for the following two sequences (i) give the first 5 terms of the sequence. (ii) determine if the sequence converges or diverges. if the sequence converges, determine the limit of the sequence

Answer:

[tex]a_9= -134[/tex]

Step-by-step explanation:

Us the formula for arithmetic sequence
[tex]a_n = a_1 + d(n -1)[/tex]

where
[tex]\rm\:a_n=\:nth\:term\\\:d\:=\:common\:difference\\n\:=\:number\:of\:terms[/tex]

Given
[tex]a_1 = -38\\d = - 12\\n = 9[/tex]

[tex]a_9 = -38 -12(9 - 1) \\\\a_9 = -38 - 12(8)\\\\a_9= -38 - 96\\\\a_9= -134[/tex]

The approximate height of the front bed 8.1ft

What is trigonometry?

The study of the relationships and characteristics of angles, triangles, and the trigonometric functions is the focus of the mathematic branch known as trigonometry (sine, cosine, tangent, cotangent, secant, and cosecant). It entails using algebraic methods and geometric principles to solve problems involving triangles and angles, such as measuring angles, computing triangle sides and angles, and analysing periodic events like waves and oscillations.

We use trigonometry to solve the problem

we have

tan (36) = opposite side/ adjacent side

tan(36) = opposite side / 12

Opposite side = tan(36) *12

Opposite side = 8.1 ft

Hence, the approximate height of the front bed 8.1ft

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The slope of the line in this situation tells us the rate of change of the balloon's altitude with respect to time.

The slope of a line represents the ratio of the change in the vertical coordinate (altitude) to the change in the horizontal coordinate (time). In this scenario, as the pilot increases the balloon's altitude to get a better view of the surroundings, the altitude changes with respect to time.

Thus, the slope of the line represents the rate of change of the balloon's altitude with respect to time. A steep slope indicates a rapid change in altitude over time, while a gentle slope indicates a slower change. By analyzing the slope, the pilot can adjust the altitude of the balloon as needed to achieve the desired view.

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6 × 3 × 3  square inches will give the total surface area of the solid figure.

What is surface area?

The surface area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface.

We are given a figure which contains six squares and the dimensions of each square are 3 inches each.

Area of one square = 3 × 3  square inches

Total surface area = 6 × 3 × 3  square inches

Hence, 6 × 3 × 3  square inches will give the total surface area of the solid figure.

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The missing figure of the question has been attached below.

The corporation should make 1000 of a certain sort of car in order to reduce production cost using minimal cost function and derivatives.

Finding the value of x that minimizes the cost function will help us determine the optimal number of automobiles to construct. [tex]C(x) = 25000 - 40x + 0.02x^2[/tex].

The derivative of C(x) with respect to x can be taken, set to zero, and then the value of x can be determined.

[tex]C'(x) = -40 + 0.04x = 0 0.04x = 40 \sx = 1000[/tex]

Hence, when 1000 cars are created, the least cost is incurred. We can check the second derivative of C(x) at x = 1000 to make sure this is a minimum.

[tex]C''(x) = 0.04 > 0[/tex]

The fact that the second derivative is positive demonstrates that the minimum of C(x) occurs at x = 1000.

As a result, the corporation should make 1000 of a certain sort of car in order to reduce production costs. Cost is reduced to $21000 at this manufacturing level.

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If the cost for the 6 new uniforms is denoted by 71.40 = (11.9)6 , then the cost per uniform is $11.9 .

The equation which shows how much it cost for a company to buy 6 new uniforms is represented as : 71.40 = (11.9)6 ,

In order to find the cost per uniform, we need to divide both sides of the cost equation by 6:

On dividing both the  sides of cost-equation by 6,

We get;

⇒ 71.40/6 = [(11.9)6]/6,

On simplifying ,

We get,

⇒ 71.40/6 = 11.9

Therefore, it cost the company 11.9 dollars each for the new uniform.

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Answer

=5

4^5=2x2x=1024x=512 

An absolute value equation to satisfy the given solution sets: -8 and -2 is |x+5|=3

In mathematics, an equation is a statement that two expressions are equal. An equation consists of variables, constants, and mathematical operations (such as addition, subtraction, multiplication, division, exponentiation, etc.). The variables in an equation are often represented by letters, and the equation indicates that certain combinations of these variables and constants have the same value. Equations are commonly used in mathematics, physics, engineering, and many other fields to model and solve problems.

From the diagram you can see that the solutions of the equation are  and

1. Determine the middle number between -8 and -2:

1/2(-8-2)=-5

2. Find the distance between points x=-5and x=-2:

d=-2+5=3

3. Writhe an absolute value equation :

|x+5|=3

Image is attached below.

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The number of cavities each person has had is an example of a survey involving quantitative data.

Quantitative data is any data that can be expressed in numerical terms and can be measured or counted. It includes variables such as counts, amounts, measurements, or ratings. In the given options, the number of cavities each person has had is a numerical variable that can be counted and analyzed statistically, making it an example of quantitative data. Other options, such as favorite food or color of the walls, are qualitative data, which is non-numerical and cannot be measured in numerical terms.

Quantitative data is commonly used in surveys, experiments, and statistical analyses to study patterns and relationships between variables. It allows for precise measurements, comparisons, and statistical modeling. Examples of quantitative data include age, height, weight, temperature, test scores, sales figures, and population counts. By contrast, qualitative data is often used to explore attitudes, beliefs, perceptions, or opinions, and is typically recorded as text or verbal data. Examples of qualitative data include interviews, open-ended survey questions, observations, and focus group discussions.

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The complete question is:

Which survey uses quantitative data, as an example?

each person individual's preferred food.

how many cavities each individual has had.

the color of each person's bedroom's walls.

the type of car each individual person owns.

The reasonable domain and range of the function is option (A) Domain: {1, 2, 3, 4, 5, …}; Range: {2, 6, 18, 54, 162, …}.

The sequence appears to be an exponential sequence with a common ratio of 3. That is, each term is obtained by multiplying the previous term by 3.

If this sequence defines a function, a reasonable domain would be the set of positive integers starting from 1 since the sequence begins with the first term being 2.

The range of the function appears to be the set of positive powers of 3 since each term is a power of 3 multiplied by the initial term, 2. Therefore, a reasonable range would be the set {2, 6, 18, 54, 162, ...}.

Therefore, the correct option is (A) Domain: {1, 2, 3, 4, 5, …}; Range: {2, 6, 18, 54, 162, …}.

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The cost of one glossy print is $7.84.

A quadratic equation is a polynomial equation of degree 2, where the largest exponent of the variable is 2.

An example of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable.

Let the cost of one regular print be "x" and the cost of one glossy print be "y".

From the first row, we can set up the equation:

45x + 30y = 465

From the second row, we can set up another equation:

15x + 10y = 155

We can solve for one variable in terms of the other in the second equation:

15x + 10y = 155

10y = 155 - 15x

y = (155 - 15x)/10

We can substitute this expression for y into the first equation:

45x + 30y = 465

45x + 30((155 - 15x)/10) = 465

Multiplying both sides by 10 to eliminate the fraction:

450x + 300(155 - 15x) = 4650

Simplifying:

450x + 46500 - 4500x = 4650

-4050x = -41850

x = 10.32 (rounded to the nearest hundredth)

Now we can substitute this value for x into the expression for y:

y = (155 - 15x)/10

y = (155 - 15(10.32))/10

y = 7.84 (rounded to the nearest hundredth)

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Answer: x=51

Step-by-step explanation: Add 7 to both sides of the equation.

Please give brainliest !!

Answer:

x = 51

Step-by-step explanation:

44 = -7 + x

+7   +7

51 = x

x = 51

the temperature in Austria will be 10 degrees Celsius at half past 11.

We can start by calculating how much the temperature will increase from 8 am to 12 pm:

From 8 am to 9 am: temperature increases by 2 degrees Celsius

From 9 am to 10 am: temperature increases by 2 degrees Celsius

From 10 am to 11 am: temperature increases by 2 degrees Celsius

From 11 am to 12 pm: temperature increases by 2 degrees Celsius

Therefore, the temperature at 12 pm will be:

-5 + 2 + 2 + 2 + 2 = -5 + 8 = 3 degrees Celsius

Now, we need to calculate how much the temperature will increase from 12 pm to 11:30 am:

From 12 pm to 1 pm: temperature increases by 2 degrees Celsius

From 1 pm to 2 pm: temperature increases by 2 degrees Celsius

From 2 pm to 3 pm: temperature increases by 2 degrees Celsius

From 9 pm to 10 pm: temperature increases by 2 degrees Celsius

From 10 pm to 11 pm: temperature increases by 2 degrees Celsius

From 11 pm to 11:30 pm: temperature increases by 1 degree Celsius

Therefore, the temperature at half past 11 will be:

3 + 2 + 2 + 2 + 1 = 10 degrees Celsius

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Answer: x = 0 represents the price of the drink

Step-by-step explanation:

The sequence type is a recursive function and the first five terms cannot be determined from the formula

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

a(n-2)ᵃ⁽ⁿ ⁻ ¹⁾ + 1 where a1 = 3

The formula a(n-2)ᵃ⁽ⁿ ⁻ ¹⁾ + 1 is recursive because it defines the nth term in terms of the two previous terms a(n-2) and a(n-1).

To find the first five terms of the sequence, we can use the initial value a1=3 and the recursive formula.

So, we have

a1 = 3

a2 = a(0)ᵃ¹

The second term cannot be calculated because we do not have a(0)

This means that other terms cannot be calculated with the formula

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The length of the rectangle is 63 cm and the Breadth of the rectangle is 12 cm, for this, we have to know something about rectangles.

Rectangle, It is a plane shape, as opposed to a square, with four(4) straight sides and four(4) right angles, particularly one(1) with uneven neighboring sides.

Square, A square is a regular quadrilateral in Euclidean geometry, which means that it has four(4) equal(same) sides and four(4) equal angles. It can alternatively be explained as a rectangle with two(2) neighboring sides that are of equal(same) length.

Given, Perimeter = 150 cm, Length, l = 5b+3 , Breadth = b

150 = 2(5b + 3 + b)

150 = 2(6b +3)

6b +3 = 75

6b = 72

b = 12 cm, So l = 63 cm (By putting the b value in the l equation

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The maximum number οf apples she can purchase is 15.

Let's start by finding the cοst οf οne apple and οne οrange using the infοrmatiοn frοm twο Saturdays agο:

3a + 4ο = 3.47, where "a" is the cοst οf οne apple and "ο" is the cοst οf οne οrange.

We can simplify this equatiοn by dividing bοth sides by 3: a + 4/3 ο = 1.1567

Nοw, let's use the infοrmatiοn frοm last Saturday:

12ο = 6.36

ο = 0.53

We can substitute this value οf "ο" intο οur simplified equatiοn tο find the cοst οf οne apple:

a + 4/3(0.53) = 1.1567

a = 0.63

Sο, οne apple cοsts $0.63 and οne οrange cοsts $0.53.

If Shefali has οne $10 bill and she wants tο buy the maximum number οf apples, she can spend at mοst $10 οn apples. Let "n" be the number οf apples she can buy:

0.63n ≤ 10

n ≤ 15.87

Since Shefali can't buy a fractiοnal part οf an apple, the maximum number οf apples she can purchase is 15.

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In response to the stated question, we can state that The new balance is equation therefore $55.59.

An equation is a mathematical assertion that establishes the equality of two expressions that are joined together by the equals sign ('='). For example, 2x – 5 = 13. 2x-5 and 13 are examples of expressions. The letter '=' connects the two expressions. A mathematical formula is called an equation if it contains two algebraic expressions on either side of the equal sign (=). It shows how the right and left formulas are equivalent to one another. Any formula will result in L.H.S. = R.H.S. (left side = right side).

We must ascertain the balance that is still owing after the payment and purchase transactions have been executed in order to calculate the unpaid balance.

The balance drops to $35.51 on April 15 ($50.51 - $15.00), a reduction of $15.00.

The account balance climbs to $54.78 ($35.51 + $19.27) on April 25.

The remaining balance is $54.78 as a result.

$44.29 * (0.18 / 365) * 30 = $0.81

The finance fee is therefore $0.81.

We combine the outstanding balance and the finance charge to determine the new balance:

$54.78 + $0.81 = $55.59

The new balance is therefore $55.59.

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The length of y is given as follows:

y = 7.8 cm.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

In the context of this problem, we have that y is the hypotenuse, while 6.1 cm is the side length adjacent to the angle of 39º, hence:

cos(39º) = 6.1/y

y = 6.1/cosine of 39 degrees

y = 7.8 cm.

6.1 cm is adjacent to the angle of 39º, while y is the hypotenuse.

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The half-life of Potassium-40 is 1.25 billion years. The decay equation for Potassium-40 can be expressed as N(t) = N0e-kt, where N(t) is the amount of Potassium-40 at time t, N0 is the initial amount of Potassium-40, and k is the decay constant.

Decay constant is a measure of the rate at which a radioactive sample decays. It is usually expressed as the probability of a given radioactive nucleus decaying per unit time. It is related to the half-life of a radioactive sample, which is the time it takes for half of the sample to decay.

To answer part b, we need to solve N(t) = 15 mg. When rearranged, this equation becomes t = ln(15/N0)/(-k). Using the given initial amount of 36 mg and the calculated decay constant of 0.00056, we find that it will take 1.44 billion years for the specimen to decay to 15 mg.

For part c, we can use the same equation and solve for N(t). We get N(t) = N0e-kt, where N(t) is the amount of Potassium-40 at time t, N0 is the initial amount of Potassium-40, and k is the decay constant. Using the initial amount of 36 mg and the decay constant of 0.00056, we find that after 300 million years, there will be 27.72 mg of Potassium-40 left.

For part d, we can solve N(t) = N0/8. When rearranged, this equation becomes t = ln(N0/8)/(-k). With the initial amount of 36 mg and the decay constant of 0.00056, we find that it will take 2.68 billion years for Potassium-40 to decay to one-eighth of its original amount.

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After simplifying we get, the solution to the equation as -2x + 15 = 30 is x = -7.5.

To solve the equation -2x + 15 = 30, we need to isolate the variable x on one side of the equation. We can do this by performing the same operation on both sides of the equation to maintain its balance.

First, we will subtract 15 from both sides of the equation to get:

-2x + 15 - 15 = 30 - 15

Simplifying the left-hand side and the right-hand side of the equation, we obtain:

-2x = 15

Next, we will divide both sides of the equation by -2 to isolate x:

-2x/-2 = 15/-2

Simplifying, we get:

x = -7.5

Therefore, the solution to the equation -2x + 15 = 30 is x = -7.5.

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The given sequence -1, -2, -6, -24 is not arithmetic.

An arithmetic sequence is a sequence where the difference between any pair of consecutive terms is a constant knowed as the common difference, and if d is that common difference, we can write the recursive formula as:

f(n) = f(n - 1) + d

Here we have the sequence:

-1, -2, -6, -24

Taking the differences we will get:

-2 - (-1) = -1

-6 - (-2) = -4

-24 - (-6) = -18

The differences are different, thus, this is not an arithmetic sequence.

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The expressions (3x+19) and (5x-9) when set equal gives the solution x = 14

Equivalent equation is an assertion that two expressions are equal, expressed by writing the two expressions separated by an equal sign from which one is to determine a particular quantity.

(3x + 19) = (5x - 9)

open parenthesis

3x + 19 = 5x - 9

combine like terms

3x - 5x = -9 - 19

-2x = -28

divide both sides by -2

x = -28/-2

x = 14

Therefore, x = 14 is the solution to the expressions when set equal.

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Answer:

Linear positive association

Step-by-step explanation:

If these are the 4 answer choices then it would be linear positive, because it is single line and moving up  on the x-axis

Applying the power rules, it was found that the equivalent expressions are:  [tex]6^{(x+7)}*(2)^{5x}[/tex] and [tex](2)^{5x+1}*6^{(x+6)}*3[/tex].

The main power rules are presented below.

For solving this question, you should apply the power rules and check the options are equivalent to the given expression [tex]6*(36)^{\frac{x}{2}+3}*(2)^{5x}[/tex].

From the power rules, you can simplify the given expression, as shown below.

[tex]6*(36)^{\frac{x}{2}+3}*(2)^{5x}=6*(6^2)^{\frac{x}{2}+3}*(2)^{5x}\\ \\ 6*(36)^{\frac{x}{2}+3}*(2)^{5x}=6*(6)^{x+6}*(2)^{5x}\\ \\ 6*(36)^{\frac{x}{2}+3}*(2)^{5x}=6*6^x*6^6*(2)^{5x}\\ \\ 6*(36)^{\frac{x}{2}+3}*(2)^{5x}=6^{(x+7)}*(2)^{5x}[/tex]

Then, you should find an expression equivalent to [tex]6^{(x+7)}*(2)^{5x}[/tex].

This expression is exactly the result of the simplification done in the expression given [tex]6*(36)^{\frac{x}{2}+3}*(2)^{5x}[/tex].

It is equivalent to [tex]6^{(x+7)}*(2)^{5x}[/tex].

The expression [tex]6^{(2x+6)}*(2)^{5x}[/tex] is not equivalent to  [tex]6*(36)^{\frac{x}{2}+3}*(2)^{5x}[/tex].

[tex](2)^{5x+1}*6^{(x+6)}*3= 2^{5x}*2^1*6^x*6^6*3\\ \\ (2)^{5x+1}*6^{(x+6)}*3= 2^{5x}*6^x*6^6*6\\ \\ (2)^{5x+1}*6^{(x+6)}*3= 2^{5x}*6^x*6^7\\ \\ (2)^{5x+1}*6^{(x+6)}*3= 2^{5x}*6^{x+7}[/tex]

The expression [tex](2)^{5x+1}*6^{(x+6)}*3[/tex] is equivalent to  [tex]6*(36)^{\frac{x}{2}+3}*(2)^{5x}[/tex].

[tex]32^x*(216)^{\frac{x}{2}+3} =2^{5x}*(6^3)^{\frac{x}{2}+3}\\ \\ 32^x*(216)^{\frac{x}{2}+3} =2^{5x}*(6^\frac{3x}{2} )*6^9}\\ \\[/tex]

The expression [tex]32^x*(216)^{\frac{x}{2}+3}[/tex] is not equivalent to  [tex]6*(36)^{\frac{x}{2}+3}*(2)^{5x}[/tex].

[tex]32^x*(6)^{\frac{x}{2}+4}=2^{5x}*6^{\frac{x}{2} }*6^4[/tex]

The expression [tex]32^x*(6)^{\frac{x}{2}+4}[/tex] is not equivalent to  [tex]6*(36)^{\frac{x}{2}+3}*(2)^{5x}[/tex].

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the expression 15*3y with all perfect squares removed is 9 * 5y, or simply 45y if you prefer not to factor it further.

In mathematics, a factor is a number or expression that divides another number or expression exactly, leaving no remainder. For example, 2 and 3 are factors of 6, because 6 can be divided by 2 and by 3 without any remainder. Similarly, (x - 3) is a factor of the expression x^2 - 9, because if we divide [tex]x^{2}[/tex]- 9 by (x - 3), we get x + 3 with no remainder. Factoring is the process of breaking down a number or expression into its factors. Factoring is an important concept in many areas of mathematics, including algebra, number theory, and calculus.

by the question.

Remove all the perfect squares from 15*3y

The expression 15*3y can be simplified as follows:

15*3y = 45y

To remove all perfect squares from this expression, we need to find the perfect squares that divide into 45.

The prime factorization of 45 is:

45 = [tex]3^{2}[/tex] * 5

So, the perfect squares that divide into 45 are[tex]3^{2}[/tex] = 9.

To remove the perfect squares from 45y, we can factor out 9 from 45, and get:

45y = 9 * 5y

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the optimal price and quantity for the bags of concrete should be amount $100 and 10,000 bags, respectively. This combination would yield a total economic surplus of $500,000.

Q = 10,000 - 100P

Where Q is the quantity of bags and P is the price per bag.

The goal of the regulation is to maximize total economic surplus.

To maximize total economic surplus, the optimal price and quantity for the bags of concrete should be determined. The total economic surplus for this situation can be calculated by finding the area of the triangle formed between the demand curve and the price line.

The optimal price is calculated by setting the demand equation equal to zero, giving P = 100.

The optimal quantity is calculated by substituting the optimal price into the demand equation, giving Q = 10,000.

The total economic surplus is calculated by finding the area of the triangle formed between the demand curve and the price line, which is (100*10,000)/2 = $500,000 amount.

Therefore, the optimal price and quantity for the bags of concrete should be $100 and 10,000 bags, respectively. This combination would yield a total economic surplus of $500,000.

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Therefore , the solution of the given problem of fraction comes out to be 81/56 is the result of adding the three decimals.

Any combination of like-sized pieces or portions can represent a whole. Standard English defines "quantity" as "a portion" of a particular measure. 8, 3/4. Wholes also include fractions. In mathematics, numerals are expressed by the ratio of quotient to ratio. Every one of these fractions of integers are simple fractions. The fraction contains a fraction, but the fraction's remainder is a challenging fraction. because the values, 4.91, and numerators of real fractions can vary.

Here,

We must identify a common denominator in order to combine these fractions. Finding the denominators' least common multiple (LCM), in this instance 56, is one way to accomplish this.

=> 4/7 + 3/4 + 1/8 = (4/7) * (8/8) + (3/4) * (14/14) + (1/8) * (7/7)

=> 32/56 + 42/56 + 7/56

=> (32 + 42 + 7)/56

=> 81/56

Therefore, 81/56 is the result of adding the three decimals. The ultimate solution is this fraction because it cannot be further condensed.

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Answer:

  17/25

Step-by-step explanation:

You want to know which of 5/16 or 17/25 is closer to 1/2.

For the sake of argument, let's assume that 17/25 is closer to 1/2. This means the difference from 1/2 is smaller than for 5/16:

  (17/25 -1/2) < (1/2 -5/16)

We can add (5/16 + 1/2) to both sides and we get ...

  17/25 + 5/16 < 1

The sum on the left is easily computed:

  (17·16 +25·5)/(25·16) < 1

  (272 +125)/400 < 1

  397/400 < 1 . . . . . . true

Our original premise is true: 17/25 is closer to 1/2.

__

Additional comment

A straightforward solution involves finding the positive difference of each number from 1/2, then comparing those differences. The attached calculator screen does that. It shows the difference of 17/25 from 1/2 is smaller than for 5/16, in agreement with the above.

Effectively, we're comparing the midpoint between the two numbers to 1/2. If it is below 1/2 (which it is), then the upper number doesn't have as great a distance from 1/2 as the lower number does.

This sort of comparison only works if the numbers are on either side of 1/2. If they are on the same side, the sign of their difference tells the tale.