The revenue over 30 weeks for a small landscaping company is modeled by the graph shown. Which of the following is true?

The minimum value of C is 42.

To solve the linear programming problem, we can graph the feasible region and find the minimum value of C within that region. The feasible region is defined by the constraints:

1) 6x + 7y ≥ 42

2) x, y ≥ 0

Let's solve the inequalities to find the vertices of the feasible region:

For 6x + 7y ≥ 42:

When x = 0, 7y ≥ 42, y ≥ 6

When y = 0, 6x ≥ 42, x ≥ 7

When x = 7, 6(7) + 7y ≥ 42, 7y ≥ 0, y ≥ 0

The vertices of the feasible region are (0, 6), (7, 0), and (7, 0).

Now, let's evaluate the objective function C = 6x + 9y at each vertex:

C(0, 6) = 6(0) + 9(6) = 54

C(7, 0) = 6(7) + 9(0) = 42

C(7, 0) = 6(7) + 9(0) = 42

The minimum value of C is 42 at the points (7, 0) and (7, 0).

Therefore, the correct choice is:

A. C = 42

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Answer:

\(x=\sqrt{33}\)

Step-by-step explanation:

We can use the Pythagorean theorem to solve this

in the 11, 13 triangle,

\(11^2 + h^2 = 13^2\\121 + h^2 = 169\\h^2 = 48\\h = 4\sqrt{3}\)

to find x

\(x^2 + (4\sqrt{3} )^2=9^2\\x^2 + 48 = 81\\x^2 = 33\\x = \sqrt{33}\)

Answer:

28

Step-by-step explanation:

sry if I'm wrong although I used calculator

The height of the 10th bounce of the ball will be 0.6 feet.

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.

The nth term of the geometric sequence is given by

\(\sf T_n=ar^{n-1}\)

Where,

According to the given question.

During the first bounce, height of the ball from the ground, a = 4.5 feet

And, the each successive bounce is 73% of the previous bounce's height.

So,

During the second bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 10\)

\(=\dfrac{73}{100}(10)\)

\(\sf = 0.73 \times 10\)

\(\sf = 7.3 \ feet\)

During the third bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 7.3\)

\(=\dfrac{73}{100}(7.3)\)

\(\sf = 5.33 \ feet\)

Like this we will obtain a geometric sequence 7.3, 5.33, 3.11, 2.23,...

And the common ratio of the geometric sequence is 0.73

Therefore,

The sixth term of the geometric sequence is given by

\(\sf T_{10}=10(0.73)^{10-1\)

\(\sf T_{10}=10(0.73)^{9\)

\(\sf T_{10}=10(0.059)\)

\(\sf T_{10}=0.59\thickapprox0.6 \ feet\)

Hence, the height of the 10th bounce of the ball will be 0.6 feet.

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1 . Price of car 8 years later is $4305.

The price of a car that was bought for $10,000 and has depreciated 10% yearly can be calculated by multiplying the original price of the car ($10,000) by (1 - 0.10) raised to the power of the number of years (8). It means the car will lose 10% of its value each year for 8 years. Therefore, the price of the car 8 years later would be $4304.67. This is the final amount after 8 years of deprecation on the original price of the car.

2. The yearly value of the card 25 years later is $16.93 and equation of price is given by 5 * (1 + 0.05)^t where t is time.

The formula used to calculate the future value of an item that appreciates at a certain annual rate is called compounding. In this case, the baseball card was bought for $5 and has appreciated at a rate of 5% per year. The formula used to find the value of the card 25 years later is "Price = initial value * (1 + interest rate)^number of years". Plugging in the given values, we get: "Price = 5 * (1 + 0.05)^25"

Price=5(1+0.05)^25

Price=5(1.05)^25

Price=16.93

so the final price of baseball is $16.93

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Aya can make 14 mats of 1 foot long.

Division is one of the fundamental arithmetic operation, which is performed to get equal parts of any number given, or finding how many equal parts can be made. It is represented by the symbol "÷" or sometimes "/"

Given that, Aya has 14\(\frac{2}{5}\) feet of chain. She wants to make pieces foot long mat.

Let can make x mats out of the given chain, since each mat is 1 foot long, so,

1×x =  14\(\frac{2}{5}\)

x = 72/5

x = 14.4

x ≈ 14

Hence, She can make 14 mats out of the given chain.

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oFYORYODYIYDOCYODYODYODOYYDSOYSITTIsst.isti.ti.s.sitsi.ttsliyd.i.odygis.x.ittxi.x,jgxfj,.jtxtis.x.tii.ts.kdttic.

Answer:

24 hours for the following conditions. (Round your answers to the nearest whole number.) (a) No antibiotic is

The exact length of the curve: y = ln 1 − x^2 , 0 ≤ x ≤ 1 6 will be\($$\int \frac{d x}{a^2-x^2}=\frac{1}{2 a} \ln \left|\frac{a+x}{a-x}\right|+c$$\)

\($$\begin{aligned}y & =\ln \left(1-x^2\right), \quad 0 \leq x \leq \frac{1}{6} \\\frac{d y}{d x} & =\frac{1}{1-x^2} \cdot \frac{d}{d x}\left(1-x^2\right) \quad\left\{\frac{d}{d u} \ln u=\frac{1}{u}\right\} . \\& =\frac{-2 x}{1-x^2}\end{aligned}$$\)

Now, the length of the curve is given by

\($$\begin{aligned}L & =\int_a^b \sqrt{1+\left(\frac{d y}{d x}\right)^2} d x \\& =\int_0^{1 / 6} \sqrt{1+\left(\frac{-2 x}{\left.1-x^2\right)^2}\right.} d x \\& =\int_0^{1 / 6} \frac{\sqrt{\left(1-x^2\right)^2+4 x^2}}{\left(1-x^2\right)} d x \\& =\int_0^{1 / 6} \frac{\sqrt{1+x^4-2 x^2+4 x^2}}{\left(1-x^2\right)} d x\end{aligned}$$\)

\(=\int_0^{1 / 6} \frac{\sqrt{1+x^4+2 x^2}}{1-x^2} d x\\\\=\int_0^{1 / 6} \frac{\sqrt{\left(1+x^2\right)^2}}{1-x^2} d x\\\\=\int_0^{1 / 6} \frac{1+x^2}{1-x^2} d x\)

Now, since the degree of Numerator & degree of Denominator are the same,

So, we will perform a long division process

\($$\begin{aligned}& \therefore \frac{1+x^2}{1-x^2}=-1+\frac{2}{1-x^2} \quad\left\{\begin{array}{l}1-x^2 \frac{-1}{\frac{x^2+1}{x^2+1}} \\\frac{2}{2}\end{array}\right. \\& \therefore L=\int_0^{1 / 6}\left(-1+\frac{2}{1-x^2}\right) d x \\&\end{aligned}$$\)

\($$\begin{aligned}& =\left[-x+2 \cdot \frac{1}{(271} \ln \left|\frac{1+x}{1-x}\right|\right]_0^{1 / 6} \\& =\left(-\frac{1}{6}+\ln \left|\frac{1+1 / 6}{1-1 / 6}\right|\right)-\left(0+\ln \left|\frac{1+0}{1-0}\right|\right) \\& =-\frac{1}{6}+\ln \left(\frac{7 / 6}{5 / 6} \cdot-(0+0)\right.\end{aligned}$$\)

\(L=\frac{-1}{6}+\ln \left(\frac{7}{5}\right)\\\)

L=0.1698 approximately 0.17 units

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\(\purple{\underline{{\boxed{\bf{QUESTION: }}}}}\)

What Is The Formula Of Triangle, Rhombus, Parallelogram

\(\purple{\underline{{\boxed{\bf{ ANSWER: }}}}}\)

➬ The formula of Triangle is:

\( \frac{1}{2} \times base \times height \: \)

➬ The formula of rhombus is:

\(diagonal1 \times diagonal2\)

➬ The formula of parallelogram:

\(base \times height\)

\(\purple{\underline{{\boxed{\bf{MORE\: TO \: KNOW: }}}}}\)

➬ The Area of Triangle: \( \frac{1}{2}base \times height\)

Perimeter of Triangle: \(sum \: of \: three \: sides\)

➬ The Area of Rhombus: \(d1 \times d2\)

The Perimeter of Rhombus: \(4 \: Sides\)

➬ The Area of Parallelogram: \(base \times height\)

The perimeter of Parallelogram: \(4 \: sides\)

The number which represents the gain as per the question is +12. Hence, option "d" is correct.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the information given in the question,

Firstly, the team returned the ball to the 30-yard line.

Then, hey ran to the 42-yard line for a gain.

Then, the number that shows the change will be,

= 42 - 30

= +12, there is gain of +12.

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Angles 6 and 8 are adjacent, they are Linear pair οf angles.

Linear pair οf angles are fοrmed when twο lines intersect each οther at a single pοint. The angles are said tο be linear if they are adjacent tο each οther after the intersectiοn οf the twο lines. The sum οf angles οf a linear pair is always equal tο 180°. Such angles are alsο knοwn as supplementary angles.

Angles 1 and 4 are not adjacent, they are vertically opposite.

Angles 5 and 8 are not adjacent, they are vertically opposite.

Angles 6 and 8 are adjacent, they are Linear pair οf angles

Angles 1 and 5 are corresponding exterior angle, so the are not linear pair.

Thus, Angles 6 and 8 are adjacent, they are Linear pair οf angles

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Answer:

Let's use a Venn diagram to solve this problem.

First, let's label the three regions of the Venn diagram: Computer only (C), Optional Maths only (M), and both Computer and Optional Maths (C ∩ M). We can also label the region outside the circles as neither Computer nor Optional Maths (N).

We know that 30% of the students like Computer only, which means that the percentage of students in region C is 30%. Similarly, 25% of the students like both Computer and Optional Maths, so the percentage of students in region C ∩ M is 25%.

We are also given that 5% of the students don't like either subject, so the percentage of students in region N is 5%.

Finally, we are told that 390 students like Optional Maths, which includes the students in regions M and C ∩ M. We don't know the percentage of students in region M, but we do know that the percentage of students in region C ∩ M is 25%.

Using this information, we can set up an equation to solve for the total number of students:

C + M + C ∩ M + N = 100%

Substituting the percentages we know, we get:

30% + M + 25% + 5% = 100%

Simplifying the equation, we get:

M = 40%

This means that 40% of the students like Optional Maths only, which is the percentage of students in region M.

Now we can use the fact that 390 students like Optional Maths to solve for the total number of students:

M + C ∩ M = 390

0.4T + 0.25T = 390

0.65T = 390

T = 600

Therefore, the total number of students is 600.

Answer:

Step-by-step explanation:A = 2 π r h + 2 π r 2

Answer:\(-\frac{11}{3}\)

Step-by-step explanation:

Convert the mixed number to an improper fraction

\(-\frac{49}{9}\)+\(\frac{8}{9}\); Then calculate the sum

The answer is \(-\frac{11}{3}\)

Answer:

I believe not statistical.

Step-by-step explanation:

Answer:

im fanna join      

Step-by-step explanation:

Answer:

No solution.

Step-by-step explanation:

\(x-6-8=-19+x\)

Subtract x from both sides:

\(x-6-8-x=-19+x-x\)

\(-6-8=-19\)

\(-14=-19\)

Since both sides are not equal, there is no solution.

We have shown that both (0.1) and (0.2) hold, based on the properties of the exponential distribution and the application of the Borel-Cantelli Lemma.

The second Borel-Cantelli lemma, which is frequently referred to as a related conclusion, is a partial converse of the first Borel-Cantelli lemma. According to the lemma, an event will have a probability of either zero or one under specific circumstances.

To prove both (0.1) and (0.2), we can use the Borel-Cantelli Lemma along with the properties of the exponential distribution. Let's start with (0.1):

(0.1) lim sup \(X_n\) / log(n) = 0 almost surely.

First, note that for an exponential random variable X with parameter λ, the cumulative distribution function (CDF) is given by F(x) = 1 - \(e^{(-\lambda x)\).

Given X_i ~ Exp(a), we have\(F(x) = 1 - e^{(-ax)\).

Now, consider the event \(E_n\) = {\(X_n\) / log(n) > ε}, where ε > 0 is a fixed constant.

We want to show that P(\(E_n\) i.o.) = 0, where "i.o." denotes "infinitely often."

Since \(X_i\) are independent and identically distributed (i.i.d.) random variables, we can write:

P(\(E_n\) i.o.) = P(lim sup (\(X_n\) / log(n)) > ε).

Using the Borel-Cantelli Lemma, it suffices to show that the sum of the probabilities of \(E_n\) is finite, i.e., Σ P(\(E_n\)) < ∞.

Now, let's calculate P\((E_n)\):

P\((E_n)\) = P(\(X_n\) / log(n) > ε)

      = P(\(X_n\) > ε * log(n))

      = 1 - P(\(X_n\) ≤ ε * log(n))

      = 1 - (1 - \(e^{(-a * \epsilon * log(n))\))   [Using the CDF of \(X_n\)]

      = \(e^{(-a * \epsilon * log(n))\).

Taking the logarithm of both sides, we have:

log(P(\(E_n\))) = -a * ε * log(n).

Now, let's consider the summation:

Σ log(P(\(E_n\))) = Σ (-a * ε * log(n))

             = -a * ε * Σ log(n).

The sum Σ log(n) diverges, as it is the harmonic series. Thus, Σ log(P(\(E_n\))) also diverges.

Since Σ log(P(\(E_n\))) diverges, we can conclude that Σ P(\(E_n\)) must also diverge.

By the Borel-Cantelli Lemma, this implies that P(\(E_n\) i.o.) = 0, which means that lim sup (\(X_n\) / log(n)) = 0 almost surely. Hence, we have proven (0.1).

Now, let's move on to (0.2):

(0.2) lim inf \(X_n\) / (1 + log(n)) = 0 almost surely.

We want to show that P(\(E'_n\) i.o.) = 0, where \(E'_n\) = {\(X_n\) / (1 + log(n)) > ε}.

Using similar steps as in (0.1), we can calculate P(\(E'_n\)) as:

P(\(E'_n\)) = \(e^{(-a * \epsilon * (1 + log(n))\)).

Taking the logarithm of both sides, we have:

log(P(\(E'_n\))) = -a * ε * (1 + log(n)).

Now, consider the summation:

Σ log(P(\(E'_n\))) = Σ (-a * ε * (1 + log(n)))

              = -a * ε * Σ (1 + log(n)).

The sum Σ (1 + log(n)) also diverges, as it is the sum of two divergent series. Thus, Σ log(P(\(E'_n\))) diverges.

Since Σ log(P(\(E'_n\))) diverges, we can conclude that Σ P(\(E'_n\)) must also diverge.

By the Borel-Cantelli Lemma, this implies that P(\(E'_n\) i.o.) = 0, which means that lim inf (\(X_n\) / (1 + log(n))) = 0 almost surely. Hence, we have proven (0.2).

Therefore, we have shown that both (0.1) and (0.2) hold, based on the properties of the exponential distribution and the application of the Borel-Cantelli Lemma.

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Answer: The value of the triangle = 3.

               The value of the square = -2,

               The value of the star = 7

               The value of the rhombus = 18.

               The value of the circle  = 4,

               The value of the right angle triangle  = -5

Step-by-step explanation:

Define Linear equation:

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has an exponent more than 1. The graph of a linear equation always forms a straight line.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Given that,

Let us assume the values is,

(Option 1) : A shape puzzle is given that,

Let's assume, the triangle shape represents = a

Let's assume, the square shape represents = b

Let's assume, the star shape represents = c

The equation becomes,

clue 1 : 2a-1 = 5

clue 2 : a + b = 1

clue 3 : a-2b = c

First take, clue 1 :         2a-1 = 5

                                       2a = 5+1

                                        2a = 6

                                         a = 6/2

                                          a = 3

Therefore,       triangle (a) = 3

Take, clue 2 :                      a + b = 1

Replace 'a' value in this equation,

                                            a + b = 1

                                            3+b = 1

                                              b = 1-3

                                              b = -2

 Therefore,         square (b) = -2

Take clue 3 :                     a-2b = c

Replace with 'a' and 'b' values in this equation,

                                          a-2b = c

                                           3-2(-2) = c

                                            3+4 = c

                                              c = 7

Therefore,             star (c) = 7

we can substitute these values,

Then,      clue 1 : 2(3) -1 = 6-1 = 5

               clue 2 : 3 + (-2) = 3-2 = 1

               clue 3 : 3-2(-2) = 3+4 = 7

Thus, The value of the triangle = 3.

         The value of the square is = -2,

          The value of the star = 7

after using the concept of linear equation in two variables.

(Option 2) : A shape puzzle is given that,

Let's assume, the rhombus shape represents = x

Let's assume, the circle shape represents = y

Let's assume, the right angle triangle shape represents = z

The equation becomes,

clue 1 : x+2 = 5y

clue 2 : 3y = 12

clue 3 : 2y = x+2z

Take, clue 2 :                     3y = 12

                                            y = 12/3 = 4

Therefore,      circle (y) = 4

First take, clue 1 :         x+2 = 5y

                                      x+2=5(4)

                                      x+2=20

                                      x = 20-2 = 18

Therefore,       rhombus (x) = 18

Take clue 3 :                      2y = x+2z                

Replace with 'x' and 'y' values in this equation,

                                         2y = x+2z

                                         2(4) = (18)+2z

                                          2(4) = (18)+2z

                                           8 = (18)+2z

                                            8-18 = 2z

                                             -10 = 2z

                                              z = -10/2

                                              z = -5

Therefore,         right angle triangle (z) = -5

we can substitute these values,

Then,      clue 1 : 18+2=5(4)

                            20 = 20

               clue 2 : 3(4) = 12

                             12 = 12

               clue 3 : 2(4) = 18+2(-5)

                             8 = 18-10

                             10+8 = 18

                              18 = 18  

Thus, The value of the rhombus = 18.

         The value of the circle  = 4,

          The value of the right angle triangle  = -5

after using the concept of linear equation in two variables.

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The fundamental question addressed by the correlational method is whether two or more variables are related in some systematic way. So the correct option is D.

Correlational method is a research technique used to explore the relationship between two or more variables. In this method, researchers collect data on the variables of interest and analyze their patterns of association. The fundamental question addressed by the correlational method is whether two or more variables are related in some systematic way. This means that researchers are interested in exploring whether changes in one variable are associated with changes in another variable.

For instance, a researcher may be interested in exploring the relationship between stress and job performance. The researcher may collect data on the levels of stress and job performance in a sample of employees and then use statistical analysis to determine if there is a systematic relationship between the two variables. If the results show that higher levels of stress are associated with lower levels of job performance, then the researcher can conclude that there is a negative correlation between the two variables.

It is important to note that correlation does not imply causation. While a correlation between two variables indicates that they are related, it does not necessarily mean that changes in one variable are causing changes in the other variable. Therefore, researchers must be cautious when interpreting correlational data and should consider other factors that may be influencing the relationship between variables.

Therefore, the fundamental question addressed by the correlational method is whether two or more variables are related in some systematic way, and researchers must be cautious when interpreting correlational data and should consider other factors that may be influencing the relationship between variables.

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A car drives down a straight farm road. Its position x from a stop sign is described by the following equation:

(a) Average velocity from t = 0 to t = 3.00 s, 5.73 m/s

(b) Instantaneous velocity at t = 0, 0 m/s

Instantaneous velocity at t = 3.00 s,12.15 m/s

(c) Average acceleration from t = 0 to t = 3.00 s,4.05 m/s²

(d) Instantaneous acceleration at t = 0,2A ≈ 4.28 m/s²

Instantaneous acceleration at t = 3.00 s, 4.14 m/s²

To calculate the quantities requested, to differentiate the position equation with respect to time.

Given:

x(t) = At² - Bt³

A = 2.14 m/s²

B = 0.0770 m/s³

(a) Average velocity from t = 0 to t = 3.00 s:

Average velocity is calculated by dividing the change in position by the change in time.

Average velocity = (x(3.00) - x(0)) / (3.00 - 0)

Plugging in the values:

Average velocity = [(A(3.00)² - B(3.00)³) - (A(0)² - B(0)³)] / (3.00 - 0)

Simplifying:

Average velocity = (9A - 27B - 0) / 3

= 3A - 9B

Substituting the given values for A and B:

Average velocity = 3(2.14) - 9(0.0770)

= 6.42 - 0.693

= 5.73 m/s

(b) Instantaneous velocity at t = 0 and t = 3.00 s:

To find the instantaneous velocity, we differentiate the position equation with respect to time.

Velocity v(t) = dx(t)/dt

v(t) = d/dt (At² - Bt³)

v(t) = 2At - 3Bt²

At t = 0:

v(0) = 2A(0) - 3B(0)²

v(0) = 0

At t = 3.00 s:

v(3.00) = 2A(3.00) - 3B(3.00)²

Substituting the given values for A and B:

v(3.00) = 2(2.14)(3.00) - 3(0.0770)(3.00)²

= 12.84 - 0.693

= 12.15 m/s

(c) Average acceleration from t = 0 to t = 3.00 s:

Average acceleration is calculated by dividing the change in velocity by the change in time.

Average acceleration = (v(3.00) - v(0)) / (3.00 - 0)

Plugging in the values:

Average acceleration = (12.15 - 0) / 3.00

= 12.15 / 3.00

≈ 4.05 m/s²

(d) Instantaneous acceleration at t = 0 and t = 3.00 s:

To find the instantaneous acceleration, we differentiate the velocity equation with respect to time.

Acceleration a(t) = dv(t)/dt

a(t) = d/dt (2At - 3Bt²)

a(t) = 2A - 6Bt

At t = 0:

a(0) = 2A - 6B(0)

a(0) = 2A

At t = 3.00 s:

a(3.00) = 2A - 6B(3.00)

Substituting the given values for A and B:

a(3.00) = 2(2.14) - 6(0.0770)(3.00)

= 4.28 - 0.1386

= 4.14 m/s²

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The altitude of Polaris, also known as the North Star, refers to its angle above the horizon when observed from a specific location on Earth.

The altitude of Polaris varies depending on the observer's latitude.

For an observer at the North Pole (latitude 90 degrees), Polaris appears directly overhead, at an altitude of 90 degrees. This means Polaris is at the zenith, the highest point in the sky.

For observers at other latitudes in the Northern Hemisphere, Polaris will appear lower in the sky. The altitude of Polaris is equal to the observer's latitude. For example, if you are at a latitude of 40 degrees north, Polaris will have an altitude of approximately 40 degrees above the horizon.

It's important to note that the altitude of Polaris remains relatively constant throughout the night and throughout the year due to its proximity to the celestial north pole. This makes it a useful navigational reference point for determining direction and latitude in the Northern Hemisphere.

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Answer:

P(x) = (-0.2x² + 480x - 24480)

Step-by-step explanation:

1). Expression representing the "Cost" to produce the shirts is,

  C(x) = 160x + 24480

  Where 'x' represents the number of shirts.

  Cost to produce 900 printed shirts will be,

   C(900) = 160×900 + 24480

                = 144000 + 24480

                = Php 168480

2). Revenue generated by selling 900 shirts is,

   R(x) = 640x - 0.2x²

   For x = 900,

   R(x) = 640(900) - 0.2(900)²

          = 576000 - 162000

          = Php 414000

3). Expression for profit:

   Since, Profit = Revenue generated - Cost for production

   P(x) = R(x) - C(x)

          = (640x - 0.2x²) - (160x + 24480)

          = (640x - 160x) - 0.2x² - 24480

          = 480x - 0.2x² - 24480

  P(x) = (-0.2x² + 480x - 24480)

We need at least 5 tosses to be certain that the probability of getting at least one 6 is greater than or equal to 1/2.

The probability of not getting a 6 on a solitary throw of a fair six-sided kick the bucket is 5/6. Subsequently, the probability of not getting a 6 on n throws is \((5/6)^n\). The probability of getting somewhere around one 6 in n throws is 1 - \((5/6)^n\).

To view the quantity of throws expected as sure that the probability of getting somewhere around one 6 is more prominent than or equivalent to 1/2, we can set the probability equivalent to 1/2 and address for n:

1 - \((5/6)^n\) = 1/2

\((5/6)^n\) = 1/2

Taking the normal logarithm of the two sides, we get:

n ln(5/6) = ln(1/2)

n = ln(1/2)/ln(5/6) ≈ 4.807

Hence, we really want something like 5 throws to be sure that the probability of getting no less than one 6 is more prominent than or equivalent to 1/2.

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Answer:

4x-7=5

Step-by-step explanation: If you take 4(3) you get 12 -7 =5

Using the distance formula, Jet will take 2.2 hours to catch up with the airplane.

We will find the solution using distance formula.

distance formula is a formula that is used to find the distance between two points. These points can be in any dimension.

d=rt where

d is distance r is rate or speed and t is time

"distance airplane traveled" = "distance jet traveled"

Let x = hours "airplane" was flying

x-1 = hours "jet" was flying

.

180x = 330(x-1)

180x = 330x - 330

180x + 330 = 330x

330 = 150x

330/150 = x

2.2 hours = x

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slope intercept equation is represented below

Therefore,

An equivalence relation is a relation that is reflexive, symmetric, and transitive. We will show that the given relation S satisfies all these properties.

To prove that the relation S on C{0} is an equivalence relation, we need to show that it satisfies three properties: reflexivity, symmetry, and transitivity.

1. Reflexivity: For any complex number x in C{0}, (x, x) ∈ S.

To establish reflexivity, we need to show that y/x is real when x = y. In this case, y/x = x/x = 1, which is a real number. Therefore, (x, x) ∈ S and S are reflexive.

2. Symmetry: For any complex numbers x and y in C{0}, if (x, y) ∈ S, then (y, x) ∈ S.

Let's assume that y/x is a real number. We need to show that x/y is also real. Since y/x is real, it means that y/x = r, where r is a real number. Rearranging this equation, we get y = rx. Dividing both sides by y, we have x/y = 1/r, which is a real number. Therefore, if (x, y) ∈ S, then (y, x) ∈ S, and S is symmetric.

3. Transitivity: For any complex numbers x, y, and z in C{0}, if (x, y) ∈ S and (y, z) ∈ S, then (x, z) ∈ S.

Assume that y/x and z/y are both real numbers. We need to prove that (x, z) ∈ S, meaning that z/x is real. Since y/x and z/y are real numbers, we can write them as y/x = r1 and z/y = r2, where r1 and r2 are real numbers. Multiplying these equations, we have (y/x) * (z/y) = r1 * r2. Simplifying, we get z/x = r1 * r2, which is a real number.

Thus, if (x, y) ∈ S and (y, z) ∈ S, then (x, z) ∈ S, and S is transitive. Since the relation S satisfies the properties of reflexivity, symmetry, and transitivity, we can conclude that S is an equivalence relation on C{0}.

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