Please help with this problem

The two points on the line to graph the function is (0, -16) and (1, -53).

A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more integers, or coordinates. The order of the coordinates is crucial, and they are sometimes recognised by their position in an ordered tuple and occasionally by a letter, as in "the x-coordinate". In elementary mathematics, the coordinates are assumed to be real numbers, although they might instead be complex numbers or components of a more abstract system, such a commutative ring.

The given function is:

q(x)=3x−(2+5x)8

To find two points on the line to graph the function we substitute different values of x.

For x = 0:

q(x)=3x−(2+5x)8

q(0) = 3(0) - (2 + 5(0))8

q(0) = -16

For x = 1:

q(x)=3x−(2+5x)8

q(1) = 3(1) - (2 + 5(1))8

q(1) = 3 - (7)8

q(1) = -53

Hence, the two points on the line to graph the function is (0, -16) and (1, -53).

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Therefore, the probability that a randomly selected family owns a cat is 0.257. Therefore, the conditional probability that a randomly selected family doesn't own a dog given that it owns a cat is 0.778.

Probability is a branch of mathematics that deals with the study of random events or situations. It involves the quantification of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, with 0 representing impossibility and 1 representing certainty. The theory of probability provides a framework for making predictions, analyzing data, and making decisions in situations involving uncertainty or randomness.

Here,

Let's use the following events:

D: family owns a dog

C: family owns a cat

From the problem statement, we know:

P(D) = 0.3

P(C|D) = 0.2

P(C) = 0.34

1. To find the probability that a randomly selected family owns a cat, we can use the law of total probability:

P(C) = P(C|D) * P(D) + P(C|not D) * P(not D)

We don't know P(C|not D), but we can find it using the fact that P(not D) = 1 - P(D):

P(C|not D) = (P(C) - P(C|D) * P(D)) / P(not D)

P(C|not D) = (0.34 - 0.2 * 0.3) / (1 - 0.3)

P(C|not D) = 0.2857

Substituting the values:

P(C) = 0.2 * 0.3 + 0.2857 * 0.7

P(C) = 0.257

2. To find the conditional probability that a randomly selected family doesn't own a dog given that it owns a cat, we can use Bayes' theorem:

P(not D|C) = P(C|not D) * P(not D) / P(C)

Substituting the values:

P(not D|C) = 0.2857 * 0.7 / 0.257

P(not D|C) = 0.778

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Complete question:

In a certain community, 30% of the families own a dog, and 20% of the families that own a dog also own a cat. It is also known that 34% of all the families own a cat. What is the probability that a randomly selected family owns a cat? What is the conditional probability that a randomly selected family doesn't own a dog given that it owns a cat?

Net accounts receivable is calculated by subtracting allowance for uncollectible from gross accounts receivable.

1- The journal entries are used to record the business transactions.

2- Ledger accounts are used to summarize thee recorded transactions.

3- Net accounts receivable (2024) = 8,640

Net accounts receivable (2025) = 4,280

1. The Turner Corporation's transactions are recorded as follows:

Date Account Title Debit Credit Journal Entries

Accounts Receivable $35,000 on June 12, 2024

$35,000 in revenue from services

Cash $20,000, September 17, 2024

$20,000 in accounts receivable

Bad Debt Cost $5,760 as of December 31, 2024

Uncollectible Allowance: $5,760

Accounts Receivable $46,400 on March 4, 2025

$46,400 in revenue from services

Cash $10,000, May 20, 2025

$10,000 in Accounts Receivable

Allowance for Uncollectible $4,400 on July 2, 2025

$4,400 in Accounts Receivable

On October 19, 2025, the cash value is $40,000.

$40,000 in accounts receivable

Bad Debts Cost $2,400 on December 31, 2025

Uncollectible Allowance: $2,400

2. The following is the procedure for posting transactions to the chosen accounts:

Account Titles Debit Credit Cash Account Date Account Titles Debit Credit

Accounts Receivable $17,000 on September 17, 2024

Accounts Receivable $10,000 on May 20, 2025

The date is October 19, 2025 $37,000 in accounts receivable

Date Account Titles Debit Credit Accounts Receivable

Service Revenue of $31,400 on June 12, 2024

17th of September, 2024, $17,000 cash

$46,400 in service revenue on March 4, 2025

$10,000 cash, May 20, 2025

Allowance for Uncollectible Accounts $4,400 on July 2, 2025

On October 19, 2025, a cash payment of $37,000 is made.

Balance $9,400 on December 31, 202 $77,800

Provision for Uncollectible Accounts

Debit Credit Date Account Titles

Bad debt expense of $5,760 as of December 31, 2024

Accounts Receivable $4,400 on July 2, 2025

Bad Debts Cost $2,400 as of December 31, 2025

Balance of $3,760 at the end of December 2025

3. The balance sheet net accounts receivable at the end of 2024 and 2025 include:

Net accounts receivable = $8,640 in 2024

Net accounts receivable = $5,640 in 2025.

Transaction Analysis: Accounts Receivable $31,400 on June 12, 2024 $31,400 in service revenue September 17, 2024, $17,000 Cash Accounts Receivable $17,000

Bad Debt Cost $5,760 as of December 31, 2024 Provision for Uncollectible Accounts $5,760 ($31,400 minus $17,000 multiplied by 40%)

Accounts Receivable $50,000 on March 4, 2025 $50,000 in service revenue

May 20, 2025, $10,000 Cash Accounts $10,000 is available for receipt.

Allowance for Uncollectible Accounts $4,400 Accounts Receivable $4,400 July 2, 2025

The date is October 19, 2025. $37,000 in cash and accounts Receivable: $37,000

Bad Debts Cost $2,400 on December 31, 2025 Uncollectible Accounts Allowance $2,400

Net Accounts Receivable: $8,640 in 2024 ($14,400 - $5,760)

2025: $5,640 ($9,400 - $3,760).

[tex]f(-11) = 3(-11)^{2} - 5 = 3(11)^{2} - 5 = 3(121) - 5 = 363-5= \bf 358[/tex]

Answer:D

Step-by-step explanation:

if x==-11

then,

f(-11) means you should write -11 in every x you see.

[tex]f(-11)=3*(-11)^{2} -5=3*121-5=363-5=358[/tex]

The solution to the differential equation dy/dx = 3x/√(y) with initial condition (0,1) is y = ((9/4) × x² + 1)^(2/3).

Differential equations are used to model a wide variety of physical, biological, and economic systems, including the motion of objects under the influence of forces, the spread of disease in a population, and the behavior of financial markets.

There are many different types of differential equations, including ordinary differential equations (ODEs) and partial differential equations (PDEs). ODEs involve a single independent variable and its derivatives, while PDEs involve multiple independent variables and their derivatives.

To solve the differential equation dy/dx = 3x/√(y), we can separate the variables by multiplying both sides by √(y) and dividing both sides by 3x:

dy/dx = 3x/√(y)

√(y) dy/dx = 3x

√(y) dy = 3x dx

Integrating both sides:

∫√(y) dy = ∫3x dx

(2/3)*y^(3/2) = (3/2)*x² + C

where C is the constant of integration.

To find the value of C, we can use the initial condition (0,1), which means y=1 when x=0:

(2/3)*y^(3/2) = (3/2)*x² + C

(2/3)*1^(3/2) = (3/2)*0² + C

C = (2/3)

Substituting C = 2/3 back into the equation, we get:

(2/3)×y^(3/2) = (3/2) × x² + 2/3

y^(3/2) = (9/4) × x² + 1

y = ((9/4) × x² + 1)^(2/3)

Therefore, the solution to the differential equation dy/dx = 3x/√(y) with initial condition (0,1) is y = ((9/4) × x² + 1)^(2/3).

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The arc length and area of each circle sector is:

Case 1: s = 121π / 12 yd, A = 1331π / 24 yd²

Case 2: s = 35π / 3 in, A = 245π / 3 in²

Case 3: s = 17π / 6 ft, A = 17π / 4 ft²

Case 4: s = 11π / 2 in, A = 33π / 2 in²

Case 5: s = 116π / 9 yd, A = 928π / 9 yd²

Case 6: s = 13π / 12 ft, A = 13π / 8 ft²

In this problem we need to determine the arc length (s), in yards or inches, and the area (A), in square yards or square inches, of a circle sector, whose formulas are listed below:

Arc length

s = (θ / 180) · π · r

Area

A = 0.5 · (θ / 180) · π · r²

Where:

Now we proceed to determine the arc length and the area for each case:

Case 1 (r = 11 yd, θ = 165°)

s = (165 / 180) · π · 11

s = 121π / 12 yd

A = 0.5 · (165 / 180) · π · 11²

A = 1331π / 24 yd²

Case 2 (r = 14 in, θ = 150°)

s = (150 / 180) · π · 14

s = 35π / 3 in

A = 0.5 · (150 / 180) · π · 14²

A = 245π / 3 in²

Case 3 (r = 3 ft, θ = 170°)

s = (170 / 180) · π · 3

s = 17π / 6 ft

A = 0.5 · (170 / 180) · π · 3²

A = 17π / 4 ft²

Case 4 (r = 6 in, θ = 165°)

s = (165 / 180) · π · 6

s = 11π / 2 in

A = 0.5 · (165 / 180) · π · 6²

A = 33π / 2 in²

Case 5 (r = 16 yd, θ = 145°)

s = (145 / 180) · π · 16

s = 116π / 9 yd

A = 0.5 · (145 / 180) · π · 16²

A = 928π / 9 yd²

Case 6 (r = 3 ft, θ = 65°)

s = (65 / 180) · π · 3

s = 13π / 12 ft

A = 0.5 · (65 / 180) · π · 3²

A = 13π / 8 ft²

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Answer:

the number is 300

Step-by-step explanation:

just look it up next time

Answer:

300

Step-by-step explanation:

let x be the number

then, 15% of x = 45

[tex] \frac{15}{100} \times x \: = 45 \\ x \: = 45 \times \frac{100}{15} [/tex]

x = 300

pls mrk me brainliest

The probability that someone who doesn't believe in ghosts is male is 6/19.

The measure of the likelihood or chance of an event occurring is known as Probability. It is expressed as a number between 0 and 1, with 0 indicating impossibility and 1 indicating certainty, and is often used in statistics, mathematics, and science.

The frequency table shows that 12 males don't believe in ghosts, and 26 females don't believe in ghosts. So, the total number of people who don't believe in ghosts is 12+26=38.

Out of these 38 people who don't believe in ghosts, 12 are male. Therefore, the probability that someone who doesn't believe in ghosts is male is:

P(Male | Don't believe in ghosts) = P(Male and Don't believe in ghosts) / P(Don't believe in ghosts)

= 12/38

= 6/19

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Answer: To solve the system of equations using the matrix method, we first need to set up the corresponding coefficient matrix and augmented matrix:

Coefficient matrix:

[1  4]

[2 -3]

Augmented matrix:

[1  4 | 9]

[2 -3 | 7]

To solve the system using matrix method, we perform row operations on the augmented matrix to get it into row echelon form, and then back substitute to obtain the solutions.

Performing row operations:

Multiply the first row by 2 and subtract the result from the second row:

[1  4 | 9]

[0 -11| -11]

Divide the second row by -11:

[1  4 | 9]

[0  1 | 1]

Subtract 4 times the second row from the first row:

[1  0 | 5]

[0  1 | 1]

The row echelon form of the augmented matrix is:

[1  0 | 5]

[0  1 | 1]

Therefore, the solution is x = 5 and y = 1.

So the solution of the system of equations is x = 5 and y = 1.

Step-by-step explanation:

The measure of angle ZUB is 32.8°.

A triangle is a closed, double-symmetrical object composed of three line segments known as sides that intersect at three points known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all factions equal), isosceles, or scalene based on their sides.

Triangles are classified as acute (all angles are less than 90 degrees), okay (one angle is equal to 90 degrees), or orbicular (all angles are greater than 90 degrees) (all angles greater than 90 degrees). The region of a triangle can be calculated using the formula A = (1/2)bh, where an is the neighborhood, b is the triangle's base, and h is the triangle's height.

Since the angles given are 90 degrees and 57.2 yοu can add thοse tοgether then subtract them  frοm 180 tο find the answer.

180 - 90 + 57.2 = 32.8

Thus,

32.8° is the answer.

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Complete question:

Point Z is the circumcenter of ΔTUV.

Point Z is the circumcenter of triangle T U V. Lines are drawn from each point of the triangle to point Z. Lines are drawn from point Z to each side to form right angles and line segments Z A, Z B, and Z C. The line segments cut the sides into 2 equal parts. Angle Z T B is 32.8 degrees and angle B Z U is 57.2 degrees.

What is m Angle ZUB?

23.7°

32.8°

33.5°

57.2°

Answer:

5/3

1 2/3

Step-by-step explanation:

5 - 3 1/3 can be simplified as follows:

5 - 3 1/3 = 5 - (3 + 1/3) [grouping the whole number and fraction together]

= 5 - (10/3) [converting the mixed number to an improper fraction]

= 15/3 - 10/3 [finding a common denominator for subtraction]

= 5/3

Therefore, 5 - 3 1/3 is equal to 5/3.

Answer:

Step-by-step explanation:

C.

The cost of an ad algebraically as a piecewise function is 29.50x + 5.25

An algebraic function is a polynomial equation that can be constructed using only algebraic operations such as addition, subtraction, multiplication, division and exponentiation

The given statement reads:

The Fort Salonga News charges $29.50

Each line above four lines costs an additional $5.25.

Let the expression be in x

y= 29.50x + 25.5

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To divide 240g in the ratio 5:3:4, we need to find out the total number of parts of the ratio:

5 + 3 + 4 = 12

Now, we can find the value of one part of the ratio by dividing the total quantity by the total number of parts:

240g ÷ 12 = 20g

So, one part of the ratio is equal to 20g.

To find the quantities of each part of the ratio, we multiply the value of one part by the respective ratio number:

5 parts x 20g = 100g (for the first part)

3 parts x 20g = 60g (for the second part)

4 parts x 20g = 80g (for the third part)

Therefore, the quantities of 240g divided in the ratio 5:3:4 are 100g, 60g, and 80g respectively.

Thus, the solution of the expression [(-17) - (26) divided by 2] is found as the  -21.5.

A quantity is subtracted from another quantity in subtraction, which is a mathematical process. Sutraction is expressed in word puzzles by phrases like "x smaller than 3" or "9 subtracted from x."

The given expression:

= [(-17) - (26)] / 2

Open the inner most brackets.

= [-17 - 26]/2

The numbers with the same sign (either positive or negative numbers gets added retaining the same sign).

= -43 / 2

Divide the number with 2.

= -21.5

Thus, the solution of the expression [(-17) - (26) divided by 2] is found as the  -21.5.

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There are 364 men at the picnic

Equations can be written in many forms, but they all have the same basic structure: an expression on the left-hand side of the equals sign, and an expression on the right-hand side of the equals sign, with the equals sign itself indicating that the two expressions are equal.

Equations can be solved using a variety of techniques, including algebraic manipulation, substitution, and graphing. The goal of solving an equation is to find the values of the variables that make the equation true. In some cases, there may be multiple solutions to an equation, or no solutions at all.

Let the number of men be 4x, and the number of women be 5x.

According to the problem, the total number of people is 819, so:

4x + 5x = 819

Simplifying and solving for x, we get:

9x = 819

x = 91

Therefore, the number of men at the picnic is:

4x = 4(91) = 364

So there are 364 men at the picnic.

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After answering the presented question, we can conclude that triangle Therefore, the answer is A. 29 inches, since it falls within this range.

A triangle is a closed, double-symmetrical shape composed of three line segments known as sides that intersect at three places known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all factions equal), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles are fewer than 90 degrees), good (one angle is equal to 90 degrees), or orbicular (all angles are higher than 90 degrees) (all angles greater than 90 degrees). The region of a triangle can be calculated using the formula A = (1/2)bh, where an is the neighbourhood, b is the triangle's base, and h is the triangle's height.  

So, for triangle ABC with sides AB, BC, and AC, we have:

[tex]AB + BC > AC\\16 + 25 > AC\\41 > AC\\BC + AC > AB\\25 + AC > 16\\AC > -9 \\AB + AC > BC\\16 + AC > 25\\AC > 9\\[/tex]

So, the possible lengths of side AC are between 9 and 41 inches.

Therefore, the answer is A. 29 inches, since it falls within this range.

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Answer:

volume = length × width × depth

Assuming that the driveway has a rectangular shape, you can measure the length and width of the area to be covered and multiply by the depth of 3/4 ft (which is 0.75 ft) to get the volume in cubic feet.

For example, if the driveway is 20 ft long and 10 ft wide, the volume of concrete needed would be:

volume = length × width × depth

= 20 ft × 10 ft × 0.75 ft

= 150 cubic feet

Answer:

x < -3

Step-by-step explanation:

x + 5 < 2

x < -3

So, the answer is x < -3

The mathematical expression 23 - √81 has a value of 14 when evaluated, mathematically

Given the following expression

23 - √81

The expression 23 - √81 involves finding the difference between the number 23 and the square root of 81.

We know that the square root of 81 is 9, so we can simplify the expression to:

23 - √81 = 23 - 9

Evaluate the difference

23 - √81 = 14

Therefore, the value of the expression is 14.

In evaluating expressions like these, it is important to be familiar with basic arithmetic operations and the rules of exponents and radicals.

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After answering the presented question, we can conclude that They are equation still pleased with the quantity of pizza they received, although it is less than in the previous scenario.

A quotient refers to the result obtained when one quantity is divided by another. For example, if you have 10 apples and you want to divide them equally among 2 people, each person would get 5 apples. The quotient in this case is 5, which represents the number of apples that each person would receive.

The quotient can be expressed in different forms, depending on the situation. If you are dividing two integers, the quotient can be a whole number (also known as an integer quotient) or a fraction (also known as a rational quotient). For example, if you divide 10 by 3, the quotient is 3 with a remainder of 1, which can be expressed as [tex]3 + 1/3[/tex] or as the fraction 10/3.

In algebra, the quotient can also refer to the result obtained when dividing two algebraic expressions. For example, if you divide [tex]x^2 + 3x + 2[/tex] by [tex]x + 1,[/tex] the quotient is [tex]x + 2[/tex], which represents the quotient of the division.

The concept of quotient is also used in other areas of mathematics, such as in modular arithmetic and in group theory, where it refers to the result of dividing one element of a group or a ring by another.

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Answer:

108x^2 +23

Step-by-step explanation:

i think...

3x×2×18x+23

108x×x+23

final answer: 108^2 +23

The surface area of the right square pyramid is 106. 25 m²

A square pyramid is seen as a pyramid with a square base.

If the apex is vertically above the center of the square, it is called a right square pyramid, and has four vertical symmetries.

Some properties of a right square pyramid are;

The formula for the surface area of a square pyramid is half of the product of its base perimeter and its slant height:

SA = P × l / 2

where P is the base perimeter and l is the slant height.

Substitute the values;

Surface area = 25(8.5)/2 = 212.5/2 = 106. 25 m²

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Using permutation and combination we can find the total number of companies listed = 12,338,352

A permutation is a methodical arrangement of things or numbers. Combinations let you choose things or numbers from a collection without worrying about the order in which they were gathered.

N (5 member) =₂₉C₅29!/5!(29-5)!=118755

The total number of firms that can be listed on NASDAQ if the company names can be either 4 or 5 letters and the letters can repeat themselves is: 4 letter names = 26 x 26 x 26 x 26 = 264 = 456,976

5 letter names equal 26, 26, 26, 26, 26 = 11,881,376.

Total number of companies listed = 456,976 + 11,881,376‬ = 12,338,352

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After answering the given query, we can state that Therefore, we can function anticipate that 8 to 16 of the upcoming pastries will be bran muffins.

Mathematicians research numbers, their variations, equations, associated structures, shapes, and possible configurations of these. The relationship between a group of inputs, each of which has a corresponding outcome, is referred to as a "function." A function is a relationship between inputs and outputs where each input results in a unique, distinct output. Each function has a domain, codomain, or scope assigned to it. Functions are commonly denoted by the letter f. (x). An cross is entered. On functions, one-to-one capabilities, so several capabilities, in capabilities, and on functions are the four main categories of available functions.

We must determine the percentage of muffins that were bran muffins in the prior sales in order to determine how many of the subsequent 16 muffins sold would be bran muffins.

In the prior auction, the following amount of muffins were sold in total:

25 + 12 + 3 + 10 = 50

The percentage of muffins that were wheat muffins is as follows:

25/50 = 0.5

This indicates that wheat muffins accounted for 50% of all sales.

This ratio can be used to make a forecast about how many bran muffins will be sold over the course of the following 16 muffins. Therefore, we anticipate that roughly 50% of the subsequent 16 batches of muffins sold will be wheat muffins:

0.5 x 16 = 8

Therefore, we can anticipate that 8 to 16 of the upcoming pastries will be bran muffins.

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The angles in the triangles when compared are:

The triangle inequality theorem implies that

The largest angle in a triangle is opposite to the longest side of the triangle.

Using the above as a guide, we have the following comparison of angles:

The above comparison are true because the angles before the inequality symbol opposite a side length greater than the lengths faced by the other angle

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Answer: wheres the question

Step-by-step explanation:

Step-by-step explanation:

The Victoria (Old Traffic) Bridge in Saskatoon, Canada, has a length of approximately 230 meters (755 feet). To estimate the length of the bridge in both SI and imperial units, you can use the following referents:

SI Units:

To estimate the length of the bridge in SI units, you can use meters as the referent. The length of the Victoria Bridge can be measured using a distance measuring device such as a surveyor's wheel, a laser distance meter, or a tape measure. You can start at one end of the bridge and measure the distance to the other end. This will give you an accurate measurement of the length of the bridge in meters.

Imperial Units:

To estimate the length of the bridge in imperial units, you can use feet as the referent. You can use a tape measure or a distance measuring wheel that measures in feet. You can start at one end of the bridge and measure the distance to the other end. This will give you an accurate measurement of the length of the bridge in feet.

To convert the length from meters to feet or vice versa, you can use the following conversion factors:

1 meter = 3.28 feet

1 foot = 0.3048 meters

Therefore, to convert the length of the Victoria Bridge from meters to feet, you can multiply the length in meters by 3.28. For example, 230 meters x 3.28 = 754.4 feet (rounded to the nearest tenth).

To convert the length of the Victoria Bridge from feet to meters, you can multiply the length in feet by 0.3048. For example, 755 feet x 0.3048 = 230.1 meters (rounded to the nearest tenth).

Answer:

Step-by-step explanation:

We can use the identity for the cosine of the sum of two angles:

cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

In this case, we can write:

cos(60°) = cos(55° + 5°) = cos(55°)cos(5°) - sin(55°)sin(5°)

We know that cos(60°) = 1/2, and we also know that cos(55°) = p. We can solve for cos(5°):

1/2 = p cos(5°) - sin(55°)sin(5°)

sin(55°)sin(5°) = p cos(5°) - 1/2

We also know that sin²(55°) + cos²(55°) = 1, so:

sin²(55°) = 1 - cos²(55°) = 1 - p²

Substituting this into the previous equation:

(1 - p²)sin(5°)² = p cos(5°) - 1/2

Rearranging and factoring:

p cos(5°) = 1/2 - (1 - p²)sin(5°)²

Using the fact that sin²(5°) + cos²(5°) = 1, we can substitute cos²(5°) = 1 - sin²(5°):

p cos(5°) = 1/2 - (1 - p²)(1 - cos²(5°))

Simplifying:

p cos(5°) = 1/2 - (1 - p²) + (1 - p²)cos²(5°)

p cos(5°) = 1 - 2p² + (2p² - 1)cos²(5°)

Solving for cos²(5°):

cos²(5°) = (1 - p cos(5°) + 2p²) / (2p² - 1)

Substituting the value we found for p, cos²(55°) = p²:

cos²(5°) = (1 - p cos(5°) + 2cos²(55°)) / (2cos²(55°) - 1)

Finally, substituting p = cos(55°):

cos²(5°) = (1 - cos²(55°) cos(5°) + 2cos²(55°)) / (2cos²(55°) - 1)

cos²(5°) = (2cos²(55°) - cos²(55°) cos(5°) + 1) / (2cos²(55°) - 1)

cos²(5°) = (cos²(55°) + 1) / (2cos²(55°) - 1)

Therefore, the value of cos 5° in terms of p = cos 55° is:

cos 5° = ±sqrt[(cos²(55°) + 1) / (2cos²(55°) - 1)]

Note that the sign of the square root is determined by the quadrant in which 5° lies. Since 5° is in the first quadrant, cos 5° is positive.