Problem 4a
The instructions are incomplete. You set up the recursive formula, but didn't ask any question about said formula.
I'll assume that your teacher wants you to list out a few terms. I'll list out the first five terms.
The notation a_1 = 4 is the same as writing [tex]a_1 = 4[/tex] where the '1' is a subscript. It tells us that the first term is 4.
The nth term a_n or [tex]a_n[/tex] is defined as such
[tex]a_n = 2*(1/3 + a_{n-1})\\\\[/tex]
Notice how if we replaced n with 2, then we get
[tex]a_n = 2*(1/3 + a_{n-1})\\\\a_2 = 2*(1/3 + a_{2-1})\\\\a_2 = 2*(1/3 + a_1)\\\\[/tex]
So the second term is directly tied to the first term, or it is dependent on it.
We'll replace a_1 with 4 to get the following
[tex]a_2 = 2*(1/3 + a_1)\\\\a_2 = 2*(1/3 + 4)\\\\a_2 = 2*(1/3 + 12/3)\\\\a_2 = 2*(13/3)\\\\a_2 = 26/3\\\\[/tex]
So the second term is 26/3.
As you can guess, the third term is going to be found in a similar fashion
[tex]a_n = 2*(1/3 + a_{n-1})\\\\a_3 = 2*(1/3 + a_{3-1})\\\\a_3 = 2*(1/3 + a_2)\\\\a_3 = 2*(1/3 + 26/3)\\\\a_3 = 2*(27/3)\\\\a_3 = 2*(9)\\\\a_3 = 18\\\\[/tex]
So 18 is the third term.
We'll repeat for n = 4 to get the fourth term.
[tex]a_n = 2*(1/3 + a_{n-1})\\\\a_4 = 2*(1/3 + a_{4-1})\\\\a_4 = 2*(1/3 + a_3)\\\\a_4 = 2*(1/3 + 18)\\\\a_4 = 2*(1/3 + 54/3)\\\\a_4 = 2*(55/3)\\\\a_4 = 110/3\\\\[/tex]
The fourth term is 110/3.
Lastly, we'll plug in n = 5
[tex]a_n = 2*(1/3 + a_{n-1})\\\\a_5 = 2*(1/3 + a_{5-1})\\\\a_5 = 2*(1/3 + a_4)\\\\a_5 = 2*(1/3 + 110/3)\\\\a_5 = 2*(111/3)\\\\a_5 = 2*(37)\\\\a_5 = 74\\\\[/tex]
The fifth term is 74.
Answer: The first five terms are 4, 26/3, 18, 110/3, 74==============================================================
Problem 4b
Again, the instructions are missing. I'll assume the same thing as problem 4a.
[tex]a_1 = 6[/tex] is the first term
Plug n = 2 into the first equation to get
[tex]a_n = \frac{n}{a_{n-1}}\\\\a_2 = \frac{2}{a_{2-1}}\\\\a_2 = \frac{2}{a_{1}}\\\\a_2 = \frac{2}{6}\\\\a_2 = \frac{1}{3}\\\\[/tex]
The second term is 1/3.
Repeat for n = 3
[tex]a_n = \frac{n}{a_{n-1}}\\\\a_3 = \frac{3}{a_{3-1}}\\\\a_3 = \frac{3}{a_{2}}\\\\a_3 = \frac{3}{1/3}\\\\a_3 = 3\div\frac{1}{3}\\\\a_3 = 3\times\frac{3}{1}\\\\a_3 = 9\\\\[/tex]
The third term is 9
Repeat for n = 4.
[tex]a_n = \frac{n}{a_{n-1}}\\\\a_4 = \frac{4}{a_{4-1}}\\\\a_4 = \frac{4}{a_{3}}\\\\a_4 = \frac{4}{9}\\\\[/tex]
The fourth term is 4/9
Repeat for n = 5
[tex]a_n = \frac{n}{a_{n-1}}\\\\a_5 = \frac{5}{a_{5-1}}\\\\a_5 = \frac{5}{a_{4}}\\\\a_5 = 5 \div a_{4}\\\\a_5 = 5 \div \frac{4}{9}\\\\a_5 = 5 \times \frac{9}{4}\\\\a_5 = \frac{5}{1} \times \frac{9}{4}\\\\a_5 = \frac{5*9}{1*4}\\\\a_5 = \frac{45}{4}\\\\[/tex]
Answer: The first five terms are 6, 1/3, 9, 4/9, 45/4==============================================================
Problem 4c
I'm not much help here for this problem. Not only are the instructions missing, but it's not clear how this sequence is set up. If I had to guess, it's somehow recursively defined. How exactly, I'm not sure. I would ask your teacher for any clarification.
If you double then triple a number, this is the same as cutting the number in half. What is the number?
9514 1404 393
Answer:
zero
Step-by-step explanation:
3(2x) = x/2
5.5x = 0 . . . . subtract x/2
x = 0 . . . . . . . divide by 5.5
The number is zero.
HELP ASAP PLEASE! Accounting class! Lorge Corporation has collected the following information after its first year of sales. Sales were $1,575,000 on 105,000 units; selling expenses $250,000 (40% variable and 60% fixed); direct materials $606,100; direct labor $250,000; administrative expenses $270,000 (20% variable and 80% fixed); and manufacturing overhead $357,000 (70% variable and 30% fixed). Top management has asked you to do a CVP analysis so that it can make plans for the coming year. It has projected that unit sales will increase by 10% next year.
(See screenshots)
Answer:
what is thia
Step-by-step explanation:
i have no idea what you juat said like fr what topic is this im too bored to read the queation
Please I need the answer according to steps
Answer:
Factorise out x and y terms:
[tex]{ \tt{ = \frac{ {x}^{2} {y}^{4} (5x - 3y)}{45} }} \\ [/tex]
The perimeter of a fence is 64 feet. The length is 4 feet less than twice the width. What is the length of the fence?
Answer:
20 feet
Step-by-step explanation:
let the width be x
length = 2x-4
perimeter = 2 length + 2 width = 2(2x-4)+2x = 4x-8+2x = 6x-8
6x-8 = 64
6x = 72
x = 12
length = 2x-4 = 2(12)-4 = 20
PLEASE HELP MIGHT GIVE BRAINLIEST!!!!! IM BEGGING YOU!!!!
Find the equation of the line with an x intercept of 4 and a y intercept of -1.5
Answer:
y = 4x -1.5
Step-by-step explanation:
The slope intercept form of a line is given by
y = mx+b where m is the slope and b is the y intercept
y = 4x -1.5
What is the sine ratio for
Answer:
the since ratio is 5/4
Step-by-step explanation:
hope this is helpful ask manyThe perimeter of a triangle is 83 centimeters. If two sides are equally long and the third side is 8 centimeters longer than the others, find the lengths of the three sides.
Answer:
25, 33
Step-by-step explanation:
let the length of the one with equal sides be x
third side = x+8
x+x+x+8 = 83
3x+8 = 83
3x = 75
x = 25
x+8 = 25+8 = 33
Determine the input that would give an output value of 2/3
==========================================
Explanation:
The steps you have so far are correct. You just need to multiply both sides by -3
Doing so will clear out the fractions and you'll be left with 19 = x, which is the same as x = 19
Let's check that answer:
[tex]y = -\frac{1}{3}x + 7\\\\y = -\frac{1}{3}*19 + 7\\\\y = \frac{-19}{3} + 7*\frac{3}{3}\\\\y = \frac{-19}{3} + \frac{21}{3}\\\\y = \frac{-19+21}{3}\\\\y = \frac{2}{3}\\\\[/tex]
So the answer is confirmed.
find range,domains, intercepts, interval of increase decrease and asymptotes of graphs
Answer:
Product of the zeroes of polynomial 3x²-2x-4 is ?
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rewrite 7/10 and negative 2/5
Simplify the following by removing parentheses and combining terms
- (2x + 8) + 3(2x + 8) - 2x
Answer:
2x+16
Step-by-step explanation:
PEMDAS
If lan does a job in 132 hours and with the help of Danielle they can do it together in 44 hours, how long
would it take Danielle to do it alone
Answer:
88 hours
Step-by-step explanation:
Ian = 132
Daniel + Ian = 44
Daniel = Ian - 44
= 132-44 = 88 hours
40+30+10 in commutative property
Answer:
10 + 40 + 30
Step-by-step explanation:
Commutative property states that the order in which we add numbers does not affect the answer, so we just need to change the order of numbers
Answered by Gauthmath
The manager of a movie theater is standing outside the theater complex one evening. He will be asking the moviegoers questions.
Which questions can the manager ask that will result in discrete quantitative data? Check all that apply.
What movie did you just see?
What genre of movie is your favorite?
How much did you spend at the movies today?
Did you order anything from the concession stand?
Answer:
It's How much did you spend at the movies today?
Step-by-step explanation:
The question can the manager asks "How much did you spend at the movies today?". Then the correct option is C.
What is discrete quantitative data?A discrete quantitative parameter has a clear mathematical explanation but could only take certain integer values (instead of every value in intervals).
The manager of a movie theater is standing outside the theater complex one evening.
He will be asking the moviegoers questions.
Then the questions can the manager ask that will result in discrete quantitative data will be
How much did you spend at the movies today?
The question can the manager asks "How much did you spend at the movies today?"
Then the correct option is C.
More about the discrete quantitative data link is given below.
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Let x represent the average annual salary of college and university professors (in thousands of dollars) in the United States. For all colleges and universities in the United States, the population variance of x is approximately σ2
= 47.1. However, a random sample of 15 colleges and universities in Kansas showed that x has a sample variance σ2 = 83.2. Use a 5% level of significance to test the claim that the variance for colleges and universities in Kansas is greater than 47.1. Use the traditional method. Assume that a simple random sample is selected from a normally distributed population.
a. Check requirements.
b. Establish H0 and H1 and note the level of significance.
c. Find the sample test statistic.
d. Find Critical Value.
e. Conclude the test and interpret results.
Answer:
Kindly check explanation
Step-by-step explanation:
Given that :
The hypothesis :
H0 : σ²= 47.1
H1 : σ² > 47.1
α = 5% = 0.05
Population variance, σ² = 47.1
Sample variance, s² = 83.2
Sample size, n = 15
The test statistic = (n-1)*s²/σ²
Test statistic, T = [(15 - 1) * 83.2] ÷ 47.1
Test statistic = T = [(14 * 83.2)] * 47.1
Test statistic = 1164.8 / 47.1
Test statistic = 24.73
The degree of freedom, df = n - 1 ; 10 = 9
Critical value (0.05, 9) = 16.92 (Chisquare distribution table)
Reject H0 ; If Test statistic > Critical value
Since ; 24.73 > 16.92 ; Reject H0 and conclude that variance is greater.
Help please 6x + 3 > a if the inequality above is true for the constant a which of the following. coupd be a vakue of z
Answer:
[tex]\frac{a+3}{6}[/tex]
Step-by-step explanation:
Treat it like any other math problem with a equals sign:
6x + 3 = a
subtract 3 from both sides: 6x = a + 3
divide both sides by 6: [tex]x = \frac{a+3}{6}[/tex]
swap the ≥ back in: [tex]x \geq \frac{a+3}{6}[/tex]
the only time the sign flips is if you divide by a negative
An urn contains six red balls numbered 1, 2, 3, 4, 5, 6, two white balls numbered 7, 8, and two black balls numbered 9, 10. A ball is drawn from the urn. (Enter your probabilities as fractions.) (a) What is the probability that the ball is white
Answer:
2/10 = 1/5
Step-by-step explanation:
To figure out the probability of something, we can take
(number of outcomes of that something) / (number of total outcomes)
Here, we are trying to find the probability that the ball is white. The number of outcomes that are possible with the ball being white is 2, as there are two white balls and you can only pick one. You can pick either of the two white balls, but there is no way to pick one of them two times, pick two of them at once, or pick any other ball and have it be white.
The number of total outcomes is 10. There are 10 balls, and you can only pick one ball at a time. There are only 10 options to choose from.
Therefore, we can plug our numbers into the formula above and get 2/10 = 1/5 as our probability
Please help!!!!
CE is tangent to this circle, CD is a radius and ECB=48 what is BAC
Answer:
48degrees
Step-by-step explanation:
From the circle geometry shown, traingle BDC is an isosceles triangle which shows means that their base angels are the same. Hence;
<B = <C
<CBD + <BCD + <D = 180
<BCD + <BCD + <D =180
2<BCD + <BDC = 180
Get <BCD;
<BCD+ <ECB = 90
<BCD + 48 = 90
<BCD = 90 - 48
<BCD = 42degrees
Get <BDC
2<BCD + <BDC = 180
2(42)+ <BDC = 180
84 + <BDC = 180
<BDC = 180 - 84
<BDC = 96
Since angle at the centre is twice that at the circumference, then;
<BAC = 1/2(<BDC )
<BAC = 96/2
<BAC = 48degrees
Use the following graph to evaluate f’(-5) and f’(-1).
Answer:
Bonsoir,
f'(-5)=-4/3
f'(-1) =3/4
Step-by-step explanation:
f'(-5) = ?
2 points : (-6,9) and (-3,5)
f'(-5)=(9-5)/(-6-(-3))=-4/3
f'(-1) = ?
2 points : (-3,5) and (1,8)
f'(-1)=(5-8)/(-3-1)=3/4
The lines are perpendicular
The derivative at the points -5 and -1 are:
f’(-5) = -4/3
f’(-1) = 3/4
What is derivative at a point on line?The slope of the tangent line to the graph of a function at a point is called the derivative of the function at that point.
We consider the line on which where the x coordinate -5 lies.
It is the line with points (-3, 5) and (-6, 9).
Slope of the line = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] = [tex]\frac{9-5}{-6+3} = \frac{-4}{3}[/tex]
f'(-5) = -4/3
We consider the line on which where the x coordinate -1 lies.
It is the line with points (-3, 5) and (1, 8).
Slope of the line = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] = [tex]\frac{8-5}{1+3} = \frac{3}{4}[/tex]
f'(-1) = 3/4
Learn more about derivative at a point here
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What is the volume of this regular prism?
54.97 cubic inches
8.91 cubic inches
109.95 cubic inches
21.99 cubic inches
Answer:
A
Step-by-step explanation:
The volume of prism is b*h, base area is (2.5)*(3.24*(1.1)=8.91. Hence volume is 8.91*6.17=54.97
Write each of the following equations in general form.
a. 1 − 2x = y
b. 9y + 7x = 16 − 3y + x
c. x = 3
d. 2y − 4x − 1 = 7
Answer:
a)2x+y=1
b) 6x+12y=16
c) y=-x+3 (I was a bit confused on this one but I believe this is correct)
d) 4x-2y=-8
Answer:
a. -2x - y + 1 = 0
b. 6x + 12y -16 = 0
c. x - 3 = 0
d. -4x + 2y - 8 = 0
Step-by-step explanation:
The Demand function for a product is given by:
D(q) = - 0.0003q^2 - 0.04q + 23.56
where q is the number of units sold and D(q) is the corresponding price per unit, in dollars. What is the average rate of change of Demand between 40 and 175 units sold?
Answer:
The average rate of change of Demand between 40 and 175 units sold is of -0.1045.
Step-by-step explanation:
Average rate of change:
The average rate of a function f(x) in an interval [a,b] is given by:
[tex]A = \frac{f(b) - f(a)}{b - a}[/tex]
In this question:
[tex]D(q) = -0.0003q^2 - 0.04q + 23.56[/tex]
What is the average rate of change of Demand between 40 and 175 units sold?
[tex]a = 40, b = 175[/tex]. So
[tex]D(40) = -0.0003*40^2 - 0.04*40 + 23.56 = 21.48[/tex]
[tex]D(175) = -0.0003*175^2 - 0.04*175 + 23.56 = 7.3725[/tex]
So
[tex]A = \frac{f(b) - f(a)}{b - a} = \frac{7.3725 - 21.48}{175 - 40} = -0.1045[/tex]
The average rate of change of Demand between 40 and 175 units sold is of -0.1045.
If my classmate was born on April 9, two thousand and six and I was born on December 24, two thousand and four, how many months, years and days are we apart?
Answer:
I could be wrong but I calculated 2 years 8 months and 15 days.
2 years
8 months
15 days
Identify the decimals labeled with the letters A B and a C
Answer:
A=3.1
B=4.2
C=2.7
Step-by-step explanation:
SOMEONE ANSWER THIS PLSSSS
Jack jogs and rides his bike for a total of 75 minutes every day. He rides his bike for 15 minutes longer than he jogs.
Part A: Write a pair of linear equations to show the relationship between the number of minutes Jack jogs (x) and the number of minutes he rides his bike (y) every day. (5 points)
Part B: How much time does Jack spend jogging every day? Show your work. (3 points)
Part C: Is it possible for Jack to have spent 60 minutes riding his bike if he jogs and rides for a total of exactly 75 minutes and rides his bike for 15 minutes longer than he jogs? Explain your reasoning. (2 points)
Answer:
here's the answer to your question
Answer:
for B : he spend 30 minutes jogging and 45 minutes riding his bike
Step-by-step explanation:
75-15=60
60/2=30
jogging (x) =30
30+15=45
riding bike (y) =45
hopefully it help you
Which of the following is the graph of f(x−1)?
Answer:
b I think!!!!!!!!!!!##$
write an equation for a radical function that has a domain of all real numbers greater than or equal to -2 and a range of all real numbers greater than of equal to 1
[tex] y = 1 + \sqrt{x + 2} [/tex]
the root must at least be 0 to have a solution. the "1+" makes it at least 1 instead of zero
Find the measure of one interior angle of a regular 7-gon
Answer:
128.57 degrees
Step-by-step explanation:
To find the measure of an interior angle of a regular polygon with [tex]n[/tex] sides, we can use the formula: [tex]\frac{180(n-2)}{n}[/tex]
To find the measure of an interior angle of a polygon with 7 sides, all we have to do is plug in 7 into the formula:
[tex]\frac{180(7-2)}{7}[/tex]
7 minus 2 equals 5, so the answer is
[tex]180(5)[/tex]÷[tex]7[/tex]
180 times 5 is equal to 900, and 900 divided by 7 is approximately 128.57
if "-3<" x/5 < "-1" what is the value of x
Answer:
-15 < x < -5
Step-by-step explanation:
-3 < x/5 < -1
Multiply all sides by 5
-3*5 < x/5 *5 < -1*5
-15 < x < -5
The slope of the line below is to use the corners of the labeled point to find a point slope equation of the line.
Plz help
Answer: Choice A) y - 10 = 2(x - 3)
============================================================
Explanation:
We can rule out choices C and D because this diagonal line has a positive slope (as it moves uphill when moving to the right).
So m = 2 must be the slope.
---------
Recall that
y - y1 = m(x - x1)
represents the point slope form of a linear equation.
The point shown on this graph is (3,10) meaning that x1 = 3 and y1 = 10 pair up together.
So,
y - y1 = m(x - x1)
y - 10 = 2(x - 3)
which points to choice A as the final answer
