The recursive formula an = an – 1 + an – 2 describes a sequence where each term is the sum of the two previous terms. To find the first five or six terms, we substitute the given initial conditions into the formula and repeatedly apply it to find subsequent terms.
Explanation:The recursive formula an = an – 1 + an – 2 describes a sequence where each term is the sum of the two previous terms. To find the first five terms, we begin with a1 = 1.2 and a2 = 2.3. Then we use the formula to find the next terms:
a3 = a2 + a1 = 2.3 + 1.2 = 3.5a4 = a3 + a2 = 3.5 + 2.3 = 5.8a5 = a4 + a3 = 5.8 + 3.5 = 9.3So the first five terms of the sequence are 1.2, 2.3, 3.5, 5.8, and 9.3.
Similarly, to find the first six terms of the sequence with a3 = -5 and a4 = 3, we use the formula:
a5 = a4 + a3 = 3 + (-5) = -2a6 = a5 + a4 = -2 + 3 = 1So the first six terms of this sequence are -5, 3, -2, 1, -1, and 0.
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House is 50.0 ft long and 26 ft wide and has 8.0-ft- m high ceilings. what is the volume of the interior of the house in cubic meters and in cubic centimeters?
If you start with a number divide it by 4 then multiply it by two you end up with 8 squared
8 squared = 64
so
(x/4)*2 = 64
divide x/4 by 2 to get x/2=64
now multiply both sides by 2 to get x=128
x = 128
A catering service offers 12 appetizers, 6 main courses, and 7 desserts. A banquet chairperson is to select 6 appetizers, 2 main courses, and 5 desserts for a banquet. In how many ways can this be done?
PLEASE HELP!!!
The first two steps in determining the solution set of the system of equations, y = –x2 + 4x + 12 and y = –3x + 24, algebraically are shown in the table. Which represents the solution(s) of this system of equations? (3, 15) (–4, 36) (3, 15) and (4, 12) (–3, 33) and (–4, 36)
Answer:
C
Step-by-step explanation:
or (3, 15) and (4, 12)
What is the following sum in simplest form? sqrt 8 + 3 sqrt2 + sqrt 32
\
Answer:-[tex]\sqrt{8}+3 \sqrt{2}+ \sqrt{32}=9\sqrt{2}[/tex] in the simplest form.
Explanation:-
Given sum :- [tex]\sqrt{8}+3 \sqrt{2}+ \sqrt{32}[/tex]
To simplify, rewrite the numbers inside the root in the product of primes, we get
[tex]\Rightarrow\sqrt{2\times2\times2}+3 \sqrt{2}+ \sqrt{2\times2\times2\times2\times2}\\\\\Rightarrow\sqrt{2^2\times2}+3 \sqrt{2}+ \sqrt{4\times4\times2}\\\\\Rightarrow\sqrt{2^2}\sqrt{2}+3 \sqrt{2}+ \sqrt{4^2\times2}\\\\\Rightarrow2\sqrt{2}+3\sqrt{2}+\sqrt{4^2}\sqrt{2}\\\\\Rightarrow2\sqrt{2}+3\sqrt{2}+4\sqrt{2}=9\sqrt{2}[/tex]
Thus [tex]\sqrt{8}+3 \sqrt{2}+ \sqrt{32}=9\sqrt{2}[/tex] in the simplest form.
Aiden calculated the area of triangle QRS below by finding half the product of 1.5 and 1.1.
Answer: The correct option is
(B) Aiden should have found half the product of 1.1 and 5.4 because the 1.5 line is not perpendicular to 1.1 line.
Step-by-step explanation: Given that Aiden calculated the area of triangle QRS by finding half the product of 1.5 and 1.1.
We are to select the correct option which states the error made by Aiden.
The AREA of a triangle is given by
[tex]A=\dfrac{1}{2}\times \textup{base}\times \textup{altitude},[/tex]
where the altitude is perpendicular to the base.
In ΔQRS, the length of the base is given by
b = QS = 0.9 + 4.5 = 5.4 units
and
the length of the altitude is given by
h = 1.1 units.
So, the area of the triangle QRS will be
[tex]A=\dfrac{1}{2}\times b\times h=\dfrac{1}{2}\times 5.4\times 1.1[/tex]
Therefore, the area of ΔQRS will be calculated by finding half the product of 1.1 and 5.4.
So, Aiden made the error by finding half the product of 1.5 and 1.1, because 1.5 line is not perpendicular to 1.1 line.
Thus, Aiden should have found half the product of 1.1 and 5.4 because the 1.5 line is not perpendicular to 1.1 line.
Option (B) is correct.
Which answer correctly describes the relationship between two of the lines in the figure?
What would a monthly payment be on a purchase of a $10,000 car at a 5.9% for 4 years?
Answer:
$234.39
Step-by-step explanation:
Braces are used in interval or roster notation?
I won tickets to a trip for four to the Super Bowl. I have eight friends but I can only bring three of them. In how many ways can I form my Super Bowl party?
Answer:
56
Step-by-step explanation:
Solve each proportion. Show your work
identify the graph of the equation. What is the angle of rotation for the equation? 13x^2+6sprt3xy+7y^2-16=0
Answer:
The answer is ellipse; 30° ⇒ answer (d)
A restaurant offers a choice of 2 soups, 3 entrees, and 5 desserts. how many different meals consisting of a soup, an entree, and a dessert are possible?
(15 POINTS) A student is chosen at random from a school. Why are the events "choosing a student of age group 5−10" and "choosing a student of age group 11−15" mutually exclusive?
a) They are independent.
b) They are dependent.
c) A student can belong to only one age group.
d) A student can belong to both the age groups.
solve for b, then find the value of b when a = 3.
4a=2b-7
a. -9/2
b. 5/2
c. 19/2
d. 17
The value of the cumulative standardized normal distribution at z is 0.8770. the value of z is
Final answer:
To find the z-score corresponding to a cumulative area of 0.8770 in a standard normal distribution, one can look up this area in a z-table or use statistical software, yielding a z-score of approximately 1.15.
Explanation:
The question involves finding the value of z in a standard normal distribution given that the cumulative area to the left of z is 0.8770.
The z-score is a measure that describes the position of a raw score in terms of its distance from the mean, measured in standard deviations.
To find the value of z corresponding to an area of 0.8770, one would typically use a z-table or statistical software. The z-table lists areas to the left (cumulative probabilities) for different z-values.
For an area of 0.8770, the z-score is approximately 1.15. This calculation is based on the standard normal distribution, where the mean is 0 and the standard deviation is 1.
A randomly generated list of numbers from 0 to 4 is being used to simulate an event, with the number 4 representing a success. What is the estimated probability of a success?
A.75%
B.60
C.25%
D.40%
The solution would be like this for this specific problem:
Given:
{0, 1, 2, 3, 4}
Success = 2, 3, and 4
Solution:
Success = 3 numbers
Sample = 5
= 3 / 5
= .6
= .6 * 100%
= 60%
So, the estimated probability of a success based from the randomly generated list of numbers being used to simulate an event is 60%.
To add, the measure of the likelihood that an event will occur is called probability and it is quantified as a number between 0 and 1, where, loosely speaking, 0 indicates impossibility and 1 indicates certainty.
Given the equation 2x + 4 = 4x − 2, select the reasoning that correctly solves for x.
Add 2, subtract 2x, then divide by 2.
Add 2, subtract 4x, then divide by −2.
Subtract 4, subtract 2x, then divide by −2.
Subtract 4, subtract 4x, then divide by 2.
Answer:
Number One / Letter A
Step-by-step explanation:
Add 2, subtract 2x, then divide by 2.
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If x varies directly with y and x = 3.5 when y = 14, find x when y = 18.
Answer:
the value of x= 4.5
Step-by-step explanation:
If x varies directly with y and x = 3.5 when y = 14
x varies directly with y , so equation is x= ky
where k is the constant of proportionality
x = 3.5 when y = 14, use the given values and find out k
Plug in the given values in x=k y
3.5= k * 14
Divide by 14 on both sides
0.25= k
So the value of k = 0.25
Now find out x when y= 18
x= ky
x= 0.25 * 18= 4.5
PLEASE HELP
Probability allows a person to effectively measure the risks in selecting one alternative over others.
True
False
Simplify the expression 3^5*6^-6/3^3*6^-4
A. 180
B. 5/2
C. 1/4
D. 3/20
Corrugated Specialties produces boxes of all kinds, and they manufacture an average of 67,000 shirt-size boxes per month. In November, they were told to increase production by 35%. How many shirt-size boxes will they produce in November? Hint: This question requires two calculations. A. 91,125 B. 23,625 C. 23,450 D. 90,450
The sum of two numbers is 61.61. if three times three times the smaller number is subtracted from the larger? number, the result is 5.5. find the two numbers.
Joshua is 25 years old and has a high risk job making $72,000 a year. The insurance company charges him an extra 20% on top of his premium rate because of his job. If Joshua wants a policy that will replace five years of his salary, what is the annual premium for the cheapest policy?
Slope (12,-18),(11,12)
The slope of the line passing through the points (12, -18) and (11, 12) is calculated using the formula for slope (y2 - y1) / (x2 - x1). The result is -30.
Explanation:The subject of this question is Mathematics, more specifically the topic of 'Slope of a Line'. The grade level appears to be High School.
To answer the question 'Find the slope for the given coordinates (12,-18) and (11,12)', we use the formula to calculate the slope between two points which is (y2 - y1) / (x2 - x1). Let's take (12, -18) as (x1, y1) and (11, 12) as (x2, y2). Now we just input the values into the formula:
Slope (m) = (12 - (-18)) / (11 - 12).
This simplifies to Slope (m) = 30 / -1 = -30.
So, the slope of the line passing through the points (12, -18) and (11, 12) is -30.
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Your Cell Phone plane cost 55 dollars a month, plus 35 cents per minute. Write an equation to represent the monthly bill of the cell phone plan
Answer:
F( x) = 0.35 x + 55
The sum of two consecutive integers is 111. find the largest of these integers
divide 111 in half
111/2 = 55.5
take the whole number above and below 55.5
so you get 55 and 56
55 + 56 = 111
56 is the larger one
3. what is the simplified form of x+4/7 - x+3/x+5
The expression [(x + 4) / (7)] - [(x + 3) / (x + 5)] in simplified form will be (x² + 2x - 1) / 7(x + 5). Then the correct option is A.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ [(x + 4) / (7)] - [(x + 3) / (x + 5)]
Simplify the expression, then we have
⇒ [(x + 4) / (7)] - [(x + 3) / (x + 5)]
⇒ [(x + 4)(x + 5) - 7(x + 3)] / [7(x + 5)]
⇒ [x² + 9x + 20 - 7x - 21] / [7(x + 5)]
⇒ (x² + 2x - 1) / 7(x + 5)
The expression [(x + 4) / (7)] - [(x + 3) / (x + 5)] in simplified form will be (x² + 2x - 1) / 7(x + 5). Then the correct option is A.
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What is the 7th term of the geometric sequence where a1 = -5 and a5 = -1,280?
Am I doing this right?