Answer:
[tex]a_4 = 154[/tex]
Step-by-step explanation:
In this problem, we are asked to find the fourth term ([tex]\square_4[/tex]) of a sequence [tex]a[/tex] given that [tex]a_1 = 5[/tex] and [tex]a_n = na_{n-1} + 2[/tex].
To solve for this, we can first find the second term in the sequence by inputting [tex]a_2[/tex] into the sequence definition.
[tex]a_2 = 2a_{2-1} + 2[/tex]
Then, we can replace [tex]a_{2-1}[/tex] with the value that we were given: [tex]a_1 = 5[/tex].
[tex]a_2 = 2(5) + 2[/tex]
[tex]a_2 = 10 + 2[/tex]
[tex]a_2 = 12[/tex]
Next, we can solve for the third term in the sequence.
[tex]a_3 = 3a_{3-1} + 2[/tex]
And we can replace [tex]a_{3-1}[/tex] with the value that we just solved for: [tex]a_2 = 12[/tex].
[tex]a_3 = 3(12) + 2[/tex]
[tex]a_3 = 36 + 2[/tex]
[tex]a_3 = 38[/tex]
Finally, we can solve for fourth term in the sequence.
[tex]a_4 = 4a_{4-1} + 2[/tex]
We can again replace [tex]a_{4-1}[/tex] with the value that we just solved for: [tex]a_3 = 38[/tex].
[tex]a_4 = 4(38) + 2[/tex]
[tex]a_4 = 152 + 2[/tex]
[tex]a_4 = 154[/tex]
Answer:
a₄ = 154
Step-by-step explanation:
You want the value of a₄ given the recursive sequence definition ...
[tex]\begin{cases}a_1=5\\a_{n}=n\cdot a_{n-1}+2\end{cases}[/tex]
SolutionThe easiest way to find the first few terms of a recursively-defined sequence is to use the recursive definition directly:
[tex]a_2=2\cdot a_1 +2 = 2(5) +2 = 12\\\\a_3=3\cdot a_2+2=3(12)+2 =38\\\\a_4=4\cdot a_3+2=4(38)+2=154[/tex]
The value of a₄ is 154.
__
Additional comment
The terms of this sequence get rapidly larger. The 10th term is 23,357,002. The general term can be defined in terms of the Euler gamma function and the incomplete gamma function:
[tex]a_n=\Gamma(n+1)+2e\Gamma(n+1,1)[/tex]
Anyone know this? Struggling highschool student here
The monthly payment for a 15-year term mortgage with a 15% down payment on a $315,200.00 purchase price for a household with a 711 credit score is $2,408.60.
Calculate the monthly payment?The monthly payment for a 15-year term mortgage with a 15% down payment on a $315,200.00 purchase price for a household with a 711 credit score is $2,408.60.To calculate this, first you must review the Monthly Principal & Interest Factor chart.Since the credit score is 711, this falls into the range of 710-729. For a 15-year term, the interest factor is 7.0.Once you have determined the interest factor, you can then calculate the monthly payment.To do this, you must subtract the 15% down payment of $47,280.00 from the purchase price of $315,200.00, which leaves $267,920.00.Then, you must multiply the $267,920.00 by the interest factor of 7.0 and divide it by 12 to get the monthly payment of $2,408.60.To learn more about The monthly payment refer to:
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Which is the equation of the axis of symmetry of the graph of y = –3(x – 6)2 + 5?
x = –6
x = –5
x = 5
x = 6
The equation that represents the axis of symmetry of the graph of the quadratic function is the line; x = 6
What is a quadratic function?A quadratic function is a function that has 2 as the highest exponent. The shape of the graph of a quadratic function is a parabola, which is U shaped.
The equation of the axis of symmetry of the graph of y = -3·(x - 6)² + 5 is obtained as follows.
The specified equation is in the vertex form of a quadratic function, which is; f(x) = a·(x - h)² + k
Where;
(h, k) = The coordinate of the vertex
The equation of the axis of symmetry is x = h
Comparison of the equation, y = -3·(x - 6)² + 5 and the vertex form of a quadratic equation, we get.
The vertex, (h, k) = (6, 5)
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2.Find the GCF(224,264) using Euclid division algorithm.
Answer:
GCF = 8.
Step-by-step explanation:
First, we divide 264 by 224 and we get the identity:
264 = 1*224 + 40 ( That is 264 divided by 224 goes once and the remainder is 40)
Now we divide 224 by 40 to get:
224 = 5*40 + 24
Repeating this process, we get:
40 = 1*24 + 16
24 = 1*16 + 8
16 = 2*8 + 0 <------ we stop because the remainder is 0.
So, The GCF is 8.
What kind of line is Y =- 6?.
y = -6 is a horizontal line and perpendicular to y-axis.
A horizontal line is perpendicular to the y-axis and parallel to the x-axis.
The equation for a horizontal line is y = c.
where c is constant and c constant is the y-coordinate of every point on the line.
In the equation y = -6, the constant is -6.
This means that every point on this line has an y-coordinate of -6.
Every point on the line (x, y) will have a y-coordinate of -6, while the
x-coordinate can be anything.
Therefore, y = -6 represent a horizontal straight line with perpendicular to the y-axis and parallel to the x-axis.
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A game includes spinning a spinner with numbers 1–5 and rolling a number cube with numbers 1–6.
What is the probability of spinning an even number and rolling a 5?
The values of the probability from spinning the spinner and rolling the cube are;
Probability that the spinner lands on an even number = 2/5Probability of rolling a 5 on the number cube = 1/6Pthe joint probability of the spinner landing on an even number and rolling a 5 = 1/15What is the probalibilty of an evdent?Probability is a measure of the liklihood that an event will occur. The probability of an event = Number of times the event occurs ÷ Sum of the frequencies of all possible events.
Numbers on the spinner are; 1, 2, 3, 4, and 5
Numbers in the number cube = 1, 2, 3, 4, 5, and 6
The probability of an event = The number of required outcomes ÷ The number of possible outcomes
The possible even numbers on the spinner = 2, and 4
The number of even numbers in the spinner = 2
The number of possible numbers on the spinner = 5
The ratio of the number of even numbers to the number of possible numbers, which is the probability of spinning an even number, therefore is; P(E) = 2/5
The number of 5s on the cube = 1
The number of possible numbers on the cube = 6
The probability of rolling a 5 on the number cube is therefore, p(5) = 1/6
The probability of landing on an even number and rolling a 5, P(E) × P(5) is therefore;
P(E) × P(5) = (2/5) × (1/6) = 2/30 = 1/15Learn more about probability here: https://brainly.com/question/51579
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Answer:
Probability of spinner landing on an even number-2,5
Probability of rolling a 5
on number cube-1,6
Probability of spinner landing on an even number and rolling a 5-1,15
Step-by-step explanation:
bc
What i the difference between 4 x 3 and 43? Prove your anwer and explain your thinking
The difference between 4 x 3 and 43 is that 4 x 3 is the mathematical operation of multiplying 4 and 3, which equals 12, while 43 is just a number.
The Mathematical OperationsThe difference between the expression "4 times 3" and the number 43 is that the former indicates the mathematical action of multiplying "4 times 3," which results in the value 12, while the latter simply represents the number itself.
To prove this, you can perform the mathematical operation of 4 x 3 = 12 and compare it to the number 43. As 12 is not equal to 43, it is clear that these are two different values.
In general, when we see a number with multiple digits, like 43, it is generally not thought of as the result of a mathematical operation. However, when we see an expression like 4 x 3, we know that it is the result of a multiplication operation and it is not just a number.
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There were 200 members at a skating club. Membership dropped by 30%. How many members are there now?
Answer:
140 members
Step-by-step explanation:
find 70% of 200
What are characteristics of perpendicular lines?.
The characteristics of perpendicular lines:
1) Perpendicular lines are intersecting lines.
2) The perpendicular lines are coplanar.
3) The perpendicular intersect at a 90° angle.
4) The product of slopes of perpendicular lines is -1.
We know that two lines are perpendicular to each other if they intersects and these two lines are inclined at angle 90°
Since these lines are inclined at 90° to each other, hence they create right angles.
Perpendicular lines are intersecting lines.
Also, the perpendicular lines are coplanar.
Mathematically, the perpendicular lines are represented by the symbol, ‘⊥‘.
If two lines l₁ and l₂ are perpendicular to each other then they are represented as l₁ ⊥ l₂.
The product of slopes of perpendicular lines is always -1.
Let m₁ be the slope of line l₁ and m₂ be the slope of line l₂.
If line l₁ and l₂ are perpendicular to each other then m₁ × m2₂ = -1
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Please Help. The picture of the question is below. My teacher is going to fail me if I do not get this question so please make it snappy.
The roots of a function are the points at which the graph of the function crosses the x-axis.
What are the roots of the function?The definite solutions to the equation are x = -2 and x = 1.The equation for the function whose graph is shown is y = (x+2)(x-1).The roots of the function are x = -2 and x = 1.The definite solutions to the equation are x = -1 and x = 3.The equation for the function whose graph is shown is y = (x + 1)^2 - 4.The roots of the function are x = -1 and x = 3.These are the x-coordinates of the points where the graph crosses the x-axis.They are also the solutions to the equation y = 0.The roots are also known as the zeros of the function. In other words, the roots of a function are the values of x that make the function equal to zero.For example, the equation x^2 + 3x + 2 = 0 has roots at x = -1 and x = -2. This means that when x is equal to -1 or -2, the equation's left-hand side (x2 + 3x + 2) is equal to zero.To learn more about the roots of the function refer to:
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halp i need this asap
Answer: 126 mm^2 - C
Step-by-step explanation: Hello! The formula for area of a triangle is 1/2(b)(h). b = base and h = height. You would multiply the base and height by 1/2 because a triangle is 1/2 the size of a square. The formula for the area of a square is (b)(h), and you would have to multiply (b)(h) to find the area of a triangle with the same base and height. The base of this triangle is 28 mm, and the height of this triangle is 9 mm. Substitute 28 mm in for the base, and 9 mm in for the height. (28)x(9) = 252. Now you have to multiply 252 x 1/2. 252 x 1/2 = 126. The answer is C, 126.
At Jaylen’s school, students must choose a language, an elective, and a science class. Their options are listed in the table.
Course Offerings
Language
Elective
Science
Chinese
Art
Astronomy
French
Band
Biology
German
Choir
Chemistry
Spanish
Computers
Physics
How many different combinations are possible?
There are twelve possible combinations:
Chinese Art AstronomyChinese Band BiologyChinese Choir ChemistryChinese Computers PhysicsFrench Art AstronomyFrench Band BiologyFrench Choir ChemistryFrench Computers PhysicsGerman Art AstronomyGerman Band BiologyGerman Choir ChemistryGerman Computers PhysicsAt Jaylen's school, students have a variety of course offerings from which to choose. They must choose a language, an elective, and a science class. The language options are Chinese, French, German, and Spanish.
With these four language options, four elective options, and four science options, there are twelve possible combinations of courses to choose from.
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arthur benjamin says that the current top of the pyramid of mathematics curriculum is
please help me !!! i need answers asap and i’ll give brainlist
You would need to know the values of each letter in the alphabet to prove AMNO~ATUV.
What other piece of information would you need to prove MNO~TUV?In order to prove that MNO~TUV, we would need to know the values of M,N,T,U,V,O. We would need to know the relationship between these variables in order to determine if MNO~TUV is true. For example, if MNO is equal to TUV, then MNO~TUV would be true.We would also need to know the type of relationship between the variables. For example, if the variables are related by addition, then if M + N = T + U, then MNO~TUV would be true.Additionally, we would need to know the context of the equation. For example, if the equation is related to a geometric problem, then we would need to know the type of shape and the number of sides in order to prove if MNO~TUV is true.Finally, we would need to know any other constraints or conditions that would be affecting the equation. For example, if there is a time limit, then the equation would need to be solved within that time limit in order to prove if MNO~TUV is true.To learn more about to prove MNO~TUV refer to:
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What is the largest integer value that makes this inequality true?
4x-8<-2x+1
Answer:
Step-by-step explanation:
the answer would be 10
The perimeter of a rectangular garden is 4.8 meters. Its length is twice its width. How wide is the garden? (Full Answer)
Answer:
0.8 meters is the width.
Step-by-step explanation:
Answer: 0.8
Step-by-step explanation: All you have to do is set the equation up so you're looking at the length being twice the width (which in equation form would be l=2w) then you say there is two lengths, so you have 4w. Then you add the original width to the lengths (2w) so you have 6w= 0.8
The area of the quare felid i 40,000 quared and we want to but a fence diagonally through the field. What hould the length of the fence be?
The length of the fence must be 282.84 ft.
Area of the field = 40,000 ft²,
The length of the fence will be equal to the diagonal of the square.
For a square of side length S, the area is:
A = S²
Substituting the values in the formula -
S² = 40,000 ft
Applying the square root on both sides -
S = √(40,000 ft²)
Calculating, the diagonal of a square of side length S is:
D = S x√2,
Substituting the values -
D = √(40,000 ft²) x √2
= √(80,000 ft²)
= 282.84 ft
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What is the area of a triangle whose height is 6 cm and base is 10 cm?.
The area of a triangle whose height is 6 cm and the base is 10 cm is 30 cm².
Area of triangle = 1/2 × b × h
= 1/2 × 10 × 6
= 1/2 × 60
= 30 cm².
A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.
In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.
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Reason What can you conclude about the domain and the range of a relation if a vertical line at =x equals 5 passes through 2 points? 1 point? No points? Explain.
The required domain of the vertical line is {5} and the range is all real numbers.
Given that,
Domain and range of the vertical line x = 5 is to be determined.
The domain is defined as the values of the independent variable for which there is a certain value of the dependent variable exists in the range of the function.
Here,
We can infer that the domain of this relation can only be constrained if a vertical line at x = 5 passes through 0 locations. This function's range can only be a collection of real numbers or a constraint.
Thus, the required domain of the vertical line is {5} and the range is all real numbers.
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What number would you multiply the second equation by in order to eliminate the x term when adding to the first equation?.
In order for the variables in the first equation to cancel out, we must multiply a number in the second equation to make it equal to those variables. For instance, we must multiply the second equation by two in order to make it equal four in order to cancel out x.
To make the variables in the first equation cancel each other out, we must multiply a number in the second equation to make it equal to those variables. For instance, we must multiply the second equation by two in order to make it equal four in order to cancel out x. We must now multiply the second equation by 3 in order to equal 9y in order to eliminate y.To learn more about equations here
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What is the latest estimate for the likelihood of one or more M 6. 7 earthquakes in the Bay Area region before the year 2043?.
A 72 percent is the latest estimate for the likelihood of one or more M 6.7 earthquakes in the Bay Area region before the year 2043.
To estimate the likelihood of future earthquakes, scientists rely on a variety of techniques that help us understand the velocities and magnitudes of past earthquakes. Using the Global Positioning System (GPS) and other land surveys and geological techniques,scientists have determined how much current plate movement, totaling inches per year across the San Francisco Bay region, stresses these individuals. We were able to more accurately measure how well it disperses. Small earthquakes occur more frequently than large ones. There is a 98% chance that an earthquake of magnitude 6.0 or greater will occur before 2043. There is a 72% chance that at least one earthquake of magnitude 6.7 or greater will occur in the San Francisco Bay Area, and a 51% chance that at least one magnitude earthquake will occur. Therefore they concluded that there is a 72% chance (or probability) of at least one earthquake of magnitude 6.7 or greater occurring somewhere in the San Francisco Bay Area before 2043.
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What is the modulus of the complex number 4 +3i?.
The modulus of the complex number is:
|z| = 5
Now, According to the question:
Complex numbers are the numbers that are expressed in the form of a+ib where, a,b are real numbers and 'i' is an imaginary number called “iota”. The value of i = (√-1). For example, 2+3i is a complex number, where 2 is a real number (Re) and 3i is an imaginary number (Im).
The modulus of complex number z=a+bi is:
[tex]|z| = \sqrt{(a+bi)(a-bi)}[/tex]
[tex]|z| = \sqrt{a^2+b^2}[/tex]
The given complex number is :
4 + 3i.
a = 4 and b = 3
The modulus of the complex number will be:
[tex]|z|=\sqrt{4^2+3^2}[/tex]
[tex]|z|=\sqrt{16+9}\\\\|z|=\sqrt{25}[/tex]
|z| = 5
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make a the subject of the relation S(a+b) =t
Answer:
a = [tex]\frac{t-sb}{s}[/tex]
Step-by-step explanation:
s(a + b) = t Distribute the s
sa + sb = t Subtract sb from both sides
sa + sb - sb = t - sb Simplify
sa = t - sb Divide both sides by s
a = [tex]\frac{t-sb}{s}[/tex]
the cost of chesse increased by 25%. how much is the new price of the cheese that originally cost $4.20. PLEASE HELP WILL GIVE BRAINLIST FOR SOLULTIONS
Answer:
Step-by-step explanation: The answer is $48.15 hopes this helps :)
An ad for an exercise product stated: "using this product will burn 74% more calories." What is misleading about this statement
Answer:
The statement is misleading as it does not provide any context for the comparison. It does not clarify what the 74% more calories is being compared to or what amount of calories is being burned by using the product. Additionally, the advertisement does not provide any evidence to back up the claim.
if (-1)^n+(-1)^4n =0 then n is?
a) any positive number b) any negative number c)any odd number d)any even number
The correct statement regarding the value of n is given as follows:
c) any odd number.
How to obtain the value of n?The expression for this problem is given as follows:
(-1)^n+(-1)^4n.
The numeric value for the expression is given as follows:
0.
The n powers of -1 are given as follows:
Negative 1 if n is odd.Positive 1 if n is even.(-1)^4n will always be an even power due to the multiplication by the even number 4, hence it is positive.
As (-1)^4n is always positive and the numeric value of the expression is of zero, we have that (-1)^n is always negative one, meaning that the value of n is an odd number.
This means that option c is correct.
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The owner of a bookstore buys used books from customers for $1.50 each.The owner then resells the used books for 400% of the amount he paid for them.What is the price of a used book in this bookstore?
The selling price of a used book at the store where the owner buys a used book for $1.50 and resells the used book at a price of 400% the price at which buys the used book is $6.00
What is the selling price of a commodity?The selling price of an item is the price which is displayed on the item on the shelves of a store. The selling price is often different from the price at which the item is bought, or produced, which is often lesser than the price at which the item is sold.
The amount at which the owner buys each used book = $1.50
The amount at which the owner of the used book store sells the books = 400% of the amount he paid for the books
400% of an amount x is equivalent to four times the amount. (4 × x)
The price at which the owner sells a used book at his store, P, is therefore;
P = 400% × $1.50 = 400/100 × $1.50 = $6.00
The price of a used book at the store is $6.0
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B is the midpoint of AC. AB - 6x + 1 and BC - 2x + 9. Find the length of AC
The length of AC in the line segment is 26 units.
How to find the length of a line segment?B is the midpoint of AC.
AB = 6x + 1
BC = 2x + 9
A midpoint is a point lying between two points and is in the middle of the line joining the two points.
Hence,
AB = BC
6x + 1 = 2x + 9
6x - 2x = 9 - 1
4x = 8
divide both sides by 4
x = 8 / 4
x = 2
Therefore,
AC = 2AB
AC = 2(6x + 1)
AC = 2(6(2) + 1)
AC = 2(12 + 1)
AC = 26 units
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Is the solution set the answer?.
Any value of a variable that makes the equation true is a solution. The set of all variables that makes the equation true is called a solution set. Because 2(4) + 6 = 14, the solution set for 2y + 6 = 14 is 4.
How do I locate the set of solutions?Plugging each value in the domain into the equation to obtain the range values is the first step in determining the solution set for an equation with a given domain. Write these values as a set and create ordered pairs from them. Your response is that set!
Is the math answer the solution?An assignment of values to the unknown variables that achieves equality in the equation is called a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used in place of the unknowns, makes the equation equal.
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Full Question = How do you find the solution set of an equation?
K is the midpoint of GJ and H is the midpoint of GI
If IJ =z-4 and HK = z - 37, what is the value of z?
The value of z from the triangle is z = 70
What are similar triangles?If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.
Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides
Given data ,
Let the first triangle be represented as ΔIGJ
Let the second triangle be represented as ΔHGK
Now , K is the midpoint of GJ and H is the midpoint of GI
So , IH = GH and GK = KJ
And , the triangles ΔIGJ and ΔHGK are similar
So , corresponding sides of similar triangles are in the same ratio
Substituting the values in the equation , we get
The measure of HK = ( 1/2 ) measure of side IJ
And , ( z - 37 ) = ( 1/2 ) x ( z - 4 )
On simplifying the equation , we get
Multiply by 2 on both sides of the equation , we get
2z - 74 = z - 4
Subtracting z on both sides of the equation , we get
z - 74 = -4
Adding 74 on both sides of the equation , we get
z = 70
Hence , the value of z is 70
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Why do parallel lines require the undefined terms of line and plane?.
Parallel lines require the terms line and plane because line and plane that are parallel cannot cross each other. Thus, they will never create a point of intersection. The characteristics of that parallel lines consist of lines and planes.
The characteristics of parallel lines are;
The shortest distance between parallel lines is the same at all points along the lines.
The lines are on the same plane.
As the plane is prolonged indefinitely, the lines do not intersect.
The characteristic of these geometric figures that create the different requirements would be how these undefined terms are situated. In the case of parallel lines, these are lines that would not intersect no matter how long the line is extended or whether it goes infinitely; thus, the lines lie on the same plane.
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