eight hundred twenty nine and six tenths as a decimal

The largest power of 10 that is a factor of 1000! is 5^249, or 10^249.

(a) To find the largest power of 10 that is a factor of 50!, we need to count the number of factors of 5 in 50! since each factor of 5 contributes at least one factor of 10.

There are 10 multiples of 5 in 50!, namely 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50. Each of these contributes one factor of 5. There are also 2 multiples of 25 (25 and 50), each of which contributes an additional factor of 5. Therefore, the total number of factors of 5 in 50! is 10 + 2 = 12.

Since each factor of 10 contains one factor of 5 and one factor of 2, we also need to count the number of factors of 2. It is clear that there are more factors of 2 than factors of 5, so we only need to count the factors of 5. Therefore, the largest power of 10 that is a factor of 50! is 5^12, or 10^12.

(b) To find the largest power of 10 that is a factor of 1000!, we follow the same reasoning as in part (a). The number of factors of 5 in 1000! is:

⌊1000/5⌋ + ⌊1000/25⌋ + ⌊1000/125⌋ + ⌊1000/625⌋ = 200 + 40 + 8 + 1 = 249

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The firm's federal income tax is $57,168.

To calculate the firm's federal income tax, we need to determine its taxable income first. Taxable income is calculated by subtracting deductions from the firm's total income.

In this case, the firm's total income consists of income from operations, interest income, and dividend income.

Total income:

Income from operations = $231,000

Interest income = $23,100

Dividend income = $29,700

Total income = $231,000 + $23,100 + $29,700 = $283,800

Next, we deduct expenses from the total income. In this case, the only relevant expense is the interest paid to bondholders:

Total expenses = Interest paid to bondholders = $11,000

Taxable income = Total income - Total expenses = $283,800 - $11,000 = $272,800

Now, we can calculate the federal income tax by applying the federal tax rate of 21% to the taxable income:

Federal income tax = Taxable income * Federal tax rate

Federal income tax = $272,800 * 0.21 = $57,168

Therefore, the firm's federal income tax is $57,168.

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Answer:

i believe it's D since the number has to be greater than or equal to 4

The expected value of a $2 ticket is $0.63

To calculate the expected value of a $2 ticket, we need to multiply the probability of winning by the value of the prize, then sum those products:

The Probability of winning the grand prize = 1/2000

Product: (1/2000) x $500 = $0.25

The Probability of winning a secondary prize: 3/2000

Product: (3/2000) x $200 = $0.30

The Probability of winning a third level prize: 8/2000

Product: (8/2000) x $20 = $0.08

The sum of the products:

$0.25 + $0.30 + $0.08 = $0.63

So the expected value of a $2 ticket is $0.63, meaning that on average, a person can expect to win $0.63 for every $2 they spend on a ticket.

The charity is expected to make a profit, which is why the answer is negative.

That is -$2 + $0.63 = -$1.37

So the expected profit for the charity per ticket sold is -$1.37, which is approximately the same as the given answer of negative $1.358(rounding off)

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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.

Answer:

A. -8

I hope this was correct :)

Answer:

p^(m+n)

Step-by-step explanation:

p^m * p^n

We know that when they are multiplied when the bases are the same, we add the exponents

p^(m+n)

Answer:

D

Step-by-step explanation:

7 is it because it is positive

Answer:

2

Step-by-step explanation:

Answer:

The answer is 2

Step-by-step explanation:

at least I think it is

Answer:

$6.84

Step-by-step explanation:

This is quite a simple question, simply add the new deposited amount into the original balance to get your answer.

It would take approximately 17.12 years for the amount to reach Birr 56,398.43 with a deposit of Birr 500 at the end of each six-month period, compounded semi-annually at an interest rate of 6%.

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount

P = Principal amount (initial deposit)

r = Annual interest rate (in decimal form)

n = Number of compounding periods per year

t = Number of years

In this case, the principal amount is Birr 500, the annual interest rate is 6% (or 0.06), and the interest is compounded semi-annually, so there are 2 compounding periods per year.

We need to find the number of years (t) it takes for the amount to reach Birr 56,398.43.

Let's substitute the given values into the formula and solve for t:

56,398.43 = 500(1 + 0.06/2)^(2t)

Divide both sides by 500:

112.79686 = (1 + 0.03)^(2t)

Take the natural logarithm of both sides to eliminate the exponent:

ln(112.79686) = ln(1.03)^(2t)

Using the property of logarithms, we can bring down the exponent:

ln(112.79686) = 2t * ln(1.03)

Now, divide both sides by 2 * ln(1.03):

t = ln(112.79686) / (2 * ln(1.03))

Using a calculator, we find t ≈ 17.12.

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Using a trigonometric relation we can see that AB = 8.7 units.

We can see that the triangle is a right triangle, and we want to find AB, which is the bottom cathetuis.

We know the hypotenuse and two angles, then we can use the trigonometric relation:

sin(a) = (adjacent cathetus)/hypotenuse

Replacing what we know:

sin(60°) = AB/10

10*sin(60°) = AB

8.7 = AB

That is the measure of AB.

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Answer:

a. lines intersecting at a single point

b. one solution

Step-by-step explanation:

a. The equations can be rewritten as:

y = -5x+23 and y = -1/6x+1

Comparing the equations with standard equation: y=mx+c, where m is the gradient of the line formed by the linear equation.

Since the gradient of the lines are different then the lines cannot be parallel and will intersent at one point.

b. The equation will have one solution as below.

The equations can be rewritten as:

5x+y=23

5x+30y=30

Subtracting both equation will result in,

29y=7

=> y=7/29

Hence x= 660/29

Answer:

Michaels class

Step-by-step explanation:

63 kids and 70 kids One group gets 9 groups and the other gets 10. 27/9 is 3, whileas 20/10 is 2 so Michaels class had more. Hope this helps :D

The answer of the given question based on graphing and crafting is you will create a Mobius strip , and when we cut it into lengthwise  you will get a single, longer Mobius strip.

A Möbius strip is a one-sided surface with only one boundary component. It is named after the German mathematician August Ferdinand Mobius who discovered it in 1858.

A Mobius strip can be created by taking  rectangular strip of paper, giving it  half-twist, and then connecting two ends of  strip together to form  loop. The resulting loop will have interesting property of being non-orientable, which means that it only has one side.

If you take a strip of paper, put two half-twists in it, and glue the ends together, you will create a Mobius strip.

When you cut a Mobius strip length wise down the middle while hugging the right edge, you will get a single, longer Mobius strip that has two full twists instead of the original two half twists. This is because cutting down the middle of the Mobius strip results in flipping one of the twists, which combines with the original twist to create a double twist.

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The possible values for the range of f(x) are given by:

The range of a function f(x) is the set that contains all possible output values for the function. Looking at the graph of the function, the range is composed by the values of y.

In this problem, the function is not given, so I can't give you an exact answer, but since the range is composed by the values of y, the first option is not possible, and the possible values for the range of f(x) are given by:

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Answer:

B only

Step-by-step explanation:

Triangles A and C are similar, but not congruent to each other. Similar triangles have proportional sides and congruent angles, while congruent triangles have congruent sides and congruent angles.

Therefore, only B is correct

The question is asking for pairs of congruent triangles but lacks key information needed to accurately answer this, such as lengths or angles. Congruent triangles are identified in geometry based on either side-lengths or angles.

The question is about congruent triangles, which in mathematics means triangles that have the same size and shape. But to accurately answer which pairs show two congruent triangles, we need more information. The options provided include 'A', 'B', and 'C' but without knowing more about these elements (for example their lengths or angles), it is impossible to determine which are congruent. Congruent triangles are identified in geometry based on either side lengths (SSS: Side-Side-Side, SAS: Side-Angle-Side, ASA: Angle-Side-Angle) or angles (AAS: Angle-Angle-Side, HL: Hypotenuse-Leg for right triangles). Without this vital information, we cannot definitively answer the question. Be sure to verify all the properties required to prove two triangles congruent.

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Answer:

y = 78

Step-by-step explanation:

66 + 4 = 70 + 4 = 74 + 4 = 78

-12 + 3 = -9 + 3 = -6 + 3 = -3

x = -3

y = 78

The solution of the expression for r is given by:

\(r = \sqrt{\frac{3x}{2m\pi}}\)

To solve the expression for r, we must isolate r, as a function of the other variables.

The expression is modeled by:

\(m = \frac{3x}{\pi r^2h}\)

Then, isolating r:

\(mr^2 = \frac{3x}{2\pi}\)

\(r^2 = \frac{3x}{2m\pi}\)

\(r = \sqrt{\frac{3x}{2m\pi}}\)

Thus, the solution of the expression for r is given by:

\(r = \sqrt{\frac{3x}{2m\pi}}\)

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Answer: $0.576

Step-by-step explanation:

The total amount in prizes is $1800.

For there to be 60% profit, the total cost of the tickets need to be \(1800(1.6)=\$ 2880\).

Thus, each ticket must sell for \(\frac{2880}{5000}=\$ 0.576\)

Step-by-step explanation:

The given line is

y = 3x - 1

3x - y - 1 = 0 .....i)

The line perpendicular to the line I Is

x + 3y + k = 0 .....ii)

The line II) passes through the point (7, 4) so

7 + 3 *4 + k = 0

7 + 12 + k = 0

19 + k = 0

I. e k = - 19

So the required equation is x + 3y - 19 = 0

Hope it will help :)❤

Answer: 17.5 lbs of plums are required to make 20 rolls of fruit leather.

Step-by-step explanation:

Since 7 lbs of plums yield 8 rolls of fruit leather, 1 lb will yield 1 1/7 rolls of fruit leather.

To find how many pounds of fruit will yield 20 rolls of fruit leather, divide how many rolls of leather you want to get by how many rolls of leather one pound will yield.

20 divided by 8/7 equals 17 1/2.

Answer:

a plus b equals 9923

Step-by-step explanation:

Step-by-step explanation:

Find the prime factorization of 35

35 = 5 × 7

Find the prime factorization of 56

56 = 2 × 2 × 2 × 7

To find the GCF, multiply all the prime factors common to both numbers:

Therefore, GCF = 7

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hhjhg&6%%%_&__&%_

Answer:

32/45 is your required answer

Answer:

your answer will be 14/45

Step-by-step explanation:

2/5 × 7/9

= 2 × 7

  5 × 9

= 14/45

Answer:

34

Step-by-step explanation:

18656954+3666637=85496654÷3456=34

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

A Residual is just the difference between the observed value in an experiment or survey and the value predicted by the regression line.

This means that the Residual can be calculated using the formula:

Thus, if we are told that a piece of data has a residual of -1.3829, it means that the difference between one of the observations from the experiment or survey conducted and the value predicted by the regression line is -1.3829.

Mathematically,

Answer:

20!

Step-by-step explanation:

1. 20 = 10 + 10

2. 20 = 40 - 20

3. 20 = 2 × 10

4. 20 = 40 ÷ 2

5. 20 = 10 + 6 + 4

6. 20 = 5 × 4

7. 20 = ?

8. 20 = 60 ÷ 3

ohh someone already answered

1. 20 = 15 (square) + 5 (circle)

2. 20 = 26 (square) - 6 (circle)

3. 20 = 5 (square) × 4 (circle)

4. 20 = 17 (square) + 3 (circle)

5. 20 = 8 (square) + 8 (square) + 4

6. 20 = 5 (square) × 4

7. 20 = 2 × 20 (square) - 20 (square)

8. 20 = 60 ÷ 3 (circle)

9. 8 × 6 = 39 + 9 (circle)

10. 7 × 6 = 49 (square) - 7 (circle)

11. The problems with 2 of the same shape,

    and problems with only one shape,

    The problems with two alike shapes means that, since they have to be

    the same number, there is no room for modification, or increasing the

    value of one shape and subtracting the same transformation from the

    other.

    With problems #6, #8 and #9, the singular shapes work as a variable in

    an expression, with usually only one making the identity true.

12.