For the points(9,2)and(2,1), (a) Find the exact distance between the points. (b) Find the midpoint of the line segment whose endpoints are the given points. Part 1 of 2 (a) The exact distance between the points is Part 2 of 2 (b) The midpoint is

We can see that there are 3 data points in the 1-5 class, 3 data points in the 6-10 class, 2 data points in the 11-15 class, and 0 data points in the 16-20 class.

To build a frequency distribution table for the given data, we will first sort the data into the appropriate class limits and then tally the frequency of each class. We will use the following columns in our table: class limits, tally, and frequency.


 
 Class Limit   Tally              Frequency
   1-5                      |||                        3
  6-10                     |||                        3
  11-15                      ||                        2
 16-20                                               0
   

 

The distribution of the data is shown in the table above. The class limits are the ranges of values that the data falls into. The tally column is used to count the number of data points in each class, and the frequency column is the total number of data points in each class. By using this table, we can see that there are 3 data points in the 1-5 class, 3 data points in the 6-10 class, 2 data points in the 11-15 class, and 0 data points in the 16-20 class.

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Answer:

The total commission earned by the company is 10% of the selling price, which is:

0.10 x $180,000 = $18,000

Marge receives 1/4 of the company's commission, which is:

(1/4) x $18,000 = $4,500

Therefore, Marge receives $4,500 in commission.

The number in the sentence that represents the number of demos, D, that each executive will receive is 72 ÷ 6 < D. Option B

Since there are more than 72 demos

Each executive will receive at least 72/6 = 12 demos.

The number of demos that each executive will receive is 12 demos

Therefore, the number in the sentence that represents the number of demos, D, that each executive will receive is 72 ÷ 6 < D.

Hence, the correct inequality is 72 ÷ 6 < D.

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The polynomial equation in the complete 30x^(4)+83x^(3)-52x^(2)+4x+1=0. The solutions are: x = -1 and x = -1/7, 1/7, -5/7, 5/7.

The question asks you to solve the polynomial equation: 30x4 + 83x3 - 52x2 + 4x + 1 = 0.

To solve this equation, you will need to factor it into the form (ax + b)(cx + d) = 0. The solutions of this equation will be when either ax + b or cx + d are equal to 0.

First, factor out the Greatest Common Factor (GCF) of the polynomial, which is 4x. This will leave us with:

4x(7x3 + 20x2 - 13x + 1) = 0.

Now, factor this expression into two binomials. One of the binomials is already in the form ax + b, and the other will need to be factored further.

4x(7x2 + 5x - 1)(x + 1) = 0.

Therefore, the solutions of this equation are when

or

.

The solutions are: x = -1 and x = -1/7, 1/7, -5/7, 5/7.

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The set of vectors {v1, v2, v3} is linearly dependent for all real number h ≠ 4 and all real number h ≠ -4.

The set of vectors {v1, v2, v3} is linearly dependent if there exists a set of real numbers a, b, and c such that a*v1 + b*v2 + c*v3 = 0 and at least one of a, b, or c is not equal to zero. In this case, we can write the equation as:

a*1 + b*2 + c*(-1) = 0

We can rearrange this equation to solve for h:

h = -a - 2*b + c

Now we can plug in the values for v1, v2, and v3:

h = -1 - 2*2 + (-1)*(-1)

h = -4

Therefore, the set of vectors {v1, v2, v3} is linearly dependent when h = -4.

Alternatively, we can also use the determinant of the matrix formed by the vectors to determine when the set is linearly dependent. The determinant of the matrix is given by:

| 1 2 -1 |
| -1 1 3 | = (1)(1)(h) + (2)(3)(-1) + (-1)(-1)(2) - (-1)(1)(-1) - (2)(-1)(1) - (1)(3)(2)
| 2 1 h |

Simplifying this equation gives:

h - 6 - 2 + 1 + 2 - 6 = 0

h - 11 = 0

h = 11

Therefore, the set of vectors {v1, v2, v3} is also linearly dependent when h = 11.

So the set of vectors {v1, v2, v3} is linearly dependent for all real number h ≠ 4 and all real number h ≠ -4.

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Answer:

Step-by-step explanation:

1500 + 5000x 0.055 - $1775

1500 + 10000 x 0.055 = $2050

with option 1 he would make 1775 to 2050

                   2400 + 5000 x0.04 =2600

                   2400 + 10000 x 0.04 = 2800

With option 2 hw would make $2600 to $2800

                                     simple calculation  :)

Gail should pick a Beautiful bank if she plans to have her money in the account for 15 years.

To determine which bank would be better for Gail, we need to calculate the future value of her investment after 15 years for each bank and compare the results.

For Neighborhood Bank, we can use the formula:

FV = P(1 + r/n)^(n*t)

where FV is the future value,

P is the principal (the initial amount invested),

r is the annual interest rate (as a decimal),

n is the number of times the interest is compounded per year,

and t is the number of years.

Plugging in the values, we get:

FV = 5,500(1 + 0.012/1)^(1*15)

FV = 5,500(1.012)^15

FV = 7,130.34

For Beautiful Day Bank, we can use the formula:

FV = P(1 + r/n)^(n*t)

Plugging in the values, we get:

FV = 5,500(1 + 0.012/365)^(365*15)

FV = 5,500(1.000032876)^5475

FV = 7,145.25

Therefore, Beautiful Day Bank would be the better choice for Gail, as she would earn a higher amount of interest and end up with a higher future value for her investment after 15 years.

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A summary is a brief overview of the main points or important details of a text or event. In the case of the statements provided, option A, "My sister's wedding was a success," is the best example of a summary.

A summary provides a general overview of the event without going into specific details about how things looked, felt, smelled, or tasted, as does option A.

Options B and C, "I ate yummy salmon at my sister's wedding" and "My dress at my sister's wedding was blue," are not summaries because they focus on specific details rather than providing an overview of the event.

In conclusion, alternative A. My sister's wedding was a success is correct.

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The solution of the equations ​2a-b=-1 and a-2b=4 is b = -3 and a = -2. The solution of the equations 3m-n=8 and m+n=4​ is m = 3 and n = 1.

In the elimination method, the two equations are solved by eliminating one variable and by substituting the value of one variable in the equation to get the value of another variable.

The two equations can be solved as below,

2a-b=-1

a-2b=4

Multiply the second equation by two and subtract from the first equation,

2a-b=-1

2a - 4b = -8

________

       3b = - 9

         b = -3

2a + 3 = -1

2a = -4

a = -2

For the other two equations,

3m-n=8

m+n= 4

_______

4m = 12

m = 3

m + n = 4

n = 4 - 3

n = 1

Therefore, the solution of the equations ​2a-b=-1 and a-2b=4 is b = -3 and a = -2. The solution of the equations 3m-n=8 and m+n=4​ is m = 3 and n = 1.

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Lee's gross pay is $472.

First, we need to calculate the commission Lee earned. To do this, we take her total sales and multiply it by her commission rate.

Commission = Total Sales x Commission Rate

Commission = $4,000 x 0.04

Commission = $160

So, Lee earned $160 in commission.

Next, we need to calculate her base pay. To do this, we multiply her hourly rate by the number of hours she worked.

Base Pay = Hourly Rate x Hours Worked

Base Pay = $8.00 x 39

Base Pay = $312

Now that we have calculated her commission and base pay, we can add them together to find her gross pay.

Gross Pay = Base Pay + Commission

Gross Pay = $312 + $160

Gross Pay = $472

This means that before any deductions (such as taxes), Lee would earn $472 for working 39 hours and making $4,000 in sales.

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The total number of words which starts and end with the letter N formed from the letters of the word NIPUN is 4

To form words that start and end with the letter N, we need to first fix the letter N at the beginning and end of the word. This leaves us with the letters I, P, and U to arrange in the middle.

There are 3! (3 factorial) ways to arrange these 3 letters, which is equal to 3 × 2 × 1 = 6.

However, we need to divide by the number of times each letter appears in the word, which is 1 for each of the letters I, P, and U.

So the total number of words that can be formed is 6/1/1/1 = 6.

But we only want the words that start and end with the letter N, so we need to divide by the number of times the letter N appears in the word, which is 2.

So the final answer is 6/2 = 3.

Therefore, the total number of words which starts and end with the letter N formed from the letters of the word NIPUN is 3.

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Answer:

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the side lengths of the triangle, and A, B, and C are the opposite angles, respectively.

We are given A, C, and c, so we can use the Law of Sines to find B, a, and b.

a/sin(A) = c/sin(C)

a/sin(22) = 2.69/sin(51.4)

a = sin(22) * (2.69/sin(51.4))

a = 1.00

b/sin(B) = c/sin(C)

b/sin(B) = 2.69/sin(51.4)

b = sin(B) * (2.69/sin(51.4))

We can use the fact that the sum of the angles in a triangle is 180 degrees to find B:

B = 180 - A - C

B = 180 - 22 - 51.4

B = 106.6

Now we can substitute the values we have found into the Law of Sines to find b:

a/sin(A) = b/sin(B)

1/sin(22) = b/sin(106.6)

b = sin(106.6) * (1/sin(22))

b = 2.69

Therefore, B is approximately 106.6 degrees, a is approximately 1.00, and b is approximately 2.69.

The functions that are odd or even can be determined by replacing x with -x and seeing if the function remains the same or changes sign.

(a) f(x) = -tan(x) is an odd function because f(-x) = -tan(-x) = tan(x) = -f(x)

(b) f(x) = tan(x+T/2) is an odd function because f(-x) = tan(-x+T/2) = -tan(x+T/2) = -f(x)

(c) f(x) = tan(x)+cot(x) is neither an odd nor an even function because f(-x) = tan(-x)+cot(-x) = -tan(x)-cot(x) ≠ f(x) or -f(x)

(d) f(x) = 5cot(x) is an even function because f(-x) = 5cot(-x) = 5cot(x) = f(x)

(e) f(x) = (tan(x))2 is an even function because f(-x) = (tan(-x))2 = (tan(x))2 = f(x)

(f) f(x) = tan(4x) is an odd function because f(-x) = tan(4(-x)) = -tan(4x) = -f(x)

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The response to the given question would be that JK || ML is a pair of parallel sides, and JM and KL are equal in length, making JKLM a trapezoid, more particularly an isosceles trapezoid.

In terms of geometry, a quadrilateral is a four-sided polygon with four edges and four corners. Its origins are in the Latin terms quadri and latus (meaning "side"). A rectangle is a two-dimensional shape with four sides, four vertices, and four corners. Two main types of concave and convex exist. Convex quadrilaterals also have a number of subclasses, such as trapezoids, parallelograms, rectangles, rhombuses, and squares. A rectangle is a two dimensional shape with four straight sides. Quadrilaterals come in many various shapes, such as parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.

The quadrilateral JKLM's shape may be ascertained using the information provided as follows:

JK = ML signifies that the lengths of the opposing sides are equal.

JM = KL denotes that the length of neighbouring sides is the same.

Nevertheless, we lack sufficient knowledge to establish whether or not opposing angles are equal.

As a result, using the information provided, the quadrilateral JKLM would be classified in the following way:

JK || ML is a pair of parallel sides, and JM and KL are equal in length, making JKLM a trapezoid, more particularly an isosceles trapezoid.

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x1 = 5 and x2 = 0

The following LP problem in a spreadsheet MAX: 4x1 + 4x2 Subject to: 2x1 + 4x2 <= 20, 3x1 + 5x2 <= 15, and x1, x2 >= 0.A spreadsheet is a type of software that allows users to store and analyze data in a grid-like format of rows and columns. Spreadsheets are commonly used for data entry, financial modeling, and other calculations.In the given problem, we are supposed to find the maximum value of the function 4x1 + 4x2 subject to the constraints 2x1 + 4x2 <= 20, 3x1 + 5x2 <= 15, and x1, x2 >= 0.The first two constraints are represented by inequalities. That means, the values of x1 and x2 can be any non-negative values that satisfy the constraints. Mathematically, the constraints can be represented as:2x1 + 4x2 <= 20⇒ x2 <= 5 - 0.5x1--------(1)3x1 + 5x2 <= 15⇒ x2 <= 3 - 0.6x1--------(2)Note that, we have represented the constraints in such a way that x2 is the subject of the inequality. This is done to make it easier to graph and find the feasible region.To find the feasible region, we need to graph both inequalities (1) and (2) on a coordinate plane. The feasible region is the shaded area that is common to both regions. It is given below:The feasible region is the triangular-shaped region. Since x1 and x2 are both non-negative, we need to consider only the values of x1 and x2 that are within the feasible region.Now, to maximize the function 4x1 + 4x2, we need to find the optimal solution. We do this by finding the intersection points of the lines that represent the equation 4x1 + 4x2 = k, where k is a constant.The equation 4x1 + 4x2 = k can be rearranged as x2 = (-x1 + k/4)This equation represents a line with a slope of -1 and a y-intercept of k/4. We can graph this line for different values of k to find the optimal solution. The line for k = 0 is shown below:We can see that the line passes through the feasible region at point (0, 0) and (5, 0). This means that the maximum value of the function is 4x1 + 4x2 = 4(5) + 4(0) = 20 at point (5, 0).Thus, the maximum value of the function 4x1 + 4x2 subject to the constraints 2x1 + 4x2 <= 20, 3x1 + 5x2 <= 15, and x1, x2 >= 0 is 20 at x1 = 5 and x2 = 0.

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Using algebra we can conclude that Mrs. Ong brought a total of 12 fruits.

Algebra is a discipline of mathematics that studies symbols and the mathematical operations that can be applied to them.

These symbols are referred to as variables because they don't have predetermined values.

These symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations in order to ascertain the values.

Now, let the total fruits be x.

Oranges = 1/2 x - 3

Pears = [x - 1/2 (1/2x -3 ) ]- 2= x - 1/4x + 3/2 - 2 = 3x /4 - 1/2

Apples = x - 1/2 (3x /4 - 1/2) - 1

           = x - 3/8 x + 1/4 - 1 = 5x /8 - 3/4

Mangoes = 5

x - 5x/ 8 + 3/4 = 5

3x /8 + 3/4 = 5    

3x + 6 = 40

3x = 34

x = 11.333

Therefore, using algebra we can conclude that Mrs. Ong brought a total of 12 fruits.

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Complete question:

Mrs. Ong bought some fruits. 3 fewer than 1/2 of the fruits were oranges. 2 fewer than 1/2 of the remaining fruits were pears. 1 fewer than half of the remaining fruits were apples and the remaining 5 fruits were mangoes.

How many fruits did Mrs Ong buy altogether?

The solutions to the equation are w = (5 + i√(5))/(10) and w = (5 - i√(5))/(10). These are the fully simplified answers.

To solve the equation 10w(w-1)+3=0 using the Quadratic Formula, we first need to rearrange the equation to the standard form of a quadratic equation, which is ax²+bx+c=0.

In this case, we can distribute the 10w to get 10w²-10w+3=0. This gives us the values of a=10, b=-10, and c=3.

Now, we can plug these values into the Quadratic Formula, which is:

w = (-b ± √(b²-4ac))/(2a)

w = (-(-10) ± √((-10)²-4(10)(3)))/(2(10))

w = (10 ± √(100-120))/(20)

w = (10 ± √(-20))/(20)

w = (10 ± √(-1)(20))/(20)

w = (10 ± √(-1)√(20))/(20)

w = (10 ± i√(20))/(20)

w = (10 ± i√(4)√(5))/(20)

w = (10 ± 2i√(5))/(20)

w = (5 ± i√(5))/(10)

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The Circumference of the given circle with a radius of 6 meters and л’s value of 3.14 is 37.68 meters.

In 2-D Geometry, the circumference of the circle is the perimeter running around the circle.

The Circumference of a circle is given by the following formula:

C=2 лr…..(i),

Where,

C = Circumference of the circle,

Л = 3.14 (given value)

r= Radius of the circle = 6 meters (given).

Substituting the values of each variable in equation (i), we get;

C = 2 лr = 2x3.14x6 meters,

Or, C = 37.68 meters

Therefore, the circumference of the given circle is 37.68 meters

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The Ratio fractions decimal percent is as follows:

17% as a decimal = 0.17

17% as a fraction = 17/100

17% as a ratio = 17:100

3/4 as a decimal = 0.75

3/4 as a fraction = 3/4

3/4 as a ratio = 3:4

To convert 17% to a decimal, we move the decimal point two places to the left, which gives us 0.17.

To convert 3/4 to a decimal, we divide 3 by 4, which gives us 0.75.

To convert 0.17 to a fraction, we write it as 17/100 and simplify by dividing both the numerator and denominator by the greatest common factor, which is 17 in this case. Therefore, 0.17 as a simplified fraction is 17/100.

To convert 0.75 to a fraction, we write it as 75/100 and simplify by dividing both the numerator and denominator by the greatest common factor, which is 25 in this case. Therefore, 0.75 as a simplified fraction is 3/4.

To convert 17% to a ratio, we write it as 17:100.

Therefore:

17% as a decimal = 0.17

17% as a fraction = 17/100

17% as a ratio = 17:100

3/4 as a decimal = 0.75

3/4 as a fraction = 3/4

3/4 as a ratio = 3:4

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The correct option is C, the area of the triangle is 9 square units.

For a triangle of base B and height H the area is:

A = B*H/2

Here we can see that:

B = x

H = 2x

And we know that x = 6 - 3 = 3

Then we can use the value of x to find the values of H and B.

B = 3

H = 2*3 = 6

Now we can replace these two values in the formula for the area, then we will get the area of the triangle:

A = 3*6/2 = 3*3 = 9 square units.

When x = 3, the area is 9 square units.

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The equation that represents the proportional relationship between the initial height and the rebound height of the bouncy ball is D . r = 0.6 h

The proportional relationship can be found by the formula :

= Change in y / Change in x

= Change in rebound height / Change in initial height

= ( 0. 50 - 0. 30 ) / ( 0. 3 / 0 . 18 )

= 0.6 meters

The proportional relationship is :

= 0. 6 x initial height

= 0. 6 h

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Class B has higher percentage of girls than class A that is 26.6 % more.

A percentage is a number or ratio that can be expressed as a fraction of 100. If you need to calculate the percentage of a number, divide the number by the whole number and multiply by 100. Percentages therefore mean 1 in 100.

Given,

Total number of students in class A = 60

Number of girls student in class A = 28

percentage of girls in class A

= (28/60)×100

= 0.467 × 100

= 46.7%

Total number of students in class B = 60

Number of girls student in class B = 44

percentage of girls in class A

= (44/60)×100

= 0.733 × 100

= 73.3 %

Difference in percentage of girls in class A and class B.

= 73.3% - 46.7%

= 26.6%

Hence, class B has 26.6 percent more girls than class A.

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Answer:

False

Step-by-step explanation:

False, you need at least one angle and three sides to use the law of sines    or two angles  and two different sides.

sin A    sin B   sin C

------  = ------- = -------

 a           b           c

True, the law of sines can be used when you are given 3 sides of a triangle, and you are solving for an angle.

The law of sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in a given triangle. Therefore, if you know the lengths of all three sides of a triangle, you can use the law of sines to solve for one of the angles.

An angle is the measure that determines two straight lines, which when joined together create a point of origin, which is called the vertex of the angle.

The unit of measurement associated with angles is degrees.

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A) To change the rectangular coordinates (-5√3, 5) to polar coordinates, we need to find the radius r and the angle θ.

The radius r can be found using the Pythagorean theorem:
r = √(x^2 + y^2)
r = √((-5√3)^2 + (5)^2)
r = √(75 + 25)
r = √100
r = 10

The angle θ can be found using the inverse tangent function:
θ = tan^(-1)(y/x)
θ = tan^(-1)(5/(-5√3))
θ = tan^(-1)(-√3/3)
θ = -π/6

So, the polar coordinates are (10, -π/6).

B) Given a = (-5, 2) and b = <4, -7>, we need to find 3a - 4b.

3a = 3(-5, 2) = (-15, 6)
4b = 4(4, -7) = (16, -28)

3a - 4b = (-15, 6) - (16, -28) = (-15 - 16, 6 - (-28)) = (-31, 34)

So, the answer is (-31, 34).

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This is a very small number, as indicated by the negative exponent. Specifically, it is 207.7 divided by 1,000,000.

An algebraic expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that can be simplified and evaluated.

It may contain one or more variables, which are symbols that represent unknown quantities or values that can vary. Algebraic expressions can be written using letters, symbols, or a combination of both, and they can be used to model real-world situations, solve problems, and express mathematical relationships.

For example, "3x + 5" is an algebraic expression that represents a linear equation with one variable "x".

2.077×10⁻⁴ means "2.077 times 10 to the power of -4", which can be rewritten as 0.0002077. This is a very small number, as indicated by the negative exponent. Specifically, it is 207.7 divided by 1,000,000.

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The height of the flagpole is approximately 23,047.11 feet.

To resolve this issue, we can make use of the similar triangles property. The teacher, the flagpole, and each of their corresponding triangles are similar because they have the same angles.

Let h be the height of the flagpole. Then, we can set up the following proportion:

h / 3112 = 612 / 9

When we simplify this ratio, we obtain:

h = (3112 x 612) / 9

h = 207424 / 9

h ≈ 23,047.11 feet

Hence, the flagpole is roughly 23,047.11 feet tall.

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The decimal fοrm οf the mixed fractiοn 33 2/3, apprοximated tο the nearest tenth, is 33.67.

A mixed fractiοn is οne that is represented by bοth its quοtient and remainder. Sο, a mixed fractiοn is a cοmbinatiοn οf a whοle number and a prοper fractiοn. A fractiοn represents a piece οf a larger tοtal. Tο learn hοw tο determine the precise values οf mixed numbers, it is crucial tο cοnvert a mixed number tο a decimal. A mixed number can be cοnverted tο decimal fοrm using οne οf twο techniques:

the mixed number is changed intο an imprοper fractiοn.

by first changing the given mixed number's fractiοnal pοrtiοn tο decimal, then adding the whοle number pοrtiοn tο it.

Nοw the given fractiοn is 33 2/3.

This is a mixed fractiοn because it has a whοle number οf 33 and a fractiοn οf 2/3.

This mixed fractiοn can be cοnverted tο a decimal number by finding the value οf the fractiοn part οf the number and adding it tο the whοle number.

Sοlving fractiοnal parts,

2/3 = 0.66666 = 0.67 (Rοunding tο the nearest tenth)

Nοw add tο the whοle number.

33 + 0.67 = 33.67

Therefοre the decimal fοrm οf the mixed fractiοn 33 2/3 is 33.67.

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$113\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{weekly, thus 52} \end{array}\dotfill &52\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]A = 113\left(1+\frac{0.06}{52}\right)^{52\cdot 4} \implies \boxed{A \approx 143.63}\hspace{5em}\underset{ earned~interest }{\stackrel{ 143.63~~ - ~~113 }{\boxed{\approx 30.63}}}[/tex]

The total surface area of the tires making contact with the ground at any one time for the truck with 18 wheels, tire radius of 21 in, tire width of 12 in, and 20% contact area is approximately 5700.24 square inches.

The surface area of one tire making contact with the ground can be calculated as follows:

The diameter of the tire is 2 * radius = 2 * 21 in = 42 in

The length of the portion of the tire making contact with the ground is 20% of the circumference of the tire = 0.2 * π * 42 in ≈ 26.39 in

The width of the tire making contact with the ground is given as 12 in

Therefore, the surface area of one tire making contact with the ground is approximately 26.39 in * 12 in = 316.68 square inches

Since the truck has 18 wheels, the total surface area of all the tires making contact with the ground at any one time is 18 * 316.68 square inches = 5700.24 square inches.

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