Which of the following statements would not translate to the equation 8 ÷ x = -4?

A. Eight divided by a number is equal to negative four.
B. The solution of a number divided by eight is negative four.
C. The quotient of eight and a number equals negative four.
D. If eight is divided by a number, the result is negative four.

The correct answer is D. f(x) = 11x - 4 and g(x) = (x + 4)/11

To determine which pair of functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.

Let's test each option:

Option A:

f(x) = x/2 + 15

g(x) = 12x - 15

f(g(x)) = (12x - 15)/2 + 15 = 6x - 7.5 + 15 = 6x + 7.5 ≠ x

g(f(x)) = 12(x/2 + 15) - 15 = 6x + 180 - 15 = 6x + 165 ≠ x

Option B:

f(x) = ∛3x

g(x) = (x/3)^3 = x^3/27

f(g(x)) = ∛3(x^3/27) = ∛(x^3/9) = x/∛9 ≠ x

g(f(x)) = (∛3x/3)^3 = (x/3)^3 = x^3/27 = x/27 ≠ x

Option C:

f(x) = 3/x - 10

g(x) = (x + 10)/3

f(g(x)) = 3/((x + 10)/3) - 10 = 9/(x + 10) - 10 = 9/(x + 10) - 10(x + 10)/(x + 10) = (9 - 10(x + 10))/(x + 10) ≠ x

g(f(x)) = (3/x - 10 + 10)/3 = 3/x ≠ x

Option D:

f(x) = 11x - 4

g(x) = (x + 4)/11

f(g(x)) = 11((x + 4)/11) - 4 = x + 4 - 4 = x ≠ x

g(f(x)) = ((11x - 4) + 4)/11 = 11x/11 = x

Based on the calculations, only Option D, where f(x) = 11x - 4 and g(x) = (x + 4)/11, satisfies the condition for being inverses of each other. Therefore, the correct answer is:

D. f(x) = 11x - 4 and g(x) = (x + 4)/11

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A qualitative research paradigm is a research approach that focuses on understanding and interpreting subjective experiences, meanings, and social phenomena.

It involves collecting and analyzing non-numerical data to gain insights into individuals' perspectives and the social context in which they exist. Focus group techniques are one of the methods used within the qualitative research paradigm to gather data through group discussions.

The qualitative research paradigm aims to explore and understand the complexity and nuances of human experiences, behaviors, and social phenomena. It recognizes the importance of context and seeks to generate rich and in-depth understandings rather than generalizable conclusions. Qualitative research methods involve collecting data through methods such as interviews, observations, and document analysis. The data collected is typically in the form of words, images, or other non-numerical formats. Researchers then analyze the data using various techniques, such as thematic analysis or grounded theory, to identify patterns, themes, and meanings.

Focus group techniques are one of the commonly used methods within the qualitative research paradigm. Focus groups involve bringing together a small group of participants who share common characteristics or experiences to engage in a facilitated discussion on a specific topic of interest. The group interaction allows participants to share their perspectives, experiences, and opinions while also influencing and being influenced by others in the group. This method provides rich qualitative data and allows researchers to explore group dynamics, collective meanings, and shared understandings.

Overall, the qualitative research paradigm and focus group techniques emphasize the importance of understanding subjective experiences, social interactions, and contextual factors to gain insights into human phenomena.

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Answer:

Step-by-step explanation:

If a 6-ounce bottle of medicine contains 36 doses, we can use a proportion to find how many doses are in a 15-ounce bottle:

6 ounces / 36 doses = 15 ounces / x doses

Cross-multiplying, we get:

6 x = 36 * 15

6 x = 540

Dividing both sides by 6, we get:

x = 90

Therefore, a 15-ounce bottle of the same medicine contains 90 doses.

9514 1404 393

Answer:

  3

Step-by-step explanation:

Vertical angles share a vertex point, and have opposite rays for sides. In short, they are across the point of intersection from each other. Vertical angles do not have a common side (they are not adjacent).

The first part of the problem is to identify angle NCA. That is shown in red in the attachment. The vertical angle is across the point of intersection. It is angle 3.

Polynomial addition is used to determine that:

(a) T(t) = -0.028t3 - 0.32t2 + 1.6t + 59 is the total amount.

b) In the fifth year, $55.5 million was spent on the purchase of both new and secondhand cars.

We must combine like terms, or terms that have been raised to the same power, in order to add polynomials. A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division (No division operation by a variable).

The four most common types of polynomials that are used in precalculus and algebra are zero polynomial function, linear polynomial function, quadratic polynomial function, and cubic polynomial function.

The following functions are provided for this issue:

U(t) = -0.38t2 + 1.5t + 42. N(t) = -0.028t3 + 0.06t2 + 0.1t + 17.

This results in the overall quantity being: T(t) = N(t) + U(t) T(t) = -0.028t3 + 0.06t2 + 0.1t + 17 - 0.38t2 + 1.5t + 42. T(t) = -0.028t3 - 0.32t2 + 1.6t + 59.

The calculation for the fifth year is as follows: T(5) = -0.028(5)3 - 0.32(5)2 + 1.6(5) + 59 = 55.5.

In the fifth year, new and used car purchases totaled $55.5 million.

T(t) = -0.028t³ + (0.06 - 0.38) (0.06 - 0.38)

t² + (0.1 + 1.5)t + 17 + 42.

T(t) = -0.028t³ - 0.32t² + 1.6t + 59.

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1 ball and 3 board games can be chosen by Amanda in option E. 60 ways.

Here it is given that Amanda needs 1 ball and 3 board games.

The toy store only has 3 kinds of balls and 6 types of board games. Hence we will use combinations to determine the no. of ways she can choose the items

ⁿCₓ = n! / (n - r)! X r!

The ball can be chosen in

³C₁ ways

= 3! / 2! X 1!

= 6/2

= 3 ways

The board game can be chosen in  ⁶C₃ ways

= 6! / 3! X 3!

= 720 / 36

= 20 ways

Hence the total number of ways the items can be chosen is

3 X 20 ways

= E. 60 ways.

Complete Question

Amanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections of the 4 items can Amanda make?

A. 9

B. 12

C. 14

D. 15

E. 60

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Answer:

I Believe Its Eight Squares

There are 450 triangles, we can pick that do not form an equilateral triangles when 15 dots are evenly spaced on the circumference of a circle.

An equilateral triangle is a triangle with all three sides of equal length , corresponding to what could also be known as a "regular" triangle.

here, we have,

Let's calculate the total no. of possible triangles, it depends on the combination. To make a triangle, we have to choose 3 dots out of 15.

Here, we will use the combination rule to find out the possible triangles,

Thus, the total number of possible triangles = 15C3                                                                      = (15.14.13) / (1.2.3) = 455

Note that an equilateral triangle would be formed by connecting 3 equally spaced dots.

For an equilateral triangle, out of 15 dots, there would be 15 - 3 = 12 dots that will not be connected.

And 12/3 = 4 dots would be between any two connecting dots.

Taking 1st connecting dot, the second connecting dot would be

1 + 4 + 1 = 6th

Similarly, the third connecting dot would be 6 + 4 + 1 = 11th

So, the following connecting dots will form equilateral triangles: (1, 6, 11); (2, 7, 12); (3, 8, 13); (4, 9, 14); (5, 10, 15);

After applying the combination rule we found the total number of the possible triangle and there are 5 equilateral triangles:

So, there are 455 - 5 = 450 triangles that are not equilateral triangles.

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Complete question;

fifteen dots are evenly spaced on the circumference of a circle. how many combinations of three dots can we pick from these 15 that do not form an equilateral triangle?

To draw a rectangular array for 24 x 18 on graph paper, we create a grid with 24 rows and 18 columns.

The partial-products algorithm for multiplying 24 and 18 involves breaking down the multiplication into smaller, manageable steps. The array helps visualize these steps and demonstrates why the algorithm yields the correct answer. Using the array, we start by dividing the 24 x 18 rectangle into smaller squares that represent individual partial products. Each row in the array corresponds to a digit in the multiplier (24), and each column corresponds to a digit in the multiplicand (18). We fill in the array by multiplying the corresponding digits in the multiplier and multiplicand.

For example, the first partial product is obtained by multiplying the rightmost digit of the multiplier (4) by each digit in the multiplicand (8, 1). We place the result, 32, in the corresponding square in the array. Similarly, we calculate the other partial products and place them in the corresponding squares. To find the final product, we sum up all the partial products in the array. In this case, we add up the values in all the squares to get 432, which is the correct answer to 24 x 18.

The array demonstrates why the partial-products algorithm works. By breaking down the multiplication into smaller steps and organizing them in the array, we ensure that each digit in the multiplier is multiplied by each digit in the multiplicand. The array visually represents the distributive property of multiplication, where each digit in one number is multiplied by each digit in the other number. Adding up the partial products gives the total product, ensuring the correct result. The array provides a visual proof of why the partial-products algorithm yields the correct answer to the multiplication problem.

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the area of the region. 2y =4√x ; y = 5 ; and 2y+4x = 8 is 9, using the concept of area under the curve.

The region between a curve and the -axis is referred to as the "area under a curve." This region may be wholly above the -axis, entirely below the -axis, or somewhere in between. The area under a curve in calculus is a picture of an integral.

The region enclosed by the curve, the axis, and the boundary points is referred to as the "area under the curve." Using the coordinate axes and the integration formula, the area under the curve has been determined as a two-dimensional area. The area of the asymmetric plane form in a two-dimensional array is provided by the region beneath the curve.

The region bounded by the lines y = 5 and 2y + 4x = 8 and the curve

2y = 4√x

Now, finding the intersecting point between 2y + 4x = 8 and 2y = 4√x

so, 4√x + 4x = 8

or,  √x + x = 2

or, √x = (2 - x)

or, x = (2 - x)²

or, x = x² - 4x + 4

or, x² - 5x + 4 = 0

or, ( x - 4) ( x - 1) = 0

or, x = 4, 1

when x = 4 then y = 2√4 = 4

when x = 1 then y = 2 √1 = 2

when y = 4 and x = 4 then equation 2y + 4x = 8 is not satisfied.

Thus, only intersection point is: (1,2)

This is the type (II) region.

So, integrate the region with respect to y.

Now, area =

= \(\int\limits^5_2 {(y/2)^2 - ((8-2y) / 4)} \, dy\)

= \(\int\limits^5_2 {[(y^2/4) -2 + (y/2)]} \, dy\)

= \(\frac{1}{4} [y^3/3]^5_2 - 2 [y]^5_2 + \frac{1}{2} [y^2/2]^5_2\)

= \(\frac{117}{12} - 6 + \frac{21}{4}\)

= \(\frac{108}{12}\)

= 9

Thus, area = 9 of the region. 2y =4√x ; y = 5 ; and 2y+4x = 8.

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Answer:

1/17 mL of water

Step-by-step explanation:

5p = 85w

Divide both sides by 85.

5p/85 = 85w/85

p/17 = w

w = p/17

For 1 mL of papaya juice, p = 1.

w = 1/17

1/17 mL of water is used for 1 mL of papaya juice.

1/4π is area of a circle when the radius is 6 cm.

What is the circumference of a circle?

 A = πr²

differentiate both sides with respect to 't'

dA/dt = πr² dr/dt

dA/dt = 2πr dr/dt

dA/dt = 3  ,     r = 6

3 = 2π * 6dr/dt

dr/dt = 1/4π

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Answer:

C - a stack of 15.6 watermelons

Step-by-step explanation:

Lets first go through each option:

"A shopping receipt that totals $4.90":

This is an appropriate answer since many items sold are not priced at exact dollars (where there are no cents), so having $4.90 as the total cost after shopping is appropriate.

"A soccer game where the average score is 4.7":

This is also an appropriate result since it is the average score of a soccer game, so finding a decimal is appropriate.

"A stack of 15.6 watermelons":

This is not an appropriate result since it would be strange to say a 'stack' or group of something that is not a whole number.

"A classroom with 24 students":

This is an appropriate result since the number of students is a whole number not a decimal.

Hope this helps :)

Answer:

(2,4) (4,6) (6,9) (8,12)

First bracket : Add 2

Second bracket : Add 2

Third bracket : Add 3

Fourth bracket: Add 4

This is all I know

Answer:

m

=

-0.052

Step-by-step explanation:

The number of views in the four weeks round to the whole number is 48.

Here it is given that the initial number of views for a reader board was 25 and it gets increased at the rate of 18% per week.

We have to find the number of views in the fourth week.

On the first week the increase = 25 + 25× 18%

                                                   = 25 + 25 × 18/100

                                                   = 25 + 4.5

                                                   = 29.5

The second week increase = 29.5 + 29.5 × 18%

                                              = 29.5 + 5.31

                                                = 34.81

The third week increase = 34.81 + 34.81 × 18%

                                         = 34.81 + 6.2658

                                         = 41.0758

The fourth week increase = 41.0758 + 41.0758 × 18%

                                           = 41.0758 + 7.393644

                                            = 48.469444

Therefore the number of views in the four weeks is 48.

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Richard's net pay for the week, considering Social Security, Medicare, and FIT deductions, can be calculated by subtracting the total deductions from his gross earnings.

First, let's determine the amount deducted for Social Security. The Social Security rate is 6.2%, and the maximum earnings subject to this deduction are $118,500. Since Richard is $1,000 below the maximum level, the amount subject to Social Security deduction is $1,000. Therefore, the Social Security deduction is 6.2% of $1,000.

Next, we calculate the Medicare deduction. The Medicare rate is 1.45%, and it is applied to the entire earnings of $1,700.

To calculate the FIT deduction, we need additional information about Richard's taxable income, tax brackets, and exemptions. Without this information, we cannot provide an accurate calculation for the FIT deduction.

Finally, we subtract the total deductions (Social Security, Medicare, and FIT) from Richard's gross earnings of $1,700 to obtain his net pay for the week.

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During the year, Poch Co. incurred cost of goods sold of $59,823 million on net sales of $76,643 million. To find Poch's return on sales ratio, we need to divide the cost of goods sold by the net sales and multiply by 100.

The calculation would be:
Return on Sales Ratio = (Cost of Goods Sold / Net Sales) * 100
Plugging in the given values:
Return on Sales Ratio = ($59,823 million / $76,643 million) * 100
Now, let's solve the calculation:
Return on Sales Ratio = (0.7807) * 100
Return on Sales Ratio ≈ 78.07%
Since none of the provided answer options match with the calculated ratio, we cannot determine the exact return on sales ratio.

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The average velocity for the [3,4] is 27m/s and for [4,5] is 37m/s

The average velocity can be found by taking the derivative of the position function and evaluating it at the midpoint of the interval.

The average velocity on the interval [3,4] is given by (s(4) - s(3)) / (4 - 3), which is equal to (s(4) - s(3)) / 1. Using the position function, s(t) = 5t^2 - 8t + 13, we find that s(4) = 5(4²) - 8(4) + 13 = 61 and s(3) = 5(3²) - 8(3) + 13 = 34. Therefore, the average velocity on the interval [3,4] is (61 - 34) / 1 = 27 m/s.

The average velocity on the interval [4,5] is given by (s(5) - s(4)) / (5 - 4), which is equal to (s(5) - s(4)) / 1. Using the position function, s(t) = 5t² - 8t + 13, we find that s(5) = 5(5²) - 8(5) + 13 = 98 and s(4) = 5(4²) - 8(4) + 13 = 61. Therefore, the average velocity on the interval [4,5] is (98 - 61) / 1 = 37 m/s.

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Answer:

Here is the steps. 67.5 cm^3

Step-by-step explanation:

4.5 * 6 = 27

27 * 2.5 = 67.5

Answer:

67.5 cm

Step-by-step explanation:

\(4\frac{1}{2}\) × \(6\) ×\(2\frac{1}{2}\) = \(67\frac{1}{2}\) or \(67.5\)

Using fraction formula,

Each person will receive 1/2 part of left over pizzas .

Fraction : In Mathematics, a fraction defined as the part of the whole thing. For example, a cake is divided into 5 equal pieces, then each piece is denoted by ¼.

We have given that,

After party , 4+1/2 pizzas left over .

number of peoples among spliting of pizza happened = 9

Assume there is x pizzas .

left over part = (4+ 1/2 ) = 9/2

ate by other = 1- 9

9/2 pizzas is divided into 9 people's = 9/2 /9

= 1/2

thus , each person will receive 1/2 of left over pizzas i.e( 4+ 1/2 ).

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The slope of the line for Carlo's plot represents The average change in the number of hot cocoas sold for every additional degree of the day's high temperature.

Information given in the question include

A plot the number of hot cocoas he sold relative to the day's high temperature and then draw the line of best fit

The data is plotted as a linear function

A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

The slope is represented as m, The slope by definition is the change of the output values to the input values

This matches with option B

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The equation of the line that goes through the point (3,-3) and has a slope of -5/3 is y=(-5x+6)/3.

In mathematics, line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. The letter m is frequently used to represent a slope; reason for this is unclear, although it is first used in English by O'Brien in 1844, who wrote the equation for a straight line as "y = mx + b," and by Todhunter in 1888, who wrote it as "y = mx + c."

The ratio of "vertical change" to "horizontal change" between (any) two unique points on a line is used to compute slope. The ratio can also be written as quotient ("rise over run"), which produces same number for every two distinct points on the same line. A declining line has negative "rise." The line might be useful, as determined by road surveyor, or it might appear in a diagram that represents a road or a roof as a description or a design.

The slope's absolute value serves as a gauge for  line's steepness, incline, or grade. A steeper line is indicated by slope with a higher absolute value. A line can be drawn with one of four directions: upward, downward, horizontal, or vertical.

if we let y = mx + b, where m is the slope and b is the intercept, and y - y1 = m (x - x1), then:

3(y + 3) = - 5 (X - (-3))

3y + 9 = - 5 X + 15

3y = -5 X + 6

y=(-5x+6)/3

Check:

When x = 3, y should equal - 3, so:

Y = (- 5 (3) + 6)/3 = -3

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Answer:

Step-by-step explanation:

The equation of the line passing through the points \((x_{1},y_{1} ) and (x_{2} ,y_{2} )\) is

\(y-y_{1}=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}*(x-x_{1} )\)

plug the two points \((x_{1},y_{1} )=(-6,-4) and (x_{2} ,y_{2} )=(-5,-4)\) into the equation.

\(y-y_{1}=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}*(x-x_{1} )\\y+4=\frac{-4-(-4)}{-5-(-6)} *(x+6)\)

\(y-y_{1}=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}*(x-x_{1} )\\y+4=\frac{-4-(-4)}{-5-(-6)} *(x+6)\\y+4=0\\y=-4\)

The equation of line that runs through the points (-6, -4) and (-5, -4) is y = -4.

The slope-intercept form is expresses as;

y = mx + b

Where m is slope and b is y-intercept.

Given that the line that passes through the points (-6, -4) and (-5, -4).

First, we find the slope.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Slope m = ( -4 - (-4) )/( -5 - (-6) )

Slope m = ( -4 + 4 )/( -5 + 6 )

Slope m = ( 0 )/( 1 )

Slope m = 0

Next, find the y-intercept b.

y = mx + b

Plug in slope m = = and point 1( -6, -4 )

-4 = 0(-6) + b

Solve for b

-4 =  b

b = -4

Now, plug slope m = 0 and y-intercept b = -4 into the slope intercept form to determine the equation of the line.

y = mx + b

y = 0(x) + -4

y = -4

Therefore, the equation of line is y = -4.

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Answer:

74

Step-by-step explanation:

92-18=74

Answer: Barry has 92 so 92 - 18 = Heidi. Heidi has 74

Step-by-step explanation:

Answer:

17. $30

18. $2.24

19. 5

20. $2.2815 or rounded to $2.28

I think I’m right

Answer:

17. 30

18. 14

19. 5 hours

20. 15

Step-by-step explanation:

The formula to calculate the cost to rent Toyota Etios is R15 + R3 n.

The formula to calculate the cost to rent VW Polo Vivo is R11.50 + R3 n.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

We have the formula used to calculate the cost to rent the Ford Figo is cost (in rand)= R900 + R7 x n.

Now, Toyota Etios cost R15 per Km and per km charge will be R3.

So, the formula to calculate the cost to rent is

= R15 + R3 n

and, VW Polo Vivo cost R11.50 per Km and per km charge will be R3.

So, the formula to calculate the cost to rent is

= R11.50 + R3 n

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Answer:

Reflection across x = -5

Therefore, (b) x = -10 is the result that is a solution of the rational equation that must be ignored due to the context.

Any equation in algebra that can be written in standard form as where x stands for an unknown value and a, b, and c stand for known values is said to be a quadratic equation. In general, it is assumed that a > 0; equations with a = 0 are regarded as degenerate since they become linear or even simpler. ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem. The answer could be simple or complicated.

Here,

1/x+1/(x+18)=1/40

x+18+x/x(x+18)=1/40

2x+18/x²+18x=1/40

40(2x+18)=x²+18x

80x+720=x²+18x

x²-62x-720=0

On solving the quadratic equation,

x=-10,72

So, the value that is a solution of the rational equation that must be discarded because of the context is (b) x = -10.

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