Please help due in 1 hour

The inverse of the function f(x) = 3 · x / (8 + x) is f⁻¹(x) = 8 · x / (3 - x).

In this problem we must determine the inverse of a function, this can be done by means of algebra properties. First, write the entire function:

f(x) = 3 · x / (8 + x) (Step 0)

y = 3 · x / (8 + x) (Step 1)

Second, use the following substitutions:

x → y

y → x

x = 3 · y / (8 + y) (Step 2)

Third, clear y within the expression:

x · (8 + y) = 3 · y (Step 3)

8 · x + x · y = 3 · y

8 · x = 3 · y - x · y (Step 4)

8 · x = y · (3 - x)

y = 8 · x / (3 - x)

Fourth, use final notation:

f⁻¹(x) = 8 · x / (3 - x) (Step 5)

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1) The first three terms in the expansion of [tex](2 - y)^{5}[/tex] in ascending powers of y are as follows:

32, -80y, and [tex]80y^2[/tex]

2)The [tex]x^{2}[/tex] coefficient in the expansion of (2 (2x - [tex]x^{2}[/tex]))5 is 80.

As the power increases, the expansion gets more difficult to compute. The Binomial Theorem can be used to easily calculate a binomial statement that has been raised to very big power.

(i) Using the binomial theorem, we can expand [tex](2 - y)^{5}[/tex] as follows:

[tex](2 - y)^{5}[/tex] = [tex]2^{5} - 5(24)y^{1} + 10(23)y^{2} + 10(23)y^{3} + 5(2)y^{4} - y^{5}[/tex]

By combining the powers of two and simplifying, we get:

[tex]32 - 80y + 80y^{2} - 40y^3 + 10y^4 - y^5[/tex]

As a result, the first three terms in the expansion of [tex](2 - y)^{5}[/tex] in ascending powers of y are as follows:

32, -80y, and [tex]80y^2[/tex]

(ii) Using the result of section (i), we can expand [tex](2 - (2x - x^{2} ))^{5}[/tex] by substituting y with 2x - x2:

[tex](2 - (2x - x^2))^5 = 2^5 - 5(2^4)(2x - x^2) + 10(2^3)(2x - x^2)^2 - 10(2^2)(2x - x^2)^3 + 5(2)(2x - x^2)^4 - (2x - x^2)^5[/tex]

By combining the powers of two and simplifying, we get:

[tex]32 - 80x + 80x^2 - 40x^3 + 10x^4 - x^5[/tex]

As a result, the [tex]x^{2}[/tex] coefficient in the expansion of (2 (2x - [tex]x^{2}[/tex]))5 is 80.

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Answer:

log b.c^z

Step-by-step explanation:

from the theorem a log b=log b^a

z log c= log c^z

from the theorem log a + log b= log ab

log b+ log c^z= logb. c^z will be the final answer

well, let's first find out how much is 30% of 30000

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{30\% of 30000}}{\left( \cfrac{30}{100} \right)30000}\implies 9000[/tex]

ok, that means if we split that down the middle, each will get 4500.

so the remaining is 21000, and that's split on a 3:4 ratio, assuming from A to B, so let's simply divide the total 21000 by (3 + 4) and distribute accordingly.

[tex]\stackrel{A}{3}~~ : ~~\stackrel{B}{4} ~~ \implies ~~ \stackrel{A}{3\cdot \frac{21000}{3+4}}~~ : ~~\stackrel{B}{4\cdot \frac{21000}{3+4}}\implies \stackrel{A}{3\cdot 3000}~~ : ~~\stackrel{B}{4\cdot 3000} \\\\\\ \stackrel{A}{9000}~~ : ~~\stackrel{B}{12000}\hspace{9em}\underset{ \textit{share for A} }{\stackrel{ 4500~~ + ~~9000 }{\text{\LARGE 13500}}}[/tex]

7:76 - This is not a valid time. There are only 60 minutes in an hour, so the minutes place cannot be 76.

Time is a measurable and non-spatial quantity used to describe or quantify the sequence, duration, or occurrence of events. It is a concept used to understand the order in which events occur and to measure the duration of those events.

10:44 - Yes, the statement is true. The time is 44 minutes after 10:00.

9:47 - No, the statement is false. The time is 13 minutes before 10:00.

12:13 - Yes, the statement is true. The time is 13 minutes after 12:00.

11:00 - Yes, the statement is true. The time is exactly 11:00.

7:76 - This is not a valid time. There are only 60 minutes in an hour, so the minutes place cannot be 76.

1:05 - Yes, the statement is true. The time is 5 minutes after 1:00.

5:02 - No information is provided about this time on the clock.

2:00 - Yes, the statement is true. The time is exactly 2:00.

4:00 - Yes, the statement is true. The time is exactly 4:00.

3:00 - Yes, the statement is true. The time is exactly 3:00.

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The friends from the first one who is predicted to finish her book to the third one who is predicted to finish her book is given by the order Nancy > Barbara > Judy

Given data ,

The total number of pages in each friend's book as follows:

Barbara's book: 320 pages

Judy's book: 260 pages

Nancy's book: 480 pages

Now, we can calculate their reading rates as pages read per day:

Barbara's reading rate: 100 pages / 4 days = 25 pages/day

Judy's reading rate: 54 pages / 3 days = 18 pages/day

Nancy's reading rate: 160 pages / 5 days = 32 pages/day

Hence , the descending order is Nancy > Barbara > Judy

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If the archaeologist found a fossil whose length is 489.44 inches, using the conversion table, the length in feet, to the nearest tenth, is 40.8 feet.

The conversion table refers to the tabulated standard units of measurement, showing temperature, length, area, volume, weight, and metric conversions

For instance, the conversion table shows that 12 inches equal 1 foot.

The length of the fossil = 489.44 inches

12 inches = 1 foot

489.44 inches = 40.8 feet (489.44 ÷ 12)

Thus, using the conversion table, which relies on multiplication or division operations using the conversion factors, the length in feet of the fossil is 40.8 feet.

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Step-by-step explanation:

We can use the proportion of males in the sample to estimate the proportion of males in the population, and then use that proportion to find the expected number of male workers.

The proportion of males in the sample is:

p = 28/50 = 0.56

We can use this proportion to estimate the proportion of males in the population:

p' = 0.56

The expected number of male workers is then:

E(X) = n * p'

where n is the total number of workers in the population:

E(X) = 1300 * 0.56

E(X) = 728

Therefore, we would expect there to be approximately 728 male workers in the company.

first you need to find the gradient of the line and to do that you divide the height of a part of the line by its length. so to find the height we do -3-0=-3 and to find the length we do 2-1=1. then divide -3 by 1 and the gradient is -3. so now we know the equation is y=-3x+b. to find b we replace y with the y coordinate of one of the 2 points. lets take the first point. so it will be 0=-3+b. Now we can easily find b by doing 0-(-3) which is 3. so the equation of the line is y=-3x+3. Also please mark this as brainliest answer if you found it helpful thanks.

Answer:

y = - 3x + 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ )  = (1, 0 ) and (x₂, y₂ ) = (2, - 3 )

m = [tex]\frac{-3-0}{2-1}[/tex] = [tex]\frac{-3}{1}[/tex] = - 3 , then

y = - 3x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (2, - 3 )

- 3 = - 3(2) + c = - 6 + c ( add 6 to both sides )

3 = c

y = - 3x + 3 ← equation of line

The interval of times that represents the middle 99.7% of Caroline's finishing times is (63.5, 72.5) seconds

In this case, we are looking for the interval of times that represents the middle 99.7% of Caroline's finishing times.

The middle 99.7% of the data corresponds to three standard deviations from the mean in both directions

Three standard deviations from the mean is 3 x 1.5 = 4.5 seconds.

Therefore, the interval of times that represents the middle 99.7% of Caroline's finishing times is (68 - 4.5, 68 + 4.5) = (63.5, 72.5) seconds

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Answer: The length of the original side of the square is 22 units.

Step-by-step explanation:

Let x be the length of the original side of the square.

If the sides are increased by 11, the new side length is x + 11.

The area of the new square is given as 400, so we have:

(x + 11)^2 = 400

Expanding the left side: x^2 + 22x + 121 = 400

Subtracting 400 from both sides: x^2 + 22x - 279 = 0

Using the quadratic formula:

x = (-22 ± sqrt(22^2 - 41(-279))) / (2*1)

x = (-22 ± sqrt(12100)) / 2

x = (-22 ± 110) / 2

Taking the positive solution:

x = (-22 + 110) / 2

x = 44 / 2

x = 22

Answer:

28 mph

Step-by-step explanation:

let x= rate of cyclist

3/11(x)=6

x=66/3=22 mph

22mph+ 6mph=28 mph

they move towards each other with a relative speed of 28 mph

The cubic equation graphed have the functions as follows

Graph of cubic function

The equation of cubic function is

y = a(x - h)^3 + k

For horizontal inflection at (-5, -7)

y = a(x + 5)^3 - 7

passing through point (-1, -3.8)

-3.8 = a(-1 + 5)^3 - 7

4.8 = -64a

a = 4.8/64 = 3/40

hence the equation is: y = 3/40(x + 5)^3 - 7

Graph of cubic function

The equation of cubic function is

y = k - a(x - h)^3

For horizontal inflection at (-0.5, 2)

y = 2 - a(x + 0.5)^3

passing through point (-5, 38.45)

38.45 = 2 - a(-5 + 0.5)^3

38.45 -2 = -a(-4.5)^3

a = -36.45/(-4.5)^3 = 2/5

hence the equation is: y = 2 - 2/5(x + 0.5)^3

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Okay, here are the steps to solve this problem:

* There are 15 sections of English 102 to choose from

* There are 9 sections of Spanish 102 to choose from

* There are 12 sections of History 102 to choose from

* There are 13 sections of College Algebra to choose from

So for English 102 Felicia has 15 options, for Spanish 102 she has 9 options, for History 102 she has 12 options, and for College Algebra she has 13 options.

By the Fundamental Principle of Counting, the total number of possible schedules is:

15 * 9 * 12 * 13 = 16,920

Therefore, the total number of possible schedules for Felicia is 16,920

The width of the path is approximately 7.45 meters.

What is meant by width?

The width refers to the measurement of something from side to side, typically in a direction perpendicular to its length or height, such as the width of a door or the width of a piece of paper.

What is meant by meters?

Meters are a unit of measurement used to measure the length in the metric system. One meter is equal to 100 centimetres or approximately 3.28 feet. It is commonly used to measure distances, heights, and lengths.

According to the given information

The area of the pool is given by the product of its length and width:

18 × 30 = 540 square meters

The area of the entire region, including the pool and the path, is given by the product of the length and width of the outer rectangle:

(18 + 2x) × (30 + 2x)

Expanding this expression, we get:

540 + 36x + 60x + 4x²

Simplifying, we get:

4x² + 96x + 540

We are given that the area of the entire region is 1900 square meters:

4x² + 96x + 540 = 1900

Subtracting 1900 from both sides, we get:

4x² + 96x - 1360 = 0

Dividing both sides by 4, we get:

x² + 24x - 340 = 0

We can use the quadratic formula to solve for x:

x = (-24 ± √(24² - 4 × 1 × (-340))) / (2 × 1)

Simplifying, we get:

x = (-24 ± √(1216)) / 2

x ≈ -17.45 or x ≈ 7.45

Since the width of the path cannot be negative, we can ignore the negative solution.

Therefore, the width of the path is approximately 7.45 meters.

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Answer: ∠EAI and/or ∠EDG (More listed below lol)

Step-by-step explanation:

Starting Angle: ∠ADE

Possible Supplements: ∠EAI, ∠EDG, ∠DAH, ∠DEC, ∠ADF, and ∠AEB

The correct mathematical expression to find the number of tiles needed to surround a square pool would depend on how the tiles are arranged and how the dimensions of the pool and the tiles are related.

4(s+1): This expression appears to be correct if we assume that each side of the square pool is surrounded by a row of tiles, and each corner requires an additional tile.

So, the expression can be simplified to 4s+4. This is a valid expression for the number of tiles needed to surround the pool.

s²: This expression does not appear to be correct, as it only gives the area of the square pool, and does not take into account the dimensions of the tiles or the need to surround the pool.

4s+4: This expression is the same as the first expression, 4(s+1), and is a valid expression for the number of tiles needed to surround the pool.

2s+2(s+2): This expression appears to be incorrect, as it gives the total perimeter of the pool plus an additional 4 units, but does not take into account the size of the tiles or the need to surround the pool.

4s: This expression is incorrect, as it only gives the perimeter of the pool and does not take into account the need to surround the pool with tiles.

Thus, two of the given expressions (4(s+1) and 4s+4) are correct, one expression (s²) is incomplete, and two expressions (2s+2(s+2) and 4s) are incorrect.

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The slant height of the cone is about 11 cm. Using the Pythagorean theorem, the height is approximately 41.4 cm to the nearest tenth.

Use the formula for the lateral area of a cone: L = πrs, where L is the lateral area, r is the radius of the base, and s is the slant height.

Plug in the given values: L = 473π cm² and r = 43 cm. Then solve for s

L = πrs

473π = π(43)s

s = 473/43 ≈ 11

So the slant height of the cone is approximately 11 cm.

Use the Pythagorean theorem to find the height of the cone. Let h be the height of the cone. Then the Pythagorean theorem gives

h² + s² = r²

Substituting in the values for s and r, we get

h² + 11² = 43²

Simplifying this equation, we get

h² = 43² - 11²

Evaluating the right-hand side, we get

h² = 1764

Taking the square root of both sides, we get

h ≈ 41.4

So the height of the cone is approximately 41.4 cm to the nearest tenth.

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Answer:

C

Step-by-step explanation:

(x-3)(x-3)=27

x^2-3x-3x+9=27

x^2-6x+9=27

          -27.   -27

x^2-6x-18=0

Answer:

(x-3)²=27

Step-by-step explanation:

x²+6x-18=0

add 18 to both sides of the equation

To complete the square add 3² to both sides and factor what is on the left side. You will be getting

(x-3)² = 27 is the answer to this problem

Answer:

C

Step-by-step explanation:

(x-3)(x-3)=27

x^2-3x-3x+9=27

x^2-6x+9=27

          -27.   -27

x^2-6x-18=0

Answer:

(x-3)²=27

Step-by-step explanation:

x²+6x-18=0

add 18 to both sides of the equation

To complete the square add 3² to both sides and factor what is on the left side. You will be getting

(x-3)² = 27 is the answer to this problem

Answer:

240

Step-by-step explanation:

Answer:   [tex]\frac{1}{5}[/tex]

Step-by-step explanation:

Males who got a C = 4

Total amount of people who got a C = 20

[tex]\frac{4}{20}[/tex]

[tex]\frac{4}{20}[/tex]  simplifies to  [tex]\frac{1}{5}[/tex]

The height of point A is 0 feet. However, this is not the actual height of point A, as it is at the highest point on the Ferris Wheel, which is 185 feet as calculated previously.

The height of point A on the Ferris Wheel can be calculated using the sine function, as it is the vertical component of the point's position. The center of the Ferris Wheel is 100 feet off the ground, and its radius is 85 feet.

Let's denote the height of point A as h_A, which is the vertical distance from the center of the Ferris Wheel to point A.

Since point A is at the 0 radian position, it is at the highest point on the Ferris Wheel. At this point, the height of point A is equal to the sum of the radius and the center's height:

h_A = radius + center's height

h_A = 85 + 100

h_A = 185 feet

So, the height of point A off the ground is 185 feet.

To estimate the value of h_A using the sine function, we can use the fact that at any given angle θ on the unit circle, the height of the point on the circle is given by the sine of that angle multiplied by the radius. In this case, since point A is at the highest point on the Ferris Wheel, we can use the sine of 0 radians (which is 0) to estimate the height of point A:

h_A = radius * sin(0)

h_A = 85 * 0

h_A = 0

So, using the sine function, we estimate that the height of point A is 0 feet. However, this is not the actual height of point A, as it is at the highest point on the Ferris Wheel, which is 185 feet as calculated previously.

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a. Monthly payment for the bank's car loan is $407.67

b. Monthly payment for the savings and loan association's car loan is $315.99

c. Total amount paid would be $2,035 less for the bank's car loan than for the savings and loan association's car loan.

The cost of borrowing money, usually expressed as a percentage of the amount borrowed, is what a lender charges a borrower to use their money. This cost is known as an interest rate.

(a) To find the monthly payment for the bank's car loan, we can use the formula for the present value of an annuity:

[tex]PV = PMT * \frac{1 - (1 + \frac{r}{n})^{(-n*t)}}{\frac{r}{n} }[/tex]

putting the given values,

⇒ [tex]21000 = PMT * \frac{1 - (1 + \frac{0.065}{12})^{(-12*5)}}{\frac{0.065}{12} }[/tex]

Solving for PMT, we get:

PMT = $407.67

Therefore, the monthly payment for the bank's car loan is $407.67

(b) To find the monthly payment for the savings and loan association's car loan, we can use the same above formula:

where PV is still $21,000, PMT is the monthly payment, r is still 0.065, n is still 12, but t is now 7 years x 12 months/year = 84 payments.

putting the given values,

[tex]21000 = PMT * \frac{1 - (1 + \frac{0.065}{12})^{(-12*7)}}{\frac{0.065}{12} }[/tex]

Solving for PMT, we get:

PMT = $315.99

Therefore, the monthly payment for the savings and loan association's car loan is $315.99.

(c) Bank's car loan: $407.67 x 60 = $24,460.20

Savings and loan association's car loan: $315.99 x 84 = $26,495.16

Therefore, the bank's car loan would have the lowest total amount to pay off, by: $26,495.16 - $24,460.20 = $2,034.96

Therefore, the total amount paid would be $2,035 less for the bank's car loan than for the savings and loan association's car loan.

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Answer:

The common ratio of this sequence is 120/150 = 4/5, so we have:

[tex] \frac{150}{1 - \frac{4}{5} } = \frac{150}{ \frac{1}{5} } = 150 \times 5 = 750[/tex]

So the sum of all the terms in this sequence is 750.

a household with a credit score of 525 would pay $4,280.82 more than a household with a credit score of 675 for a principal balance of $8,000.

what is principal balance ?

Principal balance refers to the amount of money that you still owe on a loan or debt, not including any interest or fees that have accrued. When you make a payment towards your loan or debt, a portion of the payment goes towards paying down the principal balance,

In the given question,

To calculate the difference in payment between a household with a credit score of 525 and one with a score of 675, we need to compare the total amount paid for each score range.

For a principal balance of $8,000, based on the given information:

A household with a credit score of 525 would have a simple interest rate of 28%, and would make 60 payments of $249.08 each, for a total amount paid of $14,945.00.

A household with a credit score of 675 would have a simple interest rate of 18%, and would make 38 payments of $280.61 each, for a total amount paid of $10,664.18.

The difference in payment between these two scores would be:

$14,945.00 - $10,664.18 = $4,280.82

Therefore, a household with a credit score of 525 would pay $4,280.82 more than a household with a credit score of 675 for a principal balance of $8,000.

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Answer:2nd one

Step-by-step explanation: