Rosie is 6 years older than Mia. In 4 years, Rosie will be three times Mia's present age. How old is Mia now?

Answer: 37.68 feet

Step-by-step explanation:

Circumference = 2 x π x r

Plug in values:

C = 2 x 3.14 x 6

C = 12 x 3.14

C = 37.68

The circumference is 37.68 feet

Hope this helps!

Answer: 3x3x3x3+3x3

Step-by-step explanation:

The domain and range of C are:
Domain of C: {c, j, e}
Range of C: {h, j, c, a}

The domain and range of a relation C are the set of all x-values and y-values in the ordered pairs of C. The domain of C is the set of all x-values, and the range of C is the set of all y-values. We can find the domain and range of C by looking at the ordered pairs in C={(c,h),(j,j),(j,c),(e,a)}.

The domain of C is {c, j, e} because these are the x-values in the ordered pairs. The range of C is {h, j, c, a} because these are the y-values in the ordered pairs.

Therefore, the domain and range of C are:
Domain of C: {c, j, e}
Range of C: {h, j, c, a}

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The mathematical model for constant of proportionality is given:

1. y = k/x2
2. h = k/s1/2
3. F = kr2/g
4. R = k(T - Te)
5. F = k(m1*m2) / r2

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The dimensions that would produce the maximum enclosed area are 350ft x 350ft, which will cut off 3 equal size rectangle regions in the yard.

To understand why this is the case, let's consider the problem step-by-step. If Alex wants to cut off three equal size rectangle regions in the yard, he will need to divide the lawn into four equal size rectangles. Let's call the dimensions of two of these rectangles "x" and "y".

To maximize the enclosed area, we want to maximize the area of the lawn that is left over after the three rectangles are cut out. This area can be represented by the equation A = (350-x)(350-y). We know that the total length of the piping is 1400 ft, so the perimeter of the enclosed area (the sum of all four sides) is 1400 ft. This means that 2x + 2y + 1400 = 1400, or 2x + 2y = 0.

Solving for y, we get y = -x + 700. Substituting this equation into the area equation, we get A = (350-x)(350-(-x+700)), which simplifies to A = x(350-x). To find the maximum area, we can take the derivative of this equation with respect to x, set it equal to 0, and solve for x. Doing this, we find that x = 175, which means that y = 525 - x = 350. Therefore, the dimensions that would produce the maximum enclosed area are 350ft x 350ft.

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We can plot these points on the graph and draw a straight line passing through them to represent the line 3y-4x=12.

What is graph ?

Graphs are visual representations of data or mathematical functions that are used to help people understand and analyze the relationships between different variables. Graphs can be used to show patterns, trends, and relationships in data that might be difficult to see from a table or list of numbers.

To draw the line 3y-4x=12 on the graph, we can solve for y and plot several points for different values of x, then connect the points with a straight line.

When x = -3:

3y - 4(-3) = 12

3y + 12 = 12

3y = 0

y = 0

So one point on the line is (-3, 0).

When x = 0:

3y - 4(0) = 12

3y = 12

y = 4

So another point on the line is (0, 4).

We can plot these points on the graph and draw a straight line passing through them to represent the line 3y-4x=12. The graph should look like this:

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The function that is increasing at a faster rate, given the graph shown, is D. g ( x ) increases at a faster rate.

You can find which function is increasing faster by looking at the steepness of the line.

When the slope of a line is positive, it means that as we move from left to right along the line, the y-coordinate of a point on the line increases. This indicates that the line is moving upward and becoming steeper. The steeper the line, the larger the magnitude of the slope.

g ( x ) was more steep in the interval [ 0, 1 ] and so was increasing at a faster rate.

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The angle o lies in quadrant IV because sin 0 < 0 and cot 0 > 0. The question is a bit unclear and has multiple parts, so I will answer each part separately.

Part 1: Find the exact value of each of the remaining trigonometric functions of e.

sin 0 = 3/5
cos 0 = 4/5
tan 0 = 3/4
csc 0 = 5/3
sec 0 = 5/4
cot 0 = 4/3

Part 2: Find the lengths and area A.

The length of the arc is 80 * (15/360) = 3.333 yards.
The area of the sector is (80^2 * (15/360))/2 = 266.667 square yards.

Part 3: Find the distance from A to C across the gorge illustrated in the figure.

The distance from A to C is sqrt(170^2 + 170^2) = 240.42 feet.

Part 4: Name the quadrant in which the angle o lies.

The angle o lies in quadrant IV because sin 0 < 0 and cot 0 > 0.

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Answer:

2

Step-by-step explanation:

The fraction of the whole cake they eat is 1/10

A fraction represents the parts of a whole or collection of objects e.g. 3/4 shows that out of 4 equal parts, we are referring to 3 parts.

From the question, we have the following information:

Left over = 1/2

Fraction of left over cake eaten = 1/5

Using the above as a guide, we have the following:

Fraction eaten = 1/2 * 1/5

Evaluate

Fraction eaten = 1/10

Therefore, the fraction is 1/10

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Answer: To calculate the prevalence of chronic pain in the United States in 2019, we need to divide the number of people reporting living with chronic pain by the total population and then multiply by 100 to express the result as a percentage. We can then also express the prevalence as a number of cases per 100,000 people.

Prevalence of chronic pain = (Number of people with chronic pain / Total population) x 100

Prevalence of chronic pain = (50,200,000 / 328,239,523) x 100

Prevalence of chronic pain = 15.29%

Therefore, the prevalence of chronic pain in the United States in 2019 was 15.29%. This can also be expressed as 15,290 cases per 100,000 people.

Step-by-step explanation:

You will be able to pull out $30,956.52 each month if you want to make withdrawals for 25 years with $300,000 saved for retirement and 10% interest.

To find out how much you will be able to pull out each month if you want to make withdrawals for 25 years with $300,000 saved for retirement and 10% interest, we can use the formula:

Monthly withdrawal = (Starting balance * Interest rate) / (1 - (1 + Interest rate)^(-Number of withdrawals))

In this case, the starting balance is $300,000, the interest rate is 10% or 0.10, and the number of withdrawals is 25 years * 12 months = 300 withdrawals.

Plugging in the numbers, we get:

Monthly withdrawal = ($300,000 * 0.10) / (1 - (1 + 0.10)^(-300))

Monthly withdrawal = $30,000 / (1 - 0.031)

Monthly withdrawal = $30,000 / 0.969

Monthly withdrawal = $30,956.52

Therefore, you will be able to pull out $30,956.52 each month if you want to make withdrawals for 25 years with $300,000 saved for retirement and 10% interest.

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The length of AC would be 9.6 units.

What is the basic proportionality theorem?

The basic proportionality theorem (also known as the "Thales' theorem") is a fundamental theorem in geometry that states that if a line is drawn parallel to one side of a triangle, then it divides the other two sides proportionally. In other words, if a line intersects two sides of a triangle and is parallel to the third side, then the ratio of the lengths of the two segments formed on one of the sides is equal to the ratio of the lengths of the other two sides.

In the given figure, we can apply the basic proportionality theorem

AB/BD = AC/CE
8/10 = AC/12
4/5 = AC/12
AC = 48/5
AC = 9.6 units

Hence, the length of AC would be 9.6 units.

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1. Surface area of the pyramid  is 24.36 [tex]ft^2[/tex]

2. Surface area is 259.2 [tex]in^2[/tex]

3. Surface area is 912 [tex]m^2[/tex]

4. Surface area is 1226.08 [tex]yd^2[/tex]

5. Surface area is 204 [tex]ft^2[/tex]

6. Surface area is 67.49 [tex]ft^2[/tex]

7. Surface area is 334.2 [tex]in^2[/tex]

8. Total surface area of the pyramid is 300  [tex]m^2[/tex]

9. Total surface area of the pyramid is 257.43 [tex]yd^2[/tex]

10. Total surface area of the pyramid is 80 [tex]ft^2[/tex]

11. Total surface area is 77.96 ft²

12. Total surface area is 292.55 ft²

13. Total surface area is 429 in²

14. Total surface area is 129 m²

15. Total surface area is 1256.4 yd²

1. The following formula is used to get the surface area of a pyramid having a triangle base:

Surface area = (1/2)P x s + B

where

P is the perimeter of the base,

s is the slant height, and

B is the area of the base.

By using the given values, we have:

B = (1/2) x b x h = (1/2) x 4 x 2 = 4 [tex]ft^2[/tex]

s = [tex]\sqrt{(1/2\times4)^2 + 2^2)} = \sqrt{17}[/tex] ft

P = 12 ft

Surface area = (1/2) x 12 x [tex]\sqrt{17}[/tex]+ 4 = 24.36 [tex]ft^2[/tex]

2.The following formula is used to get the surface area of a pyramid having a square base:

Surface area = (1/2)P x s + B

By using the given values, we have:

B = [tex]s^2 = 12^2 = 144 \:in^2[/tex]

s = [tex]sqrt{(1/2\times16)^2 + 12^2}[/tex] = 14.4 in

P = 16 in

Surface area = (1/2) 1614.4 + 144 = 259.2 [tex]in^2[/tex]

3. By using the same formula as above, we have:

B = [tex]s^2 = 12^2 = 144\: m^2[/tex]

s =[tex]\sqrt{(1/2\times48)^2 + 12^2}[/tex] = 24 m

P = 48 m

Surface area = (1/2)4824 + 144 = 912 [tex]m^2[/tex]

4. By using the same formula as above, we have:

B = (1/2) x b x h = 90 [tex]yd^2[/tex]

s = [tex]\sqrt{(1/2*15)^2 + 12^2} = \sqrt{369}[/tex]  yd

P = 45 yd

Surface area = (1/2)45 [tex]\sqrt{369}[/tex] + 90 = 1226.08 [tex]yd^2[/tex]

5. By using the same formula as above, we have:

B = [tex]s^2 = 6^2 = 36 ft^2[/tex]

s = [tex]\sqrt{(1/2\times24)^2 + 6^2}[/tex]= 12 ft

P = 24 ft

Surface area = (1/2)2412 + 36 = 204 [tex]ft^2[/tex]

6. By Using the same formula as problem 1, we have:

B = (1/2) x b x h  = 10 [tex]ft^2[/tex]

s = [tex]\sqrt{(1/2\times5)^2 + 4^2} = \sqrt{41}[/tex] ft

P = 15 ft

Surface area = (1/2) 15 [tex]\sqrt{41}[/tex] + 10 = 67.49 [tex]ft^2[/tex]

7. By using the same formula as problem 2, we have:

B = [tex]s^2 = 121 in^2[/tex]

s =[tex]\sqrt{(1/2\times16)^2 + 11^2} = \sqrt{185}[/tex] in

P = 16 in

Surface area = (1/2) x 16 x [tex]\sqrt{185}[/tex] + 121 = 334.2 [tex]in^2[/tex]

8. The pyramid's base is a square with long sides. b = 10 m,

so the area of the base is A = [tex]b^2[/tex] = 100  [tex]m^2[/tex]

The lateral area of the pyramid is L = 4 × (1/2 × s × P/4) = 5P [tex]m^2[/tex]

Substituting the given values, we get L = 5 × 40 = 200  [tex]m^2[/tex]

So, the total surface area of the pyramid is then

A + L = 100 + 200 = 300  [tex]m^2[/tex]

9. A side-length equilateral triangle forms the pyramid's base.b = 15 yds,

so the area of the base is

A = ([tex]\sqrt(3)[/tex]/4) × [tex]b^2[/tex] = 97.43 [tex]yd^2[/tex]

The lateral area of the pyramid is L = (1/2 × s × P/3) × h = 160 [tex]yd^2[/tex]

The total surface area of the pyramid is then

A + L = 97.43 + 160 = 257.43 [tex]yd^2[/tex]

10. The base of the pyramid is a square with sides of length

b = P/4 = 16 ft/4 = 4 ft,

A = [tex]b^2[/tex] = 16 [tex]ft^2[/tex]

L = 4 × (1/2 × s × P/4) = 64 [tex]ft^2[/tex]

The total surface area of the pyramid

A + L = 16 + 64 = 80 [tex]ft^2[/tex]

11. The surface area may be computed as follows since the base is square and has sides that are each 5 feet long:

Area of each triangular face = (1/2) x s x h = (1/2) x 7 x 3.64 = 12.74 ft²

Area of the square base = b² = 5² = 25 ft²

Total surface area = 4 x (12.74) + 25 = 77.96 ft²

12. Calculate the length of the altitude by using the Pythagorean theorem:

a² + b² = c², where a = 8 ft,

b = (1/2) x b = (1/2) x 15 ft = 7.5 ft, c = h = unknown height

8² + 7.5² = c²

c ≈ 11.18 ft

Then, we can calculate the surface area as:

Area of each triangular face = (1/2) x b x h  = 83.85 ft²

Area of the triangular base = (1/2) x b x h= 60 ft²

Total surface area = 3 x (83.85) + 60 = 292.55 ft²

13. Surface area can be calculated as:

Area of each triangular face = (1/2) x s x h = 55 in²

Area of the square base = b² = 13² = 169 in²

Total surface area = 4 x (55) + 169 = 429 in²

14. The surface area can be calculated as:

Area of each triangular face = (1/2) x s x h = (1/2) x 8 x 5 = 20 m²

Area of the square base = b² = 7² = 49 m²

Total surface area = 4 x (20) + 49 = 129 m²

15. By using the Pythagorean theorem:

a² + b² = c², where a = 25 yds, b = (1/2) x b = (1/2) x 9 yds = 4.5 yds, c = h = unknown height

25² + 4.5² = c²

c ≈ 25.42 yds

Then, we can calculate the surface area as:

Area of each triangular face = (1/2) x b x h = 381.3 yd²

Area of the triangular base = (1/2) x b x h =112.5 yd²

Total surface area = 3 x (381.3) + 112.5 = 1256.4 yd²

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To find the rational roots of the equation x^(4)-4x^(3)-5x^(2)+16x+4=0, we can use the Rational Roots Test. This test states that any rational root of the equation can be expressed as p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

In this case, the constant term is 4 and the leading coefficient is 1. The factors of 4 are 1, 2, and 4, and the factors of 1 are 1. Therefore, the possible rational roots are 1, 2, 4, -1, -2, and -4.

We can use synthetic division to test each of these possible roots. If the remainder is 0, then the root is a rational root of the equation. For example, let's test the root 1:

1 | 1 -4 -5 16 4
 |   1 -3 12 28
 ---------------
 | 1 -3 -8 28 32

The remainder is 32, which is not 0, so 1 is not a rational root of the equation.

We can continue to test the other possible roots in the same way until we find the rational roots of the equation. Once we have found the rational roots, we can use them to factor the equation and find the remaining roots.

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For matrix g : \(\displaystyle g^{-1}=\frac{1}{\left| g \right|}\left[\begin{array}{ccc}6 & 1 & -3 \\ -8 & -3 & 2 \\ 3 & -1 & -3\end{array}\right] \)
For matrix h : \(\displaystyle h^{-1}=\frac{1}{\left| h \right|}\left[\begin{array}{ccc}1 & 0 & -1 \\ 1 & -1 & 1 \\ 0 & 1 & -1\end{array}\right] \)

For matrix g, the inverse can be found using the following equation:

\(\displaystyle g^{-1}=\frac{1}{\left| g \right|}\left[\begin{array}{ccc}6 & 1 & -3 \\ -8 & -3 & 2 \\ 3 & -1 & -3\end{array}\right] \)



For matrix h, the inverse can be found using the following equation:

\(\displaystyle h^{-1}=\frac{1}{\left| h \right|}\left[\begin{array}{ccc}1 & 0 & -1 \\ 1 & -1 & 1 \\ 0 & 1 & -1\end{array}\right] \)



Where \(\left| g \right|\) is the determinant of the matrix g and \(\left| h \right|\) is the determinant of the matrix h.

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The farmer knows that the 5 camp division is an easier practical solution than the 9 camp division because it does not require dealing with fractions or decimals.

Both fractions and decimals are just two ways to represent numbers. Fractions are written in the form of p/q, where q≠0, while in decimals, the whole number part and fractional part are connected through a decimal point.

To understand why the 5 camp division is an easier practical solution than the 9 camp division, we need to consider the common factors of 8,085 and the numbers 9 and 15.

The prime factorization of 8,085 is:

8,085 = 3 x 3 x 3 x 5 x 5 x 6

The prime factorization of 9 is:

9 = 3 x 3

The prime factorization of 15 is:

15 = 3 x 5

From the prime factorizations, we can see that 9 has a common factor of 3 with 8,085, while 15 has two common factors of 3 and 5 with 8,085. This means that dividing 8,085 into 9 or 15 camps of equal size would require dealing with fractions or decimals, which can be impractical in a farming context.

On the other hand, the prime factorization of 5 is:

5 = 5

Since 5 is a prime number, it does not have any common factors with 8,085. This means that dividing 8,085 into 5 camps of equal size would not require dealing with fractions or decimals. The farmer can simply divide the grazing land into 5 equal parts, each with an area of 1,617 hectares, without needing to perform any division calculations or deal with any fractions or decimals.

Therefore, the farmer knows that the 5 camp division is an easier practical solution than the 9 camp division because it does not require dealing with fractions or decimals.

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The minimum total cost for the gas station to store, ship, and purchase 22,032 gallons of diesel for one year is $199,152.87.

The gas station has a steady annual demand for 22,032 gallons of diesel. The cost to store 1 gallon for 1 year is $9, the cost to ship each order of diesel is $34, and the cost to purchase each gallon is $19. To calculate the total cost of storing, shipping, and purchasing the diesel for one year, we can use the following formula:

Total cost = (storage cost per gallon x annual demand) + (shipping cost per order x number of orders) + (purchase cost per gallon x annual demand)

To find the number of orders, we can divide the annual demand by the number of gallons per order. In this case, the number of gallons per order is not given, so we will use the variable "x" to represent it:

Number of orders = 22,032 / x

Plugging this back into the formula, we get:

Total cost = (9 x 22,032) + (34 x 22,032 / x) + (19 x 22,032)

Simplifying, we get:

Total cost = 198,288 + (748,288 / x)

To minimize the total cost, we can take the derivative of the total cost with respect to x and set it equal to zero:

d(Total cost) / dx = -748,288 / x^2 = 0

Solving for x, we get:

x = sqrt(748,288 / 0) = 865.12

Therefore, the gas station should order 865.12 gallons of diesel per order to minimize the total cost. The minimum total cost is:

Total cost = 198,288 + (748,288 / 865.12) = $198,288 + $864.87 = $199,152.87

The minimum total cost for the gas station to store, ship, and purchase 22,032 gallons of diesel for one year is $199,152.87.

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Expressions A, B, and F are equivalent to (a²-16(a+4)).

Equivalent is a term that means equal in value, measure, force, effect, or significance. It can be used to describe two or more things that are of the same value or having the same characteristics. For example, a 1:1 ratio is said to be equivalent because it has the same value on both sides. Equivalent can also mean having the same or similar effect, such as two different treatments for a disease that have the same outcome.

The expressions A, B, and F are equivalent to (a²-16(a+4)). Expression A is equal to a² - 16a - 64. This expression can be rewritten as a³ - 64, which is equal to A. Expression B is equal to (a - 4)³. This expression can be rewritten as a³ - 64, which is equal to A. Expression F is equal to [(a)²-(4^2)](a+4). This expression can be rewritten as (a² - 16)(a+4), which is equal to A. Therefore, expressions A, B, and F are equivalent to (a²-16(a+4)).

Expression C is equal to (a+4)³, which is not equivalent to (a²-16(a+4)). Expression D is equal to (a+4)²(a-4), which is not equivalent to (a²-16(a+4)). Expression E is equal to (a-4)²(a+4), which is not equivalent to (a²-16(a+4)). Expression G is equal to(a-4)(a+4)(a+4), which is not equivalent to (a²-16(a+4)). Therefore, expressions C, D, E, and G are not equivalent to (a²-16(a+4)).

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Answer: X':(2,2) Y':(4,4) Z":(6,0)

The division of these expressions "(-18xu+9x^(7)u^(5)+24x^(7)u^(4))-:(3x^(3)u^(2))" gives the simplified expression "3x^(4)u^(3) + 8x^(4)u^(2) - 6/(x^(2)u)":

To simplify the given expression, we need to divide each term by the divisor 3x^(3)u^(2):(-18xu)/(3x^(3)u^(2)) + (9x^(7)u^(5))/(3x^(3)u^(2)) + (24x^(7)u^(4))/(3x^(3)u^(2))

Simplifying each term by canceling out common factors gives us:

-6/(x^(2)u) + 3x^(4)u^(3) + 8x^(4)u^(2)

Combining like terms gives us the final simplified expression:

3x^(4)u^(3) + 8x^(4)u^(2) - 6/(x^(2)u).

Therefore, the simplified expression is 3x^(4)u^(3) + 8x^(4)u^(2) - 6/(x^(2)u).

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The ball is falling at 130 feet per second after 10.9375 seconds.

The height of the ball launched in the air t seconds after it is launched is given by the equation F(t) = 16t^2 – 220t + 19. We need to find the time t when the ball is falling at 130 feet per second. To do this, we need to find the derivative of the function F(t) with respect to time t, which represents the velocity of the ball at any given time t.

The derivative of F(t) with respect to t is F'(t) = 32t - 220. We can set this equal to 130 to find the time when the ball is falling at 130 feet per second:

32t - 220 = 130

32t = 350

t = 350/32

t = 10.9375 seconds

Therefore, the ball is falling at 130 feet per second after 10.9375 seconds.

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The 9th term of the geometric sequence 3, -15, 75, ... is 1171875.

The given sequence is 3, -15, 75, ... We can see that each term is obtained by multiplying the previous term by -5. Therefore, the common ratio is -5.

We can use the formula for the nth term of a geometric sequence to find the 9th term. The formula is given by:

aₙ = a₁ x rⁿ⁻¹

where,

aₙ = nth term of the sequence

a₁ = first term of the sequence

r = common ratio of the sequence

n = index of the term we want to find

Using the given sequence, we have:

a₁ = 3 (first term)

r = -5 (common ratio)

To find the 9th term, we substitute n=9 into the formula:

a₉ = a₁ x r⁹⁻¹

a₉ = 3 x (-5)⁸

a₉ = 3 x 390625

a₉ = 1171875

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The expression x^(2)((1)/(8)x^(3))(40x^(-12)) equals (5/8)/(x^(7)) where the coefficient c is 5/8 and the exponent e is -7.

The expression x^(2)((1)/(8)x^(3))(40x^(-12)) can be simplified by combining the coefficients and adding the exponents of the same base.

First, we'll combine the coefficients:

(1)(1/8)(40) = 5/8

Next, we'll add the exponents of the same base:

2 + 3 + (-12) = -7

So the simplified expression is:

(5/8)x^(-7)

Now we can see that the coefficient c is 5/8 and the exponent e is -7.

So the answer is:

The expression x^(2)((1)/(8)x^(3))(40x^(-12)) equals (5/8)/(x^(7)) where the coefficient c is 5/8 and the exponent e is -7.

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The expression that represents the total travel time is 16x − 8

To add polynomial expressions we need to add or subtract like terms and constant terms.

In the given problem to find the total travel time we need to add the time takes to travel to work and the time takes to travel from work to home.  

Here we have

The expression represents the time takes to travel to work = 5x − 7

The expression represents the time takes to travel from work = 11x – 1

The total travel time =  5x − 7 + 11x – 1  

=> 5x + 11x  − 7 – 1  

=> 16x − 8  

Therefore,

The expression that represents the total travel time is 16x − 8  

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The equation of the line passing through (2/7,7/3) and having idenfinite slope is x = 2/7.

A straight line is a geometric figure that extends infinitely in both directions.

The point slope formula is:

y - y₁ = m(x - x₁)

Where m is the slope of the line, and (x₁, y₁) is a point on the line.

In this case, the slope of the line is undefined, which means that the line is a vertical line. Therefore, the equation of the line is x = 2/7, and there is no slope-intercept form of the equation.

So, the answer is: The equation of the line is x = 2/7.

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Answer:

It should be three units

Step-by-step explanation:

Answer:

3 units. .

Step-by-step explanation:

0,1,2,3 not counting your starting number

To prove that the functions f(x)= (2)/(3)x-8 and g(x)=(3)/(2)x+12 are inverses, we can use composition of functions. We can do this by setting f(g(x)) = x and g(f(x)) = x and showing that they are equivalent.

First, let's look at f(g(x)). We can substitute g(x) into the equation for f(x), so we have: f(g(x)) = (2)/(3)((3)/(2)x+12)-8. Simplifying, we have: f(g(x)) = (4x+48)/6 - 8. Distributing the 4 and rearranging, we have: f(g(x)) = x.

Now let's look at g(f(x)). We can substitute f(x) into the equation for g(x), so we have: g(f(x)) = (3)/(2)((2)/(3)x-8)+12. Simplifying, we have: g(f(x)) = (2x-32)/3 + 12. Distributing the 2 and rearranging, we have: g(f(x)) = x.

Therefore, we have shown that f(g(x)) = x and g(f(x)) = x, which means that f(x) and g(x) are inverses of each other.

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The combination that is produced contains 57.5% corn.. It is calculated by taking the weighted average of the corn content in the two bags, accounting for their respective weights.

(50% x 20 lbs) + (65% x 30 lbs)

= 1750 lbs + 1950 lbs

= 3700 lbs

3700 lbs/50 lbs

= 57.5%

The concentration of corn in the resulting mixture is 57.5%. This is calculated by taking the weighted average of the corn content in the two bags. The first bag, containing 20 pounds of calf starter mix, contains 50% corn. The second bag, containing 30 pounds, contains 65% corn. To calculate the concentration of corn in the mixture, the percentage of corn in each bag is multiplied by its respective weight, and the sums of these two products are then divided by the sum of the two weights. In this case, (50% x 20 lbs) + (65% x 30 lbs) = 1750 lbs + 1950 lbs = 3700 lbs. The resulting concentration of corn in the mixture is 3700 lbs/50 lbs = 57.5%.

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