How many centimeters are there in 3.35 meters?

A. 115
B. 225
C. 335
D. 445

a) The number of integer-valued solutions is 61, (b) the number of solutions is 62, (c) the number of solutions is 63, and (d) the number of solutions is 6.

a) The number of integer-valued solutions to x1 + x2 + x3 + x4 + x5 = 63, where all xi > 0, can be found using the stars and bars method. We want to find the number of ways to place 63 "stars" into 5 "bars", such that each bar has at least one star.

This is equivalent to the number of solutions to (x1 - 1) + (x2 - 1) + (x3 - 1) + (x4 - 1) + (x5 - 1) = 57, where all xi are non-negative integers. The number of solutions is given by the coefficient of x57 in the expansion of (x + 1)5, which is (5 + 57 - 1) choose (57) = 5 + 57 choose 57 = 61.

b) The number of integer-valued solutions to x1 + x2 + x3 + x4 + x5 = 63, where all xi ≥ 0, can be found using the same method as above. This is equivalent to the number of solutions to x1 + x2 + x3 + x4 + x5 = 63, where all xi are non-negative integers.

The number of solutions is given by the coefficient of x63 in the expansion of (x + 1)5, which is (5 + 63 - 1) choose (63) = 5 + 63 choose 63 = 62.

c) The number of integer-valued solutions to x1 + x2 + x3 + x4 + x5 ≤ 63, where all xi ≥ 0, can be found using the generating function method.

The generating function for the sequence of non-negative integers is given by (1 - x)^-1 = 1 + x + x^2 + x^3 + ... The coefficient of x^n in this series gives the number of solutions to x1 + x2 + x3 + ... + xk = n, where all xi are non-negative integers.

The coefficient of x^63 in (1 - x)^-1 is 1, and the coefficient of x^64 is 0, so there is only 1 solution where x1 + x2 + x3 + x4 + x5 = 63.

d) The number of integer-valued solutions to x1 + x2 + x3 + x4 + x5 = 63, where all xi ≥ 0, x2 ≥ 10, can be found by subtracting the number of solutions where x2 < 10 from the total number of solutions where all xi ≥ 0.

Let's call the number of solutions where x2 < 10 as S1 and the total number of solutions where all xi ≥ 0 as S2. Then, S2 - S1 = the number of solutions where x2 ≥ 10. To find S1, we use the stars and bars method as before, but now we need to place 53 stars into 4 bars since x2 must be at least 10.

The number of solutions is (4 + 53 - 1). Choose (53) = 56. To find S2, we use the generating function method as before. The number of solutions is (5 + 63 - 1). Choose (63) = 62. Thus, S2 - S1 = 62 - 56 = 6.

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--The given question is incomplete; the complete question is

"How many integer-valued solutions are there to each of the following equations and inequalities?

a) x1 + x2 + x3 + x4 + x5 = 63,all xi > 0

b) x1 + x2 + x3 + x4 + x5 = 63,all xi ≥ 0

c) x1 + x2 + x3 + x4 + x5 ≤ 63,all xi ≥ 0

d) x1 + x2 + x3 + x4 + x5 = 63,all xi ≥ 0, x2 ≥ 10"--

The basic ratio of minutes of painting to minutes of instruction is 7 : 6

From the question, we have the following parameters that can be used in our computation:

Painting = 63 minutes

Instruction = 54 minutes

The ratio can be represented as

Ratio = Painting : Instruction

When the given values are substituted in the above equation, we have the following equation

Painting : Instruction = 63 : 54

Simplify

Painting : Instruction = 21 : 18

Simplify

Painting : Instruction = 7 : 6

This  ratio cannot be simplified

Hence, the solution is 7 : 6

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Answer:

21 ft

Step-by-step explanation:

e

The vertex of the parabola f(x) = 2x^2 - 4x + 6 is (1, 4)

The function is given as:

f(x) = 2x^2 - 4x + 6

Differentiate the function

f'(x) = 4x - 4

Set to 0

4x -4 =0

So, we have:

4x = 4

Divide by 4

x = 1

Substitute x = 1 in f(x) = 2x^2 - 4x + 6

f(1) = 2(1)^2 - 4(1) + 6

This gives

f(1) = 4

This means that the vertex is (1, 4)

Next, we set x = 0.

So, we have:

f(0) = 2(0)^2 - 4(0) + 6

This gives

f(0) = 6

This means that the parabola passes through the point (0, 6)

See attachment for the parabola

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Answer:

10 6

................

Answer:

  (c)  five raised to the fourth power divided by three raised to the tenth power

Step-by-step explanation:

You want the simplified version of the quantity five raised to the negative second power times three raised to the fifth power end quantity all raised to the negative second power.

The relevant rules of exponents are ...

  (ab)^c = (a^c)(b^c)

  a^-b = 1/a^b

  (a^b)^c = a^(bc)

The given expression can be simplified as follows:

  \((5^{-2}3^5)^{-2}=5^{(-2)(-2)}3^{(5)(-2)}=5^43^{-10}=\boxed{\dfrac{5^4}{3^{10}}}\)

__

Additional comment

We find math expressions easier to understand when they are written using math notation, instead of words.

To convert  Celsius to Fahrenheit, Josh needs to use the formula; F = (9/5)C + 32

Let C represent the degrees Celsius and F represent the degrees Fahrenheit.

The relationship between C and F is given as:

C = (F-32) × 5/9

Hence to convert Celsius to Fahrenheit, we make F the subject of formula:

C = (F-32) × 5/9

9C/5 = (F-32)

F = (9/5)C + 32

To convert  Celsius to Fahrenheit, Josh needs to use the formula; F = (9/5)C + 32

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Answer:

Step-by-step explanation: This is one of the most common examples given in math textbooks, and it's useful to know if you ever travel outside the U.S., or if you are from outside the U.S. and travel here.

C = 5/9 (F - 32)

9C = 5(F - 32)

9/5 C = F - 32

9/5 C + 32 = F

F = 9/5 C + 32

The approximate height of the pole in centimeters is 17,500 centimeters.

We have,

Let's start by calculating the total length of the pole, which is buried plus the part that protrudes from the ground.

We know that the part that protrudes is 25 meters and that it represents one-seventh of the total length.

25 = L/7

where L is the total length of the pole.

We can solve for L by multiplying both sides of the equation by 7:

L = 7 x 25

  = 175 meters

Now we need to convert this length to centimeters.

Since 1 meter is equal to 100 centimeters,

175 meters x 100

= 17,500 centimeters

Therefore,

The approximate height of the pole in centimeters is 17,500 centimeters.

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The complete question.

The Clarisse company, dedicated to the telephone business, is expanding its coverage, due to this, it is placing poles, where the seventh part of a pole is buried, and protrudes 25 meters from the ground. Calculate the approximate height of the pole in centimeters.

Answer:

15

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

to find the average, add the numbers together, then multiply by the quantity.

12+14+16=42

42/3= 14

14 is the average

hope this helped <3333333333333333

The expression (4000 - 0.03x) represents the discounted price per unit when x units are purchased and multiplying by x gives the total revenue from selling x units at that price.

Revenue can be defined as the total amount of income generated by the sale of goods and services related to the primary operations of the business.

The revenue (R) from a particular distributor that buys x units can be calculated using the following function statement:

R(x) = (4000 - 0.03x) * x

Where

The expression (4000 - 0.03x) represents the discounted price per unit when x units are purchased, and multiplying by x gives the total revenue from selling x units at that price.

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The term “inverse” in mathematics generally refers to an operation that undoes or reverses another operation. However, the phrase "inverse of maths tools" doesn't really make sense because “maths tools” is not a specific mathematical operation.

Mathematical tools can refer to various instruments or techniques used in mathematics, such as calculators, rulers, compasses, graph paper, software, etc. Each of these tools has its own purpose and may or may not have an inverse operation or tool associated with it.

For example, the inverse of addition is subtraction, the inverse of multiplication is division, and the inverse of differentiation is integration. However, it's not clear what the inverse of a “maths tool” would be.

Therefore,  a) The inverse of “Add 25” would be “Subtract 25.”What is the  b) The inverse of “Divide -18” would be “Multiply -18.” c) The inverse of “Subtract 3” would be “Add 3.” d) The inverse of “Multiply 14” would be “Divide 14.”

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Step-by-step explanation:

To eliminate x in the system of equations:

1. Multiply Equation 1 by 9 and multiply Equation 2 by -4, this gives:

Equation 1: 36x -54y = 90

Equation 2: -36x - 8y = -28

2. Add the two equations together to eliminate x:

(36x - 54y) + (-36x - 8y) = 90 - 28

Simplifying, we get:

-62y = 62

3. Solve for y:

y = -1

4. Substitute y = -1 into one of the original equations, say Equation 1:

4x - 6(-1) = 10

Simplifying, we get:

4x + 6 = 10

5. Solve for x:

4x = 4

x = 1

Therefore, the solution to the system of equations is x = 1 and y = -1. We can check that these values are correct by substituting them back into the original equations and verifying that they satisfy both equations.

9514 1404 393

Answer:

  23, 49

Step-by-step explanation:

Let s represent the smaller of the two numbers. Then the larger is s+26, and the sum is ...

  s + (s+26) = 72

  2s = 72 -26

  s = (72 -26)/2 = 23

Then the larger number is

  s +26 = 49

The two numbers are 23 and 49.

_____

The reason we wrote the solution this way is to show you that the smaller number is half the difference between the given sum (72) and difference (26). This is the generic solution to a "sum and difference" problem. The smaller number is always half the difference of the give sum and difference. (Similarly, the larger is always half the sum of the given sum and difference.)

That is, the two numbers are always half the sum ± half the difference:

  72/2 ± 26/2 = {36+13, 36-13} = {49, 23}

Answer:

Amount invested in A (8%) = $20,000

Amount invested in B (7%) = $9,000

Step-by-step explanation:

Given:

Total amount invested = $29,000

Interest rate A = 8% = 0.08

Interest rate B = 7% = 0.07

Annual return = $2,230

Find:

Amount invested in each

Computation:

Assume;

Amount invested in A = x

Amount invested in B = 29,000 - x

So,

Interest receive from A = x × 0.08

Interest receive from A = 0.08 x

Interest receive from B = (29000 - x) × 0.07

Interest receive from B = 2,030 - 0.07 x

Annual return = Interest receive from A + Interest receive from B

2,230 = 0.08 x + 2,030 - 0.07 x

x = 20,000

Amount invested in A = $20,000

Amount invested in B = 29,000 - $20,000

Amount invested in B = $9,000

Answer:

a) Brain sweep out 4 radians

b) Brian is -0.3922 km to the right of the center of the ski trail

c) Brian is -0.4541 km above of the center of the ski trail

Step-by-step explanation:

Given the data in the question;

circular ski trail radius = 0.6 km

Derek starts at the 3-o'clock position and travels 2.4 km in the counter-clockwise direction.

a) How many radians does Brian sweep out?

arc length = 2.4 km

from the diagram;

arc length = rθ

θ = arc length / r

θ = 2.4 / 0.6

θ = 4 radians

Therefore, Brain sweep out 4 radians

b) When Brian stops skiing, how many km is Brian to the right of the center of the ski trail?

from the diagram;

x = rcosθ

we substitute

x = 0.6 × cos(4)

x = 0.6 × -0.65364

x = -0.3922 km

Therefore Brian is -0.3922 km to the right of the center of the ski trail

c) When Brian stops skiing, how many km is Brian above of the center of the ski trail?

from the diagram;

m = rsinθ

m = 0.6 × -0.7568

m = -0.4541 km

Therefore, Brian is -0.4541 km above of the center of the ski trail

Answer:

492

Step-by-step explanation:

6x82

Answer:

the answer is 492 the person above me is correct!!

Step-by-step explanation:

Answer:

Step-by-step explanation:

8\(\frac{1}{3}\) + 3\(\frac{1}{3}\)

=8*3+1/3 + 3*3+1/3

=24+1/3 + 9+1/3

=25/3 + 10/3

taking LCM od denominator

=25+10/3

=35/3

11\(\frac{2}{3}\) acres

Answer:

Step-by-step explanation:

sin (B) = \(\frac{2}{5}\)

Answer:

16

Step-by-step explanation:

140 divided by 9 = 15.5

you need 16 vans to hold 140 tourists

Answer:

-33=c

Step-by-step explanation:

-11×3=c/-11×-11 which cancels out the -11 and c equals -33

Answer:

1. C. The researcher must compute an estimated standard error for the mean difference score to compute a t statistics.

2. B. 10

3. A. 12

Step-by-step explanation:

The degrees of freedom is number of independent variable factors that affect the range of parameters. The degrees of freedom is the calculation of number values that are free to vary. The degrees of freedom is calculated by N-1. Standard error is the estimated deviation of standard deviation from its sample mean distribution.

Answer:

Prime numbers only have two factors which is 1 and itself so the HCF of a prime number is itself.

LCM of prime numbers is like the LCM of any other number. See where the lowest multiple of both prime numbers are equal.

Hope this helps.

Answer:

\(0.0005\) \(= 5 * 10^{-4\)

\(7.1034 * 10^3 = 7103.4\)

Step-by-step explanation:

Solving (a):

\(0.0005\)

Standard form is represented as:

\(a * 10^n\) where \(1 \le a \le 10\)

Move the decimal point to 5 and count the number of times the decimal point is moved forward (forward represents negative).

So:

\(a = 5\)

\(n = -4\)

Hence:

\(0.0005\) \(= 5 * 10^{-4\)

Solving (b):

\(7.1034 * 10^3\)

Express \(10^3\) as \(1000\)

This gives:

\(7.1034 * 10^3 = 7.1034 * 1000\)

\(7.1034 * 10^3 = 7103.4\)

Answer:

Step-by-step explanation:

U={x|x∈N and x<10}

or U={1,2,3,4,5,6,7,8,9}

B={x|x∈N and x is even and x<10}

or

B={2,4,6,8}

C={x|x∈N and x<10}

or

C={1,2,3,4,5,6,7,8,9}

(B∩C)={2,4,6,8}

(B∩C)'={1,3,5,7,9}

The number of people at the movie is 340

Let's represent the total number people at the movie as "x".

We know that the number of adults in the movie is 187 and the percentage of children is 45%

So we can write:

187 = (1 - 45%) * x

This gives

187 = 0.55x

To solve for x, we can divide both sides by 0.55:

x = 187/0,55

Evaluate

x = 340

Hence, the number of people is 340

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m = n+ x/p

m (*p) = n (*p) + x/p (*p)

mp = np + x

x= mp - np

x= p ( m - n)