What are the 4 steps to solving inequalities?.

The steps for solving inequality is consisting of four  steps which are elaborated  below :

The first step of solving an inequality is to Eliminate divisions by multiplying all terms by the slightest common denominator of all fractions, then the next step is to Simplify by combining like terms on each side of the inequality, then subtract or add quantities to get the unknown on one side and the numbers on the other, the next step is to divide each term of the inequality by the coefficient of the unknown, just  In case the coefficient is positive, the inequality will stay the same or if the coefficient is negative, the inequality will be reversed.

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Answer:

x = 6

Step-by-step explanation:

3x - 1 = 34/2

3x - 1 = 17

3x = 17 + 1

3x = 18

3/3 x = 18/3

x = 6

The consumer surplus is $5.

Consumer surplus is defined as the amount saved based on the estimated value and actual paid price. It is the difference between the amount that customer wants to pay and the amount that customer has to pay based on the final price.

Leon is willing to pay $10. The discount offered of $10 item is 50%. Hence, the final price will be -

Final price = 10 - 50%×10

Final price = 10 - 5

Final price = 5

Surplus amount = 10 - 5

Surplus amount = $5

Thus, the surplus amount for Leon is $5.

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The complete question is -

Determine the amount of consumer surplus generated: Leon goes to the clothing store to buy a new T-shirt, for which he is willing to pay up to $10. He picks out one he likes with a price tag of exactly $10. When he is paying for it he learns that the T-shirt has been discounted by 50%

The value of x is 128, for equations x/2=y² and x/4=4y

Two or more expressions with an Equal sign is called as Equation.

Given,

x/2=y²...(1) and

x/4=4y ...(2)

We need to find value of x and  x not equal to zero

x=2y²

Substitute in equation 2

2y²/4=4y

y²/2=4y

y/2=4

y=8

Now substitute in equation 2

x/4=4(8)

x/4=32

x=128

Hence the value of x is 128, for equations x/2=y² and

x/4=4y

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Answer:

11,520

Step-by-step explanation:

If the cost of carpeting 1 sq.m of floor is Rs 120 , what is the cost of carpeting 96 sq. m of floor​?

120 * 96 = 11,520

A treaty is a series of higher-level business agreements or contracts involving two or more corporations, governments, royalty, or organizations of any kind.

Contract Basics :

To understand the basics of contracts, it is important to first know what a treaty is. Firstly, it is the first stage of a treaty, treaty, alliance, or agreement. It consists of the agreements, rights and obligations between two or more parties and the terms and conditions mutually agreed upon by all parties.

Treaties as a source of International law . The treaties are considered one of the most important sources of international law. If there is a treaty between two countries, the rights and obligations under that treaty become the laws of both countries.

The sources of international law are:

International treaty law derives from the 1969 Vienna Convention on the Law of Treaties. Treaties and their enforceability. The contract will be interpreted in accordance with international law. Types of Treaties : The treaties are classified into two he following types

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The distance between the two towns Townville and Villaville is 350 miles.

Use the formula d = st, or distance equals speed times time, to find the distance.

Since both represent a certain amount of distance per unit of time, such as miles per hour or kilometers per hour, rate and speed are comparable.

If speed s and rate r are equal, then r = s = d/t.

So, the average speed is 70 miles per hour and 50 miles per hour.

The total time taken is 12 hours.

So, the distance between 2 tows will be:

2*70*50/(70+50)

= 700/12

= 175/3 mi/hr

Then,

TR distance = r*t = (175/3)*12

700 miles/2

350 miles each way

Therefore, the distance between the two towns Townville and Villaville is 350 miles.

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Answer: A) Juan buys 3 packs of markers. Each pack has 6 markers. How many markers does Juan buy in all?

Answer: A) Juan buys 3 packs of markers. Each pack has 6 markers. How many markers does Juan buy in all?

The value of expression 51 x 57 will be;

⇒ 51 x 57 = 2,907

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The expression is,

⇒ 51 x 57

Now,

Multiply the numbers as;

⇒    51

    x 57

   ---------

    357

+255×

------------

 2907

Thus, The value of expression 51 x 57 will be;

⇒ 51 x 57 = 2,907

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Answer:

the answer is 88.36 inches

Step-by-step explanation:

because he wants a square painting and the painting each side length is 9.4 so, we use the formula l square and we get the answer

The measure of angle BDC = 100°

The smallest polygon with three sides and three internal angles is known as a triangle. According to the triangle's "angle sum property," a triangle's internal angles add up to 180°.

Sum of angles in a triangle = 180°

Here we have

3 triangles in the given picture

As we know the Sum of angles in a triangle = 180°

From triangle CBD

∠CBD + ∠BDC + ∠DCB = 180°

From figure  ∠DCB = 40° and ∠CBD = 40°

=> 40° + ∠BDC + 40° = 180°  

=> ∠BDC = 180° - 80°

=> ∠BDC = 100°

Therefore,

The measure of angle BDC = 100°

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Yes, you can be confident that your portfolio will not lose more than 30% in value over the next year.

the reason is

For this question, the portfolio has an average return of 12.5% ​​with a standard deviation of 19.5%. It is estimated that next year will be a 30% loss. Confidence intervals are 95%.

Range = Average return ± 2 x Standard deviation Low aid = 12.5% - (2 x19.5%) =12.5% -39% = -26.5%

High end = 12.5% +(2 x19.5%) =12.5%+39% = 51.5%

Thus, the low end is 26.5%

Returns range from -26.5% to 51.5% with 95% confidence intervals

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The output of the function is -1 when the input is 0

The value is -1

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be  y - y₁ = m ( x - x₁ )

Now , let us find two points from the graph

Let the two points in the graph be A ( x₁ , y₁ ) and B ( x₂ , y₂ )

And ,

A ( x₁ , y₁ )  = A ( 2 , 0 )

B ( x₂ , y₂ ) = B ( -4 , -3 )

In order to find the slope of the line ,

The equation for slope is

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values , we get

Slope m = ( -3 - 0 ) / ( -4 - 2 )

              = -3 / -6

              = 1/2

So , the slope of the line is m = 1/2

To find the equation of line

y - y₁ = m ( x - x₁ )

Substituting the values , we get

y - 0 = 1/2 ( x - 2 )

y = x/2 - 1

So , the equation of line is y = x/2 - 1

Now , when the input is 0 , the value of x = 0

So , the output will be

y = x/2 - 1

y = 0 - 1

y = -1

Hence , the output of the function is -1 when the input is 0

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The explicit formula to represent the given  situation is

Explicit: pn = 14 + 9*n

Here we want to express the number of pizza delivered. Lets try to understand the case.

If we buy one pizza (p1) the cost is 14 because of the delivery plus 9 for the cost of the pizza. So:

p1 = 14 + 9 = 23

If we buy 2 pizzas (p2) we have to pay 14 for the delivery and 9 for each pizza:

p2 = 14 + 9 + 9 = 14 + 2*9 = 32

If 3 pizzas are bought (p3) the reasoning is the same, 14 for the delivery and 9 for each pizza:

p3 = 14 + 9 + 9 + 9 = 14 + 3*9 = 41

Here we can see a pattern: for any amount of pizzas n the cost will be 14 plus n-times 9, the price of a pizza. It is:

pn = 14 + 9*n

But we can separate the last equation in such a way:

pn = 14 + 9*(n-1) + 9 , as 9*(n-1) + 9 = 9*n

But if our general formula it true, the first to terms on the right are the vost of buying n-1 pizzas, so:

pn = pn-1 + 9

We can keep on separating terms as we did to arrive to this form, this is, separating the 9n in  9*(n-2) + 9*2,  9*(n-3) + 9*3, ...,  9*(n-m) + 9*m for any m < n . Here I will keep pn = pn-1 + 9 as the Recursive Formula, but you could use other formulation with, e.g., pn-2, pn-3, etc, using the above recursion.

Now, the explicit formula is such that gives as the value of any amount, finding all the terms of the sequence with those not depending on previous terms (contrary to the recursive). This formula was showed above and is: pn = 14 + 9*n. This is, given any number of pizzas we can find the cost without knowing the cost of previous values.

So, we have:

Recursive: pn = pn-1 + 9

Explicit: pn = 14 + 9*n

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The probability of choosing a person at random who is a junior and plays video games is of:

0.32 = 32%.

These are non-independent events.

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

For the probability in the context of this problem, the outcomes are given as follows:

Hence the probability is of:

p = 48/150 = 0.32 = 32%.

The probability of being a junior is of:

60/150 = 6/15.

The probability of playing videogames is of:

99/150

The multiplication of these probabilities is of:

6/15 x 99/150 = 0.264.

Different than 0.32, hence these two events are not independent.

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The percent of men are between 64 and 66. 5 inches tall is 13.59%

The distribution of heights of adult american men is approximately normal with mean 69 inches

Standard deviation 2. 5 inches.

13.59%.  66.5 inches is 1 standard deviation shorter than the mean, while 64 inches is 2 standard deviations from the mean.  looking at a graph of the normal distribution, 13.59% of samples will fall between 1 and 2 standard deviations below the mean.

Therefore, the percent of men are between 64 and 66. 5 inches tall is 13.59%

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The volume of a pyramid with a square base, where the area of the base is 8. 3m² and the height of the pyramid is 9. 8 m is 222.7m³

Given,

Each length (l) of the base of the pyramid = 8.3 m

Height(h) of the pyramid = 9.8m

We need to find the volume of the pyramid.

Formula

Volume of the pyramid = 1/3 ×area of the base×height

Area of the base =  l²

Now,

The volume of the pyramid = 1/3 ×l²×h

= 1/3 ×8.3²×9.8 cube inch = 222.7 cube meter(approx)

Therefore, the volume of a pyramid with a square base, where the area of the base is 8. 3m² and the height of the pyramid is 9. 8 m is 222.7m³

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The x-intercept is a point of the form (x,0)

What is the x-intercept?

The intersection of a function or equation's graph with the x axis is known as the x intercept. This can be compared to a point having a value of 0.

For any given curve, the x-intercept is a coordinate that is plotted on the x-axis. To put it another way, the x-intercept is the value of the x coordinate at the point where the graph crosses the x-axis, or we can say that it is the value of the x coordinate at a point where the value of the y coordinate equals zero.

Due to its location on the horizontal axis, this is also known as the horizontal intercept.

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The sum for each geometric sequence is 62.

Given:

Geometric sequence,

2 4 8 16 32

Number of terms n = 5

First term a = 2

common ratio r = 4/2

= 2

Sum [tex]S_5 = a(r^n-1)/r-1[/tex]

= 2(2^5 - 1)/2-1

= 2(32 - 1)/1

= 2(31)/1

= 2*31

= 62

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Total subscribers that Netflix must sample to obtain the interval to estimate the proportion of their current subscribers who would pay extra for a premium membership including access to more movies and TV shows are 385 subscribers.

For the Wald-type confidence interval, the confidence limits are:

[tex]p-[/tex][tex]z_{\alpha /2}[/tex][tex]\sqrt{\frac{p(1-p)}{n} }[/tex] , [tex]p+[/tex][tex]z_{\alpha /2}[/tex][tex]\sqrt{\frac{p(1-p)}{n} }[/tex]

Where p is the sample proportion attended, n is the sample size, and z∗α/2 is the upper α/2 quantile of the standard normal distribution for a 100 (1−α) % confidence interval. If a 95% CI is needed, this corresponds to α = 0.05, thus

[tex]z_{\alpha /2}[/tex] ≈ 1.96

And, the quantity

ME = [tex]z_{\alpha /2}[/tex][tex]\sqrt{\frac{p(1-p)}{n} }[/tex]

is studied as the margin of error. Since we also need ME ≤ 0.05, we solve for n to acquire

n ≥ p (1 − p) [tex](\frac{z \alpha /2}{ME} )^{2}[/tex]

The only undetermined quantity is p; but since p (1 − p) ≤ 1/4 for all p ∈ [0,1], we identify that a sample size of at least

n ≥ [tex](\frac{z \alpha /2}{2ME} )^{2}[/tex]

undertakes the Wald interval will have a margin of error less than the needed margin no matter the sample proportion checked. Alternating the given values results in

n ≥ [tex](\frac{1.96}{2(0.05} )^{2}[/tex] = 384.16

for that we need to round up to guarantee the sample size is enough, thus n = 385.

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Total time(arithmetic) taken by app to show nearest charging port will be 30 seconds.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division.

Main body:

As the driving directions algorithm requires searching through many possible routes to calculate the optimal route. the other operations, like incrementing the index and comparing the distances, take only a few nanoseconds.

Hence total time will be 30 seconds.

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well, clearly is 4 :).

now, if we take 25 to be the 100%, what is 4 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 25 & 100\\ 4& x \end{array} \implies \cfrac{25}{4}~~=~~\cfrac{100}{x} \implies 25x=400\implies x=\cfrac{400}{25}\implies x=16[/tex]

By using x0 = 0.49 the value goes to more than 1.

Given function f(x) = x³- sinx

By newton's method x₀ = 0.49

Formula for the newton's method is

Xₙ₊₁ = Xₙ - f( Xₙ)/ f'( Xₙ)

X₀ =  0.49,f(x) = x³- sinx and  f'(x) = 3x²- cosx

X₁ = X₀ - f( X)/ f'( X)

X₁ = 0.49 - x³- sinx/3x²- cosx

X₁ = 0.49-(0.49)³-sin(0.49)/3(0.49)²-cos(0.49)

X₁ = 0.658

X2 = X1 - f(X₁)/ f'(X₁)

By substituting the values we get,

X2 = 1.012

So, Using x0 = 0.49 the value goes to more than 1.

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If the hypotenuse of a right angle is 26 ft one leg is 10 ft, and the length of the other leg is 24 feet.

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

It is given that, the hypotenuse of a right angle is 26 ft one leg is 10 ft.

We have to find the length of the other leg in feet,

To the Pythagoras theorem, the square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.

h²=p²+b²

26²=10²+b²

b²=576

b=24

Thus, if the hypotenuse of a right angle is 26 ft one leg is 10 ft, and the length of the other leg is 24 feet.

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In a systematic sample, the only samples possible are those including every k^th item from the random starting position.

Simple random sampling otherwise called probability sampling involves selecting a subset of a part of a population in which each member of the population has equal chances of being selected while systematic sampling involves the use of sampling interval which is determined by dividing the population by the sample size and a random starting point is selected. for example let say we have a population of 1000 people and we want to systematically select 50 people, 1000 /  50 = 20, it means after choosing a random starting point, we select every 20th person after the starting point until the desire sample size has been attained.

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Answer:

36√3

Step-by-step explanation:

Given a=36 and ∠α=30°,

b = √c^2 - a^2

= √72^2 - 36^2

= √3888

= 62.35383 = 36√3

Thanks.

The development of information applicable to activity that upholds by the fundamental elements of scientific inquiry is referred to as practical research.

In the given question we have to define practical in research.

The development of information applicable to activity that upholds by the fundamental elements of scientific inquiry—clearly specified research questions, reliable patterns of thought, methodical data collecting and analysis, and acceptable conclusions—is referred to as practical research.

Practical research aims to advance knowledge through scientific theories, concepts, and ideas in order to benefit society. Establishing hypotheses, gathering data, evaluating, etc. all serve practical research purposes.

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When there is relationship between two variable is in table it represents a function.

A function assigns only output to each input. The value that is put into a function is the input. The result is the output.

Relationships between input values and output values can also be represented using tables. The values in the first column are the input values. The values in the second column are the output values. The relationship represents a function if each input value is paired with only one output value.

For examples :

In Given table below , Since each input value is paired with only one output value, the relationship given in the above table is a function.

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The density function for the distance between the ambulance and the accident is  equal to  2(l-a) / l².

As given in the question,

Let 'x' and 'y' represents the position of the ambulance and location of the accident on the road.

Both variables are independent .

f(x, y)=  [tex]F_{x} (x) F_{y} (y)[/tex]

        = ( 1/l² ) for ( x, y ) ∈ 9 0, l²

Distance between the ambulance and the accident is

Z : ( x- y)

P ( z≤ a) = 1 -P ( z >a)

            = 1 - ( l - a)² / l²

Density function is given  y :

[tex]f_{z}(a)[/tex] = d/da [ 1 - ( l - a)² / l² ]

        = -2( l - a) / l² ( -1)

        = 2( l - a) / l²

Therefore, for the given condition the distance between the  ambulance and the accident is given by [tex]F_{z}(a)[/tex] = 2(l-a) / l².

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