Answers
The first five terms of the recursive sequence are 5, 12, 19, 26 and 33.
How to use recursive equations to generate a series
In this question we have a linear recursive equation that requires the value of the immediately previous element to generate the next one. Then, we need to evaluate the expression for the first five elements:
i = 1
a₁ = 5
i = 2
a₁ = 5, a₂ = a₁ + 7
a₂ = 5 + 7
a₂ = 12
i = 3
a₂ = 12, a₃ = a₂ + 7
a₃ = 12 + 7
a₃ = 19
i = 4
a₃ = 19, a₄ = a₃ + 7
a₄ = 19 + 7
a₄ = 26
i = 5
a₄ = 26, a₅ = a₄ + 7
a₅ = 26 + 7
a₅ = 33
The first five terms of the recursive sequence are 5, 12, 19, 26 and 33.
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Related Questions
Find the future value and interest earned if $8704.56 is invested for 8 years at 4% compounded (a) semiannually and (b) continuously.
intorntic compounded semiannually is approximately
Answers
a) The future value, principal plus interest, with compound interest on a principal of $8,704.56 at a rate of 4% per year compounded 2 times per year over 8 years is $11,949.50.
b) The future value, principal plus interest, with compound interest on a principal of $8,704.56 at a rate of 4% per year compounded continuously over 8 years is $11,987.29.
How is the future value determined?The future value can be determined using an online finance calculator.
Data and Calculations:
a) Compounded Semiannually:Principal (P): $8,704.56
Annual Rate (R): 4%
Compound (n): Compounding Semi-Annually
Time (t in years): 8 years
Result:
A = $11,949.50
A = P + I where
P (principal) = $8,704.56
I (interest) = $3,244.94
Calculation Steps:First, convert R as a percent to r as a decimal
r = R/100
r = 4/100
r = 0.04 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 8,704.56(1 + 0.04/2)(2)(8)
A = 8,704.56(1 + 0.02)(16)
A = $11,949.50
b) Compounded Continuously:Using the formula A = Pert
Principal (P): $8,704.56
Annual Rate (R): 4%
Compound (n): Compounding Continuously
Time (t in years): 8 years
Result:
A = $11,987.29
A = P + I where
P (principal) = $8,704.56
I (interest) = $3,282.73
Calculation Steps:First, convert R as a percent to r as a decimal
r = R/100
r = 4/100
r = 0.04 rate per year,
Then solve the equation for A, using the mathematical constant, e = 2.71828
A = Pert
A = 8,704.56(2.71828)(0.04)(8)
A = $11,987.29
Thus, while the future value of $8,704.56 at a rate of 4% per year compounded semiannually over 8 years is $11,949.50, the future value of $8,704.56 at a rate of 4% per year compounded continuously over 8 years is $11,987.29.
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HELP!
ANGLE 1 = 52°
(Show work)
Answers
The measure of the unknown angles are as shown below;
m<2 = 128 degrees = m<4
m<5 = 128 degrees
m<6 = 52 degrees
m<3 = 52 degrees = m<8
m<7 = 128 degrees
Lines and anglesAn angle is the point where the two lines meet. From the given diagram, the lines B and D are parallel to each other with a transversal.
Given the following parameters
m<1 = 52 degrees
From the given diagram, the following are true
m<1 = m<3 (corresponding angle)
m<3 = m<8 (vertical angles)
m<1 = m<6 (vertical angles)
m<2 = m<5 (vertical angles)
m<4 = m<7 (vertical angles)
Also;
m<1 + m<2 = 180
m<2 = 180 - m<1
m<2 = 180 - 52
m<2 = 128 degrees = m<4
m<5 = 128 degrees
m<6 = 52 degrees
m<3 = 52 degrees = m<8
m<7 = 128 degrees
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Working together a small pipe and large pipe can fill a big pool in 6 hour. It takes the smaller pipe 5 hours longer than the large pipe to fill the big pool working alone. How long does it take the smaller pipe to fill the pool by itself ?
Answers
The time taken for the smaller pipe to fill the pool by itself is 15.71 hours
Rate of workTime taken for both pipes = 6 hoursTime taken for long pipe = xTime taken for small pipe = x + 6Rate of work of both pipes = 1/6Rate of work of long pipe = 1/xRate of work of small pipe = 1/x + 61/6 = 1/x + 1/(x+6)
1/6 = (x+6)+(x) / (x)(x+6)
1/6 = (x+6+x) / x²+6x
1/6 = (2x+6)(x² + 6x)
cross product1(x² + 6x) = 6(2x+6)
x² + 6x = 12x + 36
x² + 6x - 12x - 36 = 0
x² - 6x - 36 = 0
Using quadratic formulax = 9.71 or -3.71
The value of x cannot be negative
Therefore, the
Time taken for long pipe = x
= 9.71 hours
Time taken for small pipe = x + 6
= 9.71 + 6
= 15.71 hours
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Identify what a, b, and c would equal in standard form.
Do not simplify the equation.
-14y= 28-10x
a=
b=
C=
Answers
Answer:
below
Step-by-step explanation:
-14y = 28 - 10x
10x - 14y - 28 = 0.
a = 10
b = -14
c = -28
Answer:
a = 10
b = -14
c = 28
Step-by-step explanation:
Goal form: Standard form
ax + by = c
Given form: linear form (not fully simplified)
-14y = 28 - 10x
Add 10x on both sides (to move the x-value to the left-hand side of the equation)
-14y + 10x = 28 - 10x + 10x
-14y + 10x = 28
10x - 14y = 28
Determine [ a ], [ b ], [ c ]
ax + by = c
10x - 14y = 28
[tex]\Large\boxed{a=10}[/tex]
[tex]\Large\boxed{b=-14}[/tex]
[tex]\Large\boxed{c=28}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
I need help with the question
Answers
Answer:
0.7
Step-by-step explanation:
Each increment is 0.1, so count the approximate number of increments needed to get from the orange circle on the left and the one on the right and multiply by 0.1 to get the difference.
If 1/2x = a= 2/3y and x + y= na, what is the value of n?
Answers
Answer:
Step-by-step explanation:
[tex]\frac{1}{2} x=a=\frac{2}{3} y\\\frac{1}{2}x=a\\x=2a \\\frac{2}{3} y=a\\y=\frac{3}{2} a\\x+y=2a+\frac{3}{2} a=\frac{4a+3a}{2} =\frac{7}{2} a=na\\n=\frac{7}{2}[/tex]
ball is thrown vertically upward at an initial speed of Its height (in feet) after t seconds is given by h(t)t(16t). After how many seconds does the ball reach its maximum height? Round answer to two decimal places.
Answers
If the height of ball is shown by h(t)=52t-16[tex]t^{2}[/tex] then the ball will reach after 1.625 seconds.
Given that height in t seconds is shown by h(t)=52t-16[tex]t^{2}[/tex].
We are required to find the time after which the ball will attain its maximum height.
The maximum height is the y coordinate of vertex of the parabola. Then we can use the following value of t.
h(t)=52t-16[tex]t^{2}[/tex]
Differentiate with respect to t.
dh/dt=52-32t
Again differentiate with respect to t.
[tex]d^{2}h/dt^{2}[/tex]=-32t
Because tim cannot be negative means the height is maximum.
Put dh/dt=0
52-32t=0
-32t=-52
t=52/32
t=1.625
Hence if the height of ball is shown by h(t)=52t-16[tex]t^{2}[/tex] then the ball will reach after 1.625 seconds.
Question is incomplete as the right and complete equation is
h(t)=52t-16[tex]t^{2}[/tex] .
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if a rectangular piece of metal has 27.75 square inches what is the length and width?
Answers
We cannot get further information about the dimensions of the piece since the number of variables is greater than the number of equations.
What are the dimensions of a rectangular piece of metal?
By geometry we know that the area of the piece of metal is equal to the product of its length and width, then we must find two real numbers such that:
l · w = 27.75, where l, w > 0.
Unfortunately, we cannot get further information about the dimensions of the piece since the number of variables is greater than the number of equations. We need at least one equation to find an unique solution.
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elsa sold 24 drawings for $12 each at the art fair. She is going to use 1/3 of the money to buy books. The rest of the money is going into her savings account. How much money will she put into her savings account?
Answers
If we multiply the 24 drawing by $12 for each drawing we get $288, the total she made at the art fair. By multiplying this total by 1/3, we get $96 which is the amount she spent on books. If we subtract the $96 spent from the $288 she made, we get $192, the amount she put into her savings account.
24 * $12 = $288
$288 * 1/3 = $96
$288 - $96 = $192
what is 4,928 will rounded to the nearest hundred
Answers
Answer:
4900
Step-by-step explanation:
When rounding a number such as 4928 to the nearest hundred, we use the following rules:
A) We round the number up to the nearest hundred if the last two digits in the number are 50 or above.
B) We round the number down to the nearest hundred if the last two digits in the number are 49 or below.
C) If the last two digits are 00, then we do not have to do any rounding, because it is already to the hundred.
In this case, Rule B applies and 4928 rounded to the nearest hundred is:
4900
Answer:
Step-by-step explanation:
4,928, look at the last two numbers 28 if they are above 50 you round up, if below 50 round down,
The answer is 4,900
a) If x = a + 7 and y = b-a, show that x + y = b + 7.
Answers
Step-by-step explanation:
x = a + 7
y = b-a
To prove
x + y = b + 7.
x+y= (a+7) + (b-a)=a+7+b-a
=a-a+7+b
=0 + 7+b
= b+7
Proved ✅
In 5-card poker, find the probability of being dealt the following hand. Refer to the table. Note that
a standard deck of playing cards has 52 cards-4 suits (clubs, diamonds, hearts, spades), where
each suit has 13 cards (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King).
no pair
The probability of being dealt no pair is
(Type an integer or decimal rounded to eight decimal places as needed.)
Event E
Royal flush
Straight flush
Four of a kind
Full house
Flush
Straight
Three of a kind
Two pairs
One pair
No pair
Total
Number of
Outcomes
Favorable to E
4
36
624
3744
5108
10,200
54,912
123,552
1,098,240
1,302,540
2,598,960
Answers
The probability of being dealt no pair is 0.5011 or 50.11% if the tandard deck of playing cards has 52 cards-4 suits.
What is probability?It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
It is given that:
In 5-card poker, find the probability of being dealt the following hand. Refer to the table.
From the table:
Total number of outcomes = 2598960
Total number of favourable outcomes = 1302540
The probability of being dealt no pair:
P(no pair) = 1302540/2598960
P(no pair) = 0.5011
In percentage:
P(no pair) = 50.11%
Thus, the probability of being dealt no pair is 0.5011 or 50.11% if the tandard deck of playing cards has 52 cards-4 suits.
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1. You have learned several techniques for solving quadratic equations. Create an equation that would be best for each technique listed below. Then explain why that technique would be best for each equation that you created.
2.What is the discriminant and what happens if you are solving and the discriminant turns out to be negative?
Answers
The techniques that can be used to best explain for each equation that I have created are:
What are the techniques?A) For graphing - This is often used in checking if your answer is correct, if the math is known to be a little tedious, graphing is recommended
(b) For factoring: x^2 -3x +4 '
Where: (x-4)(x+1)=0
Then x=-1, 4
(c) For square root method: x^2 = 64
Therefore x = + or - [tex]-\sqrt{64}[/tex] = + or - 8
(d) For completing the square: x^2 + 4x = 11 and x^2 +4x + 4
Note that: x^2 +4x + 4
= x^2 + 4x = -4
= x^2 +4x + 4 = -4 + 4
= (x+2)^2 = 0
So, x = -2
(e) For quadratic formula: 6x² + 7x -19 =0
x= [-b + or - sqr(b² - 4ac)]/2a
Note that b=7
a=6
c=-19
Therefore
x= [-7+ or - sqr(49+4(6)(9)]/2
2. if the discriminant is said to be negative, then the equation is one that is made up of two imaginary or complex solutions.
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See full question below
You have learned several techniques for solving quadratic equations. Create an equation that would be best for each technique listed below. Then explain why that technique would be best for each equation that you created.
a. graphing
b. factoring
c. square root method
d. completing the square
e. quadratic formula
2. What is the discriminant and what happens if you are solving and the discriminant turns out to be negative?
What number is six and four hundredths larger than two and five tenths?
Answers
Answer:
eight and thirty-seven fiftyths
Step-by-step explanation:
6 and 4/100 + 2 and 5/10
6 and 1/25 + 2 and 1/2
156 / 25 + 5 / 2
312 / 50 + 125 / 50
437 / 50
400 / 50 = 8
8 and 37 / 50
If one angle in a parallelogram is a right angle prove the other are the same.
Answers
Answer: If one angle of a parallelogram is a right angle, then all other angles would also be right angles and the parallelogram would be a rectangle.
△ABC has vertices A(-2, 0), B(0,8), and C(4,2) Find the equations of the three altitudes of △ABC
Answers
The equations of the three altitudes of triangle ABC include the following:
3y - 2y - 4 = 0.y + 3x - 8 = 0.4y + x - 6 = 0.What is a triangle?A triangle can be defined as a two-dimensional geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.
What is a slope?A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.
How to determine a slope?Mathematically, the slope of a straight line can be calculated by using this formula;
[tex]Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Also, the point-slope form of a straight line is given by this equation:
y - y₁ = m(x - x₁)
Assuming the following parameters for triangle ABC:
Let AM be the altitudes on BC.Let BN be the altitudes on CA.Let CL be the altitudes on AB.For the equation of altitude AM, we have:
Slope of BC = (2 - 8)/(4 - 0)
Slope of BC = -6/4
Slope of BC = -3/2
Slope of AM = -1/slope of BC
Slope of AM = -1/(-3/2)
Slope of AM = 2/3.
The equation of altitude AM is given by:
y - y₁ = m(x - x₁)
y - 0 = 2/3(x - (-2))
3y = 2(x + 2)
3y = 2x + 4
3y - 2y - 4 = 0.
For the equation of altitude BN, we have:
Slope of CA = (2 - 0)/(4 - (-2))
Slope of CA = 2/6
Slope of CA = 1/3
Slope of BN = -1/slope of CA
Slope of BN = -1/(1/3)
Slope of BN = -3.
The equation of altitude BN is given by:
y - y₁ = m(x - x₁)
y - 8 = -3(x - 0)
y - 8 = -3x
y + 3x - 8 = 0.
For the equation of altitude CL, we have:
Slope of AB = (8 - 0)/(0 - (-2))
Slope of AB = 8/2
Slope of AB = 4
Slope of CL = -1/slope of AB
Slope of CL = -1/4
The equation of altitude CL is given by:
y - y₁ = m(x - x₁)
y - 2 = -1/4(x - 4)
4y - 2= -(x - 4)
4y - 2= -x + 4
4y + x - 2 - 4 = 0.
4y + x - 6 = 0.
In conclusion, we can infer and logically deduce that the equations of the three altitudes of triangle ABC include the following:
3y - 2y - 4 = 0.y + 3x - 8 = 0.4y + x - 6 = 0.Read more on point-slope form here: brainly.com/question/24907633
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Ellen read a book a day for 10 weeks. How many books did
she read in all?
Answers
1 week = 7 days
10 weeks = 10×7 days
= 70 days
if Ellen reads 1 book in a day
Therefore,
1 day = 1 book
70 days = 70×1
= 70 books.
Thus Ellen reads 70 books in 10 weeks.
Hope helps
Answer:
70 books
Step-by-step explanation:
Ellen reads one book per day for 10 weeks.
All we need to do to know the number of books Ellen read overall is to multiply 1 (number of books he read each day) and 10 weeks (total number of days).
Each week is 7 days, so 10 weeks is equal to 70 days.
The equation will be: 1 x 70
We can conclude that Ellen read 70 books overall within 10 weeks.
CAN SOMEONE HELP PLEASE!
Answers
Answer:
None of these
Step-by-step explanation:
[tex]\frac{360}{n}=24 \implies n=15[/tex]
This is called a pentadecagon.
select the correct answer. What is the area of the triangle in the diagram
Answers
Answer:
B
Step-by-step explanation:
The area of the triangle is half the base time the height. The height is y sub 1. The length is the distance between the x values.
Find the experimental probability that only 2
of 4 children in a family are boys.
The problem has been simulated by tossing 4
coins (one to represent each child). Let "heads"
represent a boy and "tails" represent a girl. A
sample of 20 coin tosses is shown.
HTHH HTTH TTTT THTT HTHT
HHTT HHHT THHT
TTHH
HTTT HTHT TTHH THTH HTHH
TTHT HTTT HTHT HHHT HHHH
HTTH
Experimental Probability = [?]%
Answers
The experimental probability that only 2 of 4 children in a family are boys is 50%.
What is experimental probability?Experimental probability refers to the chance of an expected success being achieved in a series of experiments conducted.
Experimental probability is the number of times that the expected success occurs as a fraction of the total number of times the experiment was conducted.
Like all probabilities, the experimental probability is based on the likelihood that what the experimenter expects is achieved.
Expected number of boys = 2
The number of children in the family = 4
Experimental probability = 50% (2/4 x 100)
Thus, we can conclude, based on the experimental probability, that 50% (or 2) of the 4 children in the family are boys.
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Answer:
15%
Step-by-step explanation:
Step 1: Count samples with one H
Why; Only 1 of 4 children in families are boys. The problem is simulated with samples.
Step 2: Count samples with only one H.
Why; The H represents the one boy in the family.
Step 3: Add the samples you counted with one H.
Answer: Your answer should be 3/20 after you change it into a percentage your final answer is 15%
what is ordinary numbers
Answers
What is ordinary number?
1 : a number designating the place (such as first, second, or third) occupied by an item in an ordered sequence — see Table of Numbers. 2 : a number assigned to an ordered set that designates both the order of its elements and its cardinal number.
Se tiene 10 fichas, las 5 primeras de color
azul numeradas del 1 al 5 y las 5 restantes
blancas también numeradas del 1 al 5. Se
colocan en una caja sacando una ficha y
posteriormente otra más, entonces la
probabilidad de que ambas estén
numeradas con el valor 1, es:
Answers
Usando la distribución hipergeométrica, la probabilidad de que ambas estén numeradas con el valor 1, es: 0.0222 = 2.22%.
¿Qué es la fórmula de distribución hipergeométrica?
La fórmula es:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Los parámetros son:
x es el número de éxitos.N es el tamaño de la población.n es el tamaño de la muestra.k es el número total de resultados deseados.Los valores de los parámetros son:
N = 10, k = 2, n = 2.
La probabilidad de que ambas estén numeradas con el valor 1, es P(X = 2), entonces:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,10,2,2) = \frac{C_{2,2}C_{8,0}}{C_{10,2}} = 0.0222[/tex]
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write and solve an inequality that means a number plus four than or equal to twelve.
Answers
explanation:
x- a number
×+4 - a number plus 4
x+4>
- a number plus 4 is greater than or equal to
x+4>
12 - a number plus 4 is greater than or equal to twelve
The correct answer for the solution of inequality is [tex]x\geq 8[/tex].
Let the unknown number be "[tex]x[/tex]."
The statement "a number plus four" can be written as "[tex]x+4[/tex]."
The phrase "is greater than or equal to twelve" can be expressed as "[tex]\geq 12.[/tex]
Put these together, the inequality becomes:
[tex]x + 4\geq 12[/tex]
solve for "[tex]x[/tex]," isolate the variable on one side of the inequality:
Subtract -[tex]4[/tex] from both side of the expression:
[tex]x + 4 - 4 \geq 12 - 4[/tex]
[tex]x\geq 8[/tex]
The correct expression for the inequality is [tex]x\geq 8[/tex]
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write each number as a logarithm with base 2:-3
Answers
The number -3 written as a logarithm with a base of 2 is log₂(0.125) or log₂(1/8)
What are logarithms?As a general rule, logarithms are mathematical expressions that are written in the form log(x) or ln(x), for natural logarithms
How to rewrite the number as a logarithm?The number is given as:
x = -3
The base of the logarithm is given as:
Base = 2
To rewrite the given number as a base of 2, we take the exponent of the number where the base is 2
This is represented as:
Number =2^-3
Apply the power rule of indices
Number =1/2^3
Evaluate the exponent
Number = 1/8
Evaluate the quotient
Number = 0.125
Hence, when the number -3 is rewritten as a logarithm with base 2, the equivalent logarithm expression is log₂(0.125) or log₂(1/8)
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Find the value of x.
Answers
Answer:
x = 52
Step-by-step explanation:
Since the inscribed angle measures 64 degrees, the minor arc is 64*2 = 128 degrees. Therefore the major arc is 180-128 = 232 degrees. Angle X is the difference of major and minor arc divided by 2, so X = (232-128)/2 = 52 degrees.
Instructions: Identify the vertices of the feasible region for the given linear programming constraints.
Optimization Equation:
z=−3x+5y
Constraints:
x+y≥−2
3x−y≤2
x−y≥−4
Fill in the vertices of the feasible region:
(0, )
(−3, )
(3, )
Answers
The vertices of the feasible region are (0, -2), (-3, 1) and (3, 7)
How to identify the vertices of the feasible region for the given linear programming constraints?The optimization equation is given as
z=−3x+5y
The constraints are given as:
x+y≥−2
3x−y≤2
x−y≥−4
Next, we plot the constraints on a graph and determine the points of intersections
See attachment for the graph
From the attached graph, the points of intersections are
(-3, 1), (3, 7) and (0, -2)
So, we have:
(0, -2)
(-3, 1)
(3, 7)
Hence, the vertices of the feasible region are (0, -2), (-3, 1) and (3, 7)
So, the complete parameters are:
Optimization Equation:
z=−3x+5y
Constraints:
x+y≥−2
3x−y≤2
x−y≥−4
Vertices of the feasible region
(0, -2)
(-3, 1)
(3, 7)
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Find the gradient of the line passing through the points (– 2,– 4) and (3,5).
Answers
You can count the rise/run on the graph or use slope formula (y2-y1) over (x2 -x1)
5-(-4) over 3-(-2) = 9/5
Answer:
Gradient of the line is choice D.9/5
Step-by-step explanation:
Hello!Slope between two points:slope=(y₂-y₁)/(x₂-x₁)
(x₁.y₁)=(-2,-4)(x₂.y₂)=(3,5)slope(m)=
[tex] \frac{5 - ( - 4)}{3 - ( - 2)} \\ refine \: (m )= \frac{9}{5} [/tex]
Prove: In an equilateral triangle the three medians are equal
Answers
Step-by-step explanation:
Let ABC be the equilateral triangle. Let AE, BD and CF be the medians. A meridian divides a side into two equal parts. Hence, proved that medians of an equilateral triangle are equal .
Graph the following conditions. {(x, y): x + 2y > 6}
Answers
See attachment for the graph of the inequality expression x + 2y > 6
How to graph the conditions?The condition is given as:
{(x, y): x + 2y > 6}
This means that
x + 2y > 6
The above is an inequality expression, where the variables are x and y
So, we simply plot the graph of the inequality expression x + 2y > 6
See attachment for the graph of the inequality expression x + 2y > 6
Read more about inequality at
https://brainly.com/question/24372553
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Anthony travels from Newcastle to Manchester at an average speed of 65 miles per hour.
The journey takes him 2 hours and 15 minutes.
Declan makes the same journey in 2 hours and 35 minutes.
(a) Work out Declan's average speed for the journey.
Answers
Answer:
See below
Step-by-step explanation:
Distance = rate * time
= 65 m/hr * 2 1/4 hr = 146.25 miles
rate = distance / time
for Declan : rate = 146.25 miles / (2 hrs + 35/60 min) = 56.61 mph
