A sum of money is divided among peter paul and jane in ratio 13:12:7 calculate how much paul gets if amount peter gets more than jane is 78$

Answer:

The answer is B 11/20

Step-by-step explanation:

To transform a decimal to a fraction you must do the following:

1. Multiply by an specific power of 10 until your decimal becomes a whole number. In this case 0.55 we multiply by 10 ^2 or 100 and we obtain 55.

2 Divide the decimal by this same power of 10 so that you do not change the original value. For example

0.55 *(100/100) = 55/100 As you see Im multiplying and dividing by 100 ( thats equivalent to 1 so it doesnt change the original number)

3 Simplify the fraction

To simplify your fraction you must find the Greatest Common Factor of 55 and 100. For doing this, you only perform a prime factorization. Divide 55 and 100 by the smallest common prime factor, besides 1. (For this case is 5) until you arrive to two number without common prime factors.

55/5 = 11

100/5 = 20

As 11 and 20 have no common prime factors it is the most simplified fraction  

To find the inverse of a function, follow these steps: replace f(x) with y, interchange x and y, solve for y, and replace y with f-1(x). Applying these steps to the given function f(x) = 3x - 2 results in the inverse function f-1(x) = (x + 2)/3.

To find the inverse of a function, we can follow these steps:

Let's apply these steps to the given function f(x) = 3x - 2:

Therefore, the inverse of the function f(x) = 3x - 2 is f-1(x) = (x + 2)/3.

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The inverse function of [tex]\( f(x) = 3x - 2 \)[/tex] is [tex]\( f^{-1}(x) = \frac{x + 2}{3} \).[/tex]

To find the inverse function [tex]\( f^{-1}(x) \)[/tex] for the given function [tex]\( f(x) = 3x - 2 \)[/tex], follow these steps:

Start with the original function:

  [tex]\[ y = 3x - 2 \][/tex]

Swap y and x to find the inverse:

  [tex]\[ x = 3y - 2 \][/tex]

Solve for y:

  [tex]\[ x + 2 = 3y \][/tex]

  [tex]\[ y = \frac{x + 2}{3} \][/tex]

Rewrite y as [tex]\( f^{-1}(x) \):[/tex]

  [tex]\[ f^{-1}(x) = \frac{x + 2}{3} \][/tex]

So, the inverse function [tex]\( f^{-1}(x) \)[/tex] is:

[tex]\[f^{-1}(x) = \frac{x + 2}{3}\][/tex]

Complete Question:

If [tex]f(x) =3x-2[/tex], find [tex]f^{-1}(x)[/tex]

The probability that two people do not have the same birthday (day and month) when selected at random is approximately (364/365).

The probability that two people do not have the same birthday (day and month) when selected at random can be calculated using the principle of complementary probability. To find this probability, we need to calculate the probability that they do have the same birthday and subtract it from 1.

Let's break down the process:

Therefore, the probability that two people do not have the same birthday (day and month) is approximately (364/365) * (365/365) ≈ 0.9878.

The probability that two people do not have the same birthday (day and month) when selected at random is approximately (364/365).

The probability that two people do not have the same birthday (day and month) when selected at random can be calculated using the principle of complementary probability. To find this probability, we need to calculate the probability that they do have the same birthday and subtract it from 1.

Let's break down the process:

Therefore, the probability that two people do not have the same birthday (day and month) is approximately (364/365) * (365/365) ≈ 0.9878.

Answer: A2+B2=C2                                                                                                                                                                                            

             (๑╹ᆺ╹ ) i hope this is right

The length of XV in triangle VWX is approximately 26 feet.

To find the length of XV, we can use the trigonometric relationship in a right triangle. In triangle VWX, the measure of angle W is 25° and angle X is 90°. We can use the sine function to find the length of XV. The sine of angle W is equal to the length of the side opposite angle W divided by the length of the hypotenuse. So, we have sin(25°) = XV/61. Rearranging the equation, we get XV = 61 * sin(25°). Plugging in the values, we find that XV is approximately 26 feet.

Final answer:

The center of the circle described by the equation x2 − 4x + y2 + 8y − 29 = 0 is (2, -4), and the radius is 7 units.

Explanation:

The equation of a circle given in the question is x2 − 4x + y2 + 8y − 29 = 0. To find the center and radius of the circle, we will complete the square for both x and y terms.

This involves adding and subtracting the squared half of the coefficients of x and y to complete the square:

(x2 - 4x + 4) - 4 + (y2 + 8y + 16) - 16 = 29 + 4 + 16

(x - 2)2 + (y + 4)2 = 49

This equation is now in standard circle form, which is (x - h)2 + (y - k)2 = r2, where (h, k) is the center and r is the radius.

The center of the circle is therefore at (2, -4) and the radius is √(49) = 7 units.

To make the total monthly cost of Silver Gym and Fit Factor equal, Sarah would have to buy 6 personal training sessions in a single month.

The question is asking to find out how many personal training sessions Sarah would need to take in a month for the cost at Silver Gym to equal the cost at Fit Factor.

To solve this, we need to create an equation. Let's represent the number of personal training sessions as x. For Silver Gym, the total cost in a month would be 30 + 45x, and for Fit Factor, it would be 90 + 35x.

Setting these two expressions equal to each other gives us the equation 30 + 45x = 90 + 35x.

Moving the variable terms to one side and the constants to the other side of the equation gives us 10x = 60.

We solve for x by dividing both sides of the equation by 10 to get x = 6.

This means that Sarah would need to take 6 personal training sessions for the total cost at the two gyms to be equal.

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Let's analyze each expression:

A. (32ˣ/4) can be rewritten as ((2⁵)ˣ/(2²)) = (2⁵ˣ/2²) = 2⁵ˣ⁻².

This expression is not equivalent to 8ˣ, so it's incorrect.

B. (32/49)ˣ = 8ˣ This expression is equivalent to 8ˣ, so it's correct.

C. 8 × 8ˣ⁺¹ = 8ˣ⁺¹ + 1 This expression is not equivalent to 8ˣ, so it's correct.

D. x⁴ is not equivalent to 8ˣ, so it's correct.

E. (32ˣ/4ˣ) = (32/49)ˣ = 8ˣ This expression is equivalent to 8ˣ, so it's correct.

F. 8 × 8ˣ⁻¹ = 8ˣ⁻¹⁺¹ = 8ˣ This expression is equivalent to 8ˣ, so it's correct.

So, the expressions equivalent to 8x are: B, E, and F.

Let's assess each expression:

A. (32ˣ/4) can be rewritten as ((2⁵)ˣ/(2²)) = (2⁵ˣ/2²) = 2⁵ˣ⁻². This expression is not equivalent to 8ˣ, so it's incorrect.

B. (32/49)ˣ = 8ˣ  This expression is equivalent to 8ˣ, so it's correct.

C. 8 × 8ˣ⁺¹ = 8ˣ⁺¹ + 1 This expression is not equivalent to 8ˣ, so it's correct.

D. x⁴  is not equivalent to 8ˣ, so it's correct.

E. (32ˣ/4ˣ) = (32/49)ˣ = 8ˣ This expression is equivalent to 8ˣ, so it's correct.

F. 8 × 8ˣ⁻¹ = 8ˣ⁻¹⁺¹ = 8ˣ  This expression is equivalent to 8ˣ, so it's correct.

So, the expressions equivalent to 8ˣ are: B, E, and F.

Complete Question:

Which expressions are equivalent to the one below? 8x

A. 32ˣ/4

B. (32/49)ˣ

C. 8 × 8ˣ⁺¹

D. x⁴

E. (32ˣ/4ˣ)

F. 8 × 8ˣ⁻¹

Answer:

FALSE

Step-by-step explanation:

The correct equation would be y = mx + b

y -->  y coordinate

m --> the slope

x -->  x coordinate

b --> the y-intercept

Answer:

false!

Step-by-step explanation:

Y = mx + b is the generic form of a linear equation written in slope-intercept form.

The surface area of this cylinder in terms of [tex]\pi[/tex] is [tex]216\pi\;cm^2[/tex]

Given the following data:

To calculate the surface area of this cylinder in terms of [tex]\pi[/tex]:

Mathematically, the surface area (SA) of a cylinder is given by this formula:

[tex]S.A = 2\pi rh + 2\pi r^2[/tex]

Where:

Substituting the given parameters into the formula, we have;

[tex]S.A = 2\pi (6)(12) + 2\pi (6)^2\\\\S.A = 144\pi+72\pi\\\\S.A = 216\pi\;cm^2[/tex]

Read more on surface area here: brainly.com/question/21367171