 3, and n = 1 in the recursive formula
[tex]a_2=a_{2-1}\times 3[/tex]
[tex]a_2=a_1\times \:3\:\:\:\:\:\:[/tex]
as
a₁ = 6
so
[tex]a_2=6\times \:3\:\:\:\:\:\:[/tex]
[tex]a_2=18[/tex]
(b) What is the iterative rule for the sequence?
Given the sequence
6, 18, 54, 162,...
A geometric sequence has a constant ratio 'r' and is defined as
[tex]a_n=a_1\cdot r^{n-1}[/tex]
[tex]\frac{18}{6}=3,\:\quad \frac{54}{18}=3,\:\quad \frac{162}{54}=3[/tex]
The ratio of all the adjacent terms is the same and equal to, so
r = 3
as
a₁ = 6
so substituting r = 3 and a₁ = 6 in the nth term of the sequence
[tex]a_n=a_1\cdot r^{n-1}[/tex]
[tex]a_n=6\cdot \:3^{n-1}[/tex]
Thus, the iterative rule for the sequence is
[tex]a_n=6\cdot \:3^{n-1}[/tex]a) The recursive rule for the sequence is [tex]a_n=3a_{n-1}[/tex]
b) The iterative rule for the sequence is [tex]a_n=2(3^n)[/tex]
The given sequence is:
6, 18, 54, 162, …
The common ratio, r = 18/6
r = 3
Let the last term be [tex]a_n[/tex]
Let the preceding term be [tex]a_{n-1}[/tex]
The recursive rule for the sequence is given as:
[tex]a_n=a_{n-1}r\\\\a_n=3a_{n-1}[/tex]
b) The iterative rule is gotten by using the formula:
[tex]a_n=ar^{n-1}[/tex]
Substitute a = 6 and r = 3 into the formula above
[tex]a_n=6(3)^{n-1}\\\\a_n=\frac{6}{3}(3^n )\\\\a_n=2(3^n)[/tex]
Learn more on sequence here: https://brainly.com/question/6561461
If the interest of sum of money is 6 yrs in 3/8 of the principal . what is the rate of interest?
Answer :
R = 6.25%
Solution,
Let P is the principal. It means interest will be :
I=3/8 P
The formula for the interest is given by :
[tex]I=\dfrac{PRT}{100}\\\\\dfrac{3}{8}P=\dfrac{PR\times 6}{100}\\\\\dfrac{3}{8}=\dfrac{6R}{100}\\\\R=\dfrac{300}{8\times 6}\\\\=6.25\%[/tex]
Hence, the rate of interest is 6.25%.
The freshman basketball coach’s office has a doorway that is 77 inches high. The coach will only recruit those student athletes who have to duck to enter the office. Of all the freshmen who wish to play basketball, the mean height is 75 inches with a standard deviation of 2.82 inches. Meanwhile, the football coach will only recruit student athletes to play linebacker (a defensive position) who weigh 210 pounds or more. Of all the freshmen who wish to play linebacker, the mean weight is 190 inches with a standard deviation of 12.32 pounds. Who do you think will have a harder time recruiting players?
a coffee supplier finds that it cost $850 to roast and package 100 pounds of coffee in a day and $2850 to produce 500 pounds of coffee in a day. assume that the cost function is linear. express the cost as a function of the number of pounds of coffee they produce each day
Answer:
f(x) = 5x + 350
Step-by-step explanation:
Create 2 points using the information given, where x is the number of pounds of coffee and y is the cost.
The 2 points are (100, 850) and (500, 2850)
Then, use rise over run to find the slope:
(y2 - y1) / (x2 - x1)
(2850 - 850) / (500 - 100)
2000 / 400
= 5
Then, plug in the slope and a point into y = mx + b to find b:
y = mx + b
850 = 5(100) + b
850 = 500 + b
350 = b
Plug in the slope and y intercept into y = mx + b to get the equation:
y = 5x + 350
Put it into function form:
f(x) = 5x + 350 is the cost function
A man travels 320 miles in 8 hours. If he continues at the same rate, how many miles will he
travel in the next 2 hours?
Answer: 80 miles
Step-by-step explanation:
320miles/8hours= 40mph
40mph=xmiles/2hrs
40*2= 80 miles
It is 5:15 pm now. What time will it be in 40 minutes?
5:45 am
A5:45 pm
c5:55 pm
6:00 pm
Answer:
C:5:55
Step-by-step explanation:
5:15 plus 40 minutes will be 5:55
Answer:
C. 5:55 itssssss easyyy
Step-by-step explanation:
5:15
+40
55
Sale! 25% OFF of the original price! Laura wants to buy a sleeping bag. The original price is $56. How much will Laura pay if she buys it during the sale.
Answer:
$14
Step-by-step explanation:
56 × 0.25 = 14
to check this, you can divide 14 ÷ 56 = 0.25
to turn a percentage into a decimal, just divide it by 100
The sum of 2 numbers is 84 if one number is 4.less than the other find the numbers
Answer:
one number= x = 44
the other number= (x-4)= 40
Step-by-step explanation:
one number= x
the other number= (x-4)
x + (x-4) = 84
2x= 84+4
2x= 88
x= 88/2= 44
one number= x = 44
the other number= (x-4)= 40
Ya tengo el resultado, debe ser "y=4x-4"
Pero le doy 15 puntos al que llegue a ese resultado y explique cómo llegó a él
El método de Descartes para determinar tangentes se basa en la idea de que para muchas gráficas, la recta tangente en un punto dado es una recta "única" que intersecta la gráfica solamente en ese punto. Aplicaremos ese método para determinar la ecuación de una recta tangente a la parábola y=x^2 en el punto (2,4).
Primero, sabemos que la ecuación de la recta tangente debe tener la forma de y=mx+b. Usando el hecho de que el punto (2,4) está en la recta, podemos resolver para b en términos de m y obtener la ecuación y=mx+ (4-2m). Ahora queremos que (2,4) sea la "única" solución del sistema
{ y=x^2
y=mx+4-2m
De este sistema obtenemos x^2-mx+(2m-4)=0. Usando la fórmula cuadrática obtenemos
m+- √(m^2-4(2m-4))
x= --------------------------------
2
Para obtener una solución única para x, las dos raíces deben ser iguales, en otras palabras, el discriminante m^2-4(2m-4) debe ser 0. Completa el trabajo para obtener m y escribe una ecuación de la recta tangente
Answer:
Ver desarrollo en los parrafos que siguen
Step-by-step explanation:
El problema describe todos los pasos para llegar al sistema the equaciones:
y = x^2
y = m x + 4 - 2 m
Luego igualamos las cantidades 'y" y llegamos a la siguiente ecuacion cuadratica en "x":
x^2 = m x + 4 - 2m
luego restamos "m x" y "4" de ambos lados, y sumamos "2 m" de ambos lados para terminar con una ecuacion cuadratica igualada a cero para poder aplicar la equacion cuadratica
x^2 - m x - 4 + 2 m = 0
similar a:
a x^2 + b x + c = 0
donde
a = 1; b = "-m"; y c = "2 m - 4"
Luego usando la ecuacion cuadratica:
nos da de resultado:
[tex]x=\frac{m+/-\sqrt{m^2-4(1)(2m-4)} }{2(1)}[/tex]
Y para que la solucion sea UNICA, es necesario que la cantidad dentro de la raiz sea "cero" de modo que de solamente la solucion
x = m/2
Ahora, requiriendo que el determinante the la ecuacion cuadratica sea cero es:
[tex]m^2-4(2m-4)=0\\m^2-8m+16=0\\(m-4)^2=0\\m-4=0\\m=4[/tex]
ya que reconocemos que el trinomio m^2-8m+16 es un binomio quadrado perfecto; (m-4)^2
Y pidiendo que that binomio quadrado sea cero, es lo mismo que requerir que el binomio (m-4) sea cero, lo que significa que m = 4.
De esta manera, obtuvimos la pendiente "m" de nuestra recta:
y = m x + b
y = 4 x + b
Y como conociamos el valor de "b" usando el hecho de que el punto (2, 4) esta en la recta:
4 = 4 (2) + b
4 = 8 + b
4 - 8 = b
b = -4
Por lo tanto, la ecuacion dela recta es:
y = 4 x - 4
the letters of the word independent are written on individual card and the cards are put into a box a card is selected and then replaced and then a second card is selected find the probality of obtaining the letter p twice
Answer:
The probability of obtaining the letter p twice is 1/121
Step-by-step explanation:
Probability of Recurring Events
There are 11 letters in the word 'independent', one of which is the letter 'p'.
When those letters are written on individual cards and they are put into a box, there are 11 different choices to pick at random.
This means the individual probability of getting a 'p' is:
[tex]\displaystyle P_1=\frac{1}{11}[/tex]
The card is reinserted into the box, leaving the sample space unaltered, thus the second card has the same probability:
[tex]\displaystyle P_2=\frac{1}{11}[/tex]
We'll use the multiplication rule. Just multiply the probability of the first event by the second.
[tex]\displaystyle P=P_1*P_2=\frac{1}{11}*\frac{1}{11}[/tex]
[tex]\displaystyle P=\frac{1}{121}[/tex]
The probability of obtaining the letter p twice is 1/121
Is y=6x-4 proportional?
Answer: no
Step-by-step explanation:
it wont be proportional since if we substitute 0 for x y wont be 0
What is the Inverse function of F(x)=3x²?
Answer:
f⁻¹(x) = x+2 / 3
Step-by-step explanation:
i dont have one. i just did it.
Helpp meeeeeee plzzz (13 points )
Answer:
that they both have right angles and have a leath of 5
Step-by-step explanation:
Let f(x) = 9x and g(x) = x + 7. What's
the smallest number that is in the domain of
fºg?
Enter the correct answer.
OOOO
DONE
Clear all
Answer:
Let `f` be a function defined on [0,2]. Then find the domain of function `g(x)=f(9x^2-1)
Step-by-step explanation:
I'm not sure if that's right
Which of these affect real investment value? Check all that apply.
Answer:
Fees and expenses
nominal interest rate
taxes
Step-by-step explanation:
Find the value of x. Will give brainliest
Answer:
x = 11
Step-by-step explanation:
Angle CAB = 33 degrees (Z-figure)
Angle ACE = 180 degrees (line), therefore angle ACB = 180 - 5x.
Sum of all angles in the triangle should equate to 180 degrees.
Now the sum is of all angles in triangle ABC is:
CAB + ABC + ACB = 33 + (180 - 5x) + 2x = 213 - 3x
So 213 - 3x should equal 180.
213 - 3x = 180 <=> -3x = -33 <=> x = 11
The amount of change that goes up
Answer:
rates of change, positive or negative
Step-by-step explanation:
Plz helplplpp this is due NOWWW
Answer:
Option 2
Step-by-step explanation:
1/4 is equal to .25 or 25/100
1) Find the product of -5x2y4 and 3xy3
Answer:
Answer: -15x3y7
Step-by-step explanation:
Answer:
-15x3y7 is the answer
Step-by-step explanation:
whats 0.1 as a percent
Answer:
TO findt he percent move the decimal place to the right 2 times. THis applies for any decimal. Therefore the percent is 0.1--->10%
Step-by-step explanation:
Using point-slope form, write the equation of the line that passes through (–3, 2) and has a slope of 5. A. (y – 2) = 5(x + 3) B. (y – 2) = 5(x – 3) C. (y + 2) = 5(x – 3) D. (y + 2) = –5(x + 3)
Answer:
A. (y - 2) = 5(x + 3)
General Formulas and Concepts:
Algebra I
Point-Slope Form: y - y₁ = m(x - x₁)
x₁ - x coordinate y₁ - y coordinate m - slopeStep-by-step explanation:
Step 1: Define
Point (-3, 2)
Slope m = 5
Step 2: Write Equation
Substitute in variables into general form.
y - 2 = 5(x + 3)
equation 1: 5x + 3y=8
equation 2: 4x + 7y= 34
9x-10y=42 true
Answer:
true
Step-by-step explanation:
5x + 4x = 9x
3y + 7y = 10y
8 + 34 = 42
Answer:
False
Step-by-step explanation:
5x+3y=8
4x+7y=34
Then:
5x+4x+3y+7y=9x+10y
9x+10y=43 not 9x-10y
What is the common difference between successive terms in the sequence?
0.36, 0.26, 0.16, 0.06, –0.04, –0.14, ...
A.)–0.1
B.)–0.01
C.)0.01
D.)0.1
Answer:
-0.1
any more help just ask :)
Answer:
up
Step-by-step explanation:
A. -1 I hope I helped ...........It was a bumper crop for hominy this year, and The Hominy Man hoped to set a price for a case that can maximize profit. The annual fixed cost for the hominy harvesting and other equipment is $200 and the variable cost per case is $20. The price (p) is related to demand (v) according to the following equation: v = 800 - 16p. To maximize the profit, the optimal price of a case should be_____. The maximized profit is_____.
Answer:
optimal price = $35
Maximum profit = $3400
Step-by-step explanation:
We are given;
The annual fixed cost for the hominy harvesting and other equipment = $200
The variable cost per case = $20
Since demand is given as v, thus total variable cost = 20v
Thus;
Overall total cost = fixed cost + total variable cost = 200 + 20v
We are given relationship between p and v as;
v = 800 - 16p
Making p the subject gives;
p = (800 - v)/16
Now, total revenue is given by;
Total Revenue = vp
Thus;
Total revenue = v[(800 - v)/16] = 50v - v²/16
Now, profit will be;
Profit(P) = Total revenue - total cost
P = (50v - v²/16) - (200 + 20v)
P = 50v - (v²/16) - 200 - 20v
P = 30v - (v²/16) - 200
Maximum profit will be at dP/dv = 0
Thus;
dP/dv = 30 - (v/8)
At dP/dv = 0
30 - (v/8) = 0
v/8 = 30
v = 30 × 8
v = 240
Optimal price will be gotten by putting 240 for v in the price equation which is p = (800 - v)/16.
Thus;
p = (800 - 240)/16
p = 560/16
p = $35
So, optimal price = $35
Maximum profit will be at v = 240.so let's plug in 240 for v into the profit equation.
Thus;
P = 30(240) - (240²/16) - 200
P = 3400
Maximum profit = $3400
Please stat Brainlist who ever answers first OR! Who ever answers with a fluent explanation.
Answer:
Yes it is a proportional relationship
Step-by-step explanation:
You can see a clear pattern, every time time goes up by a minute earning go up by 6. There is no random numbers without pattern. So it’s proportional.
Answer:
Yes it is a proportional relationship.
Step-by-step explanation:
It is because You can see a clear pattern, every time time goes up by a minute earning go up by 6. There is no random numbers without pattern. So it’s proportional.
what is the largest prime number?
Answer:
28258933-1
Step-by-step explanation:
hope it helps you
Jack is 2 times as old as Lacy. 5 years ago the sum of their ages was 20. How old are they now?
Answer:
2x-6=8
2x-6=8+6
2x=24
x=12
What is the graph of y=3/4x-3?
Answer:
Graph A
Step-by-step explanation:
you can write the equation into desmos (search it up on google) and it will produce a graph for you and just match it to the ones you have shown
I need asap!!!brainliest for best answer
Answer:
D
Step-by-step explanation:
the answer is D ok so u see how she jsbdjdbd
What type of correlation does the scatter plot show?
A. Positive
B. Negative
C. Cannot tell
D. None
Hurry please
I need the answer to this one in 2 minutes
Answer:
125
Step-by-step explanation:
45 ÷9=5
5² or 5×5=25
25×5=125
Hope this helps!
Answer:
I THINK ITS
Step-by-step explanation:
5x(2025 ÷81)
5x25
125