Solve the inequality.
|x + 1| < 27
[?] < x < [ ]

Using the concept of absolute and relative change, it is found that:

a) The absolute change in the monthly cost of cable TV is of $4.15.

b) The relative change in the monthly cost of cable TV is of 5.53%.

c) The absolute change in the monthly cost of eggs is of $0.67.

d) The relative change in the monthly cost of eggs is of 39.41%.

e) Due to the higher relative change, the cost of the eggs increased the most.

Hence the absolute changes are given as follows:

The relative changes are given as follows:

Hence, for item e:

Due to the higher relative change, the cost of the eggs increased the most.

More can be learned about absolute and relative change at https://brainly.com/question/19162774

#SPJ1

Compute the characteristic polynomial of [tex]A[/tex].

[tex]p(\lambda) = \det(A - \lambda I) \\\\ ~~~~~~~~ = \begin{vmatrix} \beta - \lambda & 0 & 1 \\ 2 & 1 - \lambda & -2 \\ 3 & 1 & -2-\lambda \end{vmatrix} \\\\ ~~~~~~~~ = (\beta-\lambda)\begin{vmatrix}1-\lambda&-2\\1&-2-\lambda\end{vmatrix} + \begin{vmatrix}2&1-\lambda \\ 3 & 1 \end{vmatrix} \\\\ ~~~~~~~~ = -\lambda^3 + (\beta-1) \lambda^2 + (\beta + 3) \lambda - 1[/tex]

By the Cayley-Hamilton theorem,

[tex]p(A) = -A^3 + (\beta - 1) A^2 + (\beta + 3) A - I = 0[/tex]

Note that

[tex]A^7 - (\beta - 1) A^6 - \beta A^5 \\\\ ~~~~~~~~ = -(-A^3 + (\beta - 1) A^2 + \beta A) A^4 \\\\ ~~~~~~~~ = -(\underbrace{-A^3 + (\beta - 1) A^2 + (\beta + 3) A - I}_{p(A)=0} - 3A + I) A^4 \\\\ ~~~~~~~~ = (3A - I) A^4[/tex]

Recall that [tex]\det(AB) = \det(A) \det(B)[/tex]. Note that [tex]A[/tex] is not singular, and hence [tex]A^n[/tex] is not singular for any natural [tex]n[/tex].

[tex]\det(A) = \begin{vmatrix} \beta & 0 & 1 \\ 2 & 1 & -2 \\ 3 & 1 & -2 \end{vmatrix} \\\\ ~~~~~~~~ = \beta \begin{vmatrix}1&-2\\1&-2\end{vmatrix} + \begin{vmatrix}2&1\\3&1\end{vmatrix} \\\\ ~~~~~~~~ = -1 \neq 0[/tex]

Then [tex]3A-I[/tex] must be singular. So

[tex]\det(3A-I) = \begin{vmatrix} 3\beta - 1 & 0 & 3 \\ 6 & 2 & -6 \\ 9 & 3 & -7 \end{vmatrix} \\\\ ~~~~~~~~ = (3\beta-1) \begin{vmatrix}2&-6\\3&-7\end{vmatrix} + 3 \begin{vmatrix}6&2\\9&3\end{vmatrix} \\\\ ~~~~~~~~ = 4 (3\beta-1)[/tex]

[tex]4(3\beta-1) = 0 \implies \beta = \dfrac13 \implies 9\beta = \boxed{3}[/tex]

If my allotted budget for a week in $500, and considering I spend $400 dollars as my complete expenses up till the end of the week, (since no information about my expenses is the question statement), the amount that I will be able save from my budget is $100, calculated using basic subtraction.

As per the question statement, my allotted budget for a week in $500 and there is no further information about my expenses for the week. Hence, Let us consider that I had to spend $400 dollars as my complete expenses for the week.

We are required to calculate the amount that I will be able save from my budget.

To solve this question, we simply have to subtract my total week's expenses from my weekly budget, i.e., [tex][(500-400)=100][/tex].

Hence, I will be able to save upto $100 from my weekly budget.

To learn more about Subtraction, click on the link below.

https://brainly.com/question/2346316

#SPJ1

The interpretation of the beam on the wall is that when the function is undefined, the light is not shining completely on the wall and  and the function rate of changes are 55.236, 68.276, 110.473 and 289.221

The given parameter is the graph of the beam

From the graph, we can see that the beam does not shine on all parts of the wall.

It shines on some part and doesn't on other parts

This means that the function is undefined

Hence, the interpretation of the beam on the wall is that when the function is undefined, the light is not shining completely on the wall

To do this, we use the following computations:

[d(0.1) - d(0)]/[0.1 - 0] = [5.5236 - 0]/[0.1 - 0] = 55.236

[d(0.2) - d(0.1)]/[0.2 - 0.1] = [12.3512 - 5.5236]/[0.2 - 0.1] = 68.276

[d(0.3) - d(0.2)]/[0.3 - 0.2] = [23.3985 - 12.3512]/[0.3 - 0.2] = 110.473

[d(0.4) - d(0.3)]/[0.4 - 0.3] = [52.3206 - 23.3985]/[0.4 - 0.3] = 289.221

Hence, the function rate of changes are 55.236, 68.276, 110.473 and 289.221

Read more about trigonometry functions at

https://brainly.com/question/24349828

#SPJ1

Reason:

Subtract 3x from both sides. They cancel out and go away. The x term is fully eliminated and we're left with the equation 8 = 9, which is a false statement. Therefore, the original equation is always false regardless of what you pick for x. This is why there aren't any solutions.

Visually you can graph y = 3x+8 and y = 3x+9. You'll get parallel lines that never intersect. We need the lines to intersect if we wanted a solution point. Parallel lines have the same slope, but different y intercepts.

Because the system has no solutions, we consider the system inconsistent.

Step-by-step explanation:

Mathematically the statement can be written as

SUPPLEMENTARY Angles add up to 180°

x+y=180°....(1)

let y be the larger angle and x be the smaller angle.

y=x+88°....(2)

plug in the (2) in the first equation

[tex]x + (x + 88) = 180 \\ 2x + 88 = 180 \\ 2x = 180 - 88 \\ 2x = 92 \\ \frac{2x}{2} = \frac{92}{2} \\ x = 46[/tex]

the measure of the larger angle is y=x+88°

[tex]y = 46 + 88 \\ y = 134[/tex]

The bigger angle is equal to 134°

HOPE THIS HELPS!!!!

Answer: 134°

here's your answer

Answer:

D

Step-by-step explanation:

[tex]h(x)=2x^5+(a+s)x^4+(b+t)x^3[/tex]

For the polynomial to be divisible by x⁴, the coefficient od the x³ term must be 0, and thus the answer is D.

The half-life of carbon-14 is 5,730 years. Assuming you start with 100% of carbon-14, what is the expression for the percent, P(t), of carbon-14 that remains in an organism that is t years old and what is the percent of carbon-14 remaining (rounded to the nearest whole percent) in an organism estimated to be 20,000 years old

Carbon-14, C-14, 14

C or radiocarbon, is a radioactive isotope of carbon with an atomic nucleus containing 6 protons and 8 neutrons. Its presence in organic materials is the basis of the radiocarbon dating method pioneered by Willard Libby and colleagues (1949) to date archaeological, geological and hydrogeological samples. Carbon-14 was discovered on February 27, 1940, by Martin Kamen and Sam Ruben at the University of California Radiation Laboratory in Berkeley, California. Its existence had been suggested by Franz Kurie in 1934.[2]

There are also trace amounts of the unstable radioisotope carbon-14 (14C) on Earth. Carbon-14 has a relatively short half-life of 5,730 years, meaning that the fraction of carbfon-14 in a sample is halved over the course of 5,730 years due to radioactive decay to nitrogen-14.

To know more about carbon14

visit-: https://brainly.com/question/27861556

SPJ9

The equation of the function is h(x) = ∛[(1/4)x - 5] + 3 if the cube root parent function is horizontally stretched by a factor of 4.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The cube root parent function is horizontally stretched by a factor of 4, then translated 5 units right and 3 units up.

The parent function is:

f(x) = ∛x

Horizontally stretched by a factor of 4:

g(x) = ∛[(1/4)x]

Translated 5 units right:

G(x) = ∛[(1/4)x - 5]

Translated 3 units up:

h(x) = ∛[(1/4)x - 5] + 3

Thus, the equation of the function is h(x) = ∛[(1/4)x - 5] + 3 if the cube root parent function is horizontally stretched by a factor of 4.

Learn more about the function here:

brainly.com/question/5245372

#SPJ1

Based on the values in the table of values, the expected value of the data is -3.3

The dataset is given as

x −5 −4 −3 −2 −1

P(X=x) 0.1 0.3 0.1 0.2 0.3

The expected value of the dataset is calculated as

E(x) = ∑x * P(x)

Substitute the known values in the above equation

So, we have

E(x) = (-5 * 0.1) + (-4 * 0.3) + (-3 * 0.3) + (-2 * 0.2) +(-1 * 0.3)

Evaluate the products in the above equation

So, we have

E(x) = -0.5 - 1.2 - 0.9 - 0.4 - 0.3

Evaluate the difference in the above equation

So, we have

E(x) = -3.3

Hence, the expected value of the data is -3.3

Read more about expected values at

https://brainly.com/question/15858152

#SPJ1

To find the probability of an outcome the steps are as follows:

Urn -some objects of real interest are represented as colored balls .

Given data

space Ω = {a, b, c}

p(a )= 1/7,

p(b) = 2/7 and

p(c) = 4/7.

p(E) = p(a) + p(b) +p(c).

where p(E) = random experiment i. e. union

p(E) = 1/7 + 2/7 + 4/7

p(E) = 7/7

p(E) =1

An outcome is a result of a random experiment. The set of all possible outcomes is called the sample space. Thus in the context of a random experiment, the sample space is our universal set. Here are some examples of random experiments and their sample spaces:

Random experiment: toss a coin; sample space: S={heads,tails} or as we usually write it, {H,T}.

Random experiment: roll a die; sample space: S={1,2,3,4,5,6}.

Random experiment: observe the number of iPhones sold by an Apple store in Boston in 2015; sample space: S={0,1,2,3,⋯}.

Random experiment: observe the number of goals in a soccer match; sample space: S={0,1,2,3,⋯}.

To learn more about Random Experiment

Visit - https://brainly.com/question/28107339

#SPJ9

Solving a system of equations we can see that the two numbers are 727 and 4

Let's define x as the 3-digit number and y as the one-digit number.

Then we know that the sum is equal to 731:

x + y = 731

And the product is equal to 2,908, then:

x*y = 2,908

So we have a system of equations:

x + y = 731

x*y = 2,908

Isolating x on the first equation gives:

x = 731 - y

Now we can replace that in the other equation to get:

(731 - y)*y = 2,908

Now we can solve this quadratic equation to find the value of y.

731*y - y^2 = 2,908

-y^2 + 731*y - 2,908 = 0

The solutions are:

y = (-731 ± √( 731^2 - 4*(-2,908)*(-1))/(-2)

y = (-731 ± 723)/-2

Now, y is an one digit number, then:

y = (-731 + 723)/-2 = 4

And x will be the 3 digit number:

x = 731 - x = 731 - 4 = 727

So the two numbers are 727 and 4

Learn more about systems of equations:

https://brainly.com/question/13729904

#SPJ1

The mathematical statement given as 0.09 is 1/10 as much as 0.90 is true

The mathematical statement is given as:

0.09 is 1/10 as much as 0.90

To determine if the above statement is true, we start by representing the statement as an equation

So, we have

0.09 = 1/10 * 0.90

Express 1/10 as decimal

So, we have

0.09 = 0.10 * 0.90

Evaluate the product

So, we have

0.09 = 0.09

The above equation is true

Hence, the mathematical statement given as 0.09 is 1/10 as much as 0.90 is true

Read more about expressions at

https://brainly.com/question/723406

#SPJ1

Possible question

Determine if the following statement is true or false

Answer:

x + 7

Step-by-step explanation:

5(2x + 2) - 3(3x -1)

10x + 10 - 9x - 3

x + 7

Answer:

hey the answer is d(0,4)

Answer:

It is D

Step-by-step explanation:

I've done this problem before

The raw score x, corresponding to z = 2 is calculated as; 90

We are given;

Population Mean; μ = 78

Sample mean; x' = ?

Population standard deviation; σ = 6

z-score; z = 2

The formula for z-score is;

z = (x' - μ)/σ

Thus, making x' the sample mean the subject of the formula gives;

x' = zσ + μ

Plugging in the relevant values gives;

x' = (2 * 6) + 78

x' = 12 + 78

x' = 90

Thus, the raw score x, corresponding to z = 2 is 90

Read more about statistics raw score at; https://brainly.com/question/26925971

#SPJ1

Answer:

x, y =8 -3

Step-by-step explanation:

System of Linear Equations entered :

  [1]    x - 4y = 20

  [2]    2x + 5y = 1

Graphic Representation of the Equations :

   -4y + x = 20        5y + 2x = 1  

Solve by Substitution :

// Solve equation [1] for the variable  x

 [1]    x = 4y + 20

// Plug this in for variable  x  in equation [2]

  [2]    2•(4y+20) + 5y = 1

  [2]    13y = -39

// Solve equation [2] for the variable  y

  [2]    13y = - 39

  [2]    y = - 3

// By now we know this much :

   x = 4y+20

   y = -3

// Use the  y  value to solve for  x

   x = 4(-3)+20 = 8

Solution :

{x,y} = {8,-3}

Answer:

6

Step-by-step explanation:

6 times 6 = 36, so 6 is the answer

Hope this helps. Please mark me brainliest!

The answer to the question 36/12=3

Answer:

you should cook it for 19 hours

The distance between two points A (-10, -7) and B(-8,1) will be equal to 8.2 units.

What do you mean by the distance between points ?

Distance between two points is the length of the line segment that connects the two locations in a plane.

It is given that the distance between points A (-10, -7) and B(-8,1) is to be calculated.

We can find out the distance by using the distance formula which is given by :

AB = [tex]\sqrt({x_{2} - x_{1})^2 + (y_{2}- y_{1})^2}[/tex]

AB = √ [( -8 -(-10)]^2 + [ 1 - (-7)]^2}

AB = √ (2² + 8²)

AB = √68

AB = 8.24 units

If we round off it to the nearest tenth then , hundredth place is less than 5 that meant 2 will be at the tenths place.

or

AB = 8.2 units.

Therefore , the distance between two points A (-10, -7) and B(-8,1) will be equal to 8.2 units.

Learn more about distance between two points click here :

https://brainly.com/question/7243416

#SPJ1

Answer:

-6 = 1

-4 = 2

0 = 4

2 = 5

8 = 8

Answer:

[tex](x^2y^5)5 = 5x^2y^5[/tex]

Step-by-step explanation:

Remove the parentheses to factor.

[tex]= x^2y^5 \times 5[/tex]

Flip the expression, creating a leading term and simplifying the equation.

[tex]= 5x^2y^5[/tex]

Answer:

∠ 2 = 122°

Step-by-step explanation:

given ∠ 2 = 2 ∠ 1 + 6

a linear pair of angles sum to 180° , then

∠ 1 + ∠ 2 = 180° , that is

∠ 1 + 2∠ 1 + 6 = 180° ( subtract 6 from both sides )

3∠ 1 = 174° ( divide both sides by 3 )

∠ 1 = 58° , then

∠ 2 = 180° - 58° = 122°

Answer:

36 min

Step-by-step explanation:

rate b = 1 / 90

rate m = 1/60

now add the rates together for 1 lawn

1 lawn / (1/60 + 1/90) = 36 min

The measure of the angles 1,2 and 3 are 75, 42 and 138 respectively.

The value of ∠1 = 180- 105             [supplementary angles]

∠1 = 75°

∠1 + ∠2 + 63° = 180                          [angle - sum property]

75 + ∠2 + 63 = 180

∠2 = 180 - (75 + 63)

∠2 = 42°

∠2 + ∠3 = 180                                       [supplementary angles]

42 + ∠3 = 180

∠3 = 180 - 42

∠3 = 138°

To learn more about angles from given link

https://brainly.com/question/25770607

#SPJ9

Answer:

x(down 1)=-11/5, x(down 2) =3

Step-by-step explanation:

The probability of P(A and B) based on the information given will be E. None of the above.

It should be noted that probability is used to illustrate the likelihood that something will occur.

In this case, P(A) = 0.1 and P(B) = 0.4. Therefore, the probability of P(A and B) will be

= P(A) + P(B)

= 0.1 + 0.4

= 0.5

Sine the value of 0.5 isn't given, the correct option is E.

Learn more about probability on:

brainly.com/question/24756209

#SPJ1

The image of the translation is shape WYX is shown by option 2.

The process of substituting the axes inside a Cartesian coordinate system with such a new set of axes parallel to the first, which is used to write equations for curves that are not centered about the origin.

As, from the rule of translation along x axis;

The coordinates of the x axis are not changed and y are changed.

Thus, for the given figure XWY the image after translation about the x axis is shown by the option 2 graph.

To know more about the translation, here

https://brainly.com/question/1046778

#SPJ1

The value equal to the direct opposite of Samantha's hike from her camp = -18 yards.

As per the given question;

Samantha descends a mountain from her camp.

Samantha discovered that she was 18 yards below the camp on the path she was on.

To locate the value that is the inverse of the distance Samantha hiked from her camp.

Samantha was 18 yards away from the camp.

Samantha hiked for 18 yards underneath the camp (in downwards )

Therefore;

Samantha hiked the opposite distance of 18 yards from the camp.

Samantha hiked for -18 yards.

Thus, the value equal to the inverse of the distance Samantha hiked from her tent = -18 yards

To know more about inverse, here

https://brainly.com/question/3831584

#SPJ9

Answer: 18

Step-by-step explanation: