Look at the sequence in the table. Which recursive formula represents the sequence shown?A) an = an-1 + 4C) an = 2an-1 + 3B) an = 4an-1 + 1D) an = 2an-1 - 1

The most appropriate choice for function will be given by-

The first option is correct

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Here,

For the first table,

Slope of function from x = 1 to x = 2

= [tex]\frac{1 - \frac{1}{2}}{2 - 1}[/tex]

=[tex]\frac{1}{2}[/tex]

Slope of function from x = 2 to x = 3

= [tex]\frac{\frac{3}{2}-1}{3 - 2}[/tex]

= [tex]\frac{1}{2}[/tex]

Slope of function from x = 3 to x = 4

= [tex]\frac{2-\frac{3}{2}}{4 - 3}[/tex]

= [tex]\frac{1}{2}[/tex]

Here the slope is same. So the function is linear

For the second table,

Slope of function from x = 1 to x = 2

= [tex]\frac{\frac{1}{2} - 1}{2 - 1}[/tex]

=[tex]-\frac{1}{2}[/tex]

Slope of function from x = 2 to x = 3

= [tex]\frac{\frac{1}{3}-\frac{1}{2}}{3 - 2}[/tex]

= [tex]-\frac{1}{6}[/tex]

Here the slope is not same. So the function is not linear

For the third table,

Slope of function from x = 1 to x = 2

= [tex]\frac{9 - 7}{2 - 1}[/tex]

= 2

Slope of function from x = 2 to x = 3

= [tex]\frac{13 - 9}{3 - 2}[/tex]

= 4

Here the slope is not same. So the function is not linear

For the Fourth table,

Slope of function from x = 1 to x = 2

= [tex]\frac{6 - 0}{2 - 1}[/tex]

=[tex]6[/tex]

Slope of function from x = 2 to x = 3

= [tex]\frac{16 - 6}{3 - 2}[/tex]

= 10

Here the slope is not same. So the function is not linear

So the first option is correct

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Given the system of equations:

8x - 6y = 3

-3y + 4x = 4

To find how many times the lines will intersect. let's solve the system of equation using substitution method.

8x - 6y = 3 ........................................1

-3y + 4x = 4 ......................................2

From equation 1, make x the subject:

8x - 6y = 3

8x = 3 + 6y

We have:

Multiply through by 2 to eliminate the fraction:

Since we have 0 = 5, it means the system of equations has no solution.

Therefore, the lines will not intersect, because this system has no solution.

ANSWER:

A. The lines will not intersect, because this system has no solution.

MATHEMATICALLY we say

[tex]0 \leqslant x \leqslant 4[/tex]

THAT IS THE DOMAIN OF THE GRAPH

THAT IS THE DOMAIN OF THE GRAPHOPTION A IS THE ANSWER.

The vertical angle theorem states that two opposite angles that are formed when two lines intersect each other are always equal, graphically this looks like this:

Then, if we apply this theorem to the figure shown we can say that

This means that:

The orthogonal trajectories of the family of curves y² = 6Kx³ will be [tex]y = \sqrt{6(C-\frac{x^2}{4}}[/tex]

An orthogonal trajectory of a family of curves is any curve that forms right angles with each member of the family. The curve does not always have to cross each member of the family.

It is given that,

y² = 6Kx³

Differentiate both sides we get,

[tex]\rm 2y = 6k(3x^2) \frac{dy}{dx} \\\\ \frac{dy}{dx} =\frac{2y}{18Kx^2}[/tex]

Substitute the value of K as

[tex]\rm K = \frac{y^2}{6x^3}[/tex]

[tex]\frac{2y}{18(\frac{y^2}{6x^3})x^2} = \frac{dy}{dx} \\\\ \frac{dy}{dx} = \frac{2x}{3y}[/tex]

Consider the negative reciprocal to find the perpendicular slope.

[tex]\frac{-3y}{2x} =\frac{dy}{dx} \\\\ - \int {\frac{1}{2x} \ dx = \int \frac{1}{3y} dy \\\\[/tex]

[tex]-\frac{x^2}{4}+C = \frac{y^2}{6}[/tex]

Simplify,

[tex]\rm 6(-\frac{x^2}{4}+C)= y^2 \\\\ y = \sqrt{6(C-\frac{x^2}{4}}[/tex]

Thus, the orthogonal trajectories of the family of curves y² = 6Kx³ will be [tex]y = \sqrt{6(C-\frac{x^2}{4}}[/tex]

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The answer to the given functions are:

1)  f (3) = 3 × 3 + 5 = 14

2)  f( 3 ) = (3)² - 1.5 = 7.5

3)  f (3) = 3×2 = 6

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

A function is a type of rule that produces one output for a single input.. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.

Given : Functions are f(x) = 3x + 5 ------- 1

f(x)=x²-1.5 --------- 2 and f(x) = 2x -----------3

Thus when we put x = 3 we will get the following values that is ;

1 becomes  f (3) = 3 × 3 + 5 = 14

and 2 becomes f( 3 ) = (3)² - 1.5 = 7.5

And 3 becomes f (3) = 3×2 = 6

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Answer:

B. 2.7136 x 10^22

Step-by-step explanation:

Hope this helps :))

We have that in 70 minutes 120 players of an orchestra play Beethoven's 9th symphony because it always lasts 70 minutes.

The lenght of a musical piece does not depend in the number of musicians playing it. The orchestra could have 2 violinists more or less and they still will play the same 70 minutes musical piece.

Then, an orchestra of 60 players would take the same 70 minutes to play Beethoven's 9th symphony.

Answer

(8m + 1)^2 = (8m + 1)² = 64m² + 16m + 1

Explanation

The question simply wants us to simplify the expression

(8m + 1)^2

= (8m + 1)²

= (8m + 1) (8m + 1)

= 8m (8m + 1) + 1 (8m + 1)

= 64m² + 8m + 8m + 1

= 64m² + 16m + 1

Hope this Helps!!!

To solve this problem, we will use the following expression:

In this case:

Substituting the above values in the expression, we get:

Finally, simplifying the above result, we get that the probability that his shirt number is from 67 to99 given that he weighs at most 210 pounds is:

Answer:

The point-slope form of a line is

where (x_1, y_1) are the coordinates of a point on the line.

From the given point we find the slope m.

With the value of the slope in hand, we now use one of the points given to write down the point-slope form:

where we have used the point (6, 10).

A) The inequality for the situation is 41x + 16y < 6900

B) The painter can work less than 97 hours without exceeding the budget of Hanson.

Given,

The total money spend by Hanson = < $6900

The charge for carpenters = $41 per hour

The charge for painters = $16 per hour

A) We have to find an inequality for this situation.

Lets take,

Carpenters working hours = x

Painters working hours = y

So, the inequality will be like:

41x + 16y < 6900

B) Now, we have to find the number of hours the painter can work without exceeding his budget if he hires carpenter.

Carpenters working hours = 50

Then, the charge will be = 50 × 41 = 2050

Then,

6900 - 2050 = 4850

The balance amount will be less than 4850.

So, the working hours of painter:

y < 4850 / 50

y < 97

That is, the painter can work less than 97 hours without exceeding the budget of Hanson.

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The question is incomplete. Completed question is given below:

Hanson is fixing up his home and must spend less than $6,900 to hire carpenters and painters. Carpenters charge$41 per hour and painters charge $16 per hour.

Part A: Write an inequality to represent the situation.

Part B: If he hires a carpenter for 50 hours, what is the maximum number of hours the painter can work without exceeding his budget?

The two diameters that separate the top 35 from the bottom 35 in the normal distribution are 5.35 mm and 5.61 mm .

Normal distributions are crucial to statistics because they are widely used in the natural and social sciences to represent real-valued covariates whose distributions are unknown.

First we will find the bottom 3% such that P(X ≤ x) = 0.03

⇒ [tex]P(\frac{X-5.48}{0.07}\leq \frac{x-5.48}{0.07} )=0.03[/tex]

⇒[tex]P(Z\leq \frac{x-5.48}{0.07} )=0.03[/tex]

Now we will use the normal table to calculate the corresponding z-score.

[tex]\frac{x-5.48}{0.07} =-1.88\\\\\implies x = 5.348[/tex]

Now we will find the same for the top part of the distribution.

[tex]P(\frac{X-5.48}{0.07}\leq \frac{x-5.48}{0.07} )=0.97\\\\\implies P(Z\leq \frac{x-5.48}{0.07} )=0.97[/tex]

Now we will use the normal table to calculate the corresponding z-score.

[tex]\frac{x-5.48}{0.07} =1.88\\\\\implies x = 5.612[/tex]

The two diameters that separate the top 35 from the bottom 35 in the normal distribution are 5.35 mm and 5.61 mm .

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We have in total 700 students

252 students are on the students council

700 is 100%

252 is x

x represents the percentage of the student's council, in order to calculate x we need to do the next operation

252 is the 36%

the percent of students that are on the student council is 36%

Matching the following function

What is a Function?

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

The function of f^(-1)(x) = 5x is:

f(x)= x / 5

The function of f^(-1)(x) = x^3 / 2 is:

f(x)=3√2x

The function of f^(-1)(x) = x+10 is:

x - 10

The function of f^(-1)(x) = 3(x + 17) / 2 is:

(2x / 3) - 17

Hence, These are the Match of one-to-one functions with their inverse functions.

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Since there is no overlapping the area of the polygon must be equal to the combined area of the cards.

The quadratic equation is y = 4. (x + 2)(x - 1).

Given,

The roots are -2 and 1 and whose leading coefficient is 4 using the letter x to represent the variable.

To Write the Quadratic Equation by using above given:
Now, According to the question:

Roots are -2 and 1

Leading Coefficient is = 4

Using Variable is =  x  

Formulate the equation of polynomial function is

y = 4. (x + 2)(x - 1)

Hence, The quadratic equation is y = 4. (x + 2)(x - 1).

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The sine law is described by the equation

1) Given angle C, length of side b, and length of side c, we are looking for the value of angle B. The angle B can be computed using

Substitute the values on the equation above and solve, we get

Thus, angle B is equal to 83.7 degrees.

2) Given angle B, length of side a, and length of side b, we are looking for the value of angle A. The angle A can be computed using

Substitute the values on the equation above and solve, we get

There are no valid measurements for angle A on this solution.

3) Given angle C, length of side c, and length of side b, we are looking for the value of angle B. The angle B can be computed using

Substitute the values on the equation above and solve, we get

Thus, angle B is equal to 21.9 degrees.

4. Given angle A, length of side c, and length of side a, we are looking for the value of angle C. The angle C can be computed using

Substitute the values on the equation above and solve, we get

Thus, angle C is equal to 72.74 degrees.

5. Given angle A, length of side c, and length of side a, we are looking for the value of angle C. The angle C can be computed using

Substitute the values on the equation above and solve, we get

Thus, angle C is equal to 25.0 degrees.

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{0}}} \implies \cfrac{ -3 }{ 4 } \implies {\Large \begin{array}{llll} - \cfrac{ 3 }{ 4 } \end{array}}[/tex]

The die has 6 faces

Given the area of the triangle:

You can identify in the figure provided in the exercise that the height of the triangle is:

The area of a triangle can be calculated using this formula:

Where "A" is the area, "b" is the base, and "h" is the height.

If you solve for "b", you obtain this formula:

Therefore, knowing the Area and the height of the triangle, you can substitute them into the formula and then evaluate, in order to find the length of its base:

Hence, the answer is:

Given:

The tabular representation of the data is given.

Required:

Histogram and Median of the given data.

Explanation:

The histogram of the given data is calculated as follows:

Figure 1

The median of the given set of data is calculated as,

Answer:

Thus figure 1 represents the histogram of the given data. The median of the given set of data is 27.7353.

System A

solve the first equation for x

replace in the second equation

The system has infinitely many solutions, They must satisfy the following equation

System B

solve for x for the first equation

replace in the second equation

The system has no solution.

1. The probability that they win both contract will be 23.4%.

It should be noted that probability simply means the likelihood that an event will occur.

The probability of winning the contract will be:

= Probability of A winning × Probability of B winning

= 45% × 52%

= 0.45 × 0.52

= 0.234

= 23.4%

The probability is 23.4%

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The given system of equation :

x +2y =4

2x -2y =5

On adding both equation we get

x+2y+2x-2y=4+5

3x=9

x=3

So, for y, substitute x=3

x+2y=4

3+2y=4

2y=4-3

2y=1

y=1/2

The solutions is (3,1/2)

The system of linear equation have infintely many solution if they are coincidient, i.e. slope are equal

The given expression :

x+2y =4

2y=4-x

y=(4-x)/2

y = 2-x/2

So slope is (-1/2)

The second equation : 2x-2y=5

2y=2x-5

y=(2x-5)/2

y=x-

Answer: $325

Step-by-step explanation:

a. The formula for the perimeter of a square is P=4L, where L is the length of it's sides.

b. The formula for the area of a square is A=LxL=L^2, where L is the length of it's sides.

Range of a Data Set :

The range of a set of data is the difference between the highest and lowest values in the set

MEAN :

The mean is the mathematical average of a set of two or more numbers

Set A: 2, 10, 8, 19, 23

Arrange the data of set A in ascending order;

Set A : 2, 8, 10, 19, 23

For range; the highest term is 23, lowers term is 2

Range = highest - lowest

Range = 23 - 2

Range = 21

for Mean; the sum of all entries divided by the total number of entries in data set.

In data A, total number of entries are : 5

Thus, mean of set A is 12.4

Now, for set B;

Set B : 14 16 15 17 16

Arrange the elements of set B in the ascending order;

Set B : 14, 15, 16, 16, 17

For range; the highest term is 17, lowers term is 14

Range = highest - lowest

Range = 17-14

Range = 3

Thus, range of set B is 3

for mean of set B;

The sum of all entries divided by the total number of entries in data set.

In data B, total number of entries are : 5

Thus, the mean for set B is 15.6

Answer : The mean of set A is 12.4 and range is 21

The mean of set B is 15.6 and range is 3