For the sequence a n =a n−1 +a n−2 and a 1 =2,a 2 =3 its first term is its second term is its third term is its fourth term is its fifth term is quence a n =a n−1 +a n−2 and a 1 =2,a 2 =3 its first term is its second term is its third term is its fourth term is its fifth term is

Answers

Answer 1

A function assigns the value of each element of one set to the other specific element of another set. The third, fourth, and fifth terms of the sequence are 5, 8, and 13 respectively

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

Given the nth term of the sequence is given by the formula,

[tex]a_n = a_{(n-1)}+a_{(n-2)}[/tex]

Also, the first term and the second term of the sequence are 2 and 3 respectively, therefore, the other terms of the sequence are,

[tex]a_3 = a_{(3-1)}+a_{(3-2)}\\\\a_3 = a_2 + a_1\\\\a_3 = 3 + 2\\\\a_3 = 5[/tex]

[tex]a_4 = a_{(4-1)}+a_{(4-2)}\\\\a_4 = a_3 + a_2\\\\a_4 = 5 + 3\\\\a_4 = 8[/tex]

[tex]a_5 = a_{(5-1)}+a_{(5-2)}\\\\a_5 = a_4 + a_3\\\\a_5 = 8 + 5\\\\a_5 = 13[/tex]

Hence, the third, fourth, and fifth terms of the sequence are 5, 8, and 13 respectively.

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Related Questions

Mr. Parks begins to fill a large container with water for the dunk tank at the school
fair before asking Brian to finish the job. The container has 25 gallons of water in it
before Brian uses a hose to finish filling it up. The container fills at a rate of 10
gallons per minute. Suppose that y is the amount of water in the tank after x
minutes. Which equation could be graphed to help Brian find out how much water is
in the tank at any time?
y = 25x + 10
y= 10x + 25
y= 10x - 25
y = 10x

Answers

Answer:

The answer is B / y= 10x+25

Step-by-step explanation:

your welcome

The population f(x), in millions, of State A of a country after x years is represented by the function shown below:

f(x) = 4(1.08)x

The graph shows the population g(x), in millions, of State B of the country after x years:

graph of exponential function g of x that curves up from left to right and goes through points 0 comma 2 and 9 comma 4

Which conclusion is correct about the populations of State A and State B?

Answers

Option 1 is correct. The correct solution about these functions is that The original population of State A was double of the original population of State B.

How to solve for the solution

The function in the question is given as

For A:

[tex]F(x) = 4*(1.08)^x[/tex]

For B

[tex]g(x) = 2*(1.08)^x[/tex]

The exponential growth equation that is used to solve this is

[tex]h(x) = A(r)^x[/tex]

such that A is the initial and r is the rate of growth.

f(x) and g(x) are at the same rate but the exponential function is known to grow faster.

Hence the correct option is The original population of State A was double of the original population of State B.

Complete question:

Which conclusion is correct about the population of State A and State B? 1. The original population of State A was double of the original population of State B.

2. The original population of State A was half of the original population of State B.

3. The original population of State B was one-fourth of the original population of State A.

4. The original population of State A was one-fourth of the original population of State B.

Answers

Step-by-step explanation:

From the conversation of angular momentum

Initial momentum=final momentum

Here,

Since body is initially resting, it's momentum must be zero.

Let v be velocity of third piece. Then

0= 10(-3i+2j) + 18(5i-4j) + 22v

Solving this we get,

v= 4/22(15i+13j).

The velocity of third piece is 2/11(13 j - 15i)

What is velocity?

Velocity defines the direction of the movement of the body or the object.

Given:

As the body is at rest so the initial momentum is zero.

Let v be velocity of third piece.

so,

0= 10(-3i+2j) + 18(5i-4j) + 22v

0= -30i + 20j + 90i -72j + 22 v

0= 60i - 52j + 22 v

-60i +52j = 22v

v= 2/11( 13j - 15 i)

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Pat needs to determine the height of a tree before cutting it down to be sure that it will not fall on a nearby fence. The angle of elevation of the tree from one position on a flat path from the tree is H=60 and from a second position L=30 farther along this path it is B=50 What is the height of the tree?

Answers

The height of the tree based on the information is 229.23.

How to calculate the height?

Based on the information given,

tan 50 = h/x + 60

h = (x + 60)tan 50°

x tan 60 = (x + 60)tan 50°

x(tan 60° - ta 50°) = 60 ta 60

x = 132.34

Therefore, the height will be:

= x tan60°

= 132.34 × tan 60

= 229.23

Therefore, the height is 229.23.

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Exploring Systems of Linear Equations 2x +3y =8 and 3x+y= -2

Answers

The solution of the linear equations will be ( -2, 4).

What is an equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

Given equations are:-

2x +3y = 8 and 3x+y= -2

Solving the equations by elimination method:-

2x +3y = 8

3x+y= -2

Multiply the second equation by 3 and subtract from the first equation.

2x +3y = 8

-9x -3y = 6

----------------

-7x = 14

x = -2

Out of the value of x in any one equation, we will get the value of y.

3x+y= -2

3 ( -2) + y = -2

-6 + y = -2

y = 4

The graph of the equations is also attached with the answer below.

Therefore the solution of the linear equations will be ( -2, 4).

The complete question is given below:-

Exploring Systems of Linear Equations 2x +3y =8 and 3x+y= -2. Find the value of x and y and draw a graph for the system of linear equations.

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mark: 3,2,0,1,9,12,3,5
if the pass mark is 5, how many students failed the text

Answers

Answer:

Step-by-step explanation:

Anything below 5 is a fail:

3, 2, 0, 1, 3

That's 5 students.

Write the number in numerical form-twenty-six thousandths

Answers

The answer is 0.026 in numerical form

The cleaning service requires $39 in variable costs for cleaning materials. The fixed costs of labor, the company's truck, and administrative support are $349,200 per year. Chimneysweep averages 200 service calls per month. What is the average cost per cleaning service call?

Answers

The average cost per cleaning service call charge by the company is $184.5.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Let y represent the total cost for x number of service calls in a year. Hence:

y = 39x + 349200

For 200 service call, in a year, x = 200 * 12 = 2400

y = 39(2400) + 349200 = $442800

Average cost = $442800 / 2400 = 184.5

The average cost per cleaning service call charge by the company is $184.5.

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Whats the correct answer answer asap for brainlist

Answers

Answer:

option C: Asian

explanation:

Asian countries, such as China, produce goods like the European products, but for much cheaper prices.

Halfway through the season, a soccer player has made 12 penalty kicks in 18 attempts.
Based on her performance to date, what is the relative frequency probability that she will miss
her next penalty kick?

Answers

Answer:

Step-by-step explanation:

18÷6=3 attemps

13÷6=2 makes

she will probably missed I next 3rd pe alty kick

21st attempts

Simplify the following.
7² =
4⁰ =
6-¹=

Answers

Answer:

1/6

Step-by-step explanation:

7^2 is just 7 * 7 = 49

4^0 = 1, since anything to the power of 0, is 1.

[tex]6^{-1}[/tex] is equal to [tex]\frac{1}{6}[/tex] since [tex](\frac{a}{b})^{-x}=(\frac{b}{a})^x=\frac{b^x}{a^x}[/tex]. Whenever you have a negative exponent, you flip the fraction, in this case the fraction is 6/1 so it becomes 1/6. then distribute the exponent across the division and you get 1^1/6^1 which is just 1/6

Answer:

491

Step-by-step explanation:

hey

please like my question

How do you do 56 through 58? Thanks to anyone who awnsers!

Answers

Hello !

56)

[tex]5 {x}^{2} + 8x = - 1 \\ 5 {x}^{2} + 8x + 1 = 0[/tex]

[tex]\Delta = {b}^{2} - 4ac \\ = {8}^{2} - 4 \times 5 \times 1 \\ = 64 - 20 \\ = 44[/tex]

The value of the discriminant is 44.

57) ∆>0 : there are two solutions.

58)

[tex]x_1 = \frac{ - b + \sqrt{\Delta} }{2a} \\ = \frac{ - 8 + \sqrt{44} }{2 \times 5} \\ = \frac{ \sqrt{11} - 4 }{5} [/tex]

[tex] x_2 = \frac{ - b - \sqrt{\Delta} }{2a} \\ = \frac{ - 8 - \sqrt{44} }{2 \times 5} \\ = \frac{ - \sqrt{11} - 4 }{5} [/tex]

Have a nice day

56. 44

57. 2

58. Image attached.

First, let's simplify some things. Let's make this a quadratic equation.

Moving the -1 (by adding 1 to both sides) gives us 5x^2 + 8x + 1 = 0. Note that this is the standard form of a quadratic, which is ax^2 + bx + c = 0.

Now, the discriminant. The discriminant is helpful because it tells us if we have 2 real solutions, 1 real solution, or if this equation is imaginary and thus impossible to solve using elementary techniques. If the discriminant is greater (>) than 0, then it has 2 solutions. If the discriminant equals (=) 0, it has 1 solution. If the discriminant is less than (<) 0, then it is imaginary.

The discriminant of a quadratic equation is defined as b^2 - 4ac (from the quadratic formula.) We just plug in b, a and c. b will be 8, a will be 5, and c will be 1. Now we just solve. (8)^2 - 4 * 5 * 1 = 64 - 20 = 44. Since 44 is greater than 0, we have 2 solutions for this. 44 is the discriminant. (Answer to 56.) We also have 2 solutions (answer to 57.)

Now, I'll solve the quadratic equation using the quadratic formula. I'll attach my work in an image (answer to 58.)

Hope this helped!

ch circle shows AB that measures 60°?
O
60⁰ -0
A
60°
B
60°
.0
Mark this and return
B
B
Save and Exit
Next
Submit

Answers

Step-by-step explanation:

there are a lot of typos and missing info in your problem and answer option definition.

based on what I understood the answer should be

"the second answer option".

this is where A and B have an arc angle (or inner angle at the center of the circle) of 60°.

one could see the 3rd answer to be right too, as the angle between A and B at Y is also 60°.

but I don't think this is really the meaning of this question here.

Which of the following shows the simplified form of sin x/1+cos x
O sin x- tan x
O sin x-cot x
O csc x-cot x
01

Answers

Answer:

csc x - cot x

Step-by-step explanation:

(sinx)/(1+cos x)

Multiplying the numerator and denominator by (1-cos x),

((sinx)(1-cos x))/(1-cos² x)

((sinx)(1-cosx))(sin²x)

(1-cosx)/(sinx)

cscx - cot x

what is the probability of getting a number less than 5 and a head when rolling a die and tossing, help someone quickly

Answers

Probability of getting a number less than 5 is=64=32

14. Find the value of X round the nearest degree 12 15

Answers

The measure of the angle x is 53.13 degrees after applying the sin ratio.

What is the trigonometric ratio?

The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

Applying sin ratio:

sinx = 12/15

sinx = 0.8

x = 53.13 degrees

Thus, the measure of the angle x is 53.13 degrees after applying the sin ratio.

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The average student loan debt for college graduates is $25,150.
Suppose that that distribution is normal and that the standard deviation
is $12,050. Let X = the student loan debt of a randomly selected college
graduate. Round all probabilities to 4 decimal places and all dollar
answers to the nearest dollar.
a. What is the distribution of X? X - N
b Find the probability that the college graduate has between $14,200
and $33,950 in student loan debt.
c. The middle 10% of college graduates' loan debt lies between what
two numbers?
Low: $
High: $

Answers

Using the normal distribution, it is found that:

a) [tex]X \approx N(25150, 12050)[/tex]

b) There is a 0.5859 = 58.59% probability that the college graduate has between $14,200 and $33,950 in student loan debt.

c) Low: $23,519.65, High: $26,580.35.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 25150, \sigma = 12050[/tex].

Hence the distribution of X can be described as follows:

[tex]X \approx N(25150, 12050)[/tex]

The probability that the college graduate has between $14,200 and $33,950 in student loan debt is the p-value of Z when X = 33950 subtracted by the p-value of Z when X = 14200, hence:

X = 33950:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{33950 - 25150}{12050}[/tex]

Z = 0.73

Z = 0.73 has a p-value of 0.7673.

X = 14200:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{14200 - 25150}{12050}[/tex]

Z = -0.91

Z = -0.91 has a p-value of 0.1814.

0.7673 - 0.1814 = 0.5859.

There is a 0.5859 = 58.59% probability that the college graduate has between $14,200 and $33,950 in student loan debt.

Considering the symmetry of the normal distribution, the middle 10% is between the 45th percentile(X when Z = -0.127) and the 55th percentile(X when Z = 0.127), hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-0.127 = \frac{X - 25150}{12050}[/tex]

X - 25150 = -0.127(12050)

X = $23,519.65.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.127 = \frac{X - 25150}{12050}[/tex]

X - 25150 = 0.127(12050)

X = $26,580.35.

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9. The measure of each exterior angle of a regular pentagon is
the measure of each exterior
angle of a regular nonagon.

Answers

Answer:

55,55

Step-by-step explanation:

hereakaigdidjuwjapwwjshd

The actual length of the ship is 575 feet. The scale of the model is 1 inch: 25 feet. What will be the length of the model?

Answers

The length of the model as described in the task content would be; 23 inches.

What is the length of the model?

According to the task content, it follows that for every 25 feet measure of the actual ship length, the representation is 1 inch on the model.

On this note, for 575 feet length of the actual ship, the length of the model is; 575/25 = 23 inch.

Answers

Answer:

f⁻¹(1/5) = 2

Explanation:

If f(x) = (2x -3)/5

To find inverse of f(x), make x the subject.

[tex]f(x) = \dfrac{2x - 3}{5}[/tex]

[tex]5 f(x) = 2x - 3[/tex]

[tex]2x = 5 f(x) + 3[/tex]

[tex]x = \dfrac{5 f(x) + 3}{2}[/tex]

Then,

[tex]f^{-1}(x) = \dfrac{5x+3}{2}[/tex]

To find f⁻¹(1/5), simplify insert [x = 1/5 or 0.2]

[tex]f^{-1}(0.2) = \dfrac{5(0.2)+3}{2}[/tex]

which yields

[tex]f^{-1}(0.2) = 2[/tex]

Can someone help me with this step by step with explanation im confused need help

Answers

The construction is to draw a parallel line to a given line AB passing through point P. To fix the error, the 3rd arc must be reconstructed. Thus the correct option is D. The third arc should be drawn centered at F.

The given construction involves drawing a parallel line through a given point P to a given line AB.

From the construction shown, drawing a straight line through P and G would not be parallel to the given line AB. Thus there is an error in the construction of the 3rd arc. To draw the required corresponding angle, the 3rd arc has to be reconstructed.

Therefore to fix the error the correct step to follow is: Option D. The third arc should be drawn centered at F.

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Kindly contact a 1-on-1 tutor if more explanations are needed.

Find the area of this triangle.
Round to the nearest tenth.
10 cm
55°
12 cm
[? ]cm²
Enter

Answers

Answer:

Area = 49.15

Step-by-step explanation:

area = 0.5 * side a * side b * sin(Angle)

area = 0.5 * 10 * 12 * sin(55)

area = 60 * 0.8192

49.15

I can't figure this out

Answers

The equation of the function g(x) will be g(x) = - ln (x + 2).

What is a logarithm?

Exponents can also be written as logarithms. A number base logarithm is similar to some other number. It is the exact inverse of the exponent expression.

Let the equation of the function f will be

f(x) = ln x

If the function is multiplied with negative sign, then the function gets flipped about the x-axis.

And if we add 2 in the variable of the function, then the function gets shifted towards left.

Then the equation of the function g(x) will be

g(x) = - ln (x + 2)

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I put what I thought but came out wrong, please help

Answers

Answer:

Sir, as for as I can tell that is the correct answer. Maybe you put it in wrong or added a space but that’s correct 100%.

Unless it’s not supposed to be in y = mx + b format?

Step-by-step explanation:

Answer:

y = -x - 1

Step-by-step explanation:

The equation of the line is written in the slope-intercept form,

y = mx + b

where m represents the slope

number that describes both the direction and the steepness of the line

slope = rise/run

b represents the y-intercept

point where crosses the y-axis

The y-intercept is -1rise = -1, run = 1 so rise / run = -1 / 1 = -1line is downward slope

y = mx + b → y = -1x + (-1)

this can be simplified by -x - 1

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Solution
We are given two endpoints here

Point 1: (−1, Answer
)
Point 2: ( Answer
,4)
We know our rise between the two points is 1. So

12= Answer

And our run between the two points is 4. So

42= Answer

We now have rise2+run2=distance2, so we have

1+16=distance2

Answer
=distance2

So once we take the square root of both sides we have

distance=√ Answer

We could also use the actual distance formula we developed to get the same answer.

d=(4−3)2+(−5−(−1)2)−−−−−−−−−−−−−−−−−−−√

d=(12+(−4)2)−−−−−−−−−−√

d=(1+16)−−−−−−−√

d=√ Answer

Answers

The distance between the two points on the plane is √17

Distance between two points

The formula for calculating the distance between two points is expressed as;

D = √(x2-x1)²+(y2-y1)²

From the given plane, we have the following coordinates

(-5, 4) and (-1, 3)

Substitute

D = √(3-4)²+(-1-(-5))²

D = √(-1)²+(4)²

D= √1+16
D=√17

Hence the distance between the two points on the plane is √17

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The sum of two numbers is 32. One number is 3 times the other. Find the numbers.

Answers

The numbers whose sum is 32 in which one number is 3 times the other is 8 and 24 respectively.

Equation of the unknown

Let

x = one of the unknowns3x = second unknown

x + 3x = 32

4x = 32

x = 32/4

x = 8

So,

3x = second unknown

= 3(8)

= 24

Check:

x + 3x = 32

8 + 24 = 32

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Question 1 of 10
The Quadratic Formula gives which roots for the equation 2x²+x-6=0?

Answers

Answer:

x=-3/2 or-2

Step-by-step explanation:

hope this helps

In the video, the water level was 15 milliliters before adding the chain, and 20 milliliters after adding the chain. When I weighed the chain, its mass was 73.5 grams.

I believe the chain is solid metal (not gold plated), but is probably a blend of gold and other metals. I looked up that gold has a density of 19.3 g/ml, while the other metals like silver and copper usually blended with gold have a combined density of about 9.7 g/ml.

Determine what percentage of the chain is gold, by mass, to at least 1 decimal place?

%

Answers

The answer would be 0.27

A simple random sample of 50 items from a population with 7 resulted in a sample mean of 35.

Answers

The 90% , 99% confidence interval for the population mean is 32.145 < [tex]\rm \mu[/tex] < 35.855 and 31.093 < [tex]\rm \mu[/tex] < 36.907

What is Probability ?

Probability is the study of likeliness of an event to happen.

It is given that

Total Population = 50

Mean = 35

The confidence interval is given by

[tex]\rm CI = \mu + z \dfrac{s}{\sqrt n}[/tex]

[tex]\rm \mu[/tex] is the mean

z is the confidence level value

s is the standard deviation

n is the population width

(a) The 90% confidence interval for the population mean

90% [tex]\rm \alpha / 2[/tex] = 0.05

Z = 1.64

34 [tex]\rm \pm[/tex] 1.64 * 8 / √50

34 [tex]\rm \pm[/tex] 1.855

32.145 < [tex]\rm \mu[/tex] < 35.855

(b) The 99% confidence interval for the population mean

99% [tex]\rm \alpha / 2[/tex] = 0.005

Z=2.57

34 [tex]\rm \pm[/tex] 2.57 * 8 / √50

34 [tex]\rm \pm[/tex] 2.907

31.093 < [tex]\rm \mu[/tex] < 36.907

Therefore the confidence interval for population mean has been determined.

The complete question is

A simple random sample of 50 items from a population width =7 resulted in a sample mean of 35. If required, round your answers to two decimal places.

a. Provide a 90% confidence interval for the population mean

b. Provide a 99% confidence interval for the population mean

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A 4-sided dice is rolled. The set of equally likely outcomes is {1,2,3,4}. Find the probability of rolling a number less than 14

The probability of rolling a number less than 14 is?

Answers

The probability of rolling a number less than 14 among {1,2,3,4} is 1.

Given The dice is 4 sided. Likely outcomes is {1,2,3,4} and we have to find the probability of rolling a number less than 4.

Probability is the likeliness of happening an event among all the events possible. The value of probability cannot be negative or greater than 1. It lies between 0 to 1. The formula of calculating probability is:

Probability= number of events/ total number of events.

Total likely outcomes=4 {1,2,3,4}

Numbers less than 14 = 4

Probability of rolling a number less than 14=1/4

=0.25 because all number less than 14 is present.

1,2,3,4 are all less than 14.

and because all numbers are included that's why the value of probability is 1.

Hence the probability of rolling a number less than 14 is 1.

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