Which expression is equivalent to x6 – 9?

(x3)2 – 33

(x3)2 – 32

(x3)3 – 32

Answer:  The correct answers are:

8) x=5/2 and y=0  

9) An infinite number of solutions

10) x=1/4 and y=-1/2

Step-by-step explanation:

QUESTION 8:

Rewrite equations

y+3y=0

2x-5=-y

2x+y=5

Solve for y

y+3y=0

4y=0

y=0

Substitute 0 for y in 2x+y=5

2x+0=5

2x=5

Divide both sides by 2

x=5/2

x=5/2 and y=0

QUESTION 9:

Rewrite equations

3x-y=5

y=3x-5

Linear equation

a1/a2 = b1/b2 = c1/c2

3/-3 = -1/1 = -5/5

-1 = -1 = -1

Answer: An infinite number of solutions

QUESTION 10:

Rewrite equations

2x+y=0

4x-2y=2

Substitute and Simplify

2(2x-y)=2⋅1

2x-y=1

Solve for y

2x+y=0

y=-2x

Substitute y=-2x in 2x-y=1

2x-1(-2x)=1

2x+2x=1

4x=1

x=1/4

Substitut3 1/4 for x:

y=-2x

y=-2(1/4)

y=-1/2

x=1/4 and y=-1/2

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The correct option which represents  sum expressed in sigma notation is A.

What is sigma notation?

A series is represented in an exceedingly compact type, referred to as summation or sigma notation. The greek capital letter, ∑ , is employed to represent the total.

The series 4+8+12+16+20+24 is expressed as ∑n= 4n . The expression is browse because the total of 4n as n goes from one to six . The variable n is termed the index of summation.

The geometric series.

Main body:

∑ 125 (1/5)ⁿ⁻¹ ; where, n = 1 to 4.

Now, Calculate the partial sum of the geometric series as;

The geometric series = ∑ 125 (1/5)ⁿ⁻¹

Substitute n = 1, 2, 3, 4, we get;

= 125 (1/5)¹⁻¹ + 125 (1/5)²⁻¹ + 125 (1/5)³⁻¹ + 125 (1/5)⁴⁻¹

= 125 (1/5)⁰ + 125 (1/5)¹ + 125 (1/5)² + 125 (1/5)³

= 125 + 25 + 125/25 + 125/125

= 125 + 25 + 5 + 1

Thus, The partial sum of the geometric series is;

⇒ 125 + 25 + 5 + 1

Option A is true.

The correct question is in the figure.

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Answer: x= 27/5

Step-by-step explanation:

This equation can rewrite as -2/3x + 4 = 2/5

We separate x by subtracting 4 from both sides

-2/3x = -20/5 +2/5

-2/3x = -18/5

Then we divided both sides by -2/3

Ad we will get x= 27/5

The value of [tex]z_{\alpha /2}[/tex] that corresponds to a 90% confidence interval is

The confidence level is the likelihood that, if you repeat your experiment or resample the population in the same manner, you will come close to arriving at the same estimate.

The estimate's upper and lower bounds are what make up the confidence interval for a particular level of confidence.

For 90%confidence interval = 0.9

significance level, α = 1 - 0.9 = 0.10

For two tailed test, α/2 = 0.05

using z table

0.0505 = -1.64

0.05 = x

0.0495 = -1.65

solving for x by interpolation

(0.0505 - 0.05) / (0.05 - 0.0495) = (-1.64 - x) / (x - -1.65)

0.0005(x + 1.65) = 0.0005(-1.64 - x)

x + x = -1.64 - 1.65

x = -1.645

from z tables at 90% confidence interval in two tailed test the score is found to be 1.645

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The type of automobile insurance coverage that is needed in this problem is of:

Liability coverage.

The types of car insurance coverage are listed as follows:

In this problem, the situation is that Harold caused a collision that resulted in injuries to Tyler, who has to pay the ambulance/hospital bill.

This means that Harold is liable to the injuries caused to Tyler, meaning that he needs liability coverage to help pay the hospital/ambulance bill, as collision coverage and personal injury coverages are for the victim and not for the person that caused an accident.

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The expected value of the random variable is 5.37, the variance of the random variable is 0.8531 and the standard deviation of the random variable is 0.9236.

Given that,

The number of days it takes for packages to arrive from an online shop, together with the probability that it will happen, are provided in the table below.

The table is

Number of days           Probability

A-3                                    0.01

B-4                                    0.14

C-5                                    0.46

D-6                                    0.25

E-7                                     0.14

We have to find the expected value of the random variable, the variance of the random variable and the standard deviation of the random variable.

We know that,

The random variable's predicted value is now shown.

Expected value = summation (x ×P(x))

= 3×0.01+4×0.14+5×0.46+6×0.25+7×0.14

= 5.37

Now the variance of the random variable

Variance =summation ((x - mean)² ×P(x))

= (3-5.37)² × 0.01 + (4-5.37)² × 0.14 + (5-5.37)² × 0.46 + (6-5.37)² × 0.25 + (7-5.37)² × 0.14

= 0.8531

The random variable's standard deviation is now available.

σ  = √(0.8531)

= 0.9236

Therefore, the expected value of the random variable is 5.37, the variance of the random variable is 0.8531 and the standard deviation of the random variable is 0.9236.

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1. The skew segment to line AB is of: GF.

2. The parallel segment to line AD is of: EH.

3. The plane parallel to plane DCH is of: ABF.

4. The plane that is not parallel to plane EFG is of: EFB.

Skew lines are lines that share these two features:

Hence the skew line to line AB is of:

Line GF.

Parallel lines are planes are defined as lines or planes that never intersect as they have the same orientation and inclination, hence:

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Answer:75

Step-by-step explanation:

Since the total angle in the rhombus adds to 360, we minus the 2 110 and get 140. The 65 degrees is reflected on the other side, so we subtract 65 from 140, leaving 75.

Answer:

It is the first answer.

Step-by-step explanation:

The second answer is incorrect, because this has a negative slope which means that it has a negative association.

The third one is wrong because you can see that it does show that most of the points are clustered around a path that would be a line through the points.

The line of best fit does not have to go through any of the original points.

By using Venn Diagram, it can be calculated

I) The number of students taking all courses = 2

II) The number of students taking mathematics biology and chemistry = 2

III) The number of students taking biology and chemistry = 5

What is a Venn Diagram?

Venn Diagram is a diagram used to show the relationship between two or more sets.

This problem can be solved using Venn diagram

The Venn diagram has been attached here

Number of students taking maths and biology =7

Number of students taking chemistry and biology = 7

Number of students taking maths and chemistry = 7

Let the number of students taking all three courses be x

Number of students taking Maths = 40

Number of students taking maths only = 40 - 7 - 7 + x = 26 + x

Number of students taking Biology = 35

Number of students taking Biology only = 35 - 7 - 7 + x = 21 + x

Number of students taking Chemistry = 38

Number of students taking chemistry only = 38- 7 - 7 + x = 24 + x

Number of students taking maths and biology only = 7 - x

Number of students taking maths and Chemistry only = 7 - x

Number of students taking chemistry and biology only = 7 - x

Total number of students = 26 + x + 21 + x + 24 + x + 7 - x + 7 - x + 7 - x + x

                                           = 92 + x

By the problem,

92 + x = 94

x = 94 - 92

x = 2

I) The number of students taking all courses = 2

II) The number of students taking mathematics biology and chemistry = 2

III) The number of students taking biology and chemistry = 7 - 2 = 5

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According to Fleming's left hand rule, the thumb points along + y direction, so the magnetic force will be directed along + y axis (or in the direction of flow of current.

From relation vector F= qvB [i (–k )] = + qvB(j)

Magnetic force vector F along + y axis.

The Fleming Left-hand Rule According to Fleming's left-hand rule, if we stretch the thumb, middle finger, and index finger of the left hand to make an angle of 90 degrees (perpendicular to each other) and the conductor placed in the magnetic field experiences the magnetic force.

This rule was invented in the late 1800s by John Ambrose Fleming as a simple method of determining the direction of electric current in an electric generator or the direction of motion in an electric motor.

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The expression which is equivalent to the given expression as in the task content by virtue of the laws of indices is; ( 3 )^2n.

It follows from the task content that the expression which is equivalent to the given expression is to be determined.

Since the given expression is;

( 3^4n ) ^(1/2)

However, it follows from the power of power law of indices that the expression above can be written as follows;

( 3 ) ^ (4n × 1/2)

= ( 3 )^2n

Therefore, the required equivalent expression is; ( 3 )^2n.

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to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below.

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{2}}} \implies \cfrac{ -3 }{ 1 } \implies \text{\LARGE - 3}[/tex]

The measure of angle RPT is 122° if the measure of an angle RST is 64°.

In Euclidean geometry, an angle is the figure formed by two rays, known as the sides of the angle, that have a common termination, known as the vertex of the angle. These are referred to as dihedral angles. An angle can also be defined by two intersecting curves, which is the angle of the rays lying tangent to the respective curves at their point of intersection.

Angle can also refer to a rotation or the measurement of an angle. This measurement is the ratio of the length of a circular arc to its radius.

The total of a triangle's angle measurements is 180°. Because ∠RST = 64°, the other two angles must equal to  180-64 = 116°.

The diagram shows that RST is an isosceles triangle. This suggests that the basis angles, SRT and STR, are equivalent, with each equaling 116/2 = 58°.

RP will cut RST, and PT will cut STR.

PTR = 58/2 = 29° and PRT = 58/2 = 29°.

This suggests that the base angles are 29+29 = 58°, leaving RPT at 180-58 = 122°.

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Answer: 32%

Step-by-step explanation: add up the total and divide 16 by the total number of all people surveyed

Answer:

x =50

Explanation:

[tex]\frac{2}{100}[/tex] = [tex]\frac{1}{x}[/tex]

Cross multiply 100 and 1, which makes 100. Then cross divide 100 by two, which makes 50.

Then check if 2% of 50 is 1, which is true.

x = 50

Para calcular la tasa de inflación, debemos seguir una serie de pasos.

Para ello, hemos propuesto un ejemplo en el que, paso a paso, calcularemos para un caso real la tasa de inflación.

Imaginemos que hacemos un listado de las compras realizadas en un año determinado, el cual tomamos como base. Esta compra incluye, a la hora de elaborar un listado, una serie de productos, todos ellos con sus respectivos precios. Productos que, en este caso, son barras de pan, cafés, servicios de taxi y un pantalón de vestir.

En primer lugar, lo que debemos hacer es calcular el gasto de cada producto, para ello, multiplicando las cantidades de cada producto o servicio adquiridas, por el precio que se pagó por cada una de ellas, así como por los servicios.

En este caso, sería lo siguiente:

Barras de pan: 1,50€ x 150 = 225€.

Cafés: 2,40€ x 100 = 240 €.

Taxi: 5€ x 40 = 200€.

Pantalón: 120€.                    

espero haberte ayudado

The Value of probability for the distribution is 0.24 and -0.29

Probability distribution is a statistical function that describes all the possible values and probabilities for a random variable within a given range

F(x) = P(X ≤ x) = P(a < X ≤ b) = f(b) - f(a)

The Probability Distribution is given

(1) By looking at the table ,

Value P(x = 0 ) at x =0 is 0.24

Hence , P(x=0) = 0.24

Option b is correct

(2) P(-10 ≤x ≤ 15) = P(x = 15) - P(x = -10)

By using the table ,

=> 0.05 - 0.34

=> -0.29

Option c is correct.

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Although horror book sales appear to be only 50% of fantasy sales, but they are actually only about 8% smaller, that is, option a.

Here, we are given a graph as shown in the figure below.

Just by looking at the graph it appears that that horror books are 50% of fantasy book sales.

From the graph we have the following data-

Number of horror books sold = 55

Number of fantasy books sold = 60

Number of extra fantasy books than horror books = 60 - 55

= 5

Thus, in percentage terms horror books will be - (5/60) % smaller than fantasy books

= 8.33%

Therefore, although horror book sales appear to be only 50% of fantasy sales, but they are actually only about 8% smaller, that is, option a.

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Your question was incomplete. Check for the missing graph below.

In a technique called stub testing, the programmer simulates each program outcome or result and displays a message to indicate whether or not the program executed successfully.

Test stubs are programs that imitate the behaviors of software components that a module undergoing tests rely on in advanced polymorphism computer science. Test stubs react to calls with pre-programmed prefabricated responses; they typically don't respond at all to calls that aren't part of the test. A stub is a brief piece of code used in testing to replace another component. Using a stub has the advantage of returning consistent results, which makes the test easier to write. And tests can be performed even if the other components are not yet operational.

The programmer simulates each program outcome or result and displays a message to show whether or not the program executed successfully. This process is known as stub testing.

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The sets that represent the union and intersection of set F and set H will be (-∞, 4) ∪ [7, ∞) and the null set, respectively.

Sets are groups of clearly specified components. The number of items in a finite set is denoted by a curly bracket.

The two sets are given below.

F = {v | v < 4}
H = {v | v ≥ 7}

The sets that represent the union of set F and set H will be given as,

F∪H = (-∞, 4) ∪ [7, ∞)

The sets that represent the intersection of set F and set H will be given as,

F∩H = {null}

The sets that represent the union and intersection of set F and set H will be (-∞, 4) ∪ [7, ∞) and the null set, respectively.

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Answer:

  a) 80

  b) -80

  c) -41

Step-by-step explanation:

For g = -4 and h = -5, you want the values of ...

To evaluate these expressions, put the value of the variable where the variable is, and do the arithmetic. A calculator can help.

  = 4(-4)(-5) = 80

  = (-4)²(-5) = -80

  = 5(-5) -(-4)² = -25 -16 = -41

The solution is Option 4.

Roman numeral representing the least 3 digit number which is 100 is C

The Roman numeral for 100 = C

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the least 3 digit number be A

Now , the value of A = 100

where 100 is the lease 3 digit number

And , the Roman numeral for 100 is given by C

Therefore , the value of 100 in Roman Numeral is C

Hence , The Roman numeral representing the least 3 digit number which is 100 is C

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Main answer: mean = 23

supporting answer: Agraphical representation of a normal distribution is sometimes called a bell curve because of its flared shape. The precise shape can vary according to the distribution of the population but the peak is always in the middle and the curve is always symmetrical. In a normal distribution, the mean, mode and median are all the same.

body of the answer: given total number of samples=15

 percentage of failure stain=25 percent=0.25

 standard deviation=3.5

a. formula used=z=x- mean/standard deviation

p(0.25<x<0)

z=25-mean  /3.5

0.6*3.5=25-mean

mean=25-0.6*3.5

           =22.9

since A(0.25)=0.6

b. for 15 adults the mean is 23

for one adult =23/15

                     =1.533

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The mean for the given statistic problem is 23.

The strain for a single adult in a way that conveys information about precision and reliability is 1.533.

What is normal distribution?

A graphical representation of a normal distribution is sometimes called a bell curve because of its flared shape. The precise shape can vary according to the distribution of the population but the peak is always in the middle and the curve is always symmetrical. In a normal distribution, the mean, mode and median are all the same.

Given total number of samples=15

percentage of failure stain=25 percent=0.25

standard deviation=3.5

a. formula used=z=x- mean/standard deviation

p(0.25<x<0)

z=25-mean  /3.5

0.6*3.5=25-mean

mean=25-0.6*3.5

          =22.9

since A(0.25)=0.6

b. For 15 adults the mean is 23

For one adult =23/15

                    =1.533

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56.8 is the commision

Answer: 1/54

Step-by-step explanation:

5 2/5 = 27/5

1/10 divide by 27/5 =

1/10 times 5/27 =

5/ 270 = 1/54

a) T( K₁A₁+K₂A₂)= K₁T(A₁)+K₂T(A₂). So, T is a linear transformation.

b) T(A)=B, if B be any element of M₂

c) Range of T=={A∈ [tex]M_{ 2*2}[/tex]/[tex]A^{T}[/tex]=-A}

A matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions arranged in rows and columns that is used to represent a mathematical object or an attribute of such an item.

A square matrix's determinant is a number connected with the matrix that is crucial for studying a square matrix; for example, a square matrix is invertible if and only if it has a nonzero determinant, and a square matrix's eigenvalues are the roots of a polynomial determinant.

Define T: [tex]M_{ 2*2}[/tex] ⇒ [tex]M_{ 2*2}[/tex] by T(A)=A+[tex]A^{T}[/tex]

a) Let T is a linear transformation

Consider K₁A₁+K₂A₂ ∈  [tex]M_{ 2*2}[/tex]

T( K₁A₁+K₂A₂)= K₁A₁+K₂A₂+( K₁A₁+K₂A₂)[tex]( K₁A₁+K₂A₂)^{T}[/tex]

= K₁T(A₁)+K₂T(A₂)

T( K₁A₁+K₂A₂)= K₁T(A₁)+K₂T(A₂)

Therefore, T is a linear transformation.

b) Let B∈ [tex]M_{ 2*2}[/tex] such that [tex]B^{T}[/tex]=B

Therefore, B is a symmetric matrix.

Let A=(1/2)B∈ [tex]M_{ 2*2}[/tex]

T(A)=A+[tex]A^{T}[/tex]

=(1/2)B+[tex](1/2B)^{T}[/tex]

T(A)=B

A=(1/2)B such that T(A)=B

c) Range of T is the set of B in  [tex]M_{ 2*2}[/tex], [tex]B^{T}[/tex]=B

T( [tex]M_{ 2*2}[/tex])={B∈ [tex]M_{ 2*2}[/tex]/ [tex]B^{T}[/tex]=B}

d) Kernel of T={A∈ [tex]M_{ 2*2}[/tex]/T(A)=0)

={A∈ [tex]M_{ 2*2}[/tex]/A+[tex]A^{T}[/tex]=0}

={A∈ [tex]M_{ 2*2}[/tex]/[tex]A^{T}[/tex]=-A}

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Three points Assuming M22 is the vector space containing all 22 matrices, T: M22 M22 is defined as T(A) = A + AT.

T is a linear transformation, therefore demonstrate it.

b) Assume that B is any element from M22 where BT = B. In M22, look for an A such that T(A) = B.

c) Explain the T kernel.

a) Verifying that T preserves sums and multiplication by scalars—which implies that T(0) = 0 in particular—is sufficient to determine if T is linear.

Additions: T(A+B) = A+B+A+B T = A+B+A T +B

T = (A + A T ) + (B + B T ) = T(A) + T (B).

Scalar multiplication

T(c · A) = (c · A)

T = c · A

T = c · T(A) (A).

b) Calculate A = 1 2B. Since AT = 1 2BT = 1 2B, T(A) = A + A.

T = \s1 \s2 \sB + \s1 \s2 \sB = B.

c) If 0 0 0 0 = A + A, then and only if A = a b c d, A is in the kernel of T.

If and only if 2a = b + c = 2d = 0, i.e., a = d = 0 and c = b, then T = a b c d + a c b d = 2a b + c b + c 2d. Therefore, the set ker(T) = 0 b b 0 : b R is the kernel of T.

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The percent change for people living with the disease is 36.78% and with the number of deaths is 60%

In 2005 there were 29.9 million people worldwide living with a certain disease

By 2015, the number of people living with the disease had fallen to 28.8 million

Decrease in number of people living with a disease = 29.9 - 28.8 = 1.1

decrease in percentage of people living with a disease = (1.1/29.9)/100 = 36.78%

In 2005, 1.5 million deaths from the disease

In 2015,  2.6 million deaths were reported

change in number of deaths from the disease = 2.6 - 1.5 = 0.9

Change in percentage = (0.9/1.5) 100 = 60%

Therefore,  the percent change for people living with the disease is 36.78% and with the number of deaths is 60%

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