I need a detailed explanation of how 0.667 as a fraction equals 2/3. this isn't making sense.

The inverse function of f(x) = (x^2+1)^2 step by step is given below.

The inverse of f(x) is √(√x - 1).

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = (x² + 1)²

The steps for finding the inverse of a function.

Step 1:

Keep y = f(x)

y = (x² + 1)²

Step 2:

Interchange x and y.

x = (y² + 1)²

Step 3:

Solve for y.

x = (y² + 1)²

Square root on both sides.

√x = y² + 1

(√x - 1) = y²

Square root on both sides.

y = √(√x - 1)

Thus,

The inverse of f(x) is √(√x - 1).

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The worker B has a higher variance of σ² = 9 and standard deviation of 3

The standard deviation refers to a measurement of the data dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

Standard Deviation is calculated by

Each number's deviation from the mean must be determined, and then squared.

Next, add up all of these values.

Divide the result by the quantity of numbers.

Then calculate its square root.

Given data ,

Let the data of worker A = { 5, 4, 4, 6, 7, 5, 6, 3 }

Let the data of worker B = { 4, 8, 1, 9, 2, 9, 4, 3 }

Now , the mean of worker A = 5

The mean of worker B = 5

So , the standard deviation of worker A is calculated as

The sum of the difference of the data from mean is

SD = √ ( 5 - 5 )² + ( 5 - 4 )² + ( 5 - 4 )² + ( 5 - 6 )² + ( 5 - 7 )² + ( 5 - 5 )² + ( 5 - 6)² + ( 5 - 3 )² / 8

On simplifying the equation , we get

SD = √ ( 12/8 )

SD = √1.5

Standard deviation σ = 1.2247449

And , the variance of worker A is σ² = 1.5

Now ,

The standard deviation of worker B is calculated as

The sum of the difference of the data from mean is

SD = √ ( 5 - 4 )² + ( 5 - 8 )² + ( 5 - 1 )² + ( 5 - 9 )² + ( 5 - 2 )² + ( 5 - 9 )² + ( 5 - 4)² + ( 5 - 3 )² / 8

On simplifying the equation , we get

SD = √ ( 72/8 )

SD = √9

Standard deviation σ = 3

And , the variance of worker A is σ² = 9

Hence , the worker B has higher standard deviation

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The discounted price of the set of dishes would be = $63.89

The original cost of the dishes = $57.68

The percentage increase of the cost of the dishes = 125%

That is,

= 125/100 × 57.68

= 7210/100 = $72.10+57.68 = $129.78

After one month, the store marked it down by 50%, therefore the discounted price;

= 50/100 × 129.78/1

= 6489/100

= $65.89

= 129.78-65.89 = $63.89

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The discounted price is $64.89

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

Cost =  $57.68

Mark up = 125%

Mark down = 50%

The discounted price is then calculated as

price = cost * (1 + mark up) * (1 - mark down)

So, we have

price = 57.68 * (1 + 125%) * (1 - 50%)

Evaluate

price = 64.89

Hence, the price is 64.89

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Answer:

14q/25

Step-by-step explanation:

14q/25

Answer:

the correct answer to this equation would be: >

The value of x is 13 and the angles in the triangle are 38,69 and 73 respectively.

What is triangle ?

Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.

From the given figure,

In the given triangle ,

The triangles are 3x - 1 , 8x - 35  and 6x - 5

The sum of all angles is always is 180 degrees.

so,

we get,

3x - 1 + 8x - 35 + 6x - 5 = 180

17x - 41 = 180

17x = 180 + 41

17x = 221

x = 221 / 17

x = 13

so,

3x - 1  = 3*13 - 1 = 38

8x - 35  = 8* 13 - 35 = 104 - 35 = 69

6x - 5 = 6*13 - 5 = 78 - 5 = 73

Therefore, The value of x is 13 and the angles in the triangle are 38,69 and 73 respectively.

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, The fraction equivalent to 3/9 with denominator 3 is the proper fraction p=1/3

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Given here: The fraction 3/9

Now we can simplify the fraction further by dividing both the numerator and denominator by 3

let p=3/9

then p=3/3 / 9/3

       p= 1/3

Hence, The fraction equivalent to 3/9 with denominator 3 is the proper fraction p=1/3

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Answer:

70 percent of what number is 90?

90 is 70% of 128.57

Steps to solve "90 is 70 percent of what number?"

We have, 70% × x = 90

or,

70

100

× x = 90

Multiplying both sides by 100 and dividing both sides by 70,

we have x = 90 ×

100

70

x = 128.57

If you are using a calculator, simply enter 90×100÷70, which will give you the answer.

Answer:  70 % of 90 = 63

Step-by-step explanation:

   70 %  x  90.

= (70/100) x 90

= (70*90)/100

= 6300/100

= 63

The solution is Option C.

The value of the function is f ( x ) = 3 ( x - 3 ) ( x - 7 )

Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.

Identify the even and odd multiplicities of the polynomial functions' zeros.

Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.

The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = 3 ( x - 3 ) ( x - 7 )   be equation (1)

On simplifying the equation , we get

y = 3 ( x - 3 ) ( x - 7 )

And , the point ( 8 , 15 ) lies on the graph

Substituting the values in the equation , we get

when x = 8

y = 3 ( 8 - 3 ) ( 8 - 7 )

y = 3 ( 5 )

y = 15

Therefore , the point P ( 8 , 15 ) lies on the graph of the function

And , the graph has two zeros at (3,0) and (7,0)

Hence , the graph of the function is f ( x ) = 3 ( x - 3 ) ( x - 7 )

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Answer:

c

Step-by-step explanation:

c

The required description of the given piecewise function is graphed below.

f(x) = 3 if [-5, -2]; f(x) = -3 if (-2, 3]; and f(x) = 3 if (3, 4]

A piecewise-defined function (also known as a piecewise function or a hybrid function) is a function defined by multiple sub-functions, each of which applies to a different interval of the main function's domain (a sub-domain).

The graph is given in the question, as shown

f(x) = 3 if [-5, -2]

This the sub-function define between the interval [-5, -2].

f(x) = -3 if (-2, 3]

This the sub-function define between the interval (-2, 3].

f(x) = 3 if (3, 4]

This the sub-function define between the interval (3, 4].

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Answer: Cody gave the cashier $2.87.

Step-by-step explanation:

To determine the amount of money Cody gave to the cashier, you can subtract the amount of change he received from the cost of the carrots.

$4.41 (change) - $1.54 (cost of carrots) = $2.87

So, Cody gave the cashier $2.87.

1) The number of laps that Reuben completes is; 2 laps

2) The number of laps that Maria completes is; 3 laps

3. It will take 18 minutes for Reuben and Maria to meet again at the starting line.

The parameters to solve the problem are;

Time for each lap by Reuben = 9 minutes

Time for each lap by Maria = 6 minutes

Let us find the L.C.M(Lowest common multiple) of 6 and 9;

Factors of 6 = 2 * 3

Factor of 9 = 3 * 3

Thus, L.C.M = 2 * 3 * 3 = 18 Minutes

This represents the time it will take for them to meet again at the starting line.

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Answer:

bbbbbbbbbbbbbb

see attched image for sol

The given function  f(x) = x² + 2x when x <0 and f(x) = x³ - 2x when x > 0  is continuous at x=0

In mathematics, The function is called as continuous at the particular value of x,  if right hand limit, left hand limit and the value of function at x all are equal.

RHL   = LHL  = F(x)

Limit exist and continuous

Given that,

F(x)  = x² + 2x       {x ≤ 0}

        = x³ - 2x      { x > 0}  

To check whether it is continuous at x = 0

First taking LHL,

F(0)  = 0² + 2x0

        =  0

Now, taking RHL

F(0)  =  0³ - 2x0

At x = 0

F(0)  = 0² + 2x0

        =  0

RHL = LHL = F(0)

Hence, the given function is continuous at x =0

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Slope intercept form of equation is y = -3x + 5.

The graph of the linear equation y = mx + c is a line with m as slope and c as the y-intercept. This form of the linear equation is called the slope-intercept form, and the values of m and c are real numbers.

Given equation,

-5 = -y - 3x

Standard Slope intercept form of equation y = mx + c

Given equation can be written as

y = -3x + 5

Hence, y = -3x + 5 is the slope intercept form of given equation

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The required equation in the slope-intercept form is given as y = -3x + 5.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
The equation of line passes through points (x, y) and has a slope and intercept of m and c respectively is given as,
y = mx + c

The above expression is the standard slope intercept form of a line.

Trasform the given equation,

-5 = -y - 3x
y - 5 = -3x

y = -3x + 5

Thus, the required equation in the slope-intercept form is given as y = -3x + 5.

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The congruence postulate used to prove the congruence of triangles KLM and KLN is given as follows:

E. ASA.

The Angle-Side-Angle (ASA) congruence theorem states that if any of the two angles on a triangle are the same, along with the side between them, then the two triangles are congruent.

For this problem, we have that the two angles between segment LK are equal for each triangle, as LK is a bisection of these two angles, along with segment LK, hence the ASA congruence postulate was used and the correct option is given by option E.

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The ratio the unit rate comparing all runners to boys is 5:1.

How to Calculate Unit Rate The denominator of a unit rate is always 1. Therefore, divide the denominator by the numerator so that the denominator equals one in order to determine the unit rate. The unit rate is 50km/5.5 hours = 9.09 km/hour, for instance, if 50km are travelled in 5.5 hours.

A unique form of ratio called a unit rate has a denominator (second number) of one. You are comparing a quantity to one when using a unit rate. Miles per gallon, price per pound, and pay rate per hour are a few examples of popular unit rates.

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The solutions of the equation are x < 18 and x < - 30.  

Solutions of equations are the numerical values of the variables that will satisfy the condition in the given equation. Similarly, the solutions of inequalities are the values of variables that can satisfy the given inequality.

We can solve an inequality by adding or subtracting the same integer on both sides, or we can multiply or divide by the same number on both sides until we get the value of 'x'.

Here we have

3/4 |1/3x + 2| < 6  

We can solve the above equation as follows

3/4 |1/3x + 2| < 6    

Multiply by 4 on both sides

=> 4 [ 3/4 |1/3x + 2| ] < 4 × 6    

=>  3 |1/3x + 2| < 24  

=> | x + 6| < 24      

=> x + 6 < ± 24      

=> x + 6 < 24      and     x + 6 < - 24

Subtract - 6 on both sides

=> x + 6 - 6 < 24 - 6      and     x + 6 - 6 < - 24 - 6

=> x < 18       and       x < - 30

Therefore,

The solutions of the equation are x < 18 and x < - 30.  

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Note that where Will C. Lowe wishes to purchase an ordinary whole life insurance policy with a face value Of $50,000, his annual premium, if his age for insurance purposes is thirty-one is: $7,665.

The insured pays a premium to the insurer on a regular basis to cover his risk. The risk is transferred from the insured to the insurer under an insurance arrangement. The premium is the amount charged by the insurer for accepting this risk.

To compute the Premium Payable, you must apply the stipulated rate against the sum insured.

Since the Sum assured is $50,000; and

The applicable rate for a 31-year-old is 15.33%

Thus the Insurance Premium for an Ordinary Whole Life Insurance Policy is:

(50,000 * 15.33)/100

= 766500/100

=  $7,665.

Thus Lowe to be entitled to an annual Life Insurance cover of $50,000 must pay $ $7,665 every year.

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The solution to the linear equations are;

20. x = 3. 200

21. x = 4. 333

22. x = 11. 438

23. x = 1.417

24. y = 0. 223

25. 45%

From the information given, we have to solve the linear equations, we have;

20. -15x + 73 = 26

collect like terms

-15x = 26 - 74

-15x = -48

Make 'x' the subject

x = 3. 200

21. 1.5x + 7.4 = -1.8x - 6.9

collect the like terms

3.3x = 14.3

Make 'x' the subject

x = 4. 333

22. 14.1 - 0.3x = 1.3x - 4.2

collect like terms

1.6x = 18.3

Make 'x' the subject

x = 11. 438

23. 6.2x + 4.5 = 3.8x + 7.9

collect like terms

2.4x = 3.4

Make 'x' the subject

x = 1.417

24. 4.603y - 1.842 = -3.651y

collect like terms

8.254y = 1.842

Make 'y' the subject

y = 0. 223

25. The percentage is given as;

159/350 × 100/1

45%

Hence, the values are x = 3. 200, x = 11. 438, x = 1.417, y = 0. 223 and 45%

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The values of D, Dx, Dy , x and  y are

D=28

Dx= -56

Dy= -56

x=-2

y=-2

What are matrices ?

The word "matrix" can be used to refer to a rectangular array or table with numbers or other components arranged in rows and columns. Any number of columns and rows are allowed. Matrix operations include addition, multiplication, transposition, scalar multiplication, and many others.

Write the matrices by taking coefficients of x and y in different columns as:

[tex]\begin{bmatrix} -8 & 4 \\ 3 & -5 \end{bmatrix} =\begin{bmatrix} 8 \\ 4&\end{bmatrix}[/tex]

Determinant of LHS = D

[tex]D=\begin{vmatrix} -8 & 4 \\ 3 & -5 \end{vmatrix}[/tex]  

D=28

Substitute the  x-column with the RHS to find Dx

Substitute the  y-column with the RHS to find Dy

[tex]Dx=\begin{vmatrix} 8 & 4 \\ 4 & -5 \end{vmatrix}[/tex]  

Dx= -56

[tex]Dy=\begin{vmatrix} -8 & 8 \\ 3 & 4 \end{vmatrix}[/tex]

Dy= -56

x=Dx / D = -56/28 = -2

y=Dy / D = -56/28 = -2

The values of D, Dx, Dy , x and  y  are

D=28

Dx= -56

Dy= -56

x=-2

y=-2

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Answer:

  -1

Step-by-step explanation:

You want the slope of the line through the points (-3, 4) and (2, -1).

The slope is given by the formula ...

   m = (y2 -y1)/(x2 -x1)

Using the given points, we find the slope to be ...

  m = (-1 -4)/(2 -(-3)) = -5/5 = -1

The slope of the line through the given points is -1.

A) An equation to represents your plan to afford the iguana is,

⇒ y = $12 + $9w

Where, y is total money after w weeks.

B) The amount of money you should save each week to buy the iguana in 6 weeks is, $66.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

You want to buy a pet iguana. You already have $12 and plan to save $9 per week.

Let w represents the number of weeks until you enough Money to buy the iguana.

Hence, An equation to represents your plan to afford the iguana is,

⇒ y = $12 + $9w

Where, y is total money after w weeks.

And, The amount of money you should save each week to buy the iguana in 6 weeks is,

⇒ y = $12 + $9w

⇒ y = $12 + $9 × 6

⇒ y = $12 + $54

⇒ y = $66

Thus, A) An equation to represents your plan to afford the iguana is,

⇒ y = $12 + $9w

Where, y is total money after w weeks.

B) The amount of money you should save each week to buy the iguana in 6 weeks is, $66.

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If P is the circumcenter of ABC, the DP is 13.27 units.

The value of DP is calculated by applying the following method as shown below.

Based on the given figure, D is the midpoint of AB

Line AD = BD, so line DP is perpendicular to line AB and the following equation can be formed to determine value of x.

7x - 6 = 5x + 8

2x = 14

x = 14/2

x = 7

DB = 7x - 6

DB = (7 x 7 ) - 6 = 43

Let PC = 45

PC = PB = 45

Apply Pythagoras theorem to determine DP;

DP² = PB² - DB²

DP² = 45² - 43²

DP² = 176

DP =  √176

DP = 13.27 units

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Answer:24 sq. units

Step-by-step explanation:

The length of the base is (7-1)= 6 units. The height is 8 units.

Area =1/2*l*b=24

The horizontal distance is 150 meters

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

Gradient = 2/15

Vertical distance = 60 meters

The gradient is calculaed as

Gradient = Vertical distance/Horizontal distance

So, we have

Horizontal distance = Vertical distance/Gradient

This gives

Horizontal distance = (60)/(2/5)

Evaluate

Horizontal distance = 150

Hence, the distance is 150 meters

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From the graph, she walked at a rate of [tex]\frac{25-10}{5-2}=5 \text{ ft/s}[/tex].

Therefore, she walked faster on her next three walks compared to her first two walks.

The distance of AB is 117.992 meters.

Law of sines is a law in trigonometry which states that the ratios of the angle to the opposite side of a triangle are equal.

For triangle ABC,

sin A / a = sin B / b = sin C / c

where a, b and c are the sides opposite to the angles A, B and C respectively.

Here,

∠B = 112° 10' = 112° + 0.167° = 112.167°

∠C = 15° 20' = 15° + 0.333° = 15.333°

By the angle sum property of triangle,

∠A = 180° - (∠B + ∠C)

∠A = 180° - (112.167° + 15.333°)

     = 52.5°

Using law of sines,

sin A / BC = sin C / AB

sin (52.5°) / 354 = sin (15.333°) / AB

AB = [354 × sin (15.333°)] / [sin (52.5°)]

AB =  [354 × 0.264] / [0.793]

AB = 117.992 meters

Hence the distance across the river is 117.992 meters.

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The linear function to model how much further he'll have to go over time is h(t) = 330 - 55t

Total distance between home and college= 330 miles

Distance remaining to cover= 275 miles

Distance covered= Total distance between home and college - Distance remaining to cover

= 330 miles - 275 miles

= 55 miles

Time taken to cover 55 miles= 1 hour

h(t) = 330 - 55t

Where,

h = distance remaining to cover

t = time

Ultimately, h(t) = 330 - 55t is the linear function which represents how much further he'll have to go over time.

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