Part A: In complete sentences, explain the relationships between all pairs of special angles 1, 2, 3, and 4 created by transversal line b and parallel lines d and e.

The probability that of 6 randomly selected patients, 4 will recover is 0.03295

The chance of an event occurring is defined by probability.

Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1. Additionally, the proportion of positive outcomes cannot be negative.

The ratio of good outcomes to all possible outcomes of an event is known as the probability.

Let X represent the binomial random variable that represents the patient count. Let p represent the likelihood that the patient will survive, and q represent the probability that they will pass away. The solution to the problem is q = 75% = 0.75, p = 25% = 0.25, and n = 6.

Required probability = 6C4[tex](0.25)^{4} (0.75)^{2}[/tex]

                                = 0.03295

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Based on the calculations, the interest rate on the stock in four (4) years is equal to 7.1%.

Given the following data:

Amount borrowed (Principal) = $22,000.

Simple interest, I = $78.40.

Time = 4 year.

To determine the interest rate on the stock in four (4) years:

Mathematically, simple interest can be calculated by using this formula:

I = PRT

Where:

Making R the subject of formula, we have:

R = I/PT

Substituting the given parameters into the formula, we have;

R = 6260/(22,000 × 4)

R = 6260/(88,000)

Interest rate = 0.071 = 7.1%.

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Answer:

Step-by-step explanation:

Begin by filling in x as -2 and y as √12 in the given expression:

[tex]2(3(-2)^3+2(\sqrt{12})^2)[/tex].  Work inside the parenthesis first and deal with those exponents:

(-2)³ is the same as (-2)(-2)(-2) which is -8;

(√12)² is the same as (√12)(√12) which is √144 which is 12.

Filling those simplifications in:

[tex]2(3(-8)+2(12))=2(-24+24)=2(0)=0[/tex]

[tex]\begin{cases} -5x+y=-3\\ 3x-8y=24 \end{cases} \\\\\\ \stackrel{\textit{using the 1st equation}}{-5x+y=-3}\implies \underline{y=-3+5x} \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{3x-8(\underset{y}{-3+5x})=24}\implies 3x+24-40x=24\implies 3x-40x=0 \\\\\\ -37x=0\implies \boxed{x=0}~\hfill \underline{y=-3+5(\stackrel{x}{0})}\implies \boxed{y=-3} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (0~~,~~-3)~\hfill[/tex]

Answer:

( 0, -3 )

Step-by-step explanation:

-5x + y = -3 ⇒ ( 1 )

3x - 8y = 24 ⇒ ( 2 )

We can make y the subject of equation 1.

y = 5x - 3 ⇒ ( 3 )

Now let us take equation 2.

Here we can replace y with ( 5x - 3 ) to find the value of x.

Value of x.

3x - 8y = 24

3x - 8 (5x - 3) = 24

3x - 40x + 24 = 24

-37x = 0

x = 0

Now let us take equation 3 to find the value of y.

Here we can replace x with 0.

Let us find it now.

y = 5x - 3

y = 5 × 0 - 3

y = 0 - 3

y = -3

Now, let us write the answer as an ordered pair.

( x, y )

( 0, -3 )

Answer:

y = 2x² − 12x + 8

Step-by-step explanation:

FIRST METHOD :

y = 2x² − 12x + 8

  = (2x² − 12x) + 8

  = 2 (x² − 6x) + 8

  = 2 (x² − 6x + 9 − 9 ) + 8

  = 2 (x² − 6x + 9) − 2×9 + 8

  = 2 (x² − 6x + 9) − 18 + 8

  = 2 (x² − 6x + 9) − 10

  = 2 (x − 3)² − 10

Then ,the equation has a extremum value of (3,-10)

Since the number 2 in the equation y = = 2 (x − 3)² − 10 is greater than 0

(2 > 0) , the graph (parabola) opens upward

Therefore ,the extremum (3,-10) is a minimum.

SECOND METHOD :

the graph of a function of the form f(x) = ax² + bx + c

has an extremum at the point :

[tex]\left( -\frac{b}{2a} ,f\left( -\frac{b}{2a} \right) \right)[/tex]

in the equation : f(x) = 2x² − 12x + 8

a = 2  ; b = -12  ; c = 8

Then

[tex]-\frac{b}{2a} = -\frac{-12}{2 \times 2} = 3[/tex]

Then

[tex]f\left( -\frac{b}{2a} \right) = f(3) = 2(3)^2- 12(3) + 8 = 18 - 36 + 8 = -18 + 8 = -10[/tex]

the graph of a function f(x) = 2x² − 12x + 8

has an extremum at the point (3 , -10)

Since the parabola opens up ,then the extremum (3,-10) is a minimum.

Based on the given entries that Jonathan Shaw owes and owns, the Balance Sheet can be drawn below.

The assets will go to the right side of the sheet and the liabilities and equity will go to the left.

                                            Jon's Shop of Gifts Balance Sheet

Assets                                                                                          Liabilities

Cash                                    $2,556           Bank loan                    $19,000

Accounts Receivable:         $450             Accounts Payable -           $900

R. Gregory                                                 Ceramic supply

Accounts Receivable:         $1,860          Accounts Payable -           $2,900

R. Gregory                                                 Jose's Art Co.

Supplies                               $1,000         Total liabilities                 $22,800

Furniture                              $10,300       Equity

Equipment                           $20,000       Jonathan Shaw capital  $51,166

Automobiles                       $37,800         Total equity                   $51,166

Total assets                       $73,966        Total liabilities and          $73,966

                                                                  equity

The equity can be found as:

= Assets - liabilities

= 73,966 - 22,800

= $51,166

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Steve's expected win from the lottery ticket purchase is $3 because his chance of winning the $300 prize is only 1%.

The expected winnings for Steve are a function of the probability of some predictable outcomes.

In this situation, the predictable outcome is the size of the lottery prize.

The probability that Steve will win the prize is 1% (1/100), depicting his chance of winning.

Sale price per ticket = $5

Lottery prize = $300

Value of lottery prize to Steve if he wins = $295 ($300 - $5)

Probability of winning = 1% (1/100 x 100)

Expected win = $3 ($300 x 1%)

Thus, Steve's expected win is $3, which outweighs the cost of a ticket.

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Answer:

16

Step-by-step explanation:

18,903

Step-by-step explanation:

It is just where it crosses the x axis

6) -3, -4

7) 1, -6

8) -5, -6

9) 3, -2.5

The expression representing the given statement is 7×(6+3)-(4÷2). Option A is correct.

Given the statement is Multiply 7 by the sum of 6 and 3, and then subtract the quotient of 4 and 2.

Firstly, we will break the statement in two parts that is Multiply 7 by the sum of 6 and 3 and second part is subtract the quotient of 4 and 2.

Multiply 7 by the sum of 6 and 3 means there is addition sign between 6 and 3 and the addition of 6 and 3 is multiply with 7, we get

7×(6+3)    ......(1)

subtract the quotient of 4 and 2 means 4 is divisible by 2 and this is subtract means there is a minus sign, we get

-(4÷2)   .....(2)

Combine equation (1) and (2), we get

7×(6+3)-(4÷2)

Hence, the expression which represents the given statement Multiply 7 by the sum of 6 and 3, and then subtract the quotient of 4 and 2 is 7×(6+3)-(4÷2).

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The average rate of change obtained from the ratio of change in y to the change in x is 27

The average rate of change can be obtained using the relation :

Rate of change = (y2 - y1) ÷ (x2 - x1)

at; x1 = -3

y1 can be calculated from the function ;

y1= 3(-3³)-1

y1=-82

At ; x2 = 3

y2 can be calculated from the function ;

y2 = 3(3³)-1

y2=80

The rate of change can be calculated thus : (y2 - y1) ÷ (x2 - x1)

[80-(-82)]/[3-(-6])

162/6

27

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Answer:

d ≈ 21.26 units

Step-by-step explanation:

calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (- 3, 8 ) and (x₂, y₂ ) = (13 - 6 )

d = [tex]\sqrt{13-(-3))^2+(-6-8)^2}[/tex]

   = [tex]\sqrt{(13+3)^2+(-14)^2}[/tex]

   = [tex]\sqrt{16^2+196}[/tex]

   = [tex]\sqrt{256+196}[/tex]

   = [tex]\sqrt{452}[/tex]

   ≈ 21.26 units ( to 2 dec. places )

Answer:

The distance is 21.3

Step-by-step explanation:

The solution is in the attached image

Answer:

Step-by-step explanation:

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Heat Factors are determined by the location-specific average daily high and low temperatures during the warmest month of the year.

According to thermodynamics, heat is a type of energy that crosses a thermodynamic system's border due to a temperature differential across the barrier. In a thermodynamic system, heat is not present.

But the phrase is also frequently used when referring to the thermal energy that makes up a system's internal energy and is reflected in the system's temperature. Heat is a type of energy in both senses of the word. Heat Factors are determined by the location-specific average daily high and low temperatures during the warmest month of the year.

Therefore, heat Factors are determined by the location-specific average daily high and low temperatures during the warmest month of the year.

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Using the triangle midsegment theorem, the length of AC in the given triangle is: 40 units.

The midsegment of a triangle can be defined as the line segment that intersects two sides of a triangle at their midpoints. This means that, the sides they intersect is bisected forming two equal halves.

In a typical triangle, there are three midsegments in the triangle. For example, in the image given in the attachment below, the midsegments of the triangle are: DF, FB, and BD. All midsegments are parallel to the third sides of a triangle.

What is the Triangle Midsegment Theorem?

According to the triangle midsegment theorem, the length of the midsegment (i,e. DF) is parallel to the third side (i.e. AC) and also half the length of the third side (AC).

We are given the following:

EC = 30

DF = 20

Applying the triangle midsegment theorem, we have:

DF = 1/2(AC)

Substitute

20 = 1/2(AC)

2(20) = AC

40 = AC

AC = 40 units.

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The given triangle has three angles with measurements: ∠A = 69°, ∠B = 52°, and ∠C = 59° respectively. Using the law of cosines, these angles are calculated from the given lengths of the triangle.

The law of cosines gives the relationship between the lengths of sides and the angles of the triangle ABC.

According to the law of cosines:

Cos A = (b² + c² - a²)/2bc

Cos B = (a² + c² - b²)/2ac

Cos C = (a² + b² - c²)/2ab

For the given triangle ABC,

a = 75, b = 63, and c = 69

So, using the law of cosines,

Cos A = (b² + c² - a²)/2bc

⇒ Cos A = (63² + 69² - 75²)/2×63×69

⇒ Cos A = 5/14

⇒ A = Cos⁻¹(5/14) = 69.07

∴ ∠A = 69°

Similarly,

Cos B = (a² + c² - b²)/2ac

⇒ Cos B = (75² + 69² - 63²)/2×75×69

⇒ Cos B = 31/50

⇒ B = Cos⁻¹(31/50) = 51.6 ≅ 52

∴ ∠B = 52°

Cos C = (a² + b² - c²)/2ab

⇒ Cos C = (75² + 63² - 69²)/2×75×63

⇒ Cos C = 179/350

⇒ C = Cos⁻¹(179/350) = 59.2

∴ C = 59°

Thus, the angles of the triangle ABC are 69°, 52°, and 59° respectively.

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a) The polynomial f(x) in expanded form is f(x) = x³ + 10 · x² - 20 · x - 24.

b) The rational function g(x) in factored form is g(x) = [(x - 6) · (x + 3)] / (x - 2). there is no slant asymptotes.

c) There is one evitable discontinuity at x = - 1, and one definitive discontinuity at x = 2, where there is a vertical asymptote.

a) In the first part of this question we need to determine the equation of a polynomial in expanded form, derived from its factor form defined below:

f(x) = Π (x - rₐ), for a ∈ {1, 2, 3, 4, ..., n}         (1)

Where rₐ is the a-th root of the polynomial.

If we know that r₁ = 6, r₂ = - 1 and r₃ = - 3, then the polynomial in factor form is:

f(x) = (x - 6) · (x + 1) · (x + 3)

f(x) = (x - 6) · (x² + 4 · x + 4)

f(x) = (x - 6) · x² + (x - 6) · (4 · x) + (x - 6) · 4

f(x) = x³ - 6 · x² + 4 · x² - 24 · x + 4 · x - 24

f(x) = x³ + 10 · x² - 20 · x - 24

The polynomial f(x) in expanded form is f(x) = x³ + 10 · x² - 20 · x - 24.

b) The rational function is introduced below:

g(x) = (x³ + 10 · x² - 20 · x - 24) / (x² - x - 2)

g(x) = [(x - 6) · (x + 1) · (x + 3)] / [(x - 2) · (x + 1)]

g(x) = [(x - 6) · (x + 3)] / (x - 2)

The slope of the slant asymptote is:

m = lim [g(x) / x] for x → ± ∞

m = [(x - 6) · (x + 3)] / [x · (x - 2)]

m = 1

And the intercept of the slant asymptote is:

n = lim [g(x) - m · x] for x → ± ∞

n = Non-existent

Hence, there is no slant asymptotes.

c) There is vertical asymptote at a x-point if the denominator is equal to zero. There is one evitable discontinuity at x = - 1, and one definitive discontinuity at x = 2, where there is a vertical asymptote.

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Answer:

Step-by-step explanation:

To solve this, you have to divide this fraction from left to right.

Fraction is a division or part of a whole number.

First, do apply the fraction rule.

[tex]\rightarrow: \sf{\dfrac{A}{B}\div \dfrac{C}{D}=\dfrac{A}{B}\times \dfrac{D}{C}}[/tex]

[tex]\sf{-\dfrac{1}{50}\times \dfrac{100}{1}}[/tex]

Cancel the common factor of 50.

[tex]\sf{-\dfrac{2}{1} }[/tex]

Divide.

-2/1=-2

[tex]\rightarrow: \boxed{\sf{-2}}[/tex]

So, the final answer is -2.

I hope this helps, let me know if you have any questions.

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5x-30y=-35

Divide both the side by 5 and we get

x-6y = -7

x = 6y -7

Answer:

x=-7+6y

You simply need to add 30y and then divide by 5 to isolate the variable.

Answer:

Step-by-step explanation:

find the prime factors of given numbers:

126= 2*3*3*7- this side can be cut into any number here or combination of numbers as per factors

108= 2*2*3*3*3 - same as above

As per prime factors, the squares can be of  sizes:

2×2, 3×3, 6×6, 9×9 and 18×18

The least number can be obtained with the biggest size option 18×18, this will give 7*6=42 square

[tex]\boldsymbol{\sf{6-\dfrac{3}{4}x+\dfrac{1}{3}=\dfrac{1}{y}x+5 }}[/tex]

Convert 6 to the fraction 18/3.

                       [tex]\boldsymbol{\sf{\dfrac{18}{3} -\dfrac{3}{4}x+\dfrac{1}{3}=\dfrac{1}{y}x+5 }}[/tex]

Since the fractions 18/3 and 1/3 have the same denominator, we add their numerators to calculate them.

                       [tex]\boldsymbol{\sf{\dfrac{18+1}{3}-\dfrac{3}{4}x=\dfrac{1}{2}x+5 \ \longmapsto \ \ [Add \ 18+1] }}[/tex]

                              [tex]\boldsymbol{\sf{\dfrac{19}{3}-\dfrac{3}{4}x=\dfrac{1}{2}x+5 }}[/tex]

Subtract [tex]\bf{\frac{1}{2}x }[/tex] on both sides.

                               [tex]\boldsymbol{\sf{\dfrac{19}{3}-\dfrac{3}{4}x-\dfrac{1}{2}x=5 }}[/tex]

Combine [tex]\bf{-\frac{3}{4}x}[/tex] and [tex]\bf{-\frac{1}{2}x}[/tex] to get [tex]\bf{-\frac{5}{4}x}[/tex].

                                [tex]\boldsymbol{\sf{\dfrac{19}{3}-\dfrac{5}{4}x=5 }}[/tex]

Subtract 19x from both sides.

                                       [tex]\boldsymbol{\sf{-\dfrac{5}{4}x=5-\dfrac{19}{3} }}[/tex]

Convert 5 to the fraction 15/3.

                                      [tex]\boldsymbol{\sf{-\dfrac{4}{5}x=\dfrac{15}{3}-\dfrac{19}{3} }}[/tex]

Since the fractions 15/3 and 19/3 have the same denominator, we add their numerators to calculate them.

                             [tex]\boldsymbol{\sf{-\dfrac{5}{4}x=\dfrac{15-19}{3} \ \longmapsto \ \ [Subtract \ 15-19] }}[/tex]

                                 [tex]\boldsymbol{\sf{-\dfrac{5}{4}x=-\dfrac{4}{3} }}[/tex]

Multiply both sides by -4/3, the reciprocal of -4/3.

                                    [tex]\boldsymbol{\sf{x=-\dfrac{4}{5}\left(-\dfrac{4}{5}\right) }}[/tex]

Multiply -4/3 by -4/5 (to do this, multiply the numerator by the numerator and the denominator by the denominator).

                   [tex]\boldsymbol{\sf{x=\dfrac{-4(-4)}{3\times5} \ \ \longmapsto \ \ Multiply, \ numerator \ and \ denominator. }}[/tex]

                                 [tex]\red{\boxed{\boldsymbol{\sf{\blue{Answer \ \ \longmapsto \ \ \ \ x=\frac{16}{15} }}}}}[/tex]

The closest point is (3.5, 1.9) and the distance is 1.96 units

The coordinate is given as:

(4, 0)

The equation of the function is

y = √x

The distance between two points is calculated using

d = √(x2 - x1)^2 + (y2 - y1)^2

So, we have the following points

(x1, y1) = (4, 0) and (x2, y2) = (x, 0)

This gives

d = √(x - 4)^2 + (√x - 0)^2

Evaluate the difference

d = √(x - 4)^2 + (√x)^2

Evaluate the exponent

d = √x^2 - 8x + 16 + x

Evaluate the like terms

d = √x^2 - 7x + 16

Next, we differentiate using a graphing calculator

d' = (2x - 7)/[2√(x^2 - 7x + 16)]

Set to 0

(2x - 7)/[2√(x^2 - 7x + 16)] = 0

Cross multiply

2x - 7 = 0

Add 7 to both sides

2x = 7

Divide by 2

x = 3.5

So, we have:

Substitute x = 3.5 in y = √x

y = √3.5

Evaluate

y = 1.9

So, the point is (3.5, 1.9)

The distance is then calculated as:

d = √(x2 - x1)^2 + (y2 - y1)^2

This gives

d = √(3.5 - 4)^2 + (1.9 - 0)^2

Evaluate

d = 1.96

Hence, the closest point is (3.5, 1.9) and the distance is 1.96 units

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Utilizando la distribución binomial, la probabilidad de resolver un problema de n problemas propuestos, es p^n.

La fórmula es:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Los parámetros son:

La probabilidad de que todos los problemas sean resolvidos es dada por P(X = n), asi:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = n) = C_{n,n}.p^{n}.(1-p)^{n-n}[/tex]

P(X = n) = p^n

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Answer:

f(4)=14

Step-by-step explanation:

a) u do it by substituting 4 in places where there r 'x'

since this one say f(4) it only can go to the function which says f(x)
f(x)=4x-2
f(4)=4(4)-2, so according to BODMAS rule multiplication comes first rather than subtraction

so, f(4)=16-2=14
f(4)=14
do the others based on this, hope i explained well, if i did, please gimme brainliest :)

Considering the definition of conditional probability, the probability that the team will win the second game given that they have already won the first game is 45.33%.

Probability is the greater or lesser chance that a given event will occur.

In other words, the probability establishes a relationship between the number of favorable events and the total number of possible events.

Conditional probability is the probability that a given event will occur given that another event occurs. The conditional probability operator is the │ sign.

In other words, the conditional probability is the probability of some event A , given the occurrence of some other event B and is denoted by P(A|B) and is read “the probability of A , given B ”.

Then, when an event influences the outcome of a second event, the probability of the second event is said to be a conditional probability and is calculated using the expression:

P(A|B)= P(A∩B) ÷ P(B)

where:

In this case, you know that:

Replacing in the definition of conditional probability:

P(A|B)= 0.34 ÷ 0.75

P(A|B)= 0.4533= 45.33%

Finally, the probability that the team will win the second game given that they have already won the first game is 45.33%.

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The probability of pulling a red or green card, written as a reduced fraction is 1/4

From the question, we have the following probabilities:

P(White) = 1/10

P(Pink) = 1/5

P(Green) = 1/20

P(Red) = 1/5

The probability of pulling a red or green card, written as a reduced fraction is the calculated as:

P(Red or Green card) = P(Red card) + P(Green card)

Substitute the known values in the above equation

P(Red or Green card) = 1/5 + 1/20

Express 1/5 as 4/20

P(Red or Green card) = 4/20 + 1/20

Take the LCM

P(Red or Green card) = (4+1)/20

Evaluate the sum

P(Red or Green card) = 5/20

Simplify the fraction

P(Red or Green card) = 1/4

Hence, the probability of pulling a red or green card, written as a reduced fraction is 1/4

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Answer:

Area = 32feet²

Step-by-step explanation:

Perimeter of a rectangule = 2(length+width)

Then:

g = 2w               Eq. 1

2(g+w) = 24       Eq. 2

g = length

w = width

From Eq. 2:

(2*g + 2*w) = 24

2g + 2w = 24      

2w = 24 - 2g            Eq. 3

Matching Eq. 1  and Eq. 3

g = 24 - 2g

g + 2g = 24

3g = 24

g = 24/3

g = 8 feet

From Eq. 1

g = 2w

8 = 2w

8/2 = w

w = 4 feet

Check:

From Eq. 2

2(g+w) = 24

2(8+4) = 24

2*12 = 24

Answer:

Area of a rexctangle = length * width

Then:

Area = 8feet * 4feet

Area = 32feet²

1. According to the affordability formulas given, Joe-Bob cannot afford to take out another loan.

2. Joe-Bob should follow the affordability formulas if he wants to live without financial stress caused by debts.

3. Joe-Bob may decide not to follow the affordability formula, if he can reduce his fixed monthly payments or increase his income.

4. Taking out the car loan will force Joe-Bob to increase his DTI and reduce his savings, investments, and discretionary spending.

Affordability refers to a person's financial ability to afford some fixed expenses without impacting negatively the variable expenses.

Affordability can be measured as a Debt To Income (DTI) ratio.

Current monthly income = $3,500

Monthly mortgage payment = $900

Monthly student loan payment = $350

Total monthly debt payment = $1,250

Debt To Income (DTI) = 35.7% ($1,250/$3,500 x 100)

Thus, with a DTI of 36%, Job Bob should not take out an additional car loan.

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Answer:

Simplified: 4X^3

Step-by-step explanation:

Simplify the expression.

The volume (in cubic centimeters) of a box) given the fixed base area of 6cm² and height of 6 cm is 36 cm³.

V = 6h

Where,

If the height = 6 cm

Fixed base area = 6 cm²

V = 6h

= 6 cm² × 6 cm

V = 36 cm³

Therefore, the volume of the box given the fixed base area of 6cm² and height of 6 cm is 36 cm³.

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The price at which equilibrium is achieved is $20.

The equilibrium point is the point where the lines of the demand and supply functions meet.

From the question, we understand that price is plotted on the vertical axis (i.e. the y-axis).

Also from the question, the lines intersect at point (15, 20).

The y-coordinate of the intersection point is 20 in this scenario.

Hence, the price at which equilibrium is achieved is $20.

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Answer:

b

Step-by-step explanation: