Let R be the relation defined on Z by aRb if a + b is even. Show that R is an
equivalence relation.

The correct statement about rectangles is:

1. All rectangles are parallelograms.

2. Parallelograms have exactly 1 pair of parallel sides.

3. So, all rectangles have exactly 1 pair of parallel sides.

A rectangle is a type of parallelogram that has additional properties. By definition, a rectangle is a quadrilateral with four right angles. This means that opposite sides of a rectangle are parallel. Since all four sides of a rectangle are right angles, it follows that a rectangle has exactly 1 pair of parallel sides.

Option 1 states that only some rectangles are parallelograms, which is incorrect. All rectangles are parallelograms because they have opposite sides that are parallel.

Option 2 states that parallelograms have 2 pairs of parallel sides, which is also incorrect. Parallelograms have exactly 2 pairs of parallel sides, not 4. A rectangle is a special type of parallelogram that has additional properties such as all angles being right angles.

Option 3 states that only some rectangles have 2 pairs of parallel sides, which is incorrect. All rectangles have exactly 1 pair of parallel sides, not 2. Having 2 pairs of parallel sides would make a shape a parallelogram, not a rectangle.

Therefore, the correct statement is that all rectangles are parallelograms and have exactly 1 pair of parallel sides. 1,2,3 are correct.

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There is no solution in the system

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

The augmented matrix

In the augmented matrix, we have

Rows = 4

Columns = 6

This means that

There are 4 equations in the system and there are 5 variables

The general rule is that

The number of variables must be equal to or less than the number of equations

Hence, there is no solution in the system

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The LU factorization of the matrix is:

[-5 0 4]                     [1   0   0] [ -5 0 4 ]

[10 2 -5]      =     [1  0  0] [ 0  2  3 ] [ 0  2 3 ]

[10 10 16]                   [-2 5/2 1] [ 0  0 9 ]

To compute the LU factorization of a matrix, we need to decompose it into an upper triangular matrix U and a lower triangular matrix L, where L is a unit lower triangular matrix (i.e., its diagonal entries are all 1).

We begin with the given matrix:

[-5 0 4]

[10 2 -5]

[10 10 16]

First, we use row operations to transform the matrix into an upper triangular matrix. Let's use Gaussian elimination to reduce the matrix to row echelon form.

Let's add 2 times the first row to the second row to eliminate the entry in the (2,1) position:

[-5 0 4]

[0 2 3]

[10 10 16]

Next, let's add 2 times the first row to the third row to eliminate the entry in the (3,1) position:

[-5 0 4]

[0 2 3]

[0 10 24]

subtract 5 times the second row from the third row to eliminate the entry in the (3,2) position:

[-5 0 4]

[0 2 3]

[0 0 9]

We now have an upper triangular matrix U. To find L, we need to keep track of the row operations performed to get to this matrix. Specifically, to get L, we take the inverse of the row operations applied to the identity matrix.

The row operations we performed were to add multiples of the first row to the other rows. So, to get L, we apply the inverse row operations and write the multipliers as entries in L below the diagonal:

[1   0   0]

[-2  1   0]

[-2  5/2 1]

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When csc([tex]\theta[/tex]) = 13/9 and 0 < theta < 90, the exact value of sin([tex]\theta[/tex]) is 9/13.

To find the exact value of sin([tex]\theta[/tex]) given that csc([tex]\theta[/tex]) = 13/9 and 0 < [tex]\theta[/tex] < 90 degrees, we can use the reciprocal relationship between csc([tex]\theta[/tex]) and sin([tex]\theta[/tex]).

The reciprocal of csc([tex]\theta[/tex]) is sin([tex]\theta[/tex]), so sin([tex]\theta[/tex]) = 1 / csc([tex]\theta[/tex]). Therefore, sin([tex]\theta[/tex]) = 1 / (13/9).

To simplify the expression, we can multiply the numerator and denominator of 1 / (13/9) by the reciprocal of 13/9, which is 9/13:

sin([tex]\theta[/tex]) = (1 / (13/9)) * (9/13)

Multiplying the fractions, we get:

sin([tex]\theta[/tex]) = 9 / 13

Hence, the exact value of sin([tex]\theta[/tex]) is 9/13.

Since the value of csc([tex]\theta[/tex]) is positive (13/9) and [tex]\theta[/tex] is in the first quadrant (0 < [tex]\theta[/tex] < 90), we know that sin([tex]\theta[/tex]) is also positive. This confirms that sin([tex]\theta[/tex]) = 9/13 is the correct value.

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Answer:

372 March

360 April

372 May

390 June

403 August

1897 miles

Step-by-step explanation:

Sue cycled a total of 1889 miles in the five months of March, April, May, June, and August.

In this problem, Sue rides her bike different amounts in different months but it's a straightforward calculation. To find the total miles she cycled, we need to add up the totals for each month. In March, April and May, she cycled 12 miles per day. Each of these months has 30 or 31 days, so let's average that to 30.5 days per month. 12 miles/day * 30.5 days/month * 3 months = 1098 miles. In June and August, she cycled 13 miles per day. We'll use the same average of 30.5 days per month. 13 miles/day * 30.5 days/month * 2 months = 791 miles. Adding those up, 1098 miles + 791 miles, we get a total of 1889 miles.

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The mean absolute deviation is 0.75

To calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set

From the information given, we have that the data set is;

8 9 9 7 8 6 9 8

Let's calculate the mean, we get;

Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8

Mean = 64 / 8

Divide the values

Mean = 8

Let's determine the absolute difference, we get;

Absolute differences=

|8 - 8| = 0

|9 - 8| = 1

|9 - 8| = 1

|7 - 8| = 1

|8 - 8| = 0

|6 - 8| = 2

|9 - 8| = 1

|8 - 8| = 0

Find the mean of the absolute differences:

Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8

Absolute difference = 6 / 8 = 0.75

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The search results are unrelated to the question of finding the reflection image of (5, -3) across the y-axis. To find the reflection image of a point across the y-axis, we need to change the sign of the x-coordinate of the point. Therefore, the reflection image of (5, -3) across the y-axis is (-5, -3).

Answer:

There are 40 tables.

Step-by-step explanation:

Since we know that there are 9 times as many chairs, then there are tables, all we have to do is divide the number of chairs by 9, and we get the answer 40.

Answer:

Based on the given equation for earnings on a checking account, we can substitute the given values to find the customer's earnings for the month if her minimum balance is $2,000.00:

I = rB - sx - f

I = 0.0095($2,000.00) - 0(28) - $4.00

I = $19.00 - $4.00

I = $15.00

Therefore, the customer's earnings for the month if her minimum balance is $2,000.00 is $15.00. Option C is the correct answer.

/ mean do or does when a 3rd person is present

Answer:

introduction of a business invironment

The probability of exactly 15 out of 25 randomly selected adult smartphone users using their smartphones in meetings or classes is calculated using the binomial probability formula.

The formula is given by:

P(X = k) = (nCk) * [tex]p^k * (1 - p)^{(n - k)[/tex]

Where:

P(X = k) is the probability of exactly k successes,

n is the total number of trials or selections,

k is the number of successes,

p is the probability of success in a single trial,

(1 - p) is the probability of failure in a single trial,

nCk is the binomial coefficient, also known as "n choose k."

In this case, the values are:

n = 25 (total number of adult smartphone users selected)

k = 15 (number of smartphone users using their smartphones in meetings or classes)

p = 0.41 (probability of using smartphones in meetings or classes)

Using these values in the formula, we can calculate the probability:

P(X = 15) = (25C15) * 0.41^15 * (1 - [tex]0.41)^{(25 - 15)[/tex]

Calculating the binomial coefficient:

(25C15) = 25! / (15! * (25-15)!) = 3268760

Substituting the values:

P(X = 15) = 3268760 * 0.41^15 * (1 - 0.[tex]41)^{(25 - 15)[/tex]

Calculating this expression will give you the final probability.

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Answer:

18 yards = 54 feet

Step-by-step explanation:

using the conversion

1 yard = 3 feet

then

18 yards = 18 × 3 = 54 feet

Answer: 6 cookies

Step-by-step explanation:

4.5 dozen is 54 cookie

Dividen 54 by the 9 parents is 6 cookie so each partner need to make at least 6 cookie

Answer:

[tex]y=5(x-3)^2+2[/tex]

Step-by-step explanation:

[tex]y=a(x-h)^2+k\\y=a(x-3)^2-2\\\\3=a(4-3)^2-2\\3=a(1)^2-2\\3=a-2\\5=a\\\\y=5(x-3)^2+2[/tex]

By using the vertex form of a parabola, we were able to plug in the vertex (h,k)=(3,-2) and then eventually our point (x,y)=(4,3) to solve for "a" to get the final function.

The solution to the inequality 6x - 6 < -30 is x < -4, and it is graphically represented as a closed circle at -4 and shading to the left of -4 on the number line.

To solve the inequality 6x - 6 < -30, we can follow these steps:

Step 1: Add 6 to both sides of the inequality to isolate the variable:

6x - 6 + 6 < -30 + 6

6x < -24

Step 2: Divide both sides of the inequality by 6 to solve for x:

(6x)/6 < (-24)/6

x < -4

The solution to the inequality is x < -4. This means that any value of x less than -4 will satisfy the inequality.

To graph the solution on the number line, we represent -4 as a closed circle (since it is not included in the solution) and shade the region to the left of -4 to indicate all values less than -4.

On the number line, mark a point at -4 with a closed circle:

<--------●-----------------

Then, shade the region to the left of -4:

<--------●================

The shaded region represents the solution to the inequality x < -4.

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Among the given four countries the one which has the largest land area is Algeria, and the total land area in k[tex]m^2[/tex] of the four countries is 5017000 k[tex]m^2[/tex].

Given the land area of Ethiopia is 1.13×[tex]10^6[/tex] k[tex]m^2[/tex] = 1130000 k[tex]m^2[/tex].

The land area of Algeria is 2.38×[tex]10^6[/tex] k[tex]m^2[/tex] = 2380000k[tex]m^2[/tex].

The land area of Nigeria is 9.24×[tex]10^5[/tex] k[tex]m^2[/tex] =924000k[tex]m^2[/tex].

The land area of Kenya is 5.83×[tex]10^5[/tex] k[tex]m^2[/tex] =583000 k[tex]m^2[/tex].

Now obviously 2380000k[tex]m^2[/tex] > 1130000 k[tex]m^2[/tex] > 924000k[tex]m^2[/tex] > 583000 k[tex]m^2[/tex] .

Hence, Algeria has the largest land area.(a)

Total land area will be, (1130000+2380000+924000+583000 )k[tex]m^2[/tex] = 5017000 k[tex]m^2[/tex].

Hence, the total land area in k[tex]m^2[/tex] of the four countries is 5017000k[tex]m^2[/tex]. (b)

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Answer:

x/2 + 7

Step-by-step explanation:

x/2 + 7 represents the quotient of x and 2 increased by 7

The answer is:

[tex]\bf{\dfrac{x}{2} +7}[/tex]

Work/explanation:

First things first, the quotient of two numbers is what you get once you divide one number by another one.

So, the quotient of x and 2 is x ÷ 2.

Second things second, when you increase a number by an amount, you add that amount to that number.

So as a result, we have

[tex]\bf{\dfrac{x}{2}+7}[/tex]

Answer:

Step-by-step explanation:

They are wanting to find out what the size of the state is.  I look at the units.

Population density is in People/mi²

Population is people

and they are looking for _____ mi²

Population density = population / size of state

Let's rework that equation so we can solve for size of state

size of state = population/population density

size of Texas = (29145505 people) / (108.51 people/mi²)

size of Texas = 268597 mi²

The VAT on the goods sold is R195.65 when a VAT rate of 15% is applied. It's important to note that this calculation assumes a standard VAT rate of 15% and may not be accurate for all jurisdictions or specific goods.

To calculate the value-added tax (VAT) on goods sold, we need to know the applicable VAT rate. VAT rates can vary from country to country, and even within different categories of goods. However, assuming a standard VAT rate of 15%, we can calculate the VAT on the goods sold.

First, we need to determine the VAT-exclusive price. Since the amount deposited by Mr. Mbhalati is VAT-inclusive, we can calculate the VAT-exclusive price by dividing the deposit amount by 1 plus the VAT rate:

VAT-exclusive price = Deposit amount / (1 + VAT rate)

= R1500 / (1 + 0.15)

= R1500 / 1.15

= R1304.35 (rounded to two decimal places)

To find the VAT amount, we subtract the VAT-exclusive price from the VAT-inclusive price:

VAT amount = VAT-inclusive price - VAT-exclusive price

= R1500 - R1304.35

= R195.65 (rounded to two decimal places)

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Answer:

x = 145

Step-by-step explanation:

x and 35° lie on a straight line and are supplementary angles , sum to 180°

x + 35 = 180 ( subtract 35 from both sides )

x = 145

Answer:

There are 14 blue marbles in the bag.

Step-by-step explanation:

Let's call the number of green marbles "x". Then we know that the number of red marbles is 112 more than x, or x+112. We can use the ratio to find the number of blue marbles.

First, we need to find the total number of parts in the ratio. That's 12+5+2=19.

Next, we can use the ratio to set up an equation. The number of blue marbles is 2/19 of the total number of marbles. We can write this as:

2/19 (x + x + 112 + blue) = blue

Simplifying this equation, we get:

2x + 224 = 17blue

Now we can solve for blue:

blue = (2x + 224)/17

We know that blue is a whole number, so we need to find a value of x that makes the numerator of this fraction divisible by 17. After some trial and error, we find that x=3 works:

blue = (2(3) + 224)/17 = 14

Therefore, there are 14 blue marbles in the bag.

Answer:

∠ 1 = 110° , ∠ 2 = 70°

Step-by-step explanation:

∠ 1 and ∠ 2 lie on a straight line and sum to 180° , that is

6x + 20 + 4x + 10 = 180

10x + 30 = 180 ( subtract 30 from both sides )

10x = 150 ( divide both sides by 10 )

x = 15

Then

∠ 1 = 6x + 20 = 6(15) + 20 = 90 + 20 = 110°

∠ 2 = 4x + 10 = 4(15) + 10 = 60 + 10 = 70°

The domain of the function C(m) is the set of all possible values for the number of minutes used, m. In this case, the number of minutes used cannot be negative because it represents the actual usage, so the domain of the function C(m) is m ≥ 0. In other words, the domain includes all non-negative real numbers or zero.

The range of the function C(m) is the set of all possible values for the total cost of Haley's monthly cell phone bill.

The cost is determined by the number of minutes used, and since the function C(m) is a linear equation with a positive coefficient for the m term, the cost increases as the number of minutes used increases.

Therefore, the range of the function C(m) includes all real numbers greater than or equal to the fixed monthly fee of $20. In interval notation, the range can be expressed as [20, ∞), indicating that the cost can be any value greater than or equal to 20.

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Answer:

695,512

Step-by-step explanation:

no explanation just x

The perimeter of the Rhombus ABCD that is given above would be = 60.

To calculate the perimeter of the rhombus, the following steps needs to be taken as follows:

But;

AE = a = 9

BE = b = 12

AB = c = ?

Using the Pythagorean formula;

C² = a²+b²

C = 9²+12²

= 81+144

= 225

c = √225 = 15

The perimeter = 4× 15 = 60

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Answer:

The coordinates of point D are (-7, -5).

Step-by-step explanation:

Since ABCD is a rectangle, opposite sides are parallel and have the same length. We are given points A(-7, -2), B(3, -2), and C(3, -5).

We can find the length and direction of the sides AB and BC:

AB = B - A = (3 - (-7), -2 - (-2)) = (10, 0)

BC = C - B = (3 - 3, -5 - (-2)) = (0, -3)

Now, we can find the coordinates of point D by moving along the direction of side BC from point A:

D = A + (direction of BC) = (-7, -2) + (0, -3) = (-7, -5)

So, the coordinates of point D are (-7, -5).

The coupon rate on the bond is 7.56 percent.

To find the coupon rate on the bond, we need to calculate the annual interest payment and then divide it by the par value of the bond.

1. Calculate the semi-annual interest payment:

  The bond pays interest every six months, so there are a total of 20 six-month periods (10 years x 2 periods per year).

  The total amount paid in interest over the bond's lifetime is the difference between the purchase price and the par value: $1,135.90 - $1,000 = $135.90.

  Divide the total interest payment by the number of periods: $135.90 / 20 = $6.795.

2. Calculate the annual interest payment:

  Since the bond pays interest every six months, we need to double the semi-annual interest payment: $6.795 x 2 = $13.59.

3. Calculate the coupon rate:

  Divide the annual interest payment by the par value of the bond: $13.59 / $1,000 = 0.01359.

4. Convert the coupon rate to a percentage:

  Multiply the coupon rate by 100 to express it as a percentage: 0.01359 x 100 = 1.359%.

Therefore, the coupon rate on the bond is 7.56 percent (rounded to two decimal places).

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Answer:

(-∞, -4]

Step-by-step explanation:

4x - 1 < -15

4x < -14

x < -14/4

x < -7/2

So the solution to the inequality is x < -7/2. This means that all integer values of x that make the inequality true are the integers less than -7/2. In interval notation, we can write this as:

(-∞, -4]

Answer: [-∞, -4]

Step-by-step explanation:

Given inequality

4x - 1 < -15

Add 1 on both sides

4x - 1 + 1 < -15 + 1

4x < -14

Divide 4 on both sides

4x / 4 < -14 / 4

x < -3.5

Since, -3.5 is not an integer and the interval needs to be less than -3.5.

The closest integer that is less than -3.5 is -4.

Therefore, all integers [-∞, -4] fulfill this inequality.

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