what is 43906 in expanded form​

9514 1404 393

Answer:

  26 players to start; 21 players after 5 withdrew

Step-by-step explanation:

We are told that the withdrawing players did not play against each other, so the total number of games they played was 5×2 = 10. Then the number of games played by the remaining players was 220 -10 = 210. When n players play each other, they play a total of n(n -1)/2 games. Here, that total is 210, so we have ...

  n(n -1)/2 = 210

  n^2 -n = 420 . . . . . . . . .multiply by 2

  (n -1/2)^2 = 420.25 . . . . add 0.25 to complete the square

  n = 1/2 +√420.25 = 0.5 +20.5 = 21 . . . . . square root and add 1/2

The number of participating players after 5 withdrew was 21. There were 26 players to start.

Answer:

Step-by-step explanation:

To show that the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\), we can simplify both sides of the equation using the properties of logarithms. Here are the steps:

Step 1: Simplify the expression on the left side:

\(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\)

Step 2: Apply the logarithmic property \(\ln(a) - \ln(b) = \ln\left(\frac{a}{b}\right)\) to combine the logarithms:

\(\ln\left(\frac{\sqrt{2} + 1}{\frac{1}{\sqrt{2}}}\right)\)

Step 3: Simplify the expression within the logarithm:

\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)}\right)\)

Step 4: Simplify the denominator by multiplying by the reciprocal:

\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)} \cdot \sqrt{2}\right)\)

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{\left(\frac{1}{\sqrt{2}}\right) \cdot \sqrt{2}}\right)\)

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)

Step 5: Simplify the numerator:

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)

\(\ln\left(\sqrt{2}(\sqrt{2} + 1)\right)\)

\(\ln\left(2 + \sqrt{2}\right)\)

Now, let's simplify the right side of the equation:

Step 1: Simplify the expression on the right side:

\(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\)

Step 2: Simplify the expression within the logarithm:

\(-\ln\left(\frac{\sqrt{2} - 1}{\sqrt{2}}\right)\)

Step 3: Apply the logarithmic property \(\ln\left(\frac{a}{b}\right) = -\ln\left(\frac{b}{a}\right)\) to switch the numerator and denominator:

\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)

Step 4: Simplify the expression:

\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)

\(-\ln\left(\frac{\sqrt{2}(\sqrt{2} + 1)}{1}\right)\)

\(-\ln\left(2 + \sqrt{2}\right)\)

As we can see, the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) simplifies to \(\ln(2 + \sqrt{2})\), which is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\).

A day on Venus is 184.379 Earth days more(longer) than A day on Mercury.

It is given that,

A day on Venus is about 243.025 Earth days

A day on Mercury is about 58.646 Earth days

So, the difference between them represents the longer one.

= 243.025 - 58.646

= 184.379 Earth days

Since Venus has the highest value and Mercury has the lowest value, a day on Venus is longer than a day on Mercury.

Thus, a day on Venus is 184.379 Earth days longer than a day on Mercury.

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Answer:

Hey mate.....

Step-by-step explanation:

This is ur answer.....

Variable costs are costs that change as the quantity of the good or service that a business produces changes. Variable costs are the sum of marginal costs over all units produced. They can also be considered normal costs. Fixed costs and variable costs make up the two components of total cost. 

Hope it helps you!

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Answer:

1.486m/s

Step-by-step explanation:

The rate of change is defined as the change in distance divided by the change in time

Rate = ∆distance/∆time

Distance = 16.5 and 5.5

Time = 10.9 and 3.5

When we put this into the formula above, we have:

Rate of change = 16.5 - 5.5 / 10.9 - 3.5

= 11/7.4

= 1.486m/s

The constant rate of change has been calculated to be equal to 1.486m/s

You can use the fact that the rate of the change of a value when some other independent value changes is the ratio of change in the dependent variable to the change in the independent variable.

The constant rate of the current is given by 1.4865 meters per second.

Suppose that we have to measure the rate of change of y as x changes, then we have:

\(Rate = \dfrac{y_2 - y_1}{x_2 - x_1}\)

where we have

\(\rm when \: x=x_1, y = y_1\\when\: x = x_2, y= y_2\)

Remember that, we divide by the change in independent variable so that we get some idea of how much the dependent quantity changes as we change the independent quantity by 1 unit.

(5 change per 3 unit can be rewritten as 5/3 change per 1 unit)

The distance traveled by the tracker depends on the time passed.

Let the variable "t" tracks the amount of time passed and let the variable "d" tracks the distance traveled by the tracker, then we have:

\(\rm At \: t = t_1 = 3.5, d=d_1 = 5.5 \: m\\At \: t = t_2 = 10.9, d = d_2 = 16.5 \: m\)

Thus, the constant rate of current is obtained by

\(Rate = \dfrac{d_2 - d_1}{t_2 - t_1} = \dfrac{16.5 - 5.5}{10.9 - 3.5} = \dfrac{11}{7.4} \\\\Rate \approx 1.4865 \: \text{meters per second}\)

Thus,

The constant rate of the current is given by 1.4865 meters per second.

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It should be noted that the power that the volunteers use to pushe the van is 200 watts.

From the information, they used a total force of 1,200 newtons and ater pushing the Van for 15 minutes, they were able to move the van 150 meters away from your house.

It should be noted that power is calculated as:

Power = Force × Displacement / Time

Force = 1200 Newton

Displacement = 150 meters

Time = 15 minutes = 15 × 60 = 900 seconds.

Therefore, the power that the volunteers use to pushe the van is:

Power = Force × Displacement / Time

=(1200 × 150) / 900

= 200 Watt.

Therefore, it should be noted that the power that the volunteers use to pushe the van is 200 watts.

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Answer:

The growth model that represents the population of this city is not linear--it is exponential:

\(f(t) = 10000( {1.025}^{t} )\)

\(t = 0 \: represents \: 2010\)

1.1. Accumulated depreciation:

The accumulated depreciation for the machine bought on 1 July 2013 would be R150,000 as of 31 March 2016.

1.2. Machine realization:

The machine bought in 2013 was sold for R120,000 on 30 June 2015, resulting in a profit/loss on the sale of R10,000.

1.1. Accumulated Depreciation:

To calculate the accumulated depreciation, we need to determine the annual depreciation expense for each machine and then accumulate it over the years.

Machine bought on 1 July 2013:

Cost: R250,000

Depreciation rate: 20% per annum on cost

Depreciation expense for the year ended 31 March 2014: 20% of R250,000 = R50,000

Depreciation expense for the year ended 31 March 2015: 20% of R250,000 = R50,000

Depreciation expense for the year ended 31 March 2016: 20% of R250,000 = R50,000

Accumulated depreciation for the machine bought on 1 July 2013:

As of 31 March 2014: R50,000

As of 31 March 2015: R100,000

As of 31 March 2016: R150,000

1.2. Machine Realisation:

To record the sale of the machine bought in 2013, we need to adjust the machine's value and the accumulated depreciation.

Machine's original cost: R250,000

Accumulated depreciation as of 30 June 2015: R100,000

Net book value as of 30 June 2015:  

R250,000 - R100,000 = R150,000.

On 30 June 2015, the machine was sold for R120,000.

Realisation amount: R120,000

To record the sale:

Debit Cash: R120,000

Debit Accumulated Depreciation: R100,000

Credit Machine: R250,000

Credit Machine Realisation: R120,000

Credit Profit/Loss on Sale of Machine: R10,000 (difference between net book value and realisation amount).

These entries will reflect the appropriate balances in the ledger accounts and properly close off the accounts for the years ended 31 March 2016.

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The Volume of the box is 12 cubic unit.

We have,

Height = 1 unit

Width = 2 unit

Length = 6 unit

So, Volume of box

= l w h

= 1 x 2 x 6

= 12 cubic unit

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Answer:

y=x-4

Step-by-step explanation:

Answer:

your answer is -1

Step-by-step explanation:

D = distributive property

S = switch

C = combine

I = inverse operations

F = finalize

\(4(3x - 5) -2x = -30\\12x -20 -2x = -30\\12x -2x = -30 + 20\\10x = -10\\x = \frac{-10}{10}\\ x = -1\)

Answer:

Simple it would be 76x - 1 whatever that is, and 72x + 3 which u shuld get like uh 75x, and 75x again on both so its 75x

PLEASE DONT QUOTE ME ON THIS

Xoxo~May

Step-by-step explanation:

1a. The percentage total return is -19.56%

1b. The dividend yield is 2.42%.

1c. The capital gains yield is -21.98%.

2a. The arithmetic average annual return on large-company stocks in nominal terms is 14.5%.

2b. The arithmetic average annual return on large-company stocks in real terms is 9.67%.

3a. The real return on long-term government bonds is 3.195%

3b. The real return on long-term corporate bonds is 3.291%

In Financial accounting, the percentage total return (P) can be calculated by using this formula;

P = [(Ending price - Initial price) + Dividend] ÷ Initial price

P = [(71 - 91) + 2.20] ÷ 91

P = -0.1956 or -19.56%

1b. For the dividend yield, we have:

Dividend yield = Dividend ÷ Initial price

Dividend yield = 2.20 ÷ 91

Dividend yield = 0.0242 or 2.42%

1c. For capital gains yield, we have:

Capital gains yield = (Ending price - Initial price) ÷ Initial price

Capital gains yield = (71 - 91) ÷ 91

Capital gains yield = -0.2198 or -21.98%.

Part 2.

a. The arithmetic average of annual return on large-company stocks in nominal terms is equal to 14.5%.

b. For arithmetic average annual return in real terms, we have:

(1 + 0.145) = (1 + r)(1 + 0.044)

r = (1.145/1.044) - 1

r = 9.67%

Part 3.

a. For real return on the long-term government bonds, we would apply Fisher equation:

(1 + i) = (1 + r)(1 + h)

Where:

(1 + 0.066) = (1 + r)(1 + 0.033)

1 + r = 1.066/1.033

r = 3.195%

b. For real return on long-term corporate bonds:

(1 + 0.067) = (1 + r)(1 + 0.033)

1 + r = 1.067/1.033

r = 3.291%

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The function representing the percent of group H in the population is given to be:

The number of years after 1990 when the population percentage of group H will be 15.6% can be calculated as follows:

Therefore, the year will be:

What this means is that from 2010 and beyond, the population percentage will be 15.6% or more.

Hence, the population percentage will be at least 15.6% in the year 2010 and after.

The area of the triangle is 97.07 units².

Given is a triangle we need to find the area,

So, let the triangle be ABC and the altitude be AD.

Using the trigonometric ratios,

Sin 52° = AB / AD

Sin 52° = 9 / AD

AD = 9 / Sin 52°

AD = 11.42

Now,

Tan 26° = DC / AD

Tan 26° = DC / 11.42

DC = 5.56

Also,

Cos 26° = AD / AC

Cos 26° = 11.42 / AC

AC = 12.7

BC = 11.42 + 5.56

BC ≈ 17

Now, the sides are BC = 17, AC = 12.7 and AB = 9,

The area of the triangle = 1/2 x BC x AD = 1/2 x 17 x 11.42

= 5.71 x 17

= 97.07

Hence the area of the triangle is 97.07 units².

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(i) Probability is a notion in Mathematics which describes the likelihood of an event or a set of events occurring. It is a measure of uncertainty when estimating the outcome of an experiment or an observation.

(ii) The axioms of probability are:

the non-negativity (that the probability of an event is greater than or equal to zero), and

the additivity (that the probability of the union of two or more mutually exclusive events is equal to the sum of their individual probabilities).

(iii) When two fair dice are thrown the probability of getting:

a) The sum of 9 = 1/9

b) Two odd numbers = 1/4

c) two prime numbers = 1/9

d)  two factors of 12 = 1/9

(iv) Statistics is a branch of mathematics that deals with data collection, analysis, interpretation, presentation, etc.

To find probability when two dice are thrown, we have:

(a) The sum of 9:

We will estimate the number of ways to get a sum of 9: (3,6), (4,5), (5,4), and (6,3) = 4 ways

A die has 6 possible outcomes, the total number of possible outcomes is 6x6=36 = 4/36 = 1/9.

(b) Two odd numbers:

We count the number of ways to get two odd numbers: (1,3), (1,5), (1,7), (3,1), (3,5), (3,7), (5,1), (5,3), and (5,7).

possible outcomes = 9,

So, the total possible outcomes = 6x6=36 = 9/36 = 1/4.

(c) Two prime numbers

We estimate the number of ways we can get two prime numbers: (2,3), (3,2), (5,2), and (2,5)

possible outcomes = 4,

So, the total possible outcomes = 6x6 =36 = 4/36, = 1/9.

(d) Two factors of 12:

We count the number of ways and divide by the total possible outcomes.

The factors of 12 are 1, 2, 3, 4, 6, and 12: (2,6), (3,4), and (4,3) = 3 ways

possible outcomes = 6

Therefore, the total number of possible outcomes = 6x6=36 = 3/36, = 1/12

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Convert them all into decimals. Percent is just 0.--, and the fraction you can calculate out which gives: 0.625=5/8,0.64=64%

5/8

64%

0.65

Answer:

x + 4 < 8

   - 4    -4

x < 4

Step-by-step explanation:

So, Basically anything less than 4 is a solution for this equation.

The probability that more than 2 students will attend is 0.9179.

Part (a) List the values that X may take on.

X may take on the values 0, 1, 2, 3, ..., 13.

Part (b) Give the distribution of X.

The distribution of X can be represented as follows: X-0:0, 1:0.23, 2:0.23, 3:0.23, 4:0.23, 5:0.23, 6:0.23, 7:0.23, 8:0.23, 9:0.23, 10:0.23, 11:0.23, 12:0.23, 13:0.23

Part (c) How many of the 13 students do we expect to attend the festivities? (Round your answer to the nearest whole number.)

We can expect 3 students to attend the festivities.

Part (d) Find the probability that at most 3 students will attend. (Round your answer to four decimal places.)

The probability that at most 3 students will attend is 0.6923.

Part (e) Find the probability that more than 2 students will attend. (Round your answer to four decimal places.)

The probability that more than 2 students will attend is 0.9179.

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Answer:

12 and 30

Step-by-step explanation:

-Both numbers are greater than 6

-Their highest common factor is 6

-Their lowest common multiple is 60

(12*5) and (30*2)

Answer:

Step-by-step explanation:

First, we need to convert the dimensions of the room from feet to yards, since the price is given per square yard.

24 feet = 8 yards (since 1 yard = 3 feet)

So the dimensions of the room are 8 yards x 1 yard.

The area of the room is 8 x 1 = 8 square yards.

The cost of the carpeting per square yard is $9.97.

So, the estimated cost of the carpeting would be:

8 x $9.97 = $79.76

Rounding this to the nearest cent gives an estimated cost of $79.76.

The ordered pairs are (1,0), (2,6/5),(3,12/5)

The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.

Given here: The equation as y = 6x/5 - 6/5

putting (1,0) in the equation we get 6×1/5-6/5=0

Similarly we can find the ordered pair as y = 6/5x - 6/5

Hence, The ordered pairs are (1,0), (2,6/5),(3,12/5)

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Answer:

15.25 is the better.

Step-by-step explanation:

you don't ounces divided by money.

The number line that shows the solutions of x < 5

A number line is a visual representation of the real numbers, ordered from left to right, with zero in the middle. It is typically a straight line that extends infinitely in both directions, with evenly spaced markings that represent specific points along the line.

The solution of x < 5 should consist of number less than 5

The inequality used is less than and hence should have values saying less than

Other options has numbers more than 5 such as 6 except option B

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Step-by-step explanation:

y=X -3/X

y=X/1 -3/x

y= 2x -3/x

y*X= 2x-3

y*X/2 = x-3

Answer:

Area = 240 cm²

Perimeter = 80 cm

Step-by-step explanation:

✔️ Area of the triangle = ½*base*height

base of the triangle = 24 cm

height = 20 cm

Plug in the known values

Area = ½*24*20

= 12*20

Area = 240 cm²

✔️Perimeter of the triangle = sum of all the three sides that make up the triangle

Perimeter = 22 + 24 + 34

= 80 cm

Answer: actually its 4

Step-by-step explanation: