Answer:
1.
Given the recursive formula:
[tex]a_3 = -11[/tex] and
[tex]a_n = 2a_{n-1} -1[/tex]
For n = 3:
[tex]a_3=2a_2 -1[/tex]
Substitute [tex]a_3 = -11[/tex] we have;
[tex]-11=2a_2 -1[/tex]
Add 1 to both sides we have;
[tex]-10 = 2a_2[/tex]
Divide both sides by 2 we have;
[tex]-5 = a_2[/tex]
or
[tex]a_2 = -5[/tex]
For n = 4, we have;
[tex]a_4=2a_3 -1[/tex]
Substitute [tex]a_3 = -11[/tex] we have;
[tex]a_4 = 2 \cdot -11 -1 = -22-1 = -23[/tex]
⇒[tex]a_4 = -23[/tex]
2.
Given:
[tex]a_4 = -36[/tex] and [tex]a_n = 2a_{n-1} -4[/tex]
For n = 4, we have;
[tex]a_4=2a_3 -4[/tex]
Substitute [tex]a_4 = -36[/tex] we have;
[tex]-36 = 2a_3 -4[/tex]
Add 4 to both sides we have;
[tex]-32 = 2a_3[/tex]
Divide both sides by 2 we have;
⇒[tex]a_3 =-16[/tex]
For n = 3:
[tex]a_3=2a_2 -4[/tex]
Substitute [tex]a_3 = -16[/tex] we have;
[tex]-16=2a_2 -4[/tex]
Add 4 to both sides we have;
[tex]-12 = 2a_2[/tex]
Divide both sides by 2 we have;
[tex]-6 =a_2[/tex]
or
⇒[tex]a_2 = -6[/tex]
The indicated terms of the sequence defined by each of the following recursive formulas are as follows:
[tex]\mathbf{a_{2} = -5}[/tex][tex]\mathbf{a_4 = -23}[/tex][tex]\mathbf{{a_3}=-16}[/tex][tex]\mathbf{{a_2}=-6}[/tex]What are recursive formulas?A recursive formula is one that describes each term in a series in terms of the term before it. The general term for an arithmetic sequence by using a recursive formula is [tex]\mathbf{a_n = a_{n-1} + d}[/tex]
From the given information:
[tex]\mathbf{a_3 = -11}[/tex] [tex]\mathbf{a_n = -2a_{n-1} -1}[/tex]Now, when n = 3
[tex]\mathbf{a_3 = -2a_{3-1} -1}[/tex]
[tex]\mathbf{-11= -2a_{2} -1}[/tex]
[tex]\mathbf{2a_{2} = -10}[/tex]
[tex]\mathbf{a_{2} = -5}[/tex]
When n = 4
[tex]\mathbf{a_4= -2a_{4-1} -1}[/tex]
[tex]\mathbf{a_4 = 2(-11) -1}[/tex]
[tex]\mathbf{a_4 = -23}[/tex]
Second Part:
[tex]\mathbf{a_4 = -36}[/tex][tex]\mathbf{a_n = 2_{an-1}-4}[/tex]When n = 4
[tex]\mathbf{a_4 = 2_{a4-1}-4}[/tex]
[tex]\mathbf{a_4= 2_{a3}-4}[/tex]
[tex]\mathbf{-36+4= 2_{a_3}}[/tex]
[tex]\mathbf{2_{a_3}=-32}[/tex]
[tex]\mathbf{{a_3}=-16}[/tex]
When n = 3
[tex]\mathbf{a_3= 2_{a3-1}-4}[/tex]
[tex]\mathbf{a_3= 2_{a2}-4}[/tex]
[tex]\mathbf{-16= 2_{a_2}-4}[/tex]
[tex]\mathbf{2_{a_2}=-12}[/tex]
[tex]\mathbf{{a_2}=-6}[/tex]
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Which complex number has a distance of √17 from the origin on the complex plane?
A;2 + 15i
B:17 + i
C:20 – 3i
D:4 – i
Answer:
The complex number 4-i has distance [tex]\sqrt{17}[/tex] from origin.
D is correct
Step-by-step explanation:
We are given the absolute value of complex plane.
If complex number is a+ib then absolute value [tex]\sqrt{a^2+b^2}[/tex]
We have to check the absolute value of each option and check which is equal to [tex]\sqrt{17}[/tex]
Option A: 2+15i
[tex]d=\sqrt{2^2+15^2}=\sqrt{4+225}=\sqrt{229}\neq \sqrt{17}[/tex]
Option B: 17+i
[tex]d=\sqrt{17^2+1^2}=\sqrt{289+1}=\sqrt{290}\neq \sqrt{17}[/tex]
Option C: 20-3i
[tex]d=\sqrt{20^2+3^2}=\sqrt{400+9}=\sqrt{409}\neq \sqrt{17}[/tex]
Option D: 4-i
[tex]d=\sqrt{4^2+1^2}=\sqrt{16+1}=\sqrt{17}= \sqrt{17}[/tex]
Hence, The complex number 4-i has distance [tex]\sqrt{17}[/tex] from origin.
4xy - 9xy + -3xy Simplify the polynomial
Which formula is used to find circular mil area?
Solve this equation using an algebraic method: (x + 4)( x - 4) = 9
Help me out please
Two spheres of the same density have a ratio of 4 to 9 in surface area. If the small sphere weighs 10 kg, what does the large sphere weigh?
The lifetime of a supertough aaa battery is normally distributed with mean of 28.5 hours and standard deviation of 5.3 hours. for a battery selected at random, what is the probability that the lifetime will be 25 hours or less?
If you had 5 green marbles and 8 red marbles, what's the probability that you'll pull out a marble that is green?
5+8 = 13 total marbles
5 are green
so you would have a 5/13 probability of picking a green one
There are 10 people in a room. if each person shakes hands with exactly 3 other people, what is the total number of handshakes?
An experiment consists of dealing 5 cards from a standard 52-card deck. what is the probability of being dealt aa 10, jack, queen, king, ace, all in the same suit
A personal identification code consists of five digits (0 through 9). how many codes are possible?
a. 50
b. 252
c. 100,000
d. 30,240
There are 30,240 codes that are possible which consist of five digits (0 through 9).
What is a permutation?A permutation is defined as a mathematical process that determines the number of different arrangements in a set of objects when the order of the sequential arrangements.
There are 10 options for each of the 5 digits in the personal identification code (0 through 9). Since the order of the digits matters, we can use the formula for the number of permutations of n items taken r at a time, which is:
n!/(n-r)!
In this case, n is the number of options (10) and r is the number of items (5). Plugging these values into the formula gives us:
10!/(10-5)! = 10!/(5!) = 109876 = 30,240
Therefore, the correct answer is (d) 30,240.
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Line k is the perpendicular bisector of (line)PQ. If line k intersects (line)PQ at point R, which of the following statements must be true?
check all that apply
A. Line k bisects PQ
B. PR is congruent to QR
C. Line k intersects PQ at a 90 angle
D. Point R is the midpoint of line k
E. Line k is parallel to PQ
Answer:
A. Line k bisects PQ
B. PR is congruent to QR
C. Line k intersects PQ at a 90 angle
Step-by-step explanation:
A perpendicular bisector of a line is a segment that cuts right in the middle a line, and that segment forms a 90º degree angle with the line. This means that the point where the segment cuts the line would be exactly the half, making both resultant segments on the line congruent. So the options that are correct are ABC.
What does b belong with?
Over what interval of time in minutes was the jogger heart rate changing at the constant rate
We have a graph of the heart rate vs time.
We want to find on what interval the heart rate increases with a constant rate.
That interval is 3min ≤ t ≤ 4 min
The general function that increases with a constant rate is the general linear function:
y = a*x + b
Where a is the slope and also defines the constant rate of change.
Then the interval where the jogger heart rate changes at a constant rate is the part where we have a linear function (not the horizontal line, there the heart rate does not change).
Then the interval where the heart rate changes with a constant rate is:
3min ≤ t ≤ 4 min
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How to determine the direction of a vector?
If 5+3+2=151012, 9+2+4=183662, 8+6+3=482466, 5+4+5= 202504 , then 7+2+5= ?
a.141035
b.143510
c.143542
d.143524
Maggie’s brother is 12 years younger that three times her age . The sun of their ages is 44 . How old is Maggie
What is the equation of a circle with a center (-2, 3) and a radius r = 5?
What are the discontinuities of the function f(x) = the quantity x squared minus 16 over the quantity 4x plus 24
Answer:
x= -6 is the point of discontinuity.
Step-by-step explanation:
We have been given the expression
[tex]\frac{x^2-16}{4x+24}[/tex]
The first thing to find the discontinuity is to factorize the given rational function:
After factorization we get:
We will use [tex]a^2-b^2=(a+b)(a-b)[/tex]
[tex]here, a=x\text{and}b=4[/tex] we will get:
[tex](x+4)(x-4)=x^2-4^2[/tex]
we will get:
[tex]\frac{(x+4)(x-4)}{4(x+6)}[/tex]
Discontinuity is the point where value of the function becomes not defined
Here, the point of discontinuity is -6 because when denominator becomes zero. function becomes not defined.
It has vertical asymptote but function is not defined.
Hence it is the point of discontinuity.
Two numbers, 3 and a, have a geometric mean of 9. Find the value of a.
Which of the following statements is the converse of the statement "If each of two angles has a measure of 28 degrees, then the two angles are equal in measure"?
Answer:
If two angles are equal in measure then each of the two angles has a measure of 28 degrees.
Step-by-step explanation:
The converse of a statement is found by switching the hypothesis and conclusion of a conditional statement.
The hypothesis is the part that comes after "if" and the conclusion is the part that comes after "then."
This means the hypothesis is "each of two angles has a measure of 28 degrees" and the conclusion is "the two angles are equal in measure."
This gives us the converse "If two angles are equal in measure then each of the two angles has a measure of 28 degrees."
Denise is a professional swimmer who trains, in part, by running. she would like to estimate the average number of miles she runs in each week. for a random sample of 20 weeks, the mean is = 17.5 miles with standard deviation s = 3.8 miles. find a 99% confidence interval for the population mean number of miles denise runs. use a graphing calculator for this one and not the t chart from the book.
Using a 99% confidence level and the given data, the confidence interval for Denise's average weekly running mileage can be calculated using the sample mean, standard deviation, and z-score for the confidence level.
Explanation:Denise, a professional swimmer, uses her running mileage as part of her training analysis. To estimate the population mean for the number of miles she runs weekly, we will calculate the 99% confidence interval using the sample mean and standard deviation from her 20 weeks of data. The formula for a confidence interval is:
CI = mean ± (z* × (s/sqrt(n)))
Where mean is the sample mean, z* is the z-score corresponding to the desired confidence level, s is the sample standard deviation, and n is the sample size.
The given data for Denise's running mileage is a mean (μ) of 17.5 miles and standard deviation (s) of 3.8 miles with a sample size (n) of 20 weeks. Since the sample size is greater than 30, we can use the z-distribution to approximate the t-distribution.
To find the appropriate z-score for a 99% confidence interval, we can use a graphing calculator or a z-table. The z-score for a 99% confidence level is approximately 2.576. Plugging the values into the confidence interval formula:
CI = 17.5 ± (2.576 × (3.8/sqrt(20)))
Calculating the margins of error and applying them to the sample mean, we will obtain the confidence interval for the average number of miles Denise runs in a week.
Your teacher is giving you a test worth 100 points containing 40 questions. there are two-point and four-point questions on the test. let the number of two-point questions be x and the number of four-point questions be y. how many of each type of question are on the test?
Answer:
t=30 f=10
Step-by-step explanation:
t= 100*1 - 40*4 = 30
2*1 - 1*4
f= 2*40 - 1*100 = 10
2*1 - 1*4
t=30 f=10
Which equation is not a quadratic equation?
y = 3x2 + 2
y = 5x - 2
y = -x2
y = 5x2 - 2x + 7
if 5(3x-7)=20 then what is 6x-8
Ship A receives a distress signal from the northeast and ship B receives a distress signal from the same vessel from the west. At what location is the vessel in distress located? Describe how you arrived at your conclusion using complete sentences.
Coordinate geometry is the use of a 2D plane to represent the location of points. The position or location of the distress is in the first quadrant.
The coordinates of ship A and B are not given. So, I will give a general explanation.
On the four cardinal points,
North is upwardsEast is at the rightWest is at the leftSouth is downwardSo, if ship A receives a distress from the northeast, then it means that the distress is coming from a location at the top right of A. i.e. the first quadrant.
Also, ship B receives distress from the west. This means that ship B is at the right-hand side of the distress.
So, we can conclude that the position or location of the distress is at the first quadrant.
It is impossible to determine the actual coordinates of the distress because the coordinates are not given (see attachment possible illustration)
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PLEASE HELP!!!!!!!dgbdgdbhdndcn
A science experiment begins with a metal at −100° Celsius. The following function describes the temperature change per minute: f(x) = 89x − 100°. How will the graph of this function change if the metal is at 25° at the start of the experiment?
Answer:
A
Step-by-step explanation:
Jacobysontop!
Could someone show me the work for 1/2 divided by 2/3 x 3/4
if a 24-day single payment loan has a periodic interest rate of 8.4% what is the approximate APR of the loan?
A. 201.6%
B. 127.8%
C. 12.8%
D. 20.2%
Answer:
Option B, 127.8%
Step-by-step explanation:
If a 24-day single payment loan has a periodic interest rate of 8.4%.
First we divide 365 by 24 to make periods of 24 days in one year.
365 ÷ 24 = 15.21
periodic interest rate of 8.4%
then Annual Percentage Rate = 15.21 × 8.4 = 1 27.76 ≈ 127.8%
127.8% is the approximate APR of the loan.
Examine the graph at right. Then in a sentence suggest why the graph rises at 11:00am and drops at 1:15pm