Consider your eight-digit student ID as a set of single-digit integers. For example, if your student ID is the number 01238586, then it represents the set S = {0, 1, 2, 3, 5, 6, 8}. Now consider your student ID as a sequence of eight digits. For example, if your student ID is the number 01238586, then it represents the sequence D = (0, 1, 2, 3, 8, 5, 8, 6). The sequence can be used to define a relation r:S -→ S by creating the elements of r as follows, r = {(d1, d2), (d3, d4), (d5, do), (d7, dz)} = > > The di, 1 < i < 8 are the digits in the sequence read left to right. For example, if your student ID is the number 01238586, then r = {(0, 1), (2, 3), (8,5), (8, 6)} 2 Questions to Answer a. Create the relation r using your student ID. Record the relation in roster notation as a set of 2- tuples (see example).
b. Extend your relation by adding the 2-tuple (d2, dị) to r, creating the relation R. That is, , R= r U {(d2, d])} Record the relation Ras a set of 2-tuples c. Find the transitive closure, T, of the relation R. Record the relation T as a set of 2-tuples.

Heron's formula states that the area of a triangle can be found using the following formula:[tex]A = √s(s-a)(s-b)(s-c)[/tex] where s is the semiperimeter of the triangle [tex](s = (a + b + c)/2)[/tex].

In the case of an equilateral triangle, all three sides (a, b, and c) are the same length. So, if we set x = y = z in the formula, we get [tex]A = √s(s-x)(s-x)(s-x).[/tex] Simplifying this expression yields [tex]A = (√s/4) * x^2[/tex].

We can also write the perimeter of the triangle as P = 3x. Substituting this into the area formula, we get [tex]A = [(P/3)*√3/4] * (P/3)^2[/tex]. This expression can be simplified to [tex]A = (1/12) * P^2 * √3.[/tex]

This shows that for a fixed perimeter, the area of an equilateral triangle is maximized. This is due to the fact that the area is proportional to the square of the sides, and in an  equilateral triangle all sides are equal, thus maximizing the area. Heron's formula states that the area of a triangle can be found using the following formula: A = √s(s-a)(s-b)(s-c) where s is the semiperimeter of the triangle (s = (a + b + c)/2).

Learn more about equilateral triangle here:

https://brainly.com/question/4268382

#SPJ4

We must establish both of the following statements in order to demonstrate that t(n) is unusual if and only if n is a perfect square.

First instruction: If t(n) is odd, n is a perfect cube.

Assume that t(n) is strange. All the positive divisors of n should be d 1, d 2, ldots, and d k. So, we understand that k=t(n) is unusual. The divisors can be combined into frack2 pairs, with a sum of n for each pair:

(d 1, d k), (d 2, d k-1)

If k is odd, only one divisor remains, which, if n is a perfect cube, is the square root of n. The conclusion is that n must be a perfect square if t(n) is unusual.

Second instruction: If t(n) is odd, then n is a perfect square and n is.

Let's assume that n is a perfect square, such as n=m2. Then, the positive divisors of n appear in pairs, denoted by (d, fracnd), where d spans all the divisors of m. We only need to tally the divisor d when d=fracnd because the product d cdot fracnd = n is not a perfect square if d is not equal to fracnd. Since m has an odd number of divisors, t(n) is only odd if and only if m.

We can look at m's prime factorization to understand why it has an odd amount of divisors. Write m=p 1,p 2,a 1,a 2,ldots,p k where p 1,p 2,a 1,a 2,ldots,p k are distinct prime numbers and a 1,a 2,ldots,a k are positive integers.

As a result, we have demonstrated that t(n) is odd only when n is a perfect square.

Learn more about square here:

https://brainly.com/question/14198272

#SPJ4

If the range of feasibility indicates that the original amount of a resource, which was 20, can increase by 5, then the amount of the resource can increase to 25. The statement is true.

If the range of feasibility for a given resource indicates that the original amount can increase by 5, that means the upper limit of the feasible range is 20 + 5 = 25. Therefore, the amount of the resource can increase up to 25, which is the upper bound of the feasible range.

However, it's important to note that just because the resource can increase up to 25 doesn't mean it will actually reach that level. The feasibility range only indicates what is possible or allowable based on certain criteria or constraints. Whether the resource actually increases to that level will depend on various factors such as availability, demand, and cost.

In summary, if the range of feasibility for a resource indicates an increase of 5 from an original amount of 20, then the amount of the resource can increase up to 25, but the actual increase will depend on other factors.

To learn more about range of feasibility visit: https://brainly.com/question/15700431

#SPJ4

The height of the building is given as follows:

205 feet.

The three trigonometric ratios are defined as follows:

Regarding the angle of 64º, we have that:

Hence the height is obtained applying the tangent of 64º, as follows:

tan(64º) = h/100

h = 100 x tangent of 64 degrees

h = 205 feet.

More can be learned about trigonometric ratios at brainly.com/question/24349828

#SPJ1

Answer:

x = 2.4

Step-by-step explanation:

[tex]2x + 4 \times \frac{1}{5} = 9 \\ = 2x + \frac{21}{5} = 9 \\ = 5 \times 2x + 5 \times \frac{21}{5} = 9 \times 5 \\ = 10x + 21 = 45 \\ = 10x = 45 - 21 \\ = 10x = 24 \\ \frac{10x}{10} = \frac{24}{10} \\ \times = 2.4[/tex]

It is false, consecutive sides of a parallelogram are not parallel.

A parallelogram is a quadrilateral, which is a four-sided polygon with straight sides. It is defined as a four-sided shape in which opposite sides are parallel and congruent (having the same length), and opposite angles are also congruent (having the same measure).

Here,
A parallelogram is a quadrilateral with two pairs of parallel sides. This means that any two opposite sides of a parallelogram are parallel to each other.

Therefore, it is false that, consecutive sides of a parallelogram are not parallel.

Learn more about parallelogram here: https://brainly.com/question/14984005

#SPJ1

Answer: the number is 12.

Step-by-step explanation:

Let's call the two-digit number "x". We know that the sum of its digits is 7, so we can represent the number as 10a + b, where a and b are the digits of the number and a is the tens digit and b is the units digit.

The statement that "reversing its digits increases the number by 9" means that the number obtained by reversing the digits is x + 9. We can represent this reversed number as 10b + a.

So, we have two equations:

10a + b = x

10b + a = x + 9

Now, we can substitute the value of x from the first equation into the second equation:

10b + a = 10a + b + 9

Expanding both sides, we get:

10b + a = 10a + b + 9

9b = 9a + 9

b = a + 1

We know that 0 < a < 9, since the number is a two-digit number. So, we can conclude that 0 < b < 10.

We can now substitute the value of b into the first equation:

10a + (a + 1) = x

11a + 1 = x

11a = x - 1

a = (x - 1) / 11

Since a is the tens digit of the number, it must be an integer. We can test different values of x to find the value that satisfies this condition.

If x = 20, then a = (20 - 1) / 11 = 1. This gives us b = a + 1 = 2. The original number is 10a + b = 10 + 2 = 12, which satisfies all the conditions.

So, the number is 12.

The vertices of the ellipse are:-

x = 3.625; x = 4.375

y = 0; y = -3

An ellipse is a plane curve surrounded by two focal points, such that the sum of the two distances to the focal points is a constant for all points on the curve. It generalises a circle, which is a special type of ellipse with the same two focal points.

We can rewrite the equation to standard form to see the centre and semi-axis lengths.

16x² -128x +y² +3y = -256

16(x² -8x +16) +(y² +3y +2.25) = -256 +256 +2.25

16(x -4)² +(y +1.5)² = 9/4 . . . . . write as squares

(x -4)²/(9/64) +(y +1.5)²/(9/4) = 1 . . . . divide by 9/4

((x -4)/0.375)² +((y +1.5)/1.5)² = 1 . . . . put in useful form

In this form, we have

((x -h)/a)² +((y -k)/b)² = 1

where (h, k) is the centre, 2a is the length of the axis in the x-direction, and 2b is the length of the axis in the y-direction. The required tangents are,

x = h±a

y = k±b

For the given ellipse, the tangent lines are,

x = 4 -0.375 = 3.625, x = 4.375

y = -1.5 -1.5 = -3, y = -1.5 +1.5 = 0

To know more about an ellipse follow

https://brainly.com/question/28701170

#SPJ1

The area of the given figure will be 145.13 m².

The area of a rectangle is calculated as length multiplied by width, while the area of a semi-circle is half the area of a circle with the same radius. We can calculate the combined area of the rectangle and semi-circle as follows:

Area of rectangle = length x width = 15 m x 8 m = 120 m^2

Area of semi-circle = 1/2 x pi x radius^2 = 1/2 x pi x 4^2 = 8 pi m^2

To find the total combined area, we add the area of the rectangle to the area of the semi-circle:

Total combined area = Area of rectangle + Area of the semi-circle

= 120 m² + 8π m²

= 120 m² + 25.13 m² (using π= 3.14159)

= 145.13 m

Therefore, the combined area of the rectangle and semi-circle is 145.13 square meters (rounded to two decimal places).

To know more about an area follow

https://brainly.com/question/29719061

#SPJ1

Answer:

if my calculation is correct the answer is 16 3/8-9 5/8 - fraction calculator. The result is 27/4 = 6 3/4 = 6.75 = twenty-seven quarters (or six and three quarters)

Step-by-step explanation:

The population size varies in several ways. The sample size was insufficient, which is the best explanation for why the simulation of the sampling distribution is not roughly normal.

A person's or a researcher's choice of sample size will limit the study's statistical power if it is too small or inadequate for the alpha level and the analyses they have decided to do.

Because of the aforementioned, it is much harder to determine from one's sample whether a statistical effect is existent in the population.

A sample size that is either too small or too large can affect the ability to extrapolate the results, with the latter increasing the detection of differences and accentuating statistical differences that are not clinically significant.

The complete question is:-

A recent survey indicated that the mean time spent on a music streaming service is 210 minutes per week for the population of a certain country. A simulation was conducted to create a sampling distribution of the sample mean for a population with a mean of 210. The following histogram shows the results of the simulation.Which of the following would be the best reason why the simulation of the sampling distribution is not approximately normal?

A. The samples were not selected at random.

B . The sample size was not sufficiently large.

C. The population distribution was approximately normal.

D. The samples were selected without replacement.

E. The sample means were less than the population mean.

To learn more about sample size, refer:-

https://brainly.com/question/25894237

#SPJ4

The density of the object is 3.4 × 10¹² mg/kL.

Density of an object is defined as the mass of the object per unit volume.

The formula to calculate the density of an object is,

D = M / V

Here D is the density, M is the mass and V is the volume of the object.

Given that,

M = 850.0 kg = 850 × 1,000,000 mg = 85 × 10⁷ mg

V = 25 cL = 25 × 10⁻⁵ kL

Substituting the values,

Density = (85 × 10⁷ mg) / (25 × 10⁻⁵ kL)

             = 3.4 × 10⁷⁻⁻⁵

             = 3.4 × 10¹² mg/kL

Hence the density of the given object is 3.4 × 10¹² mg/kL.

Learn more about Density here :

https://brainly.com/question/29775886

#SPJ9

So, one serving of Kind bars, which is two bars, contributes for roughly 13.8% of a 2,000 calorie diet's daily fat consumption.

An equation is a mathematical statement that shows that two expressions are equal. Equations can be used to represent relationships between variables, or to solve problems. Equations use mathematical symbols, such as the equal sign (=), to show the equality between the two expressions. For example, the equation 2x + 3 = 7 represents the relationship between the variable x and the constants 2 and 3. The equation can be solved for x to find its value. In this case, solving for x would give us x = 2.

Here,

The calculation for determining the percentage of daily fat intake in a serving of Kind bars is based on the Recommended Dietary Allowance (RDA) for fat. The RDA is a guideline for the average daily amount of a nutrient that is considered sufficient to meet the needs of most people.

For a 2,000 calorie diet, the RDA for total fat is about 65 grams per day. To calculate the percentage of daily fat intake in a serving of Kind bars, you divide the total amount of fat in the serving by the RDA for daily fat and multiply by 100.

For example, if one serving of Kind bars contains 9 grams of fat, you would perform the following calculation:

9 grams fat ÷ 65 grams RDA for daily fat x 100 = 13.8% daily fat intake

So, one serving of Kind bars, which is two bars, accounts for approximately 13.8% of a person's daily fat intake for a 2,000 calorie diet.

TO know more about equation,

https://brainly.com/question/2228446

#SPJ1

Answer:

The answer to your question is 1680

Step-by-step explanation:

1 day is 24 hours

So to find the answer we will multiply 70 days by 24 hours which will give us 1680 hours.

I hope this helps and have a wonderful day!

3(x + 16)< 27 is the expression for three times the sum of a number and 16 is a least 27.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We are given that three times the sum of a number and 16 is a least 27

Here we can see that  three times the sum of a number and 16 means

3(x + 16)

Therefore, 3(x + 16)< 27

Hence, 3(x + 16)< 27 is the expression.

More about the Algebra link is given below.

brainly.com/question/953809

#SPJ1

Answer: The five-number summary of the given data is a concise summary of the main characteristics of the data set and includes the following statistics:

Minimum: 2

Q1 (first quartile), or 25th percentile: 8

Median (second quartile), or 50th percentile: 16

Q3 (third quartile), or 75th percentile: 20

Maximum: 25

Note: The approximation method involves rounding the results to the nearest whole number.

Step-by-step explanation:

The function that models the data is [tex]y = 42.(\frac{1}{2})^x[/tex].

The formula for exponential growth is [tex]y = y_0e^{(kt)}.[/tex]

The formula for exponential decay is [tex]y = y_0e^{(-kt)}.[/tex]

Let, The given exponential be [tex]y = a(b)^x[/tex] .

Now, At (0, 42).

42 = ab⁰.

a = 42.

At (1, 21).

21 = 42.b¹.

b = 1/2.

Therefore, [tex]y = 42.(\frac{1}{2})^x[/tex]is the required function.

learn more about exponential functions here :

https://brainly.com/question/14355665

#SPJ1

on solving the provided question we can say that the function at  (h, k) = (1, - 3), will be [tex]g(x) = (x - 1)^2 - 3- > B[/tex]

Mathematics deals with numbers and their variants, equations and associated structures, forms and their positions, and locations where they might be found. The term "function" describes the connection between a group of inputs, each of which has a corresponding output. A function is an association between inputs and outputs where each input results in a single, unique outcome. A domain and a codomain, or scope, are assigned to each function. Functions are often denoted by the letter f. (x). The input is an x. On functions, one-to-one functions, many-to-one functions, within functions, and on functions are the four primary categories of functions that are available.

The graph of g(x) has its vertex at (1, - 3)

The equation of a parabola in vertex firm is

[tex]y = a(x - h)^2 + k[/tex]

(h, k) =coordinates of the vertex

and

a is a multiplier

(h, k) = (1, - 3),

[tex]g(x) = (x - 1)^2 - 3- > B[/tex]

To know more about function visit:

https://brainly.com/question/28193995

#SPJ1

The options that are true with respect to the lengths of the sides of the triangle and the included angle between sides a and b are;

The triangle is not a right triangle

cos(θ) < 0

The angle θ is an obtuse angle

A triangle is a polygon that has three sides and three interior angles.

The specified sides of the triangle are; a, b, and c

The relationship between the squares of the lengths of the sides, obtained from a similar question is presented as follows; a² + b² < c²

The specified measure of the angle opposite the side c = θ

According to Pythagorean Theorem, a triangle is a right triangle, if in the triangle, we can get; a² + b² = c²

The specified inequality, relating the squares of the lengths of the sides, a² + b² < c², which therefore, indicates;

According to cosine rule, we get;

c² = a² + b² - 2·a·b·cos(θ)

However; a² + b² < c²

c² - (a² + b²) = -2·a·b·cos(θ)

a² + b² < c²

0 < c² - (a² + b²)

0 < c² - (a² + b²) = -2·a·b·cos(θ)

0 < -2·a·b·cos(θ)

Dividing both sides by -1, the inequality sign is reversed, and we get;

0/(-1) > -2·a·b·cos(θ)/(-1) = 2·a·b·cos(θ)

0 > 2·a·b·cos(θ)

Therefore; 2·a·b·cos(θ) < 0

2·a·b·cos(θ)/(2·a·b) = cos(θ)  < 0/(2·a·b) = 0

cos(θ) is therefore, negative, which indicates that θ is in the second quadrant, with the solution, obtained using an online tool which can be expressed as follows;

(π/2) + 2·π·n < θ < (3·π/2) + 2·π·n

Where n = 0, we get;

(π/2) < θ < (3·π/2); The angle θ is therefore larger than π/2 = 90° and less than (3·π/2) = 270°, which in a triangle the maximum angle is 180°, indicating that the angle θ is an obtuse angle.

Part of the question includes to select the options that are true from the following;

cos(θ) < 0

The angle θ is an obtuse angle

The specified triangle is a right triangle

The triangle is not a right triangle

Learn more on the Pythagorean Theorem here: https://brainly.com/question/25958868

#SPJ1

The statement that ; "Null A is the set of all solutions of the equation Ax = 0" , is True because null space is the set of solutions of equation Ax = 0 .

The Dimensions of the matrix A is written as m × n ;

The Null Space of a matrix A, is denoted by null(A), and

The Null Space is defined as the set of all solutions to the homogeneous linear equation Ax = 0, where x is an n-dimensional column vector.

In other words, we say that  null(A) consists of all vectors x that make the  Ax = 0 that is the Zero vector.

Therefore , we can conclude that Null A is the set of all solutions of the equation Ax = 0  .

Learn more about Null Space here

https://brainly.com/question/17215829

#SPJ4

The given question is incomplete , the complete question is

Let A be an m×n matrix.  The statement is True or False ?

Null A is the set of all solutions of the equation Ax = 0  .

The solution for the given equation is 6. Therefore, option A is the correct answer.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is |2x+3=15.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Now, 2x=15-3

2x=12

x=6

Therefore, option A is the correct answer.

To learn more about an equation visit:

https://brainly.com/question/14686792.

#SPJ9

To assume that the sampling distribution of the sample mean is approximately normal -  A random sample of 10 taken from a population distribution that is skewed to the right.

There are several conditions that must be met for the sampling distribution of the sample mean to be approximately normal, including:

In these cases, the central limit theorem may not apply and the sampling distribution may not be approximately normal.

For such more question on sample:

https://brainly.com/question/24466382

#SPJ4

The following question may be like this:

For which conditions is not appropriate to assume that the sampling distribution of the sample mean is approximately normal?

3/12 =1/4  hopefully this answer works for you

Step-by-step explanation:

JKLM to J'K'L'M -

Reflection, over the line y=x

J'K'L'M to J"K"L"M -

Dilation of 1/2

Hope this helps :)

Since g(x) increases less frequently than f(x), Jeremiah is correct in saying that g(x) increases more gradually than f(x).

It seems like some of the numbers in the table are cut off. Nevertheless, we can determine if Jeremiah was correct in saying that g(x) increases more gradually than f(x).

From the given information, we know that f(x) = IlxIl (the greatest integer function). This function increases by 1 whenever x crosses an integer value.

Jeremiah's function is g(x) = [x] (the floor function), which is the greatest integer less than or equal to x. This function increases by 1 only when x is an integer.

Since g(x) increases less frequently than f(x), Jeremiah is correct in saying that g(x) increases more gradually than f(x).

To know more about integer function:

https://brainly.com/question/27250114

#SPJ4

w = amount of wagon stamps

b = amount of sailboat stamps

so hmm we know Megan bought 4 stamps, so whatever "w" and "b" are, we know that w + b = 4.

we also know that Megan spent 16 cents on all, and that the wagon ones cost 1c, so for "w" amount that's a total of 1*w or 1w.  Now, the sailboat stamps cost 5c, that will give us a total of 5*b or 5b for those.

[tex]w+b=4\implies b=4-w \\\\[-0.35em] ~\dotfill\\\\ 1w+5b=16\implies \stackrel{\textit{substituting from the 1st equation}}{1w+5(4-w)=16} \implies w+20-5w=16 \\\\\\ 20-4w=16\implies 20=4w+16\implies 4=4w\implies \cfrac{4}{4}=w\implies \boxed{1=w} \\\\\\ \stackrel{\textit{since we know that}}{b=4-w}\implies b=4-1\implies \boxed{b=3}[/tex]

The linear equation of the table is  y = 3x - 81.

Linear equation can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, let's find the slope of the table as follows:

slope = m = - 69 + 72 / 4 - 3

m = 3 / 1

m = 3

Therefore, let's find the y-intercept using (3, -72).

Hence,

y = 3x + b

-72 = 3(3) + b

b = -72 - 9

b = - 81

Hence, the equation is y = 3x - 81

learn more on linear equation here: https://brainly.com/question/30414224

#SPJ1

Answer:

400.059

How do you write this problem as a decimal?

So the first part of this question is four hundred:

400.

But then.. It says fifty nine hundredths. So lets write it out.

The closer we get to the decimal it gets " smaller " example the hundredths is all the way in back and the tenths is all the way to the front! So with that knowledge lets figure it out:

( to make it nice and simple for you ):

0.059

The " 9 " is in the hundredths zone and the " 5 " is in the tenths zone. So just like on top it looks like that.

0.059+400=

400.059

Thus, your answer is 400.059

Using percentages we know that the water that will drain in the 2nd hour will be 25% of the remaining water.

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred.

A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.

The symbol "%" is frequently written after the number to indicate percentages.

Convert both percentages to fractions of 100 or decimals, multiply them, then use the result to calculate the percentage of the %.

Calculating 50% of 40%, for instance, yields (50/100) x (40/100) = 0.50 x 0.40 = 0.20, which equals 20/100 or 20%.

NOTE: Using the percent sign and a division by 100 at the same time is improper.

So, in the first hour:

The drained water is 20%.

Remaining left: 80%

Then, 20% of 80 would be:

20/80 * 100 = 25%

Therefore, using percentages we know that the water that will drain in the 2nd hour will be 25% of the remaining water.

Know more about percentages here:

https://brainly.com/question/24877689

#SPJ1

Dylan made a mistake as he switched the values for the variables.

The graph's x-axis (horizontal line) should contain the independent variable, and the y-axis should contain the dependent variable (vertical line). At the origin, where the coordinates are, the x and y axes intersect (0,0).

Given:

We have x shows the number of toys and y axis the number of bones.

The two lines intersect at (15, 31).

As, Dylan interpreted this graph of a solution and determined that the pet store gave away 15 bones and 31 toys at a recent pet adoption event.

Dylan made a mistake as he switched the values for the variables.

Usually, 15 shows the toys and 31 shows the bones.

Learn more about Graph here:

https://brainly.com/question/17267403

#SPJ9