Graph the inequality on the axes below.
-x + 2y > 4

Using quicksort with median-of-three partitioning and a cutoff of 3. we will get  1, 1, 3, 2, 3, 4, 5, 5, 5, 6, 9.

The Original input is 3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5.

We get on the basis of the median after sorting the first, middle, and final elements 3, 1, 4, 1, 5, 5, 2, 6, 5, 3, 9.

As a result, we select pivot = 5. It also provides after the pivot is removed or hidden 3, 1, 4, 1, 5, 3, 2, 6, 5, 5, 9.

It is necessary to swap the two fives. However, in the subsequent swap, p and q cross. turn is traded back with the p:

3, 1, 4, 1, 5, 3, 2, 5, 5, 6, 9

It is now time to quickly sort the first eight elements of the array in a recursive fashion:3, 1, 4, 1, 5, 3, 2, 5,

and after sorting the three relevant elements, we get 1, 1, 4, 3, 5, 3, 2, 5.

As a result, we select the pivot value of 3, and after hiding this pivot once more, we get:

1, 1, 4, 2, 5, 3, 3, 5

A switch takes place between 4 and 3: 1, 1, 3, 2, 5, 4, 3, 5

Now, because the next swap crosses the pointer, the pivot needed to be swapped: 1, 1, 3, 2, 3, 4, 5,

and the following is the result: 1, 1, 3, 2, 3, 4, 5, 5, 5, 6, 9

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[tex]x\div 32 > 1\implies \cfrac{x}{32} > 1\implies 32\left( \cfrac{x}{32} \right) > 32(1)\implies x > 32[/tex]

and that can be any value, so long is greater than that, 33 will do, but so does 1,000,000, and so on.

Answer:  and that can be any value, so long is greater than that, 33 will do, but so does 1,000,000, and so on.

Step-by-step explanation:and that can be any value, so long is greater than that, 33 will do, but so does 1,000,000, and so on.

and that can be any value, so long is greater than that, 33 will do, but so does 1,000,000, and so on.

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

to get the equation 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}{-1}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-1)}}} \implies \cfrac{-4}{2 +1} \implies \cfrac{ -4 }{ 3 } \implies - \cfrac{ 4 }{ 3 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{- \cfrac{ 4 }{ 3 }}(x-\stackrel{x_1}{(-1)}) \implies y -3 = - \cfrac{ 4 }{ 3 } ( x +1) \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y-3)=3\left( - \cfrac{ 4 }{ 3 } ( x +1) \right)}\implies 3y-9=-4(x+1)\implies 3y-9=-4x-4 \\\\\\ 3y=-4x+5\implies \text{\LARGE 4}x+3y=5[/tex]

The following is an equation fo curve if it passes through the point (-2,3) is  y=2 x^2-x-7.

What is Slope?

A graph is a set of vertices—points—and edges—the lines connecting those vertices in discrete mathematics. Graphs come in a variety of forms, including connected and disconnected graphs, bipartite graphs, weighted graphs, directed and undirected graphs, and simple graphs.

Slope of the carne at (x, y) is 4 x-1

Let the curve is: y=2 x^2-x-7

[tex]$$\begin{gathered}\text { Slope: } \frac{d y}{d x}=\frac{d}{d x}\left[2 x^2-x-7\right] \\\frac{d y}{d x}=4 x-1\end{gathered}$$[/tex]

And passes Iowa's the point (-2,3).

[tex]$$\begin{aligned}& y=2 x^2-x-7 \\& 3=2(-2)^2-(-2)-7 \\& 3=8+2-7 \\& 3=10-7 \\& 3=3\end{aligned}$$[/tex]

Satisfied.

y=2 x^2-x-7

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The horizontal and vertical asymptotes of the hyperbola equation (x + 1)² / 25 - (y - 3)² / 16 = 1 are y = 4x / 5 + 19 / 5 and  y = -4x / 5 + 11/5 respectively

An asymptote of the curve y = f(x) or in the implicit form: f(x,y) = 0 is a straight line such that the distance between the curve and the straight line lends to zero when the points on the curve approach infinity. This can be said to be a line that a curve approaches but never touches.

Basically, we have three types of asymptotes which are horizontal asymptotes, vertical asymptotes and oblique asymptotes.

In the hyperbola equation given

(x + 1)² / 25 - (y - 3)² / 16 = 1

The equation of asymptotes are;

Horizontal asymptotes : y = 4x / 5 + 19 / 5

Vertical asymptotes : y = -4x / 5 + 11/5

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Answer: Part 1: Dan, Part 2: 55%

Step-by-step explanation:

1. By noon, Jon has painted 1/5 (or 20%) of the hallway and Dan has painted 25% of the hallway. Therefore, Dan has painted more of the hallway than Jon.

2. In total, the two have painted 45% (20% + 25% = 45%) of the hallway by lunchtime. Therefore, 55% (100% - 45% = 55%) needs to be painted after lunch.

Alfred gets pay as $2119.23 per week for a new part-time job as a butler.

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

Given that, Alfred responds to an ad position that pays $110,200 a year.

We know that, there are 52 weeks in a year

Salary for one week =110,200/52

= $2119.23

Therefore, the weekly pay for Alfred is $2119.23.

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Cost function is fixed cost added with number of hours times the variable cost.

What is cost ?

The two primary categories of costs that organizations face are fixed and variable costs. While variable costs fluctuate with output, fixed costs do not.

                         Sometimes, fixed costs are referred to as overhead costs. They are incurred regardless of whether a company produces 100 or 1,000 widgets.

Given that  charge for a service call is $80.00 and $30.00 for each hour of work. So fixed cost is 80 and variable cost is 30.

Cost function is fixed cost added with number of hours times the variable cost.

Thus we have the cost function here,

where x is the hours of work.

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Answer:

  m∠1 = m∠2 = 17°

Step-by-step explanation:

You want to know the measures of the base angles of an isosceles triangle with an a.pex angle of 146°.

The sum of angles in a triangle is 180°. We can use x to represent the measures of each of the two congruent base angles of the isosceles triangle:

  x + 146° +x = 180°

  2x = 34° . . . . . . subtract 146°

  x = 17° . . . . . . . divide by 2

The measures of the angles are ...

  m∠1 = m∠2 = 17°

Answer:

Step-by-step explanation:

Answer:

x=7

isosceles triangle

Step-by-step explanation:

To find the perimeter we just add all the sides so we do that for this too

(X+4)+(2x+2)+(16)

And we set it equal to 43 since that is perimeter

(X+4)+(2x+2)+(16)=43

Combine like terms

3x+22=43

   -22.  -22

3x=21

/3.  /3

x=7

And if we fill in the x we find BG and AG are equal so this is an Isosceles triangle

Hopes this helps

Answer:

x = 7

Isosceles triangle

Step-by-step explanation:

The perimeter of a two-dimensional shape is the distance all the way around the outside.

Given values of triangle BAG:

Therefore:

⇒ AG + AB + BG = perimeter

⇒ 16 + x + 4 + 2x + 2 = 43

⇒ x + 2x + 16 + 4 + 2 = 43

⇒ 3x + 22 = 43

⇒ 3x + 22 - 22 = 43 - 22

⇒ 3x = 21

⇒ 3x ÷ 3 = 21 ÷ 3

⇒ x = 7

Substitute the found value of x into the expressions for AB and BG to find their lengths:

⇒ AB = x + 4

⇒ AB = 7 + 4

⇒ AB = 11

⇒ BG = 2x + 2

⇒ BG = 2(7) + 2

⇒ BG = 14 + 2

⇒ BG = 16

As sides BG and AG are both 16 units in length, the triangle is an isosceles triangle (as it has two sides of equal length).

To estimate the population proportion to within plus or minus 2% with 95% confidence, a sample size of at least 804 is needed.

This can be calculated using the formula for determining sample size for estimating a population proportion:

n = (Z^2 * p * (1-p)) / (E^2)

Where n is the sample size, Z is the z-score corresponding to the desired level of confidence (1.96 for 95% confidence), p is the estimated proportion of the population with the characteristic of interest (assumed to be 0.5 for this calculation), and E is the maximum margin of error desired (2% in this case). Plugging these values into the formula, we get:

n = (1.96^2 * 0.5 * (1-0.5)) / (0.02^2) = 803.84

Since this is a sample size estimate, we should round up to the next whole number, resulting in a sample size of 804.

Therefore, the correct answer is as given above

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Answer:

Center = (-2, -3)

Radius = 5

Step-by-step explanation:

The value of (i) AC is the right angled triangle is 20 cm, For (ii) AB is 12 cm.

A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any one angle is a right angle.

(i) To calculate the value of /AC/, we use the formula below.

From the question,

Given:

Substitute these values into equation 1

(ii) To calculate AB, use Pythagoras formula:

From the diagram,

Substitute these values into equation 2 and solve for AB

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The speed of the canoe in still water is 3 miles per hour and the speed of the water current is 2 miles per hour. The correct options are B and D.

One or many equation having same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given that the system of equations;

x + y = 5

x - y = 1

Solving the above equations by elimination we get

x = 3 and y = 2

Where, x represents the canoe's speed with no water current (in still water) and y represents the speed of the water current, in miles per hour.

Therefore, the speed of the canoe in still water is 3 miles per hour and

the speed of the water current is 2 miles per hour.

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Answer + Step-by-step explanation:

In the attach pdf

Step-by-step explanation:

Using squares of integers numbers, it is found that the solution of the equation is located between the integers x = 1 and x = 2.

The equation given is:

x^2=3

The solution of the equation given is:

X=√3

The squares of the integers numbers until the square root of 3 are:

1^2=1

2^2=4

Since , the square root of 3, which is the solution to the equation, is located between the integers x = 1 and x = 2.

Answer:

[tex]x < -5[/tex]

Step-by-step explanation:

-3x-3>12

Divide by -3, since you are dividing by a negative, flip the equality sign:

x+1<-4

Subtract 1 from both sides:

x<-5

Hello,

I hope you and your family are doing well!

To solve the inequality −3x−3>12, you can start by moving everything to one side of the inequality by adding 3 to both sides. This gives you −3x>15.

Next, you can divide both sides of the inequality by -3 to get x<-5.

Finally, you can simplify the inequality to its final form by flipping the direction of the inequality symbol, since you divided it by a negative number. This gives you the final solution: x>-5.

So, the solution to the inequality −3x−3>12 is x>-5. This means that any value of x that is greater than -5 will satisfy the inequality.

The answer is: x > -5

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Happy Holidays!

There are 407.83 square feet living room.

What is linear expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Given that;

The carpet cost $4.15 per square foot and $97 to have it stalled.

And, Their total bill is $1, 789.50.

Now,

Let number of square feet living room = x

So, We can formulate;

⇒ 4.15x + 97 = 1,789.50

Solve for x as;

⇒ 4.15x = 1,789.50 - 97

⇒ 4.15x = 1,692.5

⇒ x = 1,692.5 / 4.15

⇒ x = 407.83 square feet

Thus, There are 407.83 square feet living room.

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1. In 60 weeks, both Zac and Jon will earn the same amount, equating to their different earnings.

2. The student's claim that the solution to the equation 200 + 20w = -100 + 25w is w = 50 is false as the solution shows that w = 60.

3. The two correct justifications for the given steps used in solving w are:

The fixed earnings of Zac = $200

Zac's earnings per week = $20

The total earnings of Zac in w weeks = 200 + 20w

Jon's fixed debt so far = $100

Jon's earnings per week = $25

The total earnings of Jon in w weeks = -100 + 25w

To determine the weeks when the total earnings of Zac and Jon will be equal, we can equate the two expressions above as follows and solve for w:

200 + 20w = -100 + 25w

20w - 25w = -300

-5w = - 300

w = -300/-5

w = 60

Thus, we can conclude that in 60 weeks, the earnings of Zac and Jon will become equal.

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A)the interval on which f is increasing is x ∈ (π/2, 3π/2), The interval on which f is decreasing x∈ ( 0, π/2), (3π/2,2π)

B) local minimum = -6

local  maximum = 6

C) Inflection points are (π/6,-3/4), (5π/6,-3/4).

Local maxima are points in an interval where the values of the function at those points are never greater than the values of the function nearby. Local minima, on the other hand, are locations where the values of the function nearby are higher than the values of the function itself.

A point of inflection is the location where a curve changes from sloping up or down to sloping down or up; also known as concave upward or concave downward. Points of inflection are studied in calculus and geometry. In business, the point of inflection is the turning point of a business due to a significant change.

f(x) = 3cos^2 -6sin(x)

f'(x) = 6cosx d(cosx)/dx -6cosx

f'(x) = 6cosx( -sinx) - 6cosx

f'(x) = -6cosx ( sin x +1)

f"(x) = -6d (cosx)/dx (sinx +1) + -6cosx d ( sin x +1)/dx

f"(x) = -6 ([tex]cos^{2}x - sin^{2}x[/tex]) + 6sinx

a).the interval on which f is increasing is

f'(x)>0

-6cosx ( sin x +1) >0

6cosx ( sin x +1) <0

x ∈ (π/2, 3π/2)

The interval on which f is decreasing

f'(x)<0

-6cosx ( sin x +1) <0

6cosx ( sin x +1) >0

x∈ ( 0, π/2), (3π/2,2π)

since the function is decreasing till x = π/2

so x = π/2 is local minimum (x,y) = ( π/2, -6)

it increasing till 3π/2 and then decreasing

x = 3π/2 is local  maximum values (x,y) = ( 3π/2, 6)

local minimum = -6

local  maximum = 6

c). inflection points. f"(x) = 0

f"(x) = -6 ([tex]cos^{2}x - sin^{2}x[/tex]) + 6sinx = 0

-6 (1-2sin^{2}x) + 6sinx = 0

2[tex]sin^{2}x[/tex] + 2sinx -sinx -1 = 0

sinx = 1/2,-1

x = (π/6,5π/6)

concave up f"(x) >0

-6 (1-2sin^{2}x) + 6sinx > 0

x ∈ (π/6,5π/6)

concave down f"(x) <0

(2sinx -1)(sinx+1) <0

x ∈ (0,π/6) (5π/6,3π/2),(3π/2, 2π)

Inflection points are (π/6,-3/4), (5π/6,-3/4).

A)the interval on which f is increasing is x ∈ (π/2, 3π/2), The interval on which f is decreasing x∈ ( 0, π/2), (3π/2,2π)

B) local minimum = -6

local  maximum = 6

C) Inflection points are (π/6,-3/4), (5π/6,-3/4).

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Hello,

I hope you and your family are doing well!

To find the percent of decrease in the winning time, you can use the following formula:

percent decrease = (old value - new value) / old value * 100%

Plugging in the values from the problem, we get:

percent decrease = (11.0 seconds - 10.49 seconds) / 11.0 seconds * 100% = 0.51 seconds / 11.0 seconds * 100% = 4.636363636363636%

Rounding to the nearest tenth, the percent of the decrease in the winning time is:

4.6%

This means that the winning time decreased by 4.6% between the 1960 Olympics and the 1988 Olympics.

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Answer:

15

Step-by-step explanation:

Answer:

y = 2x + 3 and y = x + 4

Step-by-step explanation:

the first equation:

y = -3x - 6

(5) =-3(1) - 6

5 = 3-6

5≠-3

second equation:

y = 2x + 3

(5) = 2(1) + 3

5 = 2 + 3

5 = 5

third equation:

y = -7x + 1

(5) = -7(1) + 1

5 = -7 + 1

5 ≠ -6

fourth equation:

y = x + 4

(5) = 1 + 4

5 = 5

last equation:

y = -2x - 9

(5) = -2(1) - 9

5 = -2 - 9

5 ≠ -11

The annual cost for the 450 Plan is $645.03.

What is cost price?

The cost price represents the particular worth that represents unit worth purchased.

Main Body;

This consumer used less than 450 minutes a month every month except June and December. In June, they used 178 extra minutes and in December they used 189 extra minutes. In total, they used 367

extra minutes throughout the year. The basic fee for the 450 Plan is $39.99 per month so their annual cost is

annual cost = monthly fee* months + cost per minutes* extra minutes

=39.99 *12 +0.45* 367

=479.88+ 165.15

=645.03

Annual Cost Monthly fee months cost per minute extra minutes

The annual cost for the 450 Plan is $645.03.

The 900 Plan costs $59.99 per month for all 12 months for a total cost of $719.88. Even though the consumer had to pay extra during June and December, the 450 Plan was still less expensive than the 900 Plan.

Hence , The annual cost for the 450 Plan is $645.03.

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The other five trigonometric function values are cos(∅) = 11/61, tan(∅) = 60/11, sec(∅) = 61/11, csc(∅) = 61/60 and cot(∅) = 11/60

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

sin(∅) = 60/61

The cosine of the angle can be calculated using

sin²(∅) + cos²(∅) = 1

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

(60/61)² + cos²(∅) = 1

This gives

cos²(∅) = 1 - (60/61)²

Evaluate the like terms

cos²(∅) = 121/3721

Take the square root of both sides

cos(∅) = 11/61

The tangent of the angle can be calculated using

tan(∅) = sin(∅)/cos(∅)

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

tan(∅) = (60/61)/(11/61)

Evaluate

tan(∅) = 60/11

The other ratios of the angle are calculated as follows

sec(∅) = 1/cos(∅) = 61/11

csc(∅) = 1/sin(∅) = 61/60

cot(∅) = 1/tan(∅) = 11/60

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The equation of the line in slope intercept form that passes through the point (3,4) and is parallel to the line represented by y=3x−2 is y = 3x - 5.  

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, the line that passes through the point (3,4) and is parallel to the line represented by y = 3x − 2.

Parallel line have the same slope. Therefore, the slope of the line is 3.

Let's find the y-intercept using (3, 4).

y = 3x + b

4 = 3(3) + b

4 - 9 = b

b = -5

Therefore, the equation is y = 3x - 5

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The equation of a parabola is y=1/8 (x-1)². Therefore, option 4 is the correct answer.

A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.

Given that, parabola has its focus at (1,2) and its directrix is y= -2.

From graph, vertex is (h, k)=(1, 0) and p=2

Substitute (h, k)=(1,0) and p=2 in (x-h)²=4p(y-k), we get

(x-1)²=4(2)(y-0)

⇒ (x-1)²=8y

⇒ y=1/8 (x-1)²

The equation of a parabola is y=1/8 (x-1)². Therefore, option 4 is the correct answer.

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