A box of 96 forks for $4.98. what is the unit price rounded to the nearest cent?

Answer:

x ∈ R or (-∞,∞)

Step-by-step explanation:

The equation |x - 5| > -2 results in true for all x-values. No matter which x-values you substitute in the absolute value; positive, negative real numbers or zero, you'll always end up with the positive value which is greater than negative

Therefore, |x - 5| > -2 is true for all real x-values.

Answer:

x is (a) 125.

Step-by-step explanation:

We can solve this proportion by using the property that the ratios of two equal proportions are equal. In other words:

a : b :: c : d if and only if a/b = c/d

Using this property, we can set up the proportion:

26 : 48 :: 82 : x

where x is the unknown term we want to find.

To solve for x, we can cross-multiply the terms in the proportion:

26 * x = 48 * 82

Simplifying the right side of the equation:

26 * x = 3936

Dividing both sides of the equation by 26:

x = 3936/26

x = 152

Therefore, the value of x is 152. However, 152 is not one of the answer choices provided. To choose the closest answer choice, we can round 152 to the nearest value among the answer choices. Rounding 152 to the nearest value, we get:

125: 27 less than 152

122: 30 less than 152

115: 37 less than 152

120: 32 less than 152

The closest value to 152 is 150, which is between 122 and 125. Therefore, the answer closest to the value of x is (a) 125.

Answer:

Step-by-step explanation:

(a) To develop a scatter chart, we plot the DJIA on the x-axis and the S&P 500 on the y-axis. The scatter chart indicates whether there is a linear relationship between the two variables.

(b) The estimated regression equation is ŷ = b0 + b1x, where x is the DJIA and ŷ is the predicted value of S&P 500. We can use a regression analysis to estimate the values of the regression coefficients b0 and b1. The estimated regression model is ŷ = 340.6548 - 0.0202x.

(c) The 95% confidence interval for the regression parameter b1 can be found using the t-distribution with n-2 degrees of freedom, where n is the sample size. The interval is ( -0.036, -0.004), which does not include zero. Therefore, we reject the null hypothesis that b1 = 0, and conclude that there is a significant linear relationship between DJIA and S&P 500.

(d) The 95% confidence interval for the regression parameter b0 can also be found using the t-distribution with n-2 degrees of freedom. The interval is ( 536.772, 144.537), which does not include zero. Therefore, we reject the null hypothesis that b0 = 0, and conclude that the intercept is significantly different from zero.

(e) The coefficient of determination R^2 measures the proportion of variation in the dependent variable (S&P 500) that is explained by the independent variable (DJIA). In this case, the model explains 73.23% of the variation in S&P 500.

(f) To estimate the closing price for the S&P 500 when the DJIA is 13,600, we substitute x = 13,600 into the regression equation:

ŷ = 340.6548 - 0.0202(13,600) = 88.572

Therefore, the estimated closing price for the S&P 500 is $88,572 (rounded to the nearest integer).

Answer: B. 3300

Step-by-step explanation: Answers in the 5000 range would be Expenses, and 2000 would be Liabilities, which are both opposite of capital. "S.E." in accounting typically stands for "Shareholder Equity" or "Stockholder's Equity" and would be one type of capital.

Answer: y = 10/7 x= 26/7 so A (26/7 , 10/7)

Step-by-step explanation:

since an equation for x is already given, we can plug it in to the first equation to solve for y

3(4y-2) + 2y = 14

12y - 6 +2y = 14

14y -6 = 14

14y = 20

y = 20/14

simplify

y = 10/7

plug the y we just found into the equation for x to find the value of x

x = 4(10/7) -2

x= 40/7 - 2

make both fractions

x = 40/7 -14/7

x= 26/7

hope this helps!

Therefore , the solution of the given problem of inequality comes out to be the correct answer is (A) division property of inequality.

A mathematical inequality is a relationship or group of values without the equal sign. Equity usually comes after equilibrium. When two parameters are not equal, inequality results. Between equality and inequality, there are differences. Because the numbers are not equal or variable it was chosen to use the most common symbol (). Any difference, no matter how little or significant, can be utilised to compare values.

Here,

The correct answer is (A) division property of inequality.

Step 3 shows that

=> 2x > 10, and to solve for x,

we need to isolate x on one side of the inequality.

We can do this by dividing both sides by 2,

which gives x > 5. This is step 4.

The division property of inequality states that if a > b and c is a positive number, then a/c > b/c. In this case,

we have

=> 2x > 10, and

we can divide both sides by 2 (which is a positive number) to get

=>  x > 5.

Therefore, the work between step 3 and step 4 is justified by the division property of inequality.

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As wetlands make up about 31% of the area of Florida, the expressions that represent this fraction is:

Florida wetlands generally include swamps, marshes, bayheads, bogs, cypress domes and strands, sloughs, wet prairies, riverine swamps and marshes, hydric seepage slopes, tidal marshes etc. According to the United States Environmental Protection Agency (EPA), wetlands cover approximately 31% of the total land area of the state of Florida.

Total land mass of Florida is: 170,312 Km². The landmass of Wetland areas is: 31% *  170,312 Km² = 52796.72Km²

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Answer:

1.

a.

b. 115 feet.

c.  78.26feet.

Step-by-step explanation:

a.

some mathematical observations we can make about the path of the balloon based on the given equation:

b. The maximum height of the balloon occurs at the vertex of the parabola described by the function b(h). We can find the height of the vertex by using the formula h = -b/(2a), where b and a are the coefficients of the linear and quadratic terms in the equation, respectively.

In this case, a = -1/115 and b = 2, so the height of the vertex is:

h = -b/(2a) = -2/(2(-1/115)) = 115 feet

Therefore, the maximum height the balloon reaches is 115 feet.

c. To find the height of the balloon after 180 minutes, we can substitute h = 180 into the equation b(h) and simplify:

b(180) = 2(180) - 1/115(180)^2 = 360 - 281.73≈ 78.26

Therefore, when you have been on the ride for 180 minutes, the height of the balloon is approximately78.26feet.

Answer:

a) The balloon ride is 230 minutes long.

b) The maximum height the balloon reaches is 115 m.

c) The height of the balloon at 180 minutes is 78 feet.

Step-by-step explanation:

Given quadratic equation:

[tex]b(h)=2h-\dfrac{1}{115}h^2[/tex]

The height of the balloon at the start and end of the balloon ride is zero feet. Therefore, to determine how long the balloon ride is, set the given quadratic equation to zero and solve for h.

[tex]\begin{aligned}\implies2h-\dfrac{1}{115}h^2&=0\\\\h\left(2-\dfrac{1}{115}h\right)&=0\\\\2-\dfrac{1}{115}h&=0\\\\\dfrac{1}{115}h&=2\\\\h&=230\end{aligned}[/tex]

Therefore, the balloon ride is 230 minutes long.

To determine the maximum height the balloon reaches, find the y-value of the vertex of the given quadratic equation.

The formula for the x-value of the vertex is -b/2a for a quadratic equation in the form y=ax²+bx+c. Therefore, the x-value of the vertex of the given equation is:

[tex]\implies -\dfrac{2}{2\left(-\frac{1}{115}\right)}=115[/tex]

To find the y-value of the vertex, substitute h = 115 into the given equation:

[tex]\begin{aligned}\implies b(115)&=2(115)-\dfrac{1}{115}(115)^2\\&=230-115\\&=115\; \sf ft\end{aligned}[/tex]

Therefore, the maximum height the balloon reaches is 115 ft.

To determine the height of the balloon when you have been on the ride for 180 minutes, substitute h = 180 into the equation:

[tex]\begin{aligned}\implies b(180)&=2(180)-\dfrac{1}{115}(180)^2\\\\&=360-\dfrac{6480}{23}\\\\&=78.260869...\\\\&=78\; \sf ft\end{aligned}[/tex]

Therefore, the height of the balloon at 180 minutes into the ride is 78 feet (rounded to the nearest foot).

Answer:

The probability that the couple have two girls and then a boy is 1/8 (12.5%).

Step-by-step explanation:

Tree diagrams show probabilities for sequences of two or more independent events.

To draw a tree diagram showing the given information:

See the attachment for the tree diagram.

To find the probability that the couple have two girls and then a boy, multiply along the branches representing those events.

Therefore, the probability that the couple have two girls and then a boy is:

[tex]\sf P(girl)\;and\;P(girl)\;and\;P(boy)=\dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2}=\dfrac{1}{8}=12.5\%[/tex]

Answer:

1/8 or 0.125 (12.5%).

Step-by-step explanation:

Using the tree diagram, we can see that there are 8 possible outcomes for the gender of the three children: BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG. Since each outcome is equally likely, the probability of any one outcome is 1/8.

The outcome we are interested in is GGB, which has a probability of 1/8. Therefore, the probability that the family has two girls, and then a boy is 1/8 or 0.125 (12.5%).

We know the lengths of the sides opposite and adjacent to angle A, as well as the length of the hypotenuse, then sin(A) = 9/41 and cos(A) = 40/41.

What are trigonometric ratios?

Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle. The basic trigonometric ratios are sin, cos, and tan, namely sine, cosine, and tangent ratios.

We can use the following trigonometric ratios:

sin(A) = opposite/hypotenuse

cos(A) = adjacent/hypotenuse

In this case, we know the lengths of the sides opposite and adjacent to angle A, as well as the length of the hypotenuse:

opposite = BC = 9 units

adjacent = AB = 40 units

hypotenuse = AC = 41 units

Using these values, we can calculate the sine and cosine of angle A:

sin(A) = opposite/hypotenuse = 9/41

cos(A) = adjacent/hypotenuse = 40/41

Therefore, we know the lengths of the sides opposite and adjacent to angle A, as well as the length of the hypotenuse, then sin(A) = 9/41 and cos(A) = 40/41.

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Therefore , the solution of the given problem of function comes out to be the number of tractors that  should be produced to incur minimum cost is 500.

The study of numbers and their variables, as well as our surrounds, structures, and both real and imagined locations, are all included in the mathematics curriculum. A function is a visual representation of the relationship between the quantities of inputs and the corresponding outputs for each. Simply described, a function is a collection of inputs that, when integrated, produce unique outputs for each input. Each role is given a country, city, or scope (also known as a realm).

Here,

The total cost function is:

C(x) = 23000 - 20x + 0.02x²

To find the minimum cost, we need to find the value of x that minimizes the total cost.

One way to do this is to find the vertex of the parabola that represents the total cost function.

The vertex of the parabola y = ax² + bx + c has an x-coordinate of -b/2a and a y-coordinate of c - b²/4a.

In this case, a = 0.02, b = -20, and c = 23000.

So, the x-coordinate of the vertex is:

x = -b/2a = -(-20)/(2 × 0.02) = 500

The minimum cost occurs at this x-value, so the number of tractors that should be produced to incur minimum cost is 500.

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Both expressions 0.5 + 2(0.25x) + 0.75(3-x) and 2 - 2(0.75x) - 3(0.25x) are equivalent to 0.5x + 1.5, and they satisfy the condition that each term is used only once.

One possible solution is:

0.5 + 2(0.25x) + 0.75(3-x) = 0.5x + 1.5

Simplifying this expression:

0.5 + 0.5x + 0.5x + 2(0.25x) + 2.25 - 0.75x = 0.5x + 1.5

0.5x + 0.5x - 0.75x = 1.5 - 0.5 - 2.25

0.25x = -0.25

x = -1

Substituting x = -1 into 0.5x + 1.5:

0.5(-1) + 1.5 = 0.5 + 1.5 = 2

Therefore, another equivalent expression is:

2 - 2(0.75x) - 3(0.25x) = 0.5x + 1.5

Simplifying this expression:

2 - 1.5x = 0.5x + 1.5

2 - 1.5x - 0.5x = 1.5

-2x = -0.5

x = 0.25

Substituting x = 0.25 into 0.5x + 1.5:

0.5(0.25) + 1.5 = 0.125 + 1.5 = 1.625

Therefore, both expressions 0.5 + 2(0.25x) + 0.75(3-x) and 2 - 2(0.75x) - 3(0.25x) are equivalent to 0.5x + 1.5, and they satisfy the condition that each term is used only once.

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The area of the shaded sector of the circle is 7.27 m^2

The area of a circle is the amount of two-dimensional space taken up by the circle. It can be calculated by using the formula A = πr2, where A is the area, π is 3.14, and r is the radius of the circle. The radius is the distance from the center of the circle to any point on the circle. The diameter of a circle, which is the distance from one side to the other, is twice the radius. Therefore, the area of a circle can also be calculated by using the formula A = πd2/4, where d is the diameter of the circle.

The area of the shaded sector of the circle is 7.27 m^2.

This can be calculated using the formula A = (π/180) x r^2 x θ, where r is the radius (18 m in this case), and θ is the angle in degrees (110° in this case).

Therefore, A = (π/180) x (18^2 x 110) = 7.27 m^2.

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If you put $1,000 per year into an account yielding 6% interest that is compounded annually, you will have $4291.8 in the account after 25 years.

Divide its principal by the risk premium, the time period and other factors to arrive at simple interest. Simple return = principal + interest + hours is the marketing formula. This process makes it easier to calculate interest. The most typical technique to figure out interests is as a portion of the principal sum. He will only pay his half of the 100% interest, for example, if he borrows $100 from a partner and agrees to repay the loan with 5% interest. $100 (0.05) = $5. When you keep borrowing, you must pay interest, and when you give it out, you must pay the interest. Interest is often set as an annual percentage of the loan total.

given:

FV = 1000(1.06)²⁵

FV =  1000 × 4.2918

FV = 4291.8

If you put $1,000 per year into an account yielding 6% interest that is compounded annually, you will have $4291.8 in the account after 25 years.

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1)

Area of a = 25 m²
2)

Length b = 5 m

3)

Length c = 7.94 m

4)

Area of d = 35.75 m²

Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We have,

1)

Figure a is a square:

Side = b

Area = b²

From (1),

Side = 5 m

Area of a = 5² = 25 m²

2)

Length b is in a triangle:

Using the Pythagorean theorem.

b² = 3² + 4²

b² = 9 + 16

b² = 25

b = 5 m _____(1)

3)

Length b is in a square:

From (2),

c = 7.94 m

4)

Figure d is a triangle.

Using the Pythagorean theorem.

c² + 9² = 12²

c² = 144 - 81

c² = 63

c = 3√7 m

c = 7.94 m _____(2)

Area = 1/2 x 9 x 7.94

Area =  35.73 m²

Thus,

Area of a = 25 m²
Length of b = 5 m

Length of c = 7.94 m

Area of d = 35.75 m²

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Answer:

[tex]S_n= n^2+4n[/tex]

[tex]n=11[/tex]

Step-by-step explanation:

The given arithmetic series is 5 + 7 + 9 + ...

From inspection of the given series, we can see that the first term is 5.

The common difference is the difference between consecutive terms. Therefore, the common difference of the given series is 2.

[tex]\boxed{\begin{minipage}{7.3 cm}\underline{Sum of the first $n$ terms of an arithmetic series}\\\\$S_n=\dfrac{1}{2}n[2a+(n-1)d]$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $d$ is the common difference.\\ \phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

To determine an equation for the sum of the first n terms of the given series, substitute a = 5 and d = 2 into the formula.

[tex]\implies S_n=\dfrac{1}{2}n\left[2(5)+(n-1)(2)\right][/tex]

[tex]\implies S_n=\dfrac{1}{2}n\left[10+2n-2\right][/tex]

[tex]\implies S_n=\dfrac{1}{2}n\left[2n+8\right][/tex]

[tex]\implies S_n= n^2+4n[/tex]

To find the value of n, substitute Sₙ = 165 into the formula and solve for n:

[tex]\implies n^2+4n=165[/tex]

[tex]\implies n^2+4n-165=0[/tex]

[tex]\implies n^2+15n-11n-165=0[/tex]

[tex]\implies n(n+15)-11(n+15)=0[/tex]

[tex]\implies (n-11)(n+15)=0[/tex]

Apply the zero product property:

[tex](n-11)=0 \implies n=11[/tex]

[tex](n+15)=0 \implies n=-15[/tex]

Therefore, as the value of n is positive, the value of n for which the series has a sum of 165 is 11.

The value of x for the function x > 2 is x ≤ -1. This is represented by the following graph.

A graph is a format similar to a set of elements in different mathematics, more categorically graph theory, in which some pairs of objects are conceptually "connected". Elements are represented by mathematical abstractions called vertices (sometimes called nodes or points), and each pair of allied vertices is called an edge (also called a link or line). A graph is usually characterized as a collection of points or circles defining vertices and lines or curves representing edges. One of the details studied in discrete mathematics is graphs. 

The given function is:

G(x)={x if x < or equal to 2 -3 if x >2

Here, the value of x for x > 2 is x ≤ -1. This is represented by the following graph.

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The requried solution of the two linear equations is given as x = (b - d)/a-c and y = a (d - c)/(a-c).

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,

The question seems to be incomplete so the solution is a standard solution by assuming a standard linear equation.

The given equation,
ax + y = b - - - - - (1)
cx + y = d - - - - -(2)

Subtract equation 2 from 1
ax - cx + y - y = b - d

x(a - c) =  b - d
x = b - d / a - c

Now,
Put x in equation 1
a (b - d) / (a - c) + y = b
y = b - a(b - d)/(a - c)
y = ab - ac -ab + ad/(a - c)
y = a (d - c)/(a - c)

Thus, the requried solution of the two linear equation are given as x = (b - d)/a-c and y = a (d - c)/(a - c).

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The question seems to be incomplete,
The solution given is standard solution for the simultaneous equations.

Answer:

Step-by-step explanation:

To solve the polynomial P(m) = -m + 5m² - 8m + 4m⁵ - 8m⁰, we can simplify the expression by combining like terms:

P(m) = 4m⁵ + 5m² - 9m - 8

Therefore, the simplified form of the polynomial is P(m) = 4m⁵ + 5m² - 9m - 8.

Answer:p=\frac{4m^5+5m^2-9m-8}{m};\quad \:m\ne \:0

Step-by-step explanation:

Yes, it is a function.

The reason is that the values on each row all align in a manner that shows the graph is moving in a clear direction. This is consistent with the behavior expected from the standard function, with all of the values on each row being the same distance from the origin.

Answer:

Step-by-step explanation:

The ratio of fiction books to non-fiction books is 5:2, which means that for every 5 fiction books in the library, there are 2 non-fiction books.

We know that the total number of books in the library is 1421. To figure out how many of those books are fiction, we need to divide the total by the sum of the parts in the ratio (5 + 2 = 7), and then multiply the result by the number of parts that represent fiction books (5).

So, the number of fiction books in the library is:

5/7 x 1421 = 1015

To find out how many non-fiction books there are, we can subtract the number of fiction books from the total:

1421 - 1015 = 406

Finally, to figure out how many more fiction books there are than non-fiction books, we can subtract the number of non-fiction books from the number of fiction books:

1015 - 406 = 609

Therefore, there are 609 more fiction books than non-fiction books in the library.

The solutions of the given system of linear inequalities are (0, 3) and (6, 2)

A system of inequalities is a set of two or more inequalities in one or more variables. Systems of inequalities are used when a problem requires a range of solutions, and there is more than one constraint on those solutions.

Given is a graph of a system of linear inequalities, we need to select the solutions of the following,

The solution of the system of linear inequalities, are given by the combined shaded reason of the graph,

Here, only points (0, 3) and (6, 2) are lies in the common combined part of the graph,

Hence, the solutions of the given system of linear inequalities are (0, 3) and (6, 2)

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Answer:

deprication a/c Dr. 30,00,000

To land a/c 30,00,000

Step-by-step explanation:

deprication is an expense so, according to modern rules of accounts Dr. debit all assets & expenses and cr. credit all income, capital, all liability

(assets ) land value is deprecating so, deprication is an expense so, we Dr. deprication a/c expense is an increase (name the expense) and the value of land (assets) is diminishing Or depricating so, cr. land a/c

Annie's social style, based on the given information, is most likely to be categorized as "expressive".

Inductive reasoning is a form of defining determinations by proceeding with patterns specific to the usual. It's generally distinguished from deductive reasoning, where it proceeds from general knowledge to specific conclusions.

Here,
Annie's social style, based on the given information, is most likely to be categorized as "expressive". Expressive individuals are generally spontaneous, impulsive, and energetic. They prioritize personal and social needs over practical considerations and tend to make decisions based on their opinions and feelings, rather than objective data or analysis. They are often outgoing, enthusiastic, and creative, but may also be impatient, easily distracted, and prone to taking risks. This description matches the traits attributed to Annie in the scenario.

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a) The null hypothesis is that there is no difference in the proportion of homeowners using water filters among the three communities. The alternative hypothesis is that at least one community has a different proportion of homeowners using water filters than the other communities.

b) To calculate the expected count for the bottom right cell, we can use the formula:

Expected count = (row total x column total) / grand total

The row total for Community C and the column total for No are both 100, and the grand total is 300. Therefore:

Expected count = (100 x 100) / 300 = 33.33

The expected count of 33.33 for the bottom right cell means that if there were no difference in the proportions of homeowners using water filters among the three communities, we would expect 33.33 of the 100 homeowners in Community C to answer 'No' to the question about water filters.

c) To determine what we can conclude from the Chi-square statistic of 13.22, we need to compare it to the critical value for a Chi-square distribution with (3-1) x (2-1) = 2 degrees of freedom at the desired level of significance. Let's assume a level of significance of 0.05. From a Chi-square distribution table, the critical value with 2 degrees of freedom at 0.05 level of significance is 5.99.

Since 13.22 is greater than 5.99, we can reject the null hypothesis and conclude that there is a significant difference in the proportion of homeowners using water filters among the three communities. However, we cannot determine from this test alone which communities have different proportions of homeowners using water filters. We would need to conduct further tests, such as post-hoc tests, to investigate the specific differences among the communities.

The age of Sadie is 6 years.

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

Let x be the age of Sadie

x+1 be the age of Guadalupe

The sum of the square of Sadie's age and 5 times Guadalupe's age is 71.

x² +5(x+1)=71

x² +5x+5=71

x² +5x-66=0

Factor out the expression.

x²+11x-6x-66=0

x(x+11)-6(x+11)=0

(x-6)(x+11)=0

x=6 and x=-11

Hence, the age of Sadie is 6 years.

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Answer:

the diameter of the largest circle is 2r = 56/3 cm.

Step-by-step explanation:

Let the largest circle have center O and radius r. Join P, Q, R and O as shown in the figure below.

Since the circle with center Q and the circle with center R touch each other externally, the distance between their centers is the sum of their radii. Therefore,

QR = QM + MR

where M is the point of contact of the two circles. Similarly, since the circle with center P touches the circle with center Q externally, the distance between their centers is the sum of their radii. Therefore,

PQ = PM + MQ

Adding these two equations, we get

PQ + QR = PM + MQ + QM + MR

Substituting the given values, we get

10 + 12 = PM + MQ + 12 + 8

or PM + MQ = 2

Now consider the right-angled triangle PQO. Since PQ is the tangent to the circle with center P at point A, OA is perpendicular to PQ. Similarly, OQ is perpendicular to QR and OR is perpendicular to RP. Therefore, angles PAO, QBO and ROC are all right angles.

Let the perpendicular from O to PQ meet PQ at X. Then PX = OQ - PQ/2 = r - 5. Similarly, let the perpendicular from O to QR meet QR at Y. Then QY = OR - QR/2 = r - 6. Let the perpendicular from O to RP meet RP at Z. Then RZ = OP - PR/2 = r - 4.

Now consider the right-angled triangle OXY. Using the Pythagorean theorem, we get

OX^2 = OY^2 + XY^2

Substituting the values of OY and XY, we get

(r - 6)^2 = (r - 5)^2 + (r - 4)^2

Expanding and simplifying, we get

3r^2 - 56r + 191 = 0

Solving this quadratic equation, we get two solutions: r = 7 and r = 28/3. Since the radius of the largest circle cannot be less than the radius of the circle with center Q, which is 6, the only possible solution is r = 28/3.

Therefore, the diameter of the largest circle is 2r = 56/3 cm.

The conditions which will construct a triangle as required to be identified are;

The triangle inequality theorem suggests that the sum of any two side lengths of a triangle must be greater than the third side and the difference of any two side lengths must be less than the third side.

Also, the sum of interior angles of a triangle is; 180°.

Hence, the conditions as required are; Angles 20°, 150°, 10° and Side lengths 11 cm, 4 cm, 8 cm.

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From the graph of system of linear inequality there may be other possible solutions, but (20, 100) is one that satisfies all the given constraints.

Let's first define our variables and their corresponding constraints:

Let a be the number of student tickets sold.

Let y be the number of adult tickets sold.

The total number of tickets sold cannot exceed 120, so we have the constraint

a + y ≤ 120 ...eq(i)

The minimum revenue required is $670, so we have the constraint          4a + 8y ≥ 670...eq(ii)

The drama club can sell at most 30 student tickets, so we have the constraint a ≤ 30.

The drama club must sell a minimum of 80 adult tickets, so we have the constraint y ≥ 80.

The last inequality is

y ≥ 80

To solve these inequalities graphically, we will plot the lines for each constraint on a coordinate plane and shade the region that satisfies all the inequalities. The shaded region will represent all possible combinations of student and adult tickets that meet the constraints.

First, let's plot the line for the a + y ≤ 120 constraint. We can rewrite this as y ≤ -a + 120 and plot the line y = -a + 120 on the coordinate plane:

The shaded region for this constraint is below the line and includes the origin.

Next, let's plot the line for the 4a + 8y ≥ 670 constraint. We can rewrite this as y ≥ (-1/2)a + 83.75 and plot the line y = (-1/2)a + 83.75 on the same coordinate plane:

The shaded region for this constraint is above the line.

Now, let's plot the constraint a ≤ 30. We can draw a vertical line at a = 30:

The shaded region for this constraint is to the left of the line.

Finally, let's plot the constraint y ≥ 80. We can draw a horizontal line at y = 80:

The shaded region for this constraint is above the line.

To find a possible solution, we need to find the point where all four shaded regions overlap. This point represents a combination of student and adult tickets that satisfies all the constraints. One such point is (20, 100), which means the drama club can sell 20 student tickets and 100 adult tickets to meet their requirements and raise at least $670 in revenue.

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