Your chess board is the shape of a square with a 12 inch diagonal (measured from one vertex to the opposite vertex). Find the area.

An integer is a whole number that can be positive, negative, or zero and is pronounced as "IN-tuh-jer."

Integers include things like -5, 1, 5, 8, 97, and 3,043.

5.643.1, -1.43, 1 3/4, 3.14,.09, and other non-integer numbers are a few examples.

Formally, the following describes the set of numbers designated Z:

Z = {..., -3, -2, -1, 0, 1, 2, 3, ...}

The four most frequent ones are p, q, r, and s.

An infinite set is the set Z. In spite of the possibility of an unlimited number of items in a set, denumerability refers to the property that each element in the set can be represented by a list that implies its identity. The fact that 356,804,251 and -67,332 are integers whereas 356,804,251.5, -67,332.89, -4/3, and 0.232323... are not can be inferred from the list "..., -3, -2, -1, 0, 1, 2, 3,...."

There are no elements missing from either set when pairing the components of Z with N, the set of natural numbers. Let N = {1, 2, 3, ...}. Following that, the pairing may go like this:

The key criterion for assessing cardinality, or size, in infinite sets is the presence of a one-to-one relationship. Z shares the same cardinality with the sets of natural and rational numbers. Real, fictitious, and complex number sets, however, have cardinality that is more than Z.

To Learn more About integer Refer To:

https://brainly.com/question/929808

#SPJ4

The probability that two randomly chosen individuals in the United States both wear a seat belt while driving is approximately 18.49%.

To calculate the probability that both randomly chosen individuals are wearing a seat belt, we can multiply the individual probabilities together.

The probability of the first person wearing a seat belt is 43%, which can be expressed as 0.43 or 43/100. Since the first person's choice does not affect the second person's probability, the probability of the second person wearing a seat belt is also 43%.

To find the probability of both events occurring, we multiply the two probabilities together:

0.43 * 0.43 = 0.1849 or 18.49%

Therefore, the probability that both randomly chosen individuals are wearing a seat belt is approximately 18.49%.

To learn more about probability click here

brainly.com/question/32117953

#SPJ11

10 and 13 are the measure of the values of x and y respectively

The given diagram is a parallelogram with unknown values x an y.

Since the measure of sum of angles in a triangle is 180 degrees, hence we will take the measure of the angles in the triangle EFY to have:

70 + 7x - 5 + 45 = 180

110 + 7x = 180

7x = 180 - 110

7x = 70

x = 10

Similarly for the triangle EDY;

45 + 70 + 5y = 180

115 + 5y = 180

5y = 180 - 115

5y = 65

y = 13

Hence the measure of the values of x and y are 10 and 13 respectively

Learn more on parallelograms here: https://brainly.com/question/970600

#SPJ1

Estimated change = 11.98 - Objective function value with a right-hand side of 9

To determine how much the objective function is expected to change when the right-hand side of the constraint is increased from 8 to 9, we need to calculate the shadow price or dual value associated with that constraint.

In the given problem:

Objective function: Minimize 3X^2 - 22X + 2XY + Y^2 - 16Y + 60

Constraint: X + 5Y ≤ 8

To find the shadow price or dual value, we can solve the problem using linear programming techniques. However, without access to the specific methodology or algorithm used to solve the problem, I am unable to provide an exact solution or calculate the shadow price accurately.

However, if we assume that the linear programming problem has been solved, and the optimal solution for the original problem with a right-hand side of 8 is X = 3.08 and Y = 0.98, with an optimal objective function value of 11.98, we can estimate the change in the objective function value.

The estimated change in the objective function value can be calculated by subtracting the optimal objective function value with the new right-hand side (9) from the original optimal objective function value (11.98).

Estimated change = 11.98 - Objective function value with a right-hand side of 9

Please note that without access to the specific methodology used to solve the problem or the actual shadow price/dual value, this calculation is an estimation based on the provided information.

To obtain the actual change and re-solve the problem with a new right-hand side of 9, I would need the specific linear programming methodology used to solve the problem or more details on the specific algorithm employed.

Learn more about constraints here:

https://brainly.com/question/30968609

#SPJ11

Answer:

Step-by-step explanation:

first you have to make this an improper fraction my multiplying -3 by 11 then add the product of that to 6 and put it all over 11

\(-3\frac{6}{11}\) → \(-\frac{39}{11}\)

once you get this you have to do the reciprocal of this to get them to equal 1

\(-\frac{39}{11}\) → \(-\frac{11}{39}\)

then multiply the number by the reciprocal

\(-\frac{39}{11}* -\frac{11}{39}=\frac{429}{429}=1\)

Answer:

Susan is riding her bike. The distance she travels varies directly with the number of revolutions (turns) her wheels make. See the graph below.

23

20

Answer:

A

Step-by-step explanation:

The first one is a function

Answer:

A

Step-by-step explanation:

The 1's and 2 's complements of the following binary numbers:

11101010 (original)

00010101 (1's complement)

00010110 (2's complement)

a) For 1's complement, we simply flip all the bits:

11101010 (original)

00010101 (1's complement)

For 2's complement, we first find the 1's complement and then add 1:

11101010 (original)

00010101 (1's complement)

00010110 (2's complement)

b) For 1's complement, we simply flip all the bits:

01111110 (original)

10000001 (1's complement)

For 2's complement, we first find the 1's complement and then add 1:

01111110 (original)

10000001 (1's complement)

10000010 (2's complement)

c) For 1's complement, we simply flip all the bits:

00000001 (original)

11111110 (1's complement)

For 2's complement, we first find the 1's complement and then add 1:

00000001 (original)

11111110 (1's complement)

11111111 (2's complement)

d) For 1's complement, we simply flip all the bits:

10000000 (original)

01111111 (1's complement)

For 2's complement, we first find the 1's complement and then add 1:

10000000 (original)

01111111 (1's complement)

10000000 (2's complement)

e) For both 1's complement and 2's complement, we simply have the original number because the number is already 0:

00000000 (original)

00000000 (1's complement)

00000000 (2's complement)

To learn more about binary numbers visit:https://brainly.com/question/31102086

#SPJ11

Answer:

B

Step-by-step explanation:

the area of the rectangle is 4x8 = 32

the area of each half of the triangle is 4x4/2 = 8.

8x2 = 16.

The triangle is 16, the rectangle is 32

The probability that Carol, the 44-year-old non-Hispanic black female, lives to be 64 years old is 0.82003.

What is mortality?

Mortality rate is a measure of the number of deaths in a given population over a specified period of time, usually expressed as the number of deaths per 1,000 or 100,000 people.

The mortality table gives the probability of survival from age 45 to 64. To calculate the probability of survival from age 44 to 64, we can subtract the probability of dying before age 45 from the probability of surviving to age 64. The probability of dying before age 45 for a non-Hispanic black female is 0.00208, and the probability of surviving to age 64 is 0.82212. Subtracting 0.00208 from 0.82212 gives us 0.82003 as the probability that Carol, a 44 year old non-Hispanic black female, will live to be 64 years old.

In conclusion, the probability that Carol, the 44-year-old non-Hispanic black female, lives to be 64 years old is 0.82003. This probability is calculated by subtracting the probability of dying before age 45 (0.00208) from the probability of surviving to age 64 (0.82212), as found in table 18 of the 2019 Annuity 2000 Mortality Table.

For more questions related to probability,

https://brainly.com/question/30034780

#SPJ1

Answer:

she is correct

Step-by-step explanation:

Jerome's sister is correct. She is correct because 6:16 is a duplicate of the recipe and is equivalent ratio of 3:8, but still is a larger amount of energy drink using the same measurements.

Answer:

she is correct

Step-by-step explanation:

because they are all the same numbers just multiplied

Histograms and box plots are graphical representations for the frequency of numeric data values. The data and explore the central tendency and variability before using advanced statistical analysis techniques.

In statistics, a histogram is a graphical representation of the distribution of data. The histogram is represented by a set of rectangles, adjacent to each other, where each bar represent a kind of data. Statistics is a stream of mathematics that is applied in various fields.

Both histograms and box plots are used to explore and present the data in an easy and understandable manner. Histograms are preferred to determine the underlying probability distribution of a data. Box plots on the other hand are more useful when comparing between several data sets. They are less detailed than histograms and take up less space.

To see the image at the bottom of the explanation.

Learn more about Histogram at:

https://brainly.com/question/28975056

#SPJ4

Answer:

60

Step-by-step explanation:

Well initial value is the starting amount or when x is 0

when x is 0 y is 60 hence 60 is the answer

Answer:

true

depending on how complete the table of values is.

Answer:

Step-by-step explanation:

Q1

A graph which uses horizontal or vertical bars with no gaps to represent data is called bar graph.

Q2

Data plotted against the frequency in a histogram is class interval.

Q3

The data plotted against the frequency in an ogive is cumulative frequency.

Q4

A score of 50 under the column > c.f. with the boundaries 23.5 - 28.5 means 50 students got a score greater than 23.5.

Q5

Mean = 2(2) + 3 + 4 + 7(3) + 10 + 11 + 2(12) / 11

Mean = 4 + 7 + 21 + 21 + 24 / 11

Mean = 77/11

The mean is 7

Q6

The median is the middle term.

The median of the distribution is 7

To construct the first simplex tableau using the Big M method. The initial artificial basic solution is x₅ = 20 and x₆ = 50. The initial entering basic variable is x₁ and the leaving basic variable is x₅.

To construct the first simplex tableau using the Big M method, we first rewrite the problem in standard form as follows:

Maximize \(Z = 2x₁ + 5x₂ + 3x₃\)
subject to
\(x₁ - 2x₂ + x₃ + x₄ = 20\\2x₁ + 4x₂ + x₃ = 50\\x₁ ≥ 0, x₂ ≥ 0, x₃ ≥ 0, x₄ ≥ 0.\)

To construct the initial simplex tableau, we introduce artificial variables x₅ and x₆ to the two equations.

The initial tableau is:

 Basis   |  x₁   |  x₂   |  x₃   |  x₄   |  x₅   |  x₆   |   RHS  
----------------------------------------------------------------------
    x₅    |   1    |   2    |   1    |   0    |   1    |   0    |   20    
    x₆    |   2    |   4    |   1    |   0    |   0    |   1    |   50    
----------------------------------------------------------------------
    -Z    |  -2    |  -5    |  -3    |   0    |   0    |   0    |   0    

The initial artificial basic solution is x₅ = 20 and x₆ = 50. The initial entering basic variable is x₁ and the leaving basic variable is x₅.

Know more about variable  here:

https://brainly.com/question/28248724

#SPJ11

Using the Big M method, the complete first simplex tableau for the given linear programming problem is constructed as follows:

┌─────────────┬──────┬───────┬───────┬─────┬─────┬─────┬─────────────┐

│     BV      │  x₁  │   x₂  │   x₃  │ s₁  │ s₂  │ a₁  │      RHS    │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────┼─────────────┤

│      Z      │  2   │   5   │   3   │  0  │  0  │  0  │      0      │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────┼─────────────┤

│   x₁ - 2x₂  │  1   │  -2   │   1   │ -1  │  0  │  0  │     20      │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────┼─────────────┤

│   2x₁ + 4x₂ │  2   │   4   │   1   │  0  │ -1  │  0  │     50      │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────┼─────────────┤

│     x₁      │  1   │   0   │   0   │  0  │  0  │ -M  │      0      │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────┼─────────────┤

│     x₂      │  0   │   1   │   0   │  0  │  0  │ -M  │      0      │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────┼─────────────┤

│     x₃      │  0   │   0   │   1   │  0  │  0  │ -M  │      0      │

└─────────────┴──────┴───────┴───────┴─────┴─────┴─────┴─────────────┘

The initial (artificial) basic solution is x₁ = 0, x₂ = 0, x₃ = 0, s₁ = 20, s₂ = 50, a₁ = 0. The initial entering basic variable is x₁, which has the most positive coefficient in the objective row. The leaving basic variable is s₁, determined by selecting the row with the smallest positive ratio of the right-hand side (RHS) to the entering column's coefficient. In this case, the ratio for the second row (20/1) is the smallest, so s₁ leaves the basis.

To construct the complete first simplex tableau using the Big M method, we first convert the given problem into standard form by introducing slack variables (s₁, s₂) for the inequalities and an artificial variable (a₁) for the equality constraint. We assign a large positive value (M) to the coefficients of the artificial variables in the objective row.

The first row represents the objective function, where the coefficients of the decision variables x₁, x₁₂₃ are taken directly from the given problem. The slack variables and the artificial variable (a₁) have coefficients of 0 since they don't appear in the objective function.

The subsequent rows represent the constraints. Each row corresponds to one constraint, where the coefficients of the decision variables, slack variables, and the artificial variable are taken from the original problem. The right-hand side (RHS) values are also copied accordingly.

The initial (artificial) basic solution is obtained by setting the decision variables to 0, the slack variables and the artificial variable to the right-hand side values. In this case, x₁ = 0, x₂ = 0, x₃ = 0, s₁ = 20, s₂ = 50, and a₁ = 0.

The initial entering basic variable is determined by selecting the most positive coefficient in the objective row, which is x₁ in this case. The leaving basic variable is determined by finding the smallest positive ratio of the RHS to the entering column's coefficient. Since the ratio for the second row (20/1) is the smallest, s₁ leaves the basis.

The resulting tableau serves as the starting point for applying the simplex method to solve the linear programming problem iteratively.

Learn more about Big M Method:

https://brainly.com/question/32588617

#SPJ11

Answer:

hi

Step-by-step explanation:

hi

Answer:

87.4 sq ft   uncovered

Step-by-step explanation:

Total room area     - rug area

  (10 * 10)                - pi (2)^2 =

Answer:

I believe that if the power went off you wouldnd see at all.

Step-by-step explanation:

Mirrors bend light to show the images of yourself and others that you see. not sure if im right but... hope it helps.

Answer:

Suppose that the wholesale of a bike is A (A is the 100% in this case). If we have an increase of 30% for the sale price, we have the new price of:

Price = A + (30%/100%)A = A + 0.3*A = (1.3)*A

Then if we know that the price tag of the bike is $125, then we have:

$125 = (1.3)*A

$125/1.3 = A = $96.15

The wholesale cost of the bike is $96.15

Answer:

1. Andre wants to buy a bike that has a price tag of $125. What was the wholesale cost of this bike?    $ 96.15

2. If the bike is discounted by 20%, how much will Andre pay (before tax)?  

                        $ 100

                                     I hope this helped <33 !

Answer:

9,000 m2

Step-by-step explanation:

If the longer rope has three times the length of the shorter rope, the perimeter and the sides of the triangle formed by the longer rope are three times the perimeter and sides of the triangle formed by the smaller rope.

The area of an equilateral triangle is:

\(Area = \frac{side^{2} * \sqrt{3}}{4}\)

So, if the side is three times bigger, the area will be 9 times bigger (3^2).

The area of the small triangle is 1000 m2, so the area of the bigger triangle is 9 * 1,000 = 9,000 m2

Answer:

26.66666666666667

Step-by-step explanation:

1200/45=

If the standard deviation of a set of data is 6, then the value of variance is 36

The formula for determining variance is variance = √Standard deviation

Variance of a set of data is equal to square of the standard deviation.

If the standard deviation of a set of data is 6 then we get variance by putting the value of standard deviation in the formula

variance = √Standard deviation

Take square root on both sides

Standard deviation² = 6²

Standard deviation= 36

Hence,  standard deviation of a set of data is 6, then the value of variance is 36

To learn more on Statistics click:

https://brainly.com/question/30218856

#SPJ1

Answer:

y= 65

x=4

Step-by-step explanation:

Hope this help!!!

Have a great day!!!

Answer:

Solution given;

m<DCA=<BCA[diagonal of a parallelogram or rhombus bisect the angle]

13x-16=9x+4

13x-9x=16+4

4x=20

x=20/4

x=5.

now

2<ADB+<BCD=180°[co interior angle]

2<ADB=180-13*5+16-9*5-4

<ADB=82/2

<ADB=41 ° is a required answer.

Answer:

$0.12

Step-by-step explanation:

10 folders - $1.20

1 folder - ?

cross multiply

1 × 1.20 / 10

= 1.20 ÷ 10

= $0.12

Answer:

$0.12 and $0.14 are the prices per folder

Step-by-step explanation:

I'm just guessing that this is the answer not entirely sure.

the value of the iterated integral is (π/8) (2 - e^(-16)).

We have the iterated integral:

∫[0,4] ∫[0,√(16-x^2)] e^(-x^2-y^2) dy dx

To convert this to polar coordinates, we need to express x and y in terms of r and θ.

We have:

x = r cos(θ)

y = r sin(θ)

We also need to express the differential element dA in terms of polar coordinates. We have:

dA = r dr dθ

Substituting these expressions into the given integral, we get:

∫[0,π/2] ∫[0,4] e^(-r^2) r dr dθ

The limits of integration for θ are 0 to π/2 because the region lies in the first and second quadrants.

We can evaluate this integral using the fact that the integral of e^(-r^2) is √π/2:

∫[0,π/2] ∫[0,4] e^(-r^2) r dr dθ

= ∫[0,π/2] [-1/2 e^(-r^2)] [0,4] dθ

= ∫[0,π/2] (1/2 - 1/2 e^(-16)) dθ

= π/4 - π/8 (1 - e^(-16))

= (π/8) (2 - e^(-16))

To know more about coordinates visit:

brainly.com/question/22261383

#SPJ11

Answer: 125

Step-by-step explanation:

\(0^{3} = 0 \\1^{3} = 1\\2^{3} = 8\\3^{3} = 27\\4^{3} = 64\\5^{3} = 25 * 5 = 125\)

Answer:

125

Step-by-step explanation:

Because 5×5×5=125

if it has 3 exponents then you multiply 3 times