Find the mean and the median of the data set. 31,32,36,31,30,35,33,30.

Answer:

59.09%

Step-by-step explanation:

35-22=13

13/2= .59090909=59.09%

q. answered

user rates 2

The matching of items and their corresponding descriptions are 1. Domain, 2.Output, 3. Input, 4. Relation, 5. Function, and 6. Range.

1. Domain - the first element of a relation or function; also known as the input value.

3. Input - the x-value of a function.

6. Range - the second element of a relation or function; also known as the output value.

4. Relation - any set of ordered pairs (x, y) that are able to be graphed on a coordinate plane.

2. Output - a relation in which every input value has exactly one output value.

5. Function - the y-value of a function.

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The value of the number is x = 34.

Let's break down the problem and solve it step by step.

1. "Five less than twice the value of a number": This can be represented as 2x - 5, where x is the number.

2. "Three times the quantity of 4 more than 1/2 the number": This can be represented as 3 * (x/2 + 4).

According to the problem statement, the two expressions are equal. We can set up the equation as follows:

2x - 5 = 3 * (x/2 + 4)

Now, let's solve the equation:

2x - 5 = 3 * (x/2 + 4)

Distribute the 3 to both terms inside the parentheses:

2x - 5 = (3/2)x + 12

Multiply through by 2 to eliminate the fraction:

2(2x - 5) = 2((3/2)x + 12)

4x - 10 = 3x + 24

Next, let's isolate the x term by moving the constant terms to the other side of the equation:

4x - 3x = 24 + 10

Simplify:

x = 34

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Answer:

ist cubes man

Step-by-step explanation:

The required number would be 2 which represents "the sum of 4 times a number, and -2 is the same as the sum of five times the number, and -2."

The sum of 4 times a number, and -2 is the same as the sum of five times the number, and -2.

Let's assume the number would be x

As per the given condition, the algebraic form would be as

⇒ 4(x - 2) = 5(x - 2)

Apply the distributive property of multiplication,

⇒ 4x - 8 = 5x - 10

Rearrange the terms of variable x,

⇒ 5x - 4x = 10 - 8

Apply the subtraction operation,

⇒ x = 2

Therefore, the required number would be 2.

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Answer: 277 ways

Step-by-step explanation:

Let’s start bycreating 10-unit pieces using the 4-unit piece.

The arrangements are:

1). 4-3-3 (3 permutations)

2). 4-3-2-1 = 4! = 24 permutations.

3). 4-3-1-1-1 (5*[4!/(3!1!)]

= 5*4

= 20permutations

4). 4-2-2-2 (4 permutations)

5). 4-2-2-1-1 (5 *[4!/(2!2!)]

= 5*6

= 30 permutations

6). 4-2-1-1-1-1(6*[5!/(4!1!)]

= 6*5

= 30 permutations

Let’s-consider the arrangements using one or more3-unit pieces and no 4-unit piece:

7). 3-3-2-2 (4!/(2!2!)

8). 3-3-2-1-1 (5*(4!/(2!2!)

= 5*6

= 30 permutations.

9). 3-3-1-1-1-1 (6!/(4!2!) = 0

10). 3-2-2-2-1 (5*4!/(3!1!)

= 5*4

= 20permutations

11). 3-2-2-1-1-1 (6*5!/(3!2!)

= 6*10

= 60 permutations

Finally we would look at the arrangements using only 1-and 2-unit pieces:

12). 2-2-2-1-1-1-1 (7!/(4!3!)

= 35 permutations

add them all up:

(3 + 24 + 20 + 4) + (30 + 30 + 6 + 30) + (15 + 20 + 60 + 35)

=51 + 96 + 130

= 277ways

The sum of the infinite geometric sequence is 3 3/4

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

The geometric sequence

In the geometric sequence, we have

First term, a = 3/5¹⁻¹

a = 3

Also, we have

Common ratio, r = 1/5

The sum of the infinite geometric sequence is calculated as

Sum = a/(1 -  r)

So, we have

Sum = 3/(1 -  1/5)

Evaluate

Sum = 3 3/4

Hence, the sum of the infinite geometric sequence is 3 3/4

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Answer: 19

Step-by-step explanation:

As per the model created by Jack; f(x) determines the area and x represents length so f(3) = 9+9+1

Therefore, f(3) = 19

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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Answer:

400,000

Step-by-step explanation:

➟ 10 × 4 ten thousand

Since, a ten thousand = 10,000 therefore 4 ten thousand = 40,000

➟ 10 × 40,000

➟ 400,000

Answer:

\(\displaystyle \frac{1}{2}\)

General Formulas and Concepts:

Math

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

\(\displaystyle (\frac{(2.7 - 0.8) \cdot 2\frac{1}{3}}{(5.2 - 1.4) \div \frac{3}{70}} + 0.125) \div 2\frac{1}{2} + 0.43\)

Step 2: Compute

The answer would be x = 2 (children) and y = 8 (adults). Therefore, the maximum number of passengers that can ride the elevator is 2 children and 8 adults.

The correct system of inequalities to model all the allowable combinations of children and adults that can ride an elevator is a and b. We can calculate the total weight of the passengers in the elevator by multiplying the number of children by the average weight of a child (60 pounds) and the number of adults by the average weight of an adult (130 pounds). Therefore, the first inequality, x + y < 10, sets the limit on the number of people in the elevator, and the second inequality, 130x + 60y < 1200, sets the limit on the total weight that the elevator can hold. To solve for the allowable combinations of passengers, we can set up and solve a system of equations. For example, if we want to find the maximum number of adults and children that can ride the elevator, we can solve the equations x + y = 10 and 130x + 60y = 1200. The answer would be x = 2 (children) and y = 8 (adults). Therefore, the maximum number of passengers that can ride the elevator is 2 children and 8 adults.

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a) The deepest that the diver went is of: 432 yards deep.

b) It took 12 minutes for the diver to return to the surface.

c) After one minute, the diver was 132 yards deep.

The quadratic function modeling the diver's height after x seconds is given as follows:

d(x) = 12x² - 144x.

The coefficients are given as follows:

a = 12, b = -144, c = 0.

The x-coordinate of the vertex is given as follows:

x = -b/2a

x = 144/24

x = 6.

Item a:

As a > 0, in item a, the minimum height is given as follows:

d(6) = 12(6)² - 144(6)

d(6) = -432 feet.

Item b:

The roots of the function, in item b, are obtained as follows:

12x² - 144x = 0

12x(x - 12) = 0

Hence:

12 - 0 = 12, hence it took 12 minutes for the diver to return to the surface.

Item c:

After one minute, the depth of the diver, in item c, is given as follows:

d(1) = 12(1)² - 144

d(1) = -132 yards.

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Answer: The commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer. The property holds for Addition and Multiplication, but not for subtraction and division.

Step-by-step explanation:

Hope this is right!!!!

Answer: See explanation

Step-by-step explanation:

a. Construct a decision tree for Wile

The solution to the question has been attached.

b. What is the expected value of the new car?

= [(0.2 × $10,000) + (0.8 × $18,000)] - $22,000

= $2000 + $14400 - $22000

= $16400 - $22000

= -$5600

c. What is the expected value of the used car?

= [(0.4 × $4000) + (0.6 ×$9000] - $12000

= $1600 + 5400 - $12000

= $7000 - $12000

= -$5000

d. What is the expected value of leasing the car?

= [(0.1 × -$2000) + (0.9 ×0)] - $8500

= -$200 - $8500

= -$8700

The complete distance in feet on the table are a=6, b=7, c=8, d=7, and e=6.

In mathematics, a revolution is a full rotation, or a full 360-degree turn. The item starts and ends in the same location during a 360-degree revolution.

The circumference of the wheel is equal to the length of a full revolution, or 2*pi*radius. The whole rotation of the wheel is 360 degrees.

The eight of the point is 6 feet, and the wheel's radius is 1 feet.

The point will be in its initial position, which is 6 feet high.

The height will thus be a = 6 + 0 = 6 ft.

The point will reach half the whole height of the wheel, or 2 feet, when the distance travelled is pi/2.

Height of b = 6 + 1 = 7 feet will result.

The point will be at the top of the wheel, which is 2 feet higher than the lower point of the wheel, when the distance travelled equals pi.

The height will thus be c = 6 + 2 = 8 ft.

The point will be half the whole height of the wheel, or 2 feet, when the distance travelled is 3 pi/2.

The height will thus be d = 6 + 1 = 7 ft.

The point will be in its initial position, which is 6 feet high, when the distance travelled is 2 pi.

The height will thus be e = 6 + 0 = 6 ft.

Hence, the complete distance in feet on the table are a=6, b=7, c=8, d=7, and e=6.

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The coefficients of the linear combination a · (1, 3, 2) + b · (1, - 5, 6) + c · (2, 1, - 2) = (4, 10, - 8) are a = 1, b = - 1 and c = 2.

Vectors can generated by combining vectors by means of fundamental operations in real fields (vector sum, multiplication of a vector by a scalar).

A vector is a linear combination of a given set of vectors when not all scalar coefficients are zero, at least one of them must not be zero. Herein we find a linear combination of vectors, that is, a vector composition of the form:

U = Σ αₙ · Vₙ, for n = {1, 2, 3, ..., m - 1, m}

Where:

Now we proceed to solve the linear combination. First, determine the vector generators and coefficients:

V₁ = (1, 3, 2), V₂ = (1, - 5, 6), V₃ = (2, 1, - 2)

α₁ = a, α₂ = b, α₃ = c

Second, create the equation of linear combination and simplify by real field operations:

U = α₁ · V₁ + α₂ · V₂ + α₃ · V₃

a · (1, 3, 2) + b · (1, - 5, 6) + c · (2, 1, - 2) = (4, 10, - 8)

(a, 3 · a, 2 · a) + (b, - 5 · b, 6 · b) + (2 · c, c, - 2 · c) = (4, 10, - 8)

(a + b + 2 · c, 3 · a - 5 · b + c, 2 · a + 6 · b - 2 · c) = (4, 10, - 8)

Where a, b, c are real coefficients (scalars).

Third, derive the resulting system of linear equations:

a + b + 2 · c = 4

3 · a - 5 · b + c = 10

2 · a + 6 · b - 2 · c = - 8

Fourth, find the solution to the system by means of numerical methods:

(a, b, c) = (1, - 1, 2)

The coefficients associated to the linear combination are (a, b, c) = (1, - 1, 2).

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9514 1404 393

Answer:

  5/4

Step-by-step explanation:

The ratio of long sides is ...

  right/left = 5/4

The scale factor is 5/4.

Answer:

\((x + (3+5i))^2 = x^2 + 6x + (10x+30)i - 16\)

Step-by-step explanation:

Complex numbers identity:

The complex numbers identity is:

\(i^2 = -1\)

Square of the sum:

\((x + y)^2 = x^2 + 2xy + y^2\)

In this question:

\((x + (3+5i))^2\)

\(x^2 + 2x(3+5i) + (3+5i)^2\)

\(x^2 + 6x + 10xi + 9 + 30i + 25i^2\)

\(x^2 + 6x + 9 + (10x+30)i - 25\)

\(x^2 + 6x + (10x+30)i - 16\)

So

\((x + (3+5i))^2 = x^2 + 6x + (10x+30)i - 16\)

Answer:

yes me me me me me ,,,,,,,,,,,,,,,,,,,, ....

The next number should be 297.

Answer:

D

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 3x + 4 ← is in slope- intercept form

with slope m = - 3

given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{-3}\) = \(\frac{1}{3}\) , then

y = \(\frac{1}{3}\) x + c ← is the partial equation

to find c substitute (- 1, 5 ) into the partial equation

5 = - \(\frac{1}{3}\) + c ( add \(\frac{1}{3}\) to both sides )

5 \(\frac{1}{3}\) = c ⇒ c = \(\frac{16}{3}\)

y = \(\frac{1}{3}\) x + \(\frac{16}{3}\) ( multiply through by 3 to clear the fractions )

3y = x + 16

Answer:

Because it makes factoring easier because the coefficient are smaller requiring less step

Answer:

10 ....................

A rectangle that could have a perimeter of 52 feet is a 12 feet by 14 feet rectangle.

The symbols W and L are variables.

The symbol P is a constant.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

P = 2(L + W)

52 = 2(12 + 14)

52 = 2(26)

52 feet = 52 feet.

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Answer:

D 12,000

Step-by-step explanation:

There is 1000 meters in every km

a. The chart is prepared below.

b. At the end of 4 years, Ross still owes his parents $1,576.92.

To solve this problem, we need to calculate the balance of Ross's loan at the end of each year.

The balance for each year can be calculated by subtracting the yearly payment from the balance at the beginning of the year and adding the interest earned for the year.

The interest for each year is calculated by multiplying the balance at the beginning of the year by the annual interest rate of 3.2%.

Here are the steps for calculating the balance for each year:

Year 1:

Beginning balance = $2,500.00

Interest for the year = $2,500.00 x 0.032 = $80.00

Ending balance = $2,500.00 + $80.00 - $300.00 = $2,280.00

Year 2:

Beginning balance = $2,280.00

Interest for the year = $2,280.00 x 0.032 = $72.96

Ending balance = $2,280.00 + $72.96 - $300.00 = $2,052.96

Year 3:

Beginning balance = $2,052.96

Interest for the year = $2,052.96 x 0.032 = $65.76

Ending balance = $2,052.96 + $65.76 - $300.00 = $1,818.72

Year 4:

Beginning balance = $1,818.72

Interest for the year = $1,818.72 x 0.032 = $58.20

Ending balance = $1,818.72 + $58.20 - $300.00 = $1,576.92

Here's a table that shows the details:

Year ,principal ,Interest rate, interest, Payment ,annual owing

1 $2,500.00 $80.00 $300.00              $2,280.00

2 $2,280.00 $72.96 $300.00              $2,052.96

3 $2,052.96 $65.76 $300.00               $1,818.72

4 $1,818.72         $58.20  $300.00       $1,576.92

b. At the end of 4 years, Ross still owes his parents $1,576.92.

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Answer: factorizar x de x ^ 2 + 5x.

x (x + 5)

Step-by-step explanation: