Solving inequalities #5
25 points!!

-√12 i is the complex conjugate of the complex number√-12

A complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit.

A conjugate of a complex number is another complex number which has the same real part as the original complex number and the imaginary part has the same magnitude but opposite sign.

It's important to remember that i²=-1

This means we can rewrite

√-12 as √12i² =√12i

For complex number z=x+iy the conjugate of complex number is z=x-iy

We have z=√-12 so conjugate is -√12 i

Hence, -√12 i is the complex conjugate of the complex number

√-12

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Answer:

Carmen's water bottle holds 1 8/10 liters of water, which can be written as 18/10 liters or 1.8 liters.

Jorge's water bottle holds 2 2/5 liters of water, which can be written as 22/5 liters or 4.4 liters.

Jorge's estimate of his water bottle holding about 1/2 liter more water than Carmen's is reasonable because:

4.4 liters (Jorge's bottle) - 1.8 liters (Carmen's bottle) = 2.6 liters

2.6 liters is close to the estimate of 1/2 liter, so Jorge's estimate is reasonable.

The cost per square inches of the circular pie is C = $ 0.164

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

Given data ,

Let the cost per square inch of the apple pie be C

Let the area of the circle be represented as A

Now , the diameter of the circle is d = 10 inches

So , the radius of the circle r = d/2 = 5 inches

And , area of the circle = πr²

Substituting the values in the equation , we get

Area of Circle A = π x ( 5 )²

Area of Circle A = 78.5398 inches²

The cost of the apple pie = $ 12.85

Now , the cost for 78.5398 inches² of apple pie = $ 12.85

So , the cost for 1 inches² of pie C = 12.85 / 78.5398

On simplifying the equation , we get

The cost per square inches C = $ 0.164

Hence , the cost per square inches is $ 0.164

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Answer: would be 0.16th

hope this helped :)

The area of a circle with a diameter of 16 meters is equal to: B. 64π square meters.

Mathematically, the area of a circle can be calculated by using this formula:

Area = πr²

Where:

r represents the radius of a circle.

Note: Radius = diameter/2 = 16/2 = 8 meters.

By substituting the radius into the formula for the area of a circle, we have the following;

Area of circle = π × 8²

Area of circle = 64π square meters.

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Answer:64 PI

Step-by-step explanation:

The final solution for the initial value problem: y = −e∫x dx√40 − ∫x2e∫x dx − ∫y2e∫x dx.

The given initial value problem is yy′+x=x2+y2 with y(3) = −√40. To solve this we make the substitution U = u' and u = y. This transforms the given equation into the linear differential equation in x, u, and u': u'+xu=x2+u2. To solve this, we can use the integrating factor method. Multiplying both sides by the integrating factor e∫x dx gives us u'e∫x dx + xue∫x dx = x2e∫x dx + u2e∫x dx. Taking the integral of both sides, we obtain ue∫x dx = ∫x2e∫x dx + ∫u2e∫x dx + c, where c is the constant of integration. Solving for u, we have u = c/e∫x dx − ∫x2e∫x dx − ∫u2e∫x dx. Using the fact that u = y, we can substitute this expression into the equation to obtain the solution in terms of x and y: y = (c/e∫x dx) − ∫x2e∫x dx − ∫y2e∫x dx. Using the initial condition y(3) = −√40, we can solve for c to get c = −e∫3 dx√40. Substituting this into the solution, we get the final solution for the initial value problem: y = −e∫x dx√40 − ∫x2e∫x dx − ∫y2e∫x dx.

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The Transformation is graph of f is translated 3 units up and 7 units to the right.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Given: y=f(x-7) + 3.

As, from the Rule the f(x, y) --> f(x-c, y) shows the horizontal shift on right side.

So, the function is shifted 7 units to the right.

Now, the rule f(x)--> f(x) + c shows the vertical translation up by c units.

So, the function is translated 3 units up.

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The simplified form is q⁹rs⁶t

Index forms are simply described as a method of writing numbers that are too large or small in more concise forms.

The other names for index forms are scientific notation and standard forms.

There are rules for index forms, some of them are;

From the information given, we have that;

qr^0s^5t^0 x q^8rst

Note that any number raised to zero is 1, then we have;

qs⁵ × q⁸rst

Now, add the exponents of the like bases

q⁹rs⁶t

Hence, the value is q⁹rs⁶t

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Statistical methods are the processes of collecting, presenting, analyzing data, and drawing conclusions.

These methods are divided into two groups: descriptive statistics and inferential statistics.

The scope of descriptive statistics includes distributions of random and random variables, discrete and continuous random variables. For inference statistics, including statistical inference from one or two populations, analysis of variance, regression analysis, and analysis of categorical data from both random and normal populations.

Statistical techniques include many ways to collect, present, analyze, and draw conclusions from data. By considering these methods, you can choose which method to use according to the characteristics of your data.

Choosing the right method leads to drawing the right conclusions.

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Answer:

hi !!

Step-by-step explanation:

first the domain of f(x) : 2*-1 -1 < 2x-1 < 2*4 -1 = -3 <2x-1 < 7

now the domain of g(x) : 4/(3-2) < 4/(x-2) < 4/(5-2) = 1.3 < 4/(x-2) < 4

now h(x) = -3 - 1.3 <f(x) - g(x) < 7-4 = - 4.3 < f(x) - g(x) < 3

it is the answer e : None of the Above

Answer:

half of 20 is 1010

Step-by-step explanation:

half of 20 is 1010 is your new radius so10^2 = 100100 x 3.14 = 314Now we multiply by the height:314 x 11 = 3,454 cm^3

The perimeter of the figure is 4(π + 9)ft.

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length.

Given is a 2 - D figure as shown in the figure attached.

We can write the perimeter as -

P = P{rectangle} + P{semicircle}

P = 2(10 + 8) + (4π)

P =  (4π) + (36)

P = 4(π + 9)

Therefore, the perimeter of the figure is 4(π + 9)ft.

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The scatterplot shows a linear relationship between left and right forearm lengths in cm, for 55 college students.

The regression line is the best fit line that describes the relationship between the two variables. The formula for a linear regression line is  y = mx + b, where m is the slope of the line and b is the y-intercept. The slope of the line in the scatterplot is 0.95, which indicates that for every 1 cm increase in the left arm, there is a 0.95 cm increase in the right arm. The y-intercept of the regression line is 8.4, meaning that when the left arm is 0, the right arm is 8.4 cm long. The equation for the regression line in the scatterplot is y = 0.95x + 8.4. This equation can be used to predict the right arm length for any given left arm length.

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The domain of the given function would be -

- 5 ≤ x < 3.

An function in mathematics defines a relationship between one variable (the independent variable {x})  and another variable (the dependent variable {y}). Example → y = f{x} = ax + b.

Given is the graph of the linear equation as shown in the image.

Domain represents the set of values along the {x} - axis.

So, we can write -

- 5 ≤ x < 3

Therefore, the domain of the given function would be -

- 5 ≤ x < 3.

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Answer:

654.85:4

Step-by-step explanation:

just took the test!

The number of 1/4 bottles is 11

From the question, we have the following parameters that can be used in our computation:

Size of bottles = 1/4

Volume of container = 2.750 liters

The nuber of bottles is then calculated as

Bottles = Volume of container/Size of bottles

Substitute the known values in the above equation, so, we have the following representation

Bottles = 2.750/(1/4)

Evaluate the quotient

Bottles = 11

Hence, the number of bottles is 11

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Consider the simple given arrangement of three resistors, the total equivalent resistance of the arrangement will be smaller than the resistor C.

Please refer to the attached picture below for the give resistors arrangement.

The three resistors are arranged in a paralel circuit. Hence, the total equivalent resistance for the arrangement will be:

1/R total = 1/Ra + 1/Rb + 1/Rc

Where:

Ra = A

Rb = b

Rc = C

A < B < C

Then, the total resistance will be:

1/R total = 1/A + 1/B + 1/C

    1       = BC + AC + AB

R total              ABC

R total =           ABC      

                BC + AC + AB

Next, we will try to choose any random numbers that meet the resistors condition to proof this condition. This time, we choose:

A = 3

B = 2

C = 1

Then, we need to subtitute each number to its positions:

R total =          3 x 2 x 1      

                  2(1) + 3(1) + 3(2)

R total =          6    

               2 + 3 + 6

R total = 6/12

R total = 1/2 < C --> proven

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In the number 240.149, how does the value of the 4 in the hundredths place compare to the value of the 4 in the tens place, is ,the correct option is 1/1000.

Place value is the basis of our entire number system. This is the system in which the position of a digit in a number determines its value.

The number 42,316 is different from 61,432 because the digits are in different positions.

here,, we have,

i) the 4 in the hundredths place will give us the value 0.04 = 4/100

ii) the value of 4 in the tens place gives us the value = 4 × 10 = 40

iii) to compare the value of 4 in the hundredths place to the value of 4 in the tens place  we divide the value obtained in i) by the value obtained in ii).

Therefore we get the value of the comparison as = (4/100)/40

                                                                                  =1/1000

Therefore the correct option is 1/1000.

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Answer:

I don't know sorry :((

Step-by-step explanation:

share in other part :(

The slope of the line is 1/3.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

Slope can also be defined as the tangent of the angle that the line is making with the positive X axis.

Slope of a line passing through (x, y) and (x', y') is given by,

Slope = (y' - y) / (x' - x)

Consider the points on the given line.

The line passes through (0, 2) and (3, 3).

Slope = (3 - 2) / (3 - 0)

         = 1/3

Hence the slope of the given line is 1/3.

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the daily number of absences at high school a in the state is approximately bormally distributed with mean 122 students and standard deviation of 11.5 students.

if more than 140 students are absent on the day the attendance count is taken for funding purposes ,

the school will lose some of its state funding in the subsequent year

We are to obtain the standard deviation of the given values :

{24, 18, 31,25, 34}

The standard deviation = √(Σ(x - mean)²/ n)

The mean = (ΣX) /n

Using calculator to save computation time :

The standard deviation, s = 6.27 (2 decimal places)

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The range of f(x) = |x - 3| + 2 is calculated to be y ≥ 2

In geometry range refers to all the possible values of the y coordinate

using the equation f(x) = |x - 3| + 2 and plotting the values shows that the range of f(x) = |x - 3| + 2 is [2, ∞),

this means that it includes all values greater than or equal to 2, but not 2 itself.

This can be visualized on a number line as all values to the right of 2, extending towards positive infinity.

The plot is attached

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The graph of the function f(X)=2(3)^x is the graph a

From the question, we have the following parameters that can be used in our computation:

f(x) = 2(3)^x

The above equation is an exponential function

An exponential function is represented as

y = ab^x

Using the above as a guide, we have the following:

a = 2

b = 3

The graph that has this prperty is (a)

Hence, the graph is a

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The proof that the vertical angles provided in the image above are congruent is given below:

Statements                                                        Reasons

1. ∠2 and ∠4 are vert. angles                           (Given)

2. ∠2 and ∠3 are a linear pair                          (Definition of Linear Pair)

3. ∠3 and ∠4 are a linear pair                           (Definition of Linear Pair)

4. m∠2 + m∠3 = 180                                          Angle addition postulate

5. m∠3 + m∠4 = 180                                           Angle addition postulate

6. m∠2 + m∠3 = m∠3 + m∠4                             Subtraction property

7. m∠2 = m∠4                                                     Subtraction property

8. ∠2 ≅ 4                                                           Definition of Congruent Angles

When two lines connect, vertical angles are generated. The angles that are opposite each other in the four produced angles are vertical angles. They are also known as vertically opposed angles. These angles are never unequal.

Congruent angles are those of equal measure. Be a result, any angles of equal measure are referred to as congruent angles. They may be found in equilateral triangles, isosceles triangles, and where a transversal connects two parallel lines.

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The equation 1 ≠ 2 is true because 1 and 2 do not have the same value

From the question, we have the following parameters that can be used in our computation:

The above statements are true

However, when both sides of the equation are multiplied by 0, we have

0 * 0/1 = 0 * 0/2

Evaluate

0 = 0

The result is 0 = 0 and not 1 = 2

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The events with a probability of 1/2 regarding the letters of the word August are given as follows:

A probability is obtained by the division of the number of desired outcomes by the number of total outcomes in the context of a problem.

For the six letters in the word August, we have that:

Hence each event has a probability of 1/2, which is the desired probability for this problem.

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Answer:

Option A will have the least amount of interest because simple interest generates earnings from principal only.

Step-by-step explanation:

got it right :D

Answer:

[tex]p=\frac{15}{24}[/tex]

Step-by-step explanation:

Correct option is B, Each box weighs 1/2 pounds.

The pound is a unit of weight that is equivalent to 16 ounces, 7,000 grains (or 0.45359237 kg) in avoirdupois and 12 ounces, 5,760 grains (or 0.3732417216 kg) in troy and apothecaries' weight. The abbreviation lb comes from the Latin word libra, which was the origin of the contemporary pound.

a weight measurement scale: The weight of one pound is about equal to 454 grams. A kilogram is equivalent to around 2.2 pounds. One pound contains 16 ounces.

From the Latin word "poundus," which means "weight," comes its name. The elaborate L in Libra is where the £ sign originated. The pound, which represented one pound of silver weight, was a monetary unit in Anglo-Saxon England as early as 775 AD.

As per shown in graph,

Corresponding to 1 on x - axis,

the total pounds on 1 box is 1/2 on y - axis.

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