Determine f –1(x) if f of x is equal to the quantity x plus 2 end quantity over the quantity x minus 3 end quantity where x ≠ 3.


f inverse of x is equal to the quantity x minus 3 end quantity over the quantity x plus 2 end quantity
b
f inverse of x is equal to the quantity x minus 2 end quantity over the quantity x plus 3 end quantity
c
f inverse of x is equal to the quantity x minus 1 end quantity over the quantity 3 times x plus 2 end quantity
d
f inverse of x is equal to the quantity 3 times x plus 2 end quantity over the quantity x minus 1 end quantity

The ratio of all flowers in the vase to roses is 9:16. The ratio of all flowers in the vase to daisies is 16:7.

An expression known as a ratio in mathematics shows how many times one number is contained in another. In a bowl of fruit, for instance, the proportion of oranges to lemons is eight to six if there are eight oranges and six lemons (that is, 8:6, which is equivalent to the ratio 4:3). In a similar vein, the proportion of oranges to the overall amount of fruit is 8:14, and that of lemons to oranges is 6:8 (or 3:4). (or 4:7).

A ratio can have any number of numbers as its components, including counts of people or things, weights, lengths, and times, among other values. Both numbers are usually limited to positive values in settings.

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we get that the expression ( 2 x + 3 ) / 3 + ( x - 4 ) / 4 can be written as an equation as 11 x / 12.

We are given an expression:

( 2 x + 3 ) / 3 + ( x - 4 )/ 4

We need to simplify it and write it as an equation.

Taking the LCM, we get that:

4( 2 x + 3) + 3 (x - 4) / 12

simplifying brackets, we get that,

8 x + 12 + 3 x - 12 / 12

Combining the like terms, we get that:

8 x + 3 x / 12

11 x / 12

Therefore, we get that the expression ( 2 x + 3 ) / 3 + ( x - 4 ) / 4 can be written as an equation as 11 x / 12.

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Answer:

6

Step-by-step explanation:

Answer:

6(x+6y)

Step-by-step explanation:

The greatest common factor is 6.

6x+36y=

=6(x+6y)

The expression with the GCF factored out is 6(x+6y)

Hope this helps!

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The probability of getting February, then a number less than 5 is:

P = 1/18

First, we need to find the two individual probabilities:

We have a total of 12 months, and we assume that the probability for each of these is the same one, then the probability of getting February will be:

p = 1/12.

Now, the standard die has 6 sides, the numbers that are less than 5 are:

{1, 2, 3, 4}

So 4 out of the 6 outcomes are less than 5, then the probability here is:

q = 4/6 = 2/3.

Then the joint probability is:

P = p*q = (1/12)*(2/3) = 2/36 = 1/18

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Answer:

So if you roll the die ten times, that means every time you roll it, it is 10%, with that knowledge, if you rolled 6, four times, that means the experimental probability is 40% to get 6.

11/12 - 3/4 = 1/6

1/2 + 4/9 = 17/18

11/12 - 3/4

= 11-9/12

= 2/12

= 1/6

1/2 + 4/9

= 9+8/18

= 17/18

Hence the solution to the expression in it's simplest form is 1/6 and 17/18

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Answer:

1/6and 17/18

Step-by-step explanation:

11/12-3/4

find the l.c.m

11/12-3/4=11-9/12=2/12=1/6

1/2+4/9=9+8/18=17/18

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Answer:

8 hours

Step-by-step explanation:

69 = 7t -8

61 = 7t

t = 8.71428571

There are 256 different pizzas can you make with anywhere from 0 to 4 toppings.

Combinations:

Combinations defines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Given,

Pizza pies with a choice of any of 4 toppings: pepperoni, mushrooms, green peppers, or sausage.

Here we need to find how many different pizzas can you make with anywhere from 0 to 4 toppings.

Here we need to assume that each pizza can have at most 1 serving of each topping.

Here we have four level of toppings like no serving, single serving, double serving and triple serving.

Suppose you had one topping, let's say mushrooms.  How many different possible pizzas would there be?

If you understand the setup right, there would be 4: no topping, single mushrooms, double mushrooms, or triple mushrooms.

Similarly, imagine that there are two toppings, mushrooms and sausage.

Then, there are 4 x 4 = 16 different combinations with two items.

We could continue this for a long time.  

If you have only sausage, mushroom, pepperoni and onion, then for a total of

=> 4 x 4 x 4 x 4 = 256 combinations.

Therefore, there are 256 different pizzas can you make with anywhere from 0 to 4 toppings.

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Answer:

T=48

Step-by-step explanation:

Now since I don’t know the height at the present moment, I’ll just make this ratio (of the tree) be represented as x/36. Which is saying that for every ‘x’ amount of feet, there will be 36 feet of shadow.

so we have 4/3=x/36. If I cross multiply 36 and 4, then divide the product by 3, then ‘x’ will be 48.

As a result, 3.0 x 10¹ litter of gasoline will be used for a 450-kilometer trip.

The correct option  is B.

In fact, a conversion factor is a number that is utilized to multiply as well as divide one set of units by another.. When converting to an equivalent value, the appropriate conversion factor must be utilized. To convert inches into feet, for example, the suitable conversion value becomes 12 inches equal to 1 foot.

Unit conversion is indeed a multi-step procedure that includes multiplying or dividing by a numerical factor, determining the appropriate number of important digits, and rounding.

The car gets 35 miles for each gallon of gas.

We need to calculate how many liters of petrol will be required for a 450-kilometer trip.

first converting km into miles:

1 km  =0.621371 miles.

So,

450 km = 450 x 0.621371

= 279.61 miles.

Now we know that :

One gallon of gasoline will get you 35 miles.

So for 279.61 miles.

Let x be the number of liters of gasoline required to travel the distance.

So

x = 279.61 / 35

x = 7.98 gallons

Now in litters:

1 gallon = 3.78541litters

So,

7.98 * 3.7854 = 30.24

                       = 3.0 x 10¹ litter

As a result, 3.0 x 10¹ litter of petrol will be used for a 450-kilometer trip.

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I understand that the question you are looking for is:

A car averages 35 miles per gallon of gasoline.  How many liters of gasoline will be needed for a trip of 450 kilometers?  Some conversion factors, which may be helpful are the following:

   1 qt = 0.946 L.

  1 mile = 0.621371 km.  

1000 m = 1 km.

  4 qt = 1 gallon.

  1 ft = 12 inches.  

a. 2.5 x 10¹ L

b. 3.0 x 10¹ L

c. 3.5 x 10¹ L  

d. 4.0 x 10¹ L    

e. 4.5 x 10¹ L  

Answer:

Answer choice "b. e"

Step-by-step explanation:

The vertex is the starting point of a line, ray, angle etc...

Answer:

42

Step-by-step explanation:

45 divided by 5 is 9.

210 divided by 5 is 42.

Hope It Helps

Sorry If I'm Wrong

The radians will the hour hand on a clock rotation for 23hr and 6hr is 23/6π and π.

We have to find the radians will the hour hand on a clock rotation for 23hr and 6hr.

One revolution is done by fully around the circle with the radius. After one full rotation, the radius subtends an angle of 2π radians at the circle's center. To illustrate the conversion of 1 radian to degrees, we will use the knowledge that 2π radians = 360 degrees.

2π radians = 360°

Divide the above equation by 2,

⇒ π radians = 180°

Divide the above equation by π,

⇒ 1 radian = 180°/π

⇒ 1 radian = 57.296°

Only 12 hours are represented by one full rotation of the hour hand. A whole rotation equals 360°, or two radians.

11 hours rotation equals to 330°, or 11π/6 radians.

23 hours=12+11

=360°+330° (or) 2π+11π/6

=690° (or) 23π/6

Now, 6 hours=12/2

=360°/2 (or) 2π/2

=180° (or) π.

Therefore, the radians will the hour hand on a clock rotation for 23hr and 6hr is 23/6π and π.

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The probability that at least one of them has been vaccinated is 0.9552

Probability:

Probability defines the possible occurrence of any particular required event.

Given,

Here we need to find in a large population, 54 % of the people have been vaccinated. if 4 people are randomly selected, what is the probability that at least one of them has been vaccinated.

Here we have to know that,

The situation where at least one out of 4 are vaccinated includes all but one possibility, that which none of the 4 are vaccinated.

The sum of all probabilities must equal 1.

Let Q be probability none of the 4 are vaccinated.

Let P be probability that at least 1 is vaccinated.

Then the probability is calculated as,

P = 1 - Q

Now if 54% are vaccinated, then 46% are not vaccinated.

Thus any given person has a probability of 0.46 of not being vaccinated.

=> Q = (0.46)⁴

=> Q = 0.0448

Then apply the value to the formula,

=> P = 1 - 0.0448

=> P = 0.9552

Therefore, the probability that at least one of them has been vaccinated 0.9552.

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Answer:

100 times bigger this is simple math

Answer:

Step-by-step explanation:

The total cost of the books will be €3276.

It should be noted the school bought 234 books at €14 each.

Therefore, the total cost of the books will be:

= Price × Total books

= €14 × 234

= €3276

Therefore, the total cost of the books will be €3276.

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Answer:

120

Step-by-step explanation:

Answer:

The correct answer is B)

Step-by-step explanation:

The values x = 2 and y = 5 make the equation true.

the reason for this is because ordered pairs are in the form (x,y), meaning  for the point (2,5), the number 2 is an x-value and the number 5 is a y-value. so when you put these numbers into the equation, you should get a true statement both sides are equal to one another.

Answer:

Step-by-step explanation: the correct answer is B) x=2 and y=5 make the equation true.

I don't think you can solve this, considering the given expression is false. However consult a tutor perhaps and see if they can help you further.

Step-by-step explanation:

⎡02413524−6⎦⎥⎥⎤ and B=⎣⎢⎢⎡−10021030−1⎦⎥⎥⎤

∴4A=⎣⎢⎢⎡081641220816−24⎦⎥⎥⎤ and 6B=⎣⎢⎢⎡−600126080−6⎦⎥⎥⎤ 

⇒4A−6B=⎣⎢⎢⎡0−(−6)8−016−04

Answer:

looking at the screenshot! it can be a or b

Step-by-step explanation:

No these lengths does not form a right triangle

There is a property of triangles which says that some of two sides of the triangle should be more than the third side of the triangle

So first case 6,30,5

30+6 =36 which is  more than 5

second case 5,30,6

5+30 =35 which is more than 6

third case 5,6,30

5+6 =11 which is not more than 30

as in third case the property is breached because sum of two sides of triangle is not more than third side so the figure cannot be a triangle .

And hence we cannot check whether it is a right angle triangle or not.

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Answer:

(2/x²y³)    

Step-by-step explanation:

(2(x^-2)y)/(y^4)

x^-2 can also be written as (1/x²)

(2(1/x²)y)/(y^4)

(2/x²)(y)/(y^4)

(2y/x²)/(y^4)

this can also be written as (2y/x²) × (1/y^4)

= 2y/(x² × y^4)

WHEN THE SAME VARIABLE IS DIVIDED THEIR POWERS ARE SUBTRACTED

= (2/x²y³)       (we got y³ by y^1 /y^4  The powers got subtracted)

Answer:

660%

Step-by-step explanation:

6 x 100= 600%

3/5 = 0.6 × 100 = 60%

600% + 60% = 660%

The general solution of the given differential equation are:  [tex]e^{\frac{-x}{3}}[/tex] [A cos(x√ 2/3) + B sin(x√ 2/3) i ]

Now,

Given: 3y'' + 2y' + y = 0

To find: General solution of the given differential equation.

Finding:

=> [tex]3\frac{d^{2}y}{dx^{2}} + 2 \frac{dy}{dx} + y = 0[/tex]

The characteristic equation of this equation is:

=> 3m² + 2m + 1 = 0

=> m = [tex]\frac{(-2)± \sqrt{4 - 4(3)(1)}}{2(3)}[/tex]

=> m = [tex]\frac{(-2)±\sqrt{4-12}}{6}[/tex]

=> m = [tex]\frac{(-2)±2\sqrt{2}i}{6}[/tex]

=> m = [tex]\frac{(-1)±\sqrt{2}i}{3}[/tex] = [tex]\frac{-1}{3}[/tex] ± [tex]\frac{\sqrt{2}}{3}[/tex]

Thus, For a = -1/3 and b = (√2)/3,

General solution of the differential equation => [tex]e^{\frac{-x}{3}}[/tex] [A cos(x√ 2/3) + B sin(x√ 2/3) i ]

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The average acceleration during the time interval 0 seconds to 10 seconds is [tex]\frac{V_{1}-V_{2} }{10}[/tex] unit per second per second.

As per the question statement, we are supposed to find out the average acceleration during the time interval 0 seconds to 10 seconds. But before solving this question we should be aware about what actually average acceleration is.

Average acceleration : [tex]\frac{change in velocity}{total time interval}[/tex]

Here in the question, we are not given information about velocity of the object hence we assume the initial and final velocities of the object to be [tex]V_{1}[/tex] and [tex]V_{2}[/tex] respectively, hence

Change in velocity = [tex]V_{1}-V_{2}[/tex]

Total time interval = [tex](10 - 0)sec=10sec[/tex]

Therefore by definition of average acceleration we get

[tex]A_{avg}[/tex][tex]= \frac{V_{1}-V_{2} }{10}[/tex] unit per sec per second

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Answer:

18.7 units (3 s.f.)

Step-by-step explanation:

The distance between two points is given by the formula below, where [tex](x_1, y_1)[/tex] is the first coordinate and [tex](x_2, y_2)[/tex] is the second coordinate.

[tex]\boxed{{\text{Distance between 2 points}= \sqrt{(y_1 - y_2)^{2} + (x_1 - x_2)^{2} } }}[/tex]

Substitute the given points into the formula:

Distance between (0, -5) and (18, -10)

= [tex]\sqrt{[-10 -(-5)]^{2} + (18-0)^{2} }[/tex]

= [tex]\sqrt{(-10+5)^2+18^2}[/tex]

= [tex]\sqrt{(-5)^2+18^2}[/tex]

= [tex]\sqrt{349}[/tex]

= 18.7 units (3 s.f.)

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The probability that at least one of them is a boy is 0.9947

The probability = (1 - P) none of these 7 is a boy

= 1 - P (all girls)

1 - 0.473^7

1 - 0.00529697

= 0.9947

Hence in a certain​ country, the true probability of a baby being a girl is 0.473 . among the next seven randomly selected births in the​ country, the probability that at least one of them is a boy is 0.9947

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The type of question is GCF .

The factor of a number is a number that can divide another number perfectly without leaving any remainder.  Highest common factor is the highest factor that is common to two or more numbers

Factors of 8, 16 and 24 = 1, 2, 4, 8,

Highest common factor = 8

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Paula shovels 3 square feet more than Melinda in 1 minute.

We are given two equations relating the distance covered by each while they shovel. Assuming the x to be representative of Melinda's speed and y to be representative of Paula's speed. Making at least one coefficient same for both the equation.

Equation 1 : 30x + 30y = 450

Equation 2 : 20x + 25y = 345

Dividing equation 1 and equation 2 by 5.

Equation 3 : 6x + 6y = 90

Equation 4 : 4x + 5y = 69

Multiplying equation 3 with 4 and equation 4 with 6.

Equation 5 : 24x + 24y = 360

Equation 6 : 24x + 30y = 414

Subtracting Equation 5 from Equation 6.

  24x + 30y = 414

- 24x + 24y = 360

6y = 54

y = 9

Keep the value of y in equation 3

6x + 6×9 = 90

6x + 54 = 90

6x = 90 - 54

6x = 36

x = 6

So, Melinda's speed is 6 square feet per minute and Paula's speed is 9 square feet per minute.

Difference between speed = 9 - 6

Difference = 3 square feet per minute

Hence, Paula's speed is 3 square feet per minute more than Melinda.

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The complete question is -

Melinda and Paula shovel driveways and sidewalks in the winter as a way to earn extra money. Together they shoveled 450 square feet of sidewalk in 30 minutes. Then Melinda shoveled for 20 minutes while Paula shoveled for 25 minutes to complete 345 square feet of driveway.

30x + 30y = 45020x + 25y = 345

How much more can Paula shovel in 1 minute than Melinda?

3 square feet per minute

6 square feet per minute

9 square feet per minute

15 square feet per minute

Answer:

A: 3 square feet per minute

Step-by-step explanation: