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2 years ago

What fraction of a year are 31 days ?

Mathematics

1 answer:

Alborosie2 years ago

5 0

9514 1404 393

Answer:

non-leap years: 31/365
leap years: 31/366

Step-by-step explanation:

As a fraction of the number of days in a calendar year, it will depend on whether the year is a leap year.

non-leap years have 365 days, so 31 days is 31/365 years.

leap years have 366 days, so 31 days is 31/366 years.

_____

If you're asking for the purpose of computing interest, you need to be aware that "ordinary interest" counts 360 days in a year. 31 days would be 31/360 years. "Exact interest" counts 365 days in a year, so 31 days would be 31/365 years.

In astronomy, the definitions of "day" and "year" may vary, depending on the frame of reference and what direction in space marks the boundary of the period. The precise fraction will depend on how you define these terms and where the clock is located.

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Two chemicals A and B are combined to form a chemical C. The rate, or velocity, of the reaction is proportional to the product o

Keith_Richards [23]

Answer:

32.1 g

Step-by-step explanation:

In each 3 grams of C, there are 2 grams of A and 1 gram of B. So, for some amount C, the amount remaining of A is 40 -(2C/3), and the amount remaining of B is (50 -C/3). Since the reaction rate is proportional to the product of these amounts, we have ...

C' = k(40 -2C/3)(50 -C/3) = (2k/9)(60 -C)(150 -C) . . . for some constant k

This is separable differential equation with a solution of the form ...

ln((150 -C)/(60 -C)) = at + b

We know that C(0) = 0, so b=ln(150/60) = ln(2.5). And we know that C(10) = 20, so ln(130/40) = 10a +ln(2.5) ⇒ a = ln(1.3)/10

Then our equation for C is ...

ln((150 -C)/(60 -C)) = t·ln(1.3)/10 +ln(2.5)

For t=20, this is ...

ln((150 -C)/(60 -C)) = 2ln(1.3) +ln(2.5) = ln(2.5·1.3²) = ln(4.225)

Taking antilogs, we have ...

(150 -C)/(60 -C) = 4.225

1 +90/(60 -C) = 4.225

C = 60 -90/3.225 ≈ 32.093 . . . . . grams of product in 20 minutes

In 20 minutes, about 32.1 grams of C are formed.

7 0

3 years ago

Solve the system of equations y=x-4, y=-3x

abruzzese [7]

Y=x-4
x=y+4
y=-3(y+4)
y=-3y-12
4y=-12
y=-3
x=1

5 0

3 years ago

Hostoso

Softa [21]

Answer:

Step-by-step explanation:

0.12 is 12 percent we also have the 0.06 percent which would just be 6 percent we need to add up those percentages to get 18 percent, for the people surveyed that cannot swim would be 18 percent.

6 0

2 years ago

Geometric mean definition

nikdorinn [45]

The central number in a geometric progression which indicates the central tendency or typical value of a set of numbers by using the product of their values as opposed to the arithmetic mean which uses their sum.

5 0

3 years ago

Solve the following quadratics. State the FACTORS AND SOLUTIONS. 1. 2x^2 - 7x + 3 2. 3x^2 + 7x +2

tekilochka [14]

Answer:

1. x = 3, 1/2 (solutions); (x - 3)(2x - 1) (factors)

2. x = -1/3, -2 (solutions); (3x + 1)(x + 2) (factors)

Step-by-step explanation:

1. 2x^2 - 7x + 3

To solve problem 1, you will need to identify your a, b, and c values in this quadratic function.

Since this problem is in standard form, it will be easy to identify these values. The standard form of a quadratic function is ax^2 + bx + c.

The a value is 2, the b value is -7, and the c value is 3 if we use our standard form and see which numbers are plugged into it.

Since we know that

a = 2
b = -7
c = 3

we can use the quadratic formula: $x = \frac{-b~\pm~\sqrt{b^2~-~4ac} }{2a}$

Substitute the a, b, and c values into the quadratic formula: $x=\frac{-(-7)\pm\sqrt{(-7)^2-4(2)(3)} }{2(2)}$

Now simplify using the laws of pemdas: $x=\frac{7\pm\sqrt{(49)-(24)} }{4}$

Simplify even further: $x=\frac{7\pm\sqrt{(25)} }{4} \rightarrow x=\frac{7\pm (5) }{4}$

Now split this equation into two equations to solve for x: $x=\frac{12 }{4} ~~and~~ x=\frac{2 }{4}$

12/4 can be simplified to 3, and 2/4 can be simplified to 1/2.

This means your solutions to problem 1 is 3, 1/2.

$\boxed {x=3,\frac{1}{2} }$

There is also another way to solve for the quadratic functions, and this was by factoring.

If you factor 2x^2 - 7x + 3 using the bottoms-up method, you will get (x - 3)(2x - 1).

After factoring, solving for the solutions is simple because all you have to do is set each factor to 0.

x - 3 = 0
2x - 1 = 0

After solving for x by adding 3 to both sides, or by adding 1 to both sides then dividing by 2, you will end up with the same solutions: x = 3 and x = 1/2.

2. 3x^2 + 7x + 2

To save time I'll be using the bottoms-up factoring method, but remember to refer back to problem 1 (quadratic formula) if you prefer that method.

Factor this quadratic function using the bottoms-up method. After factoring you will have (3x + 1)(x + 2). These are your factors.

Now to solve for x and find the solutions of the quadratic function, you will set both factors equal to 0.

3x + 1 = 0
x + 2 = 0

Solve.

First factor: 3x + 1 = 0

Subtract 1 from both sides.

3x = -1

Divide both sides by 3.

x = -1/3

Second factor: x + 2 = 0

Subtract 2 from both sides.

x = -2

Your solutions are x = -1/3 and x = -2.

$\boxed {x = -\frac{1}{3} , -2}$

7 0

3 years ago