The recursive formula for the given sequence is a(n) = 2 a(n-1) - a(n-2) + 1
A recursive formula is an equation that express the nth term as a function of preceding term(s), i.e. as function of (n-1)th term, (n-2)th terms, and so on. Mathematically it can be written as:
a(n) = f(a(n-1), a(n-2), ..., a(1))
The given sequence: 1,3,6,10, . . .
Here a(1) = 1. Notice that:
a(2) = 3 = 1 + 2
a(3) = 6 = 3 + 3
a(4) = 10 = 6 + 4
Notice that the differences between terms increase by 1.
Further, we can write:
a(2) = 3 = 1 + (1 - 0) + 1
= a(1) + a(1) + 1
= 2a(1) + 1
a(3) = 6 = 3 + (3 -1) + 1
= a(2) + a(2) - a(1) + 1
= 2a(2) - a(1) + 1
a(4) = 10 = 6 + (6 - 3) + 1
= a(3) + a(3) - a(2) + 1
= 2 a(3) - a(2) + 1
We can continue this recursive pattern to find a(n),
a(n) = 2 a(n-1) - a(n-2) + 1
We can find next term for n = 5:
a(5) = 2a(4) - a(3) + 1
= 2. 10 - 6 + 1 = 15
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What is 0.5 written as a fraction?
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]0.5*\frac{10}{10} = \frac{5}{10} = \frac{1}{2}[/tex]
The total cost to buy gloves for the football team can be found using the function \(p=24.99g+5.69\), where \(g)\ is the number of gloves bought. If there are at least \(7\) players but no more than \(14\) players on the football team, what is the domain of the function for this situation
The domain of the given function is a 180.62 to 355.55.
According to the statement
We have to find that the linear equation domain.
So, For this purpose, we know that the
The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.
From the given information:
The total cost to buy gloves for the football team can be found using the function \(p=24.99g+5.69\), where \(g)\ is the number of gloves bought. If there are at least \(7\) players but no more than \(14\) players on the football team
Then
p=24.99g+5.69
Now find the value of the g is
p=24.99g+5.69
Here the domain of the g]function is a From 1 to 14.
Then
For 7
p=24.99(7)+5.69
p=174.93+5.69
p = 180.62.
And for 14
p=24.99(14)+5.69
p=349.86+5.69
p = 355.55.
So, The domain of the given function is a 180.62 to 355.55.
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Select the reason that best supports Statement 6 in the given proof.
URGENTTTT!!!
Answer:
B) distributive propertyStep-by-step explanation:
The statements 6 covers the operation:
3(x + 7) = 3x + 21This is the reflection of the distributive property of multiplication.
The matching answer choice is B.
Find the slope of the line that contains the points (4,3) and (-2,-5).
The slope of the line that contains the points (4,3) and (-2,-5) is 4/3
In this question,
we need to find the slope of the line that contains the points (4,3) and (-2,-5).
We know that the slope of the line passing though points (x1, y1), (x2, y2) is:
m = (y2 - y1) / (x2 - x1)
Let (x1, y1) = (4, 3),
(x2, y2) = (-2, -5)
Using the formula of the slope,
m = (y2 - y1) / (x2 - x1)
m = (-5 - 3) / (-2 - 4)
m = -8 / (-6)
m = 4/3
Therefore, the slope of the line that contains the points (4,3) and (-2,-5) is 4/3
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Use the given information to determine whether LM is a perpendicular bisector, median, and/or an altitude of Δ J K L .
LM ⊥ JK
Since LM ⊥ JK, LM is an altitude by the definition of altitude. We don't know if it is a perpendicular bisector because it is not evident that M is the midpoint of JK.
What is meant by the altitude of a triangle?An altitude of a triangle is a line segment through a vertex that is perpendicular to a line containing the base in geometry. The extended base of the altitude is the line that contains the opposite side. The intersection of the extended base and the altitude is known as the altitude's foot.
A triangle's altitude is the perpendicular drawn from the triangle's vertex to the opposite side. The altitude, also known as the triangle's height, forms a right-angle triangle with the base.
Since LM ⊥ JK, LM is an altitude by the definition of altitude. We don't know if it is a perpendicular bisector because it is not evident that M is the midpoint of JK.
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Laci and Leon are saving money to go to an amusement park. Laci has $1 more than 4 times the amount of money Leon has. Together, they have $76. Write an equation to determine how much money they have together
Answer:
Step-by-step explanation:
x+4x+1=76 is the answer
We have 6 books on mathematics, 3 on physics, and 1 on chemistry, and you must choose 1 book. in how many ways can you do that? (also think why the an
The number of ways that a book can be chosen from all the books can be determined by using combination.
Combination is a method of choosing items from a set in a way that order of selection does not matter. It refers to the combination of n items taken k at a time without repetition. From example, selection of food, menu, subjects, etc.
A combination is the selection of r items from a set of n items without replacement and where order is unimportant.
nCr=n!/r!(n-r)!
Where n! = 1*2*3*….*n
In the given situation, r = 1(number of books to be chosen) and n=10(total number of books)
10C1=10!/1!(10-1)!
10C1=10!/1!(9)!
10C1=(10*9!)/1!(9)!
10C1=10
The number of ways to choose a book from the ten books is 10.
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Find the 13th term of the geometric sequence 7, 21, 63
Answer: 3720087
Step-by-step explanation:
n=term number
an=term value
terms: 7, 21, 63...
term number: 1, 2, 3, ...
7 is 1st term. 21 is 2nd term. 63 is 3rd term.
21/7=3
63/21=3
Common change in each term is multiplication by 3
Hence, the formula can be expressed in exponents.
an=3^(n-1) * 7 where n is the term number, an is the term value, and 7 is the 1st term in the sequence.
an=3^(13-1) * 7
an=3^12 * 7
an=531441 * 7
an=3720087
What are the next three terms in the sequence, 500, 100, 20?
Answer: –1, 9, 19, 29, … (1 point)
38, 37, 32
40, 51, 62
39, 49, 59
38, 47, 56.
Step-by-step explanation: tried
A boat is cruising at a speed of 24 miles per hour. The captain plans to cruise at this speed for the next 9 miles, plus or minus 3 miles. What is the minimum number of hours the boat will cruise at? Maximum number of hours?
Answer:
Minimum 1/4 Hour Maximum 1/2 Hour
Speed is the ratio of distance and time.
The maximum number of hours the boat will cruise is 1/2 hours.
The minimum number of hours the boat will cruise is 1/4 hour.
What is speed?Speed is the ratio of distance and time.
It tells us how fast a body is moving.
We have,
Boat speed = 24 miles per hour.
Speed = distance / time
Distance = 9 miles
Time = distance / speed
Minimum number of hours:
Distance = 9 - 3 = 6 miles
Time = Distance / Speed = 6 / 24 = 1/4 hours
Maximum number of hours:
Distance = 9 + 3
Time = Distance / Speed = 12 / 24 = 1 / 2 hours
Thus,
The maximum number of hours the boat will cruise is 1/2 hours.
The minimum number of hours the boat will cruise is 1/4 hour.
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what is the inverse of h(x)=7x^2+8 with the domain restriction x greater than or equal to 0
The inverse of the function is f-1(x) = √1/7(x - 8)
How to determine the inverse of the function?The function is given as
h(x) = 7x^2 + 8
Express h(x) as y
So, we have
y = 7x^2 + 8
Swap the positions of x and y
So, we have
x = 7y^2 + 8
Rewrite as
7y^2 = x - 8
Divide by 7
y^2 = 1/7(x - 8)
Take the square roots
y = √1/7(x - 8)
Hence, the inverse of the function is f-1(x) = √1/7(x - 8)
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Michele bought a chocolate cake for $12.75 plus 9 cupcakes to bring to a party. Myka bought 24 cupcakes at the same bakery. If Myka and Michele spent the same amount, how much did each cupcake, x, cost?
Considering the definition of an equation and the way to solve it, each cupcake cost $0.85.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.
The solution of a equation means determining the value that satisfies it and the equality is true. To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.Cost of the cupcakeBeing "x" thecost of the cupcake, and knowing that:
Michele bought a chocolate cake for $12.75 plus 9 cupcakes to bring to a party. → Amount spent by Michele=12.75 + 9xMyka bought 24 cupcakes at the same bakery. → Amount spent by Myka= 24xMyka and Michele spent the same amount.the equation in this case is:
Amount spent by Michele= Amount spent by Myka
12.75 + 9x= 24x
Solving:
12.75= 24x - 9x
12.75= 15x
12.75÷ 15= x
0.85=x
Finally, each cupcake cost $0.85.
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In this problem, you will investigate expected value.
b. Use the random number generator on a calculator to generate, 20 pairs of integers between 1 and 6 . Record the sum of each pair.
The 20 randomly generated pairs for the numbers 1 to 6 is (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,2), (2,3), (2,4), (2,5), (2,6), (3,3), (3,4), (3,5), (3,6), (4,4), (4,5), (4,6), (5,5), (5,6) and the sum of each pair is 2, 3, 4, 5, 6, 7, 4, 5, 6, 7, 8, 6, 7, 8, 9, 8, 9, 10, 10, 11.
Sum of the number:
When we add two or more numbers, the result or the answer we get can be defined as the SUM. The numbers that are added are called addends.
For example if we add the numbers 2 and 7 then we get the um as 9.
Given,
Here we need to generate the 20 pairs of integers between 1 and 6 . And also we have to record the sum of each pair.
The 20 pairs by using the number 1 to 6 are,
Listed as,
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,2), (2,3), (2,4), (2,5), (2,6), (3,3), (3,4), (3,5), (3,6), (4,4), (4,5), (4,6), (5,5), (5,6).
Now the sum of these 20 pairs are,
(1,1) = 1 + 1 = 2
(1,2) = 1 + 2 = 3
(1,3) = 1 + 3 = 4
(1,4) = 1 + 4 = 5
(1,5) = 1 + 5 = 6
(1,6) = 1 + 6 = 7
(2,2) = 2 + 2 = 4
(2,3) = 2 + 3 = 5
(2,4) = 2 + 4 = 6
(2,5) = 2 + 5 = 7
(2,6) = 2 + 6 = 8
(3,3) = 3 + 3 = 6
(3,4) = 3 + 4 = 7
(3,5) = 3 + 5 = 8
(3,6) = 3 + 6 = 9
(4,4) = 4 + 4 = 8
(4,5) = 4 + 5 = 9
(4,6) = 4 + 6 = 10
(5,5) = 5 + 5 = 10
(5,6) = 5 + 6 = 11
Therefore, the sum of each pair is 2, 3, 4, 5, 6, 7, 4, 5, 6, 7, 8, 6, 7, 8, 9, 8, 9, 10, 10, 11.
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Determine whether each function is linear or quadratic. Identify the quadratic, linear, and constant terms. y=x-2(x+5)
The given function y = x- 2(x+5), is a linear function.
It has no quadratic termIts linear term is -xIts constant term is -10What is a function?A function is a mathematical expression or equation that allows us to visualize graphically the behavior of a function. A function is not real when it cuts the vertical axis at the same point of x.
A function can be linear or quadratic, this is evidenced by the higher exponential degree.
We rewrite the function and reduce it to its minimum expression:
y = x- 2(x+5)
y = x + (-2x - 10)
y = x - 2x - 10
y = -x - 10 , linear function.
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Compare and contrast inscribed angles and central angles of a circle. If they intercept the same arc, how are they related?
If a central angle and an inscribed angle intersect the same arc, the central angle is twice the inscribed angle and half the central angle.
What is the relation between the central and inscribed angle on the same arc?According to the inscribed angle theorem, an angle inscribed in a circle is half the central angle 2 that subtends the same arc on the circle.
The central angle has the same length as the intercepted arc. As can be seen, if a central angle and an inscribed angle intersect the same arc, the central angle is twice as large as the inscribed angles. Similarly, the inscribed angle equals half of the central angle.
An inscribed angle is one that has its vertex on a circle and its sides are chords. The intercepted arc is the arc that is contained within the inscribed angle and has its endpoints on the angle.
If a central angle and an inscribed angle intersect the same arc, the central angle is twice the inscribed angle and half the central angle.
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Under a microscope, a single celled organism 200 microns in length appears to be 50 millimeters long. If 1 millimeter =1000 microns, what magnification setting (scale factor) was used? Explain your reasoning.
The length of the organism in millimeters is 200 ч 1000 or 0.2 mm.
What is a microscope?A microscope is a laboratory tool used to examine objects that are too small to see with the eye. Microscopy is the science of using a microscope to examine small objects and structures. Microscopic means invisible to the eye unless magnified.There are numerous types of microscopes, and they can be classified in various ways. One method is to describe the method a device uses to interact with a sample and produce images, such as sending a beam of light or electrons through a sample in its optical path, detecting photon emissions from a sample, or scanning across a short distance from a sample.In the given situation, the organism's length in millimeters is 200 ч 1000 or 0.2 mm.
Therefore, the length of the organism in millimeters is 200 ч 1000 or 0.2 mm.
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Use completing the square to solve for x in the equation (x minus 12) (x + 4) = 9.
The solution fo the equation by completing the square is x = 12.544 or -4.544
What is completing the square method?Completing the square method is a method of solving quadratic equations in which the equation is converted into a perfect square binomial.
How to use completing the square to solve the equation?Given (x - 12)(x + 4) = 9
Expanding the brackets, we have
x² - 12x + 4x - 48 = 9
x² - 8x - 48 = 9
x² - 8x - 48 - 9 = 0
x² - 8x - 57 = 0
To complete the square, we add half the square of the coefficient of x to both sides. so,
x² - 8x - 57 = 0
x² - 8x - 57 + (-8/2)² = 0 + (-8/2)²
x² - 8x - 57 + (-4)² = 0 + (-4)²
x² - 8x + (-4)² - 57 = 0 + (-4)²
(x - 4)² - 57 = 16
(x - 4)² = 16 + 57
(x - 4)² = 73
Taking square roots, we have
x - 4 = ±√73
x - 4 = ±8.544
x = 4 ± 8.544
x = 4 + 8.544 or x = 4 - 8.544
x = 12.544 or -4.544
So, the solution fo the quadratic equation by completing the square is x = 12.544 or -4.544
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Answer:
Step-by-step explanation:
x=+/-square root 73
Find the value of x2 for 8 degrees of freedom and an area of .05 in the left tail of the chi-square distribution.
The value of x² for 8 degrees of freedom and an area of .05 in the left tail of the chi-square distribution is 1.344
Chi-square Distribution:
The chi-square distribution is a continuous probability distribution. It is skewed to the right or positively skewed for low degrees of freedom but shifts towards the symmetric distribution as the degrees of freedom are increased.
Given,
Degree of freedom = 8
Area of the left = 0.05
Here we need to find the value X² of the chi-square distribution.
The value of X² of the chi-square distribution is calculated through the formula,
X² = X²₍₁ ₋ₓ₎,y
Where
x represents the area of the given tails
y represents the degree of freedom
Apply the values on the formula,
=> X² = X²₍₁ ₋₀.₀₅₎,8
=> X² = X²₍₀.₉₉₅₎,8
Now, based on the Chi square distribution table,
The value of
=> X² = 1.344
Therefore, the value of x² for 8 degrees of freedom and an area of .05 in the left tail of the chi-square distribution is 1.344
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What are multiples of 5/4?
For example; Kendal is doing math problems to study for an exam, and she has completed 5/4of the number of assigned problems. What multiple of the number of assigned problems has Kendal completed?
I need help
Also, I'm in 6th grade and its a lot harder whenever you are in SEARCH/GT(Smart people classes basically)
pls I'm failing my class and I need to do this grade and get them all right to get my grade up
The multiples of 5/4 will be 2 1/2, 3 3/4, 5, etc.
How to illustrate the information?It should be noted that multiples simply mean the answer that one gets when the number of multiplied by any whole number.
Therefore, the multiples will be:
= 5/4 × 2 = 2 1/2
= 5/4 × 3 = 3 3/4
= 5/4 × 4 = 5
Therefore, the multiples of 5/4 will be 2 1/2, 3 3/4, 5, etc.
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points A(-1.5) and b(6) are marked on a number line. find the coordinate of point m if it is know that AM:md = 1:2
The coordinates of point m if it is known that am : md = 1 : 2 is (4/3, 5)
How to find the coordinates of point m?The given parameters are
A = (-1, 5)
B = (6, 5)
Ratio, m : n = 1 : 2
The coordinates of point m are calculated using
M = 1/(m + n) * (mx2 + nx1, my2 + ny1)
So, we have
M = 1/(1 + 2) * (1 * 6 + 2 * -1, 1 * 5 + 2 * 5)
Evaluate the sum of products
So, we have
M = 1/3 * (4, 15)
Evaluate the product
M = (4/3, 5)
Hence, the coordinates of point m if it is known that am : md = 1 : 2 is (4/3, 5)
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The least preferable and reliable method of selecting people to participate in a research study is:_____.
The least preferable and reliable method of selecting people to participate in a research study is convenience sampling.
Convenience sampling is a type of sampling in which you include people who are easy to reach. Convenience sampling is included in non-probability sampling because it doesn't include a random selection of the participants. Convenience sampling can be used when you need to conduct a study quickly or when you are on a shoestring budget as it is inexpensive compared to other methods of sampling.
It is the least preferable method because of the inability to generalize the result of the survey to the population as a whole. In addition to this, there is a possibility of under or over-representation of the population as a whole. The biggest problem with convenience sampling is dependence as the sample items are connected to each another in some way. This dependency interferes with statistical analysis.
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Choose the vocabulary term that correctly completes each sentence.
If an infinite geometric series ______ then it must have a sum.
If an infinite geometric series is a convergent series then it must have a sum.
What is a convergent series?
If a series' partial sum sequence tends to a limit, it is said to be convergent (or to be convergent)This indicates that as partial sums are added in the order indicated by the indices, they approach closer and closer to a certain number. When a series becomes closer to a particular value as it gets closer to infinity, it is said to be convergent. A series in mathematics is the total of all the terms in an infinite series of numbers.Two forces must be moving in concert for there to be convergence. If a finite real number L serves as the limit of a sequence of real numbers, the sequence is said to be convergent.To learn more about convergent series, refer:
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The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of n objects where order of selection is not important is called the rule for?.
Combination is the counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects, where order of selection is not important.
The formula for combination is given by:
C = N! / n!(N - n)!
where N is the set of objects
and n is the number of objects to be selected from N
example: If the order doesn't matter, how many ways can 3 girls be selected from a group of 5 girls?
C = N! / n!(N - n)!
where N = 5 and n = 3
C = 5! / 3!(5 - 3)!
C = 120/(6)(2)
C = 10
Hence, there are 10 ways to select 3 girls from a group of 5 girls.
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O
O
-100
What is the probability of flipping tails on the coin and spinning a 2 on the spinner?
8
Tails
414
4
3
(T.1)
(T.2)
(T.3)
(T.4)
Answer:
a 50% chance of getting tails
but about the spinner It depends on what kind of spinner it is and how many sides/numbers/etc
does it have
Julia is the oldest of three siblings whose ages are consecutive integers. If the sum of their ages is 42, find Julia's age.
Answer:
Her age is 15.
Step-by-step explanation:
13 + 14 + 15 = 42
Julia is the oldest and 15 is the greatest of the 3 numbers
therefore Julia is 15
What are the domain and range of the function represented by the set of
ordered pairs?
{(-13, 9), (-7,-5), (5, 14), (11,-10)}
The function's domain and range as represented either by set of ordered pairs:
Domain = (-13 , -7 , 5 , 11)
Range = (9 , -5 , 14 , 11)
What is function's domain and range?Range and domain The domain of something like a function is the set of values that can be plugged into it. This set contains the x values in a function like f. (x). A function's range is the collection of values that the function can take. This is the set of values that the function returns after we enter an x value.
According to the data:The set of ordered pairs = {(-13, 9), (-7,-5), (5, 14), (11,-10)}.
(x,y)
x=input
y=output
As a result, the domain consists only of the first numbers.
range refers to all of the second numbers.
x=domain
y=range
So,
Domain = (-13 , -7 , 5 , 11)
Range = (9 , -5 , 14 , 11)
The function's domain and range as represented either by set of ordered pairs:
Domain = (-13 , -7 , 5 , 11)
Range = (9 , -5 , 14 , 11)
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For whole number n, n3 will be odd if n is odd and even if n is even
The table shows the results of an experiment in which a spinner numbered 1-4 was spun.
What is the experimental probability that the spinner will land on a 4?
Answer:
1/4 or 25% or 0.25
Step-by-step explanation:
Solve each equation. Check your answer. 43-3 d=d+9
d= 17/2 is the solution of the given equation 43-3 d=d+9.
According to the given question.
We have a linear equation in one variable 43 -3d = d + 9.
Since, we have to solve the above linear equation in one varible 43 -3d = d + 9, which means we have to solve the above equation for d.
As we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
Thereofore, the solution of the given linear equation in one variable 43 -3d = d + 9 is given by
43 -3d = d + 9
⇒ 43 - 9 -3d = d (subtracting 9 from both the sides)
⇒ 34 = d + 3d (adding 3d both the sides)
⇒ 34 = 4d
⇒ d = 34/4
⇒ d = 17/2
Now, we will check whether d = 17/2 is the solution of the given equation or not.
Thereofore,
LHS
= 43 - 3(17/2)
= 43 - 51/2
= 86 - 51/2
= 35/2
RHS
= 17/2 + 9
= 17 + 18/2
=35/2
Here, LHS = RHS for d = 17/2
Hence, d= 17/2 is the solution of the given equation 43-3 d=d+9.
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Expand, x³(3x - 5).
3x^4-5x³
Step-by-step explanation:
