At first, students might think that the lengths of the sides of a triangle can be any three lengths, but that is not so. The Triangle Inequality says that the length of any side must be less than the sum of the lengths of the other two sides. For the triangle in part (a) to exist, all of these

statements must be true:

?

?

?

5<3+4, 3<4+5, and 4<5+3.

In the provided problem of collection survay data the researchers use the Cluster Analysis data analysis techniques.

Cluster analysis is a statistical technique for processing data. It works by organizing items into groups or clusters based on how closely related they are.

Cluster analysis, similar to reduced-space analysis (factor analysis), deals with data matrices in which the variables have not been previously split into reference and prediction subsets. The goal of cluster analysis is to find similar groups of subjects. Here, “similarity” between each pair of subjects means a global measure of the entire set of traits.

The most common use of cluster analysis is classification. Subjects are divided into groups such that each subject is more similar to other subjects within that group than subjects outside the group.

Cluster analysis used in following areas

In the context of market research, this can be used to identify categories such as age ranges, income ranges, urban, rural, or suburban locations.

Marketing can use cluster analysis for audience segmentation to target different customer groups with the most relevant messages.

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The unit rate of Ricky purchase is $3.75 per pizza.

The unit rate of William purchase is $8 per pounds of blackberries.

Unit rate is the ratio of two different units, with denominator as 1.

In other words, a unit rate is a rate where the second quantity is one unit , such as $10 per pound, 30 miles per hour, 22 Indian Rupees per Nigerian naira, etc.

Let's find the unit rate of the situations.

Ricky spent $15.00 on 4 pizzas

unit rate = 15 / 4

unit rate = 3.75 dollars per pizza

William paid $20.00 for 2 1/2 pounds = 5 / 2 pounds of blackberries.

Therefore,

unit rate = 20 ÷ 5 / 2

unit rate = 20 × 2 / 5

unit rate = 40 / 5

unit rate = 8 dollars per pounds of blackberries

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Answer:

1.a)  Broken line.

1.b)  False.

2.a)  Solid line.

2.b)  True.

Step-by-step explanation:

When graphing inequalities:

Given inequality:

[tex]y > -2x+4[/tex]

a)  As the "<" sign has been used, the line will be a broken line.

b)  Substitute (0, 0) into the inequality:

[tex]\begin{aligned}\textsf{When $x=0$ and $y=0$}: \quad 0 & > -2(0)+4\\0 & > 0+4\\0 & > 4\end{aligned}[/tex]

As zero is not greater than 4, the solution at (0, 0) is false.

Graphing the inequality

Change the inequality sign to an equals sign, then substitute two values of x into the equation and solve for y to find two points on the line:

[tex]\begin{aligned}x=-2: \quad y & =-2(-2)+4\\y &=4+4\\y&=8\end{aligned}[/tex]

[tex]\begin{aligned}x=4: \quad y & =-2(4)+4\\y &=-8+4\\y&=-4\end{aligned}[/tex]

Plot the points (-2, 8) and (4, -4).

Draw a broken straight line through the points.

Shade above the line.

Given inequality:

[tex]3x+2y \leq 6[/tex]

a)  As the "≤" sign has been used, the line will be a solid line.

b)  Substitute (0, 0) into the inequality:

[tex]\begin{aligned}\textsf{When $x=0$ and $y=0$}: \quad 3(0)+2(0) & \leq 6\\0+0 & \leq 6\\0 & \leq 6\end{aligned}[/tex]

As zero is less than 6, the solution at (0, 0) is true.

Graphing the inequality

Change the inequality sign to an equals sign, then substitute two values of x into the equation and solve for y to find two points on the line:

[tex]\begin{aligned}x=-2: \quad 3(-2)+2y & =6\\-6+2y&=6\\2y&=12\\y&=6\end{aligned}[/tex]

[tex]\begin{aligned}x=4: \quad 3(4)+2y & =6\\12+2y&=6\\2y&=-6\\y&=-3\end{aligned}[/tex]

Plot the points (-2, 6) and (4, -3).

Draw a solid straight line through the points.

Shade below the line.

Answer:

slope and x-intercept is -1/2

y-intercept is 5

The equation which is correct is :

n + q = 104

Since we have given that:

Number of nickels and quarters = 104

Total amount from them = $22

Let the number of nickels be 'n'

Let the quarters be 'q'

So, the equation will be

n + q = 104           -------------------------------------------- (1)

Since we know that

value of nickels = 0.05 dollars

Value of quarters = 0.25 dollars

So, the equation will be

0.05n + 0.25q = $22       ------------------------------------ (2)

So, there are two system of linear equation can be used to find the number of nickels and the number of quarters. i.e.

n + q = 104

0.05n + 0.25q = $22

Using elimination we can find the value of n and q :

0.05( n + q =104 )

⇒0.05n+0.05q=5.2-----------(3)

Now, from equation (2) and (3), we get,

0.05 n + 0.05q = 5.2

0.05 n + 0.25q = 22

(-)       (-)           (-)

------------------------------------

0          + 0.2q = 16.8

q = 16.8 ÷ 0.2

q = 84

Putting the value of q = 84 in equation (1),

   n + q = 104

⇒ n + 84 = 104

⇒ n = 104 - 84

⇒ n = 20

Hence,  n +q =104 equation is correct.

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Answer: option 2

Step-by-step explanation:

The leading coefficient is positive and the degree is odd, so the correct answer is option 2.

Answer:

$67.50

Step-by-step explanation:

27(2) = 54

27/2 = 13.5

54+13.5 = 67.5

Answer:

67.5

explanation:

27/2= 13.5

5*13.5= 67.5

The additive inverse of the mentioned complex number is -13 + 2i.

The additive inverse of any number is defined as the number, which on addition to the original number, gives the sum zero. In order to make possible this situation, the additive inverse will have opposite signs for each value.

In the question, 13 has positive sign and 2i has negative sign. To cancel them out, the additive inverse will be 13 with negative sign and 2i with positive sign. Thus, third option is correct additive inverse.

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The complete question is -

what is the additive inverse of the complex number 13 - 2i?

-13 - 2i

-13 + 2i

13 - 2i

13 + 2i

To cover the area of floor, we will spend $0.65 for the entire 0.23 squared feet

Perimeter of Rectangle could be considered as one of the important formulae of the rectangle. It is the total distance covered by the rectangle around its outside. A rectangle is a quadrilateral that has two pairs of parallel sides equal and all the four angles at the vertices are right angles.

The formula of perimeter of a rectangle is given as

P = 2(L + W)

But the width the rectangle is 6 feet more than half it's length.

W = 6 + 1/2L

If the perimeter is 313 times the length;

P = 2(L + W)

P = 2(L + 6 + 1/2L)

But P = 313L

313L = 2(L + 6 + 1/2L)

313L = 2L + 12 + L

313L = 3L + 12

310L = 12

L = 12 / 310

L = 0.039 ft

The length of rectangle is 0.039ft

The width of the rectangle is 6 + 1/2(0.039) = 6.0195ft

The perimeter of the rectangle = 2(L + w)

Perimeter = 2 (0.039 + 6.0195)

Perimeter = 12.117ft

The area of the rectangle is L * w

A = L * W = 0.039 * 6.0195

A = 0.234ft^2

The cost of the materials will be 2.75 * 0.234 = $0.65

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Answer:

Step-by-step explanation:

Estimated line of best fit added to the graph (see attached).

The most reasonable value of y corresponding to x = 3 is approximately 18 gallons.

The matching answer choice is D.

Answer:

(D) 17 gallons

Step-by-step explanation:

a) The pie chart that represents this information is given at the end of the answer.

b) The amount that represents his savings is of: gh¢ 720.

A pie chart is a graph in which the values of each measure in the data-set assume a percentage equivalent to the percentage of these values in the circular graph.

In the context of this problem, these percentages are given as follows, as stated from the text:

All these percentages are inserted on the image given at the end of the answer, which represents the pie chart.

The percentage of savings is of:

12%.

Hence the amount of savings is given by the multiplication of 0.12 by 6,000. as follows:

0.12 x 6000 = gh¢ 720.

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Answer:

A = 64 m²

Step-by-step explanation:

Step 1: What is the question asking

Step 2: What is known

Step 3: Conversion

Step 4: Answer the question/solve for the area

the 60th percentile of breaking strength for this type of fishing line is

k= 6.64

assume that k pounds is the both percentile of breaking strength for this type of finishing line

p( x<k) = 0.60

p( x- 6.44/0.75 < k- 6.44/0.75)= 0.60

then k-6.44 /0.75 = 0.26

thus k= 6.64

Hence , the 60th percentile of breaking strength for this type of fishing line is 6.64

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Answers:

1st box:  [tex]\boldsymbol{90}[/tex]

2nd box:  [tex]\boldsymbol{90}[/tex]

3rd box:  [tex]\boldsymbol{\text{m}\angle 2 = \text{m}\angle 3}[/tex]

===============================================

Explanation:

Complementary angles form a corner. Note that "complementary" and "corner" both start with "C" to help remember the rule.

By "corner", I refer to a 90 degree angle.

Since [tex]\angle 1\text{ and } \angle 2[/tex] are complementary, we know that [tex]\text{m}\angle 1+\text{m}\angle 2 = 90[/tex] simply by the definition of what it means to be complementary.

---------------

Through similar logic, [tex]\angle 1\text{ and } \angle 3[/tex] are complementary which means [tex]\text{m}\angle 1+\text{m}\angle3 = 90[/tex]

We can then equate the left hand sides (LHS) of both equations since both LHS expressions equal 90. This is an example of the substitution property in action.

That's how we end up with [tex]\text{m}\angle 1+\text{m}\angle 2 = \text{m}\angle 1+\text{m}\angle 3[/tex]

After this point, subtract [tex]\text{m}\angle1[/tex] from both sides to cancel them out. We'll be left with [tex]\text{m}\angle 2 = \text{m}\angle 3[/tex], which concludes with [tex]\angle 2 \cong \angle 3[/tex] to show the two angles are congruent.

The equation to represent the situation is y = 15 + 30x.

The number of hours Sophia used for the guitar training after paying 75 dollars is 2 hours.

Sophia takes guitar lessons at home every Sunday. Her instructor charges $15 to cover home visit costs, and $30 per hour of training. One Sunday, Sophia's mother pays the instructor $75 for the guitar lessons.

The equation that can be used to represent the given situation is as follows:

let

x = number of hours used for the training

y = total cost

Therefore,

y = 15 + 30x

Now, Sophia's mother spent 75 dollars for her daughters training. Let's find the hours Sophia used.

Therefore,

75 = 15 + 30x

75 - 15 = 30x

60 = 30x

divide both sides by 30

x = 60 / 30

x = 2

Therefore, she used 2 hours for the training.

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The front and side elevation diagram along with the diagram given in question is attached with the answer.

What is elevation?

A location's elevation can be defined as its height above or below a fixed reference point, most frequently a reference geoid, a mathematical representation of the Earth's sea level as an equipotential gravitational surface (see Geodetic datum Vertical datum). In most cases, elevation is used to describe locations on the surface of the Earth, whereas altitude or geopotential height is used to describe locations above the surface, such as those of flying airplanes or orbiting satellites, and depth is used to describe locations below the surface.

Drawing the required Elevation Using the Construction Method

The scale is 2 squares to 1 meter.

16 squares total make up the plane on which the front elevation is to be drawn.

Front elevation: There are 4 squares across the front elevation's width.

4 + 1 squares make up the portion of the front closest to the observer.

The slant surface of the has a square count of 3 by 4 squares.

Side elevation: By following the same format as before, the side elevation is provided as follows;

The lower side of the side elevation's breadth is 2 meters wide, or 4 squares.

The side elevation's height is 2 meters, or 4 squares.

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Step-by-step explanation:

it is a parallelogram.

that means both pairs of opposite sides are parallel and the sides of each pair are equally long.

the sum of all internal angles is 360°.

the opposing angles are equal.

and therefore neighboring angles are complementary angles (or a linear pair) : together they have 180°.

so,

76 = 4x - 8

84 = 4x

x = 21

-3z + 8 + 76 = 180

-3z + 84 = 180

-3z = 96

z = -32

-3z + 8 = -6y - 10

-3×-32 + 8 = -6y - 10

96 + 8 = -6y - 10

104 = -6y - 10

114 = -6y

y = -19

According to the Pythagoras theorem, the value of ED is 8.4 cm

Pythagoras theorem:

Pythagoras theorem defines that the right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Given,

A, B, C, D, E, F, G and H form a cuboid.

AB = 6.7cm, BC = 2.3cm, and CG = 8.1cm.

Now, we need to find the value of Ed and round off it into 1 decimal place.

Here we have the cuboid with the edges named as A, B, C, D, E, F, G and H.

Now, we have to use the value of BC and CG to find the value of hypotenuse of BG.

Because, BG and ED are opposite to each other.

Which means both have the same hypotenuse value.

So, according to the Pythagoras theorem,

=> BG² = BC² + CG²

=> BG² = (2.3)² + (8.1)²

=> BG² = 5.29 + 65.61

=> BG² = 70.9

So, the value of BG is 8.42.

Therefore, the value of ED is 8.4 When we round off this into one decimal place.

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The solution of the given equation is x = 10/3

The replacement value is 10/3.

This is incorrect question

Correct question is :

What is the solution to the equation 6x−5=15, given the replacement set {5/6, 5/3, 10/3}

Given,

In the question:

The equation is given as:

6x - 5 = 15

To find the solution of the given equation.

Now, According to the question:

The equation is:

6x - 5 =15

Combine the like terms:

6x = 15 + 5

6x = 20

x = 20 /6

x = 10/3

Hence, The solution of the given equation is x = 10/3

The replacement value is 10/3.

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The pounds of chocolate chips that were left is B. eleven-twelfths pounds

Given that Eva bought seven and one-half pounds of chocolate chips. She used three and three-fourths pounds in some cookies and two and five-sixths pounds in some muffins

The fraction left will be:

= Total pounds bought - The amount used

= 7 1/2 - (3 3/4 + 2 5/6)

= 7 1/2 - (3 9/12 + 2 10/12)

= 7 1/2 - 6 7/12

= 11/12

In conclusion, the correct option is B.

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Answer: $28.89

Step-by-step explanation: 2% of 1,444.50 is $28.89

the sampling distribution of the sample means is 0.03

According to the central limit theorem (n>= 30), the sampling distribution of the sample mean is approximately normal with a mean of 4.9 and a standard deviation of 3.

So:

x = standard dev/sample size

= 3 / 100

= 0.03; it is normal due to its large sample size.

Distribution is the technique of promoting and handing over services and products to clients. The term is related to marketing channels that are used to reach customers in special methods and exceptional areas. distribution characteristic, a mathematical expression that describes the chance that a machine will take on a particular value or set of values. The traditional examples are related to games of hazard.

distributing objects is an act of spreading them out similarly. Algebraic distribution method to multiply every one of the phrases inside the parentheses by way of another time period this is outside the parentheses. To distribute a term over several different terms, you multiply each of the alternative phrases by the primary term. the statistical distribution suggests which values are common and uncommon. there are numerous styles of statistical distributions, along with the bell-shaped everyday distribution.

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Answer: m1=2 and m2=88

Step-by-step explanation:

90=x-9+8x

99=9x

x=11

Heidi earned $30 in commission.

The amount of money that the store made from Heidi's sales is equal to $720.

In this exercise, you're required to determine the amount of money earned by the salesperson as commission based on the price at which she sold a jewelry.

Mathematically, the amount of commission earned on the sales of a product can be calculated by using this mathematical expression:

Commission = Percent commission × Sales price

Given the following data:

Percent commission = 4%

Sales price = $750.

Substituting the given parameters into the formula, we have;

Commission = 4/100 × 750

Commission = 0.04 × 750

Commission = $30.

Next, we would determine the amount of money that the store made from her sales:

Sales = $750 - $30.

Sales = $720.

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Rama had used 0.10 as an approximation for the length of each bead, the row would have been too short and would have dropped outside of the allowed length range.

Rama is stringing beads whose lengths are each 0.19 inches.

A bead's length is 0.19 inches, which is approximately 0.2 inches. If the row has 9 beads, we must double the length of each bead by the number of beads. Therefore

Because the beads are approximately 0.20 inches in length, the length of a row of 9 beads is

will be approximately 9 × 0.20 = 1.80 inches.

Thus, if she had used 0.10 as an approximation for the length of each bead, the row would have been too short and would have dropped outside of the allowed length range.

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Answer:

a = -1
b = -9

Step-by-step explanation:

when x = -2 put -2 for x in the equation:

a(3- (-2)) = -2*(-2) + b and then solve
a(3+2) = 4+b
5a = 4+b

then look at the numbers in the box and try for which number this equation will work. when you put a = -1 and b = -9 you will see it is equal on both sides because each side is -5

The standard deviation of the monthly amount charged is 346.41

Step 1: Identify the values of a and b, where [a , b] is the interval over which the continuous uniform distribution is defined.

Since it takes between 300 and 1500 minutes to be seated at the restaurant, we have:

a = 300

b = 1500

Step 2: Calculate the variance using the formula Var(x) = [tex]\frac{(b-a)^{2} }{12}[/tex]

Using the formula for the variance and the values identified in step 1

(a = 300 , b = 1500), we have:

Var(x) = [tex]\frac{(b-a)^{2} }{12}[/tex]

         = [tex]\frac{(1500 - 300)^{2} }{12}[/tex]

         = 1440000/12

         = 120,000

the variance is 120,000

Step 3: Calculate the standard deviation by taking the square root of the variance. σ = [tex]\sqrt{Var(x)}[/tex]

The standard deviation is the square root of the result from step 2 (variance = 120,000)

σ = [tex]\sqrt{Var(x)}[/tex]

σ = [tex]\sqrt{120000}[/tex]

   = 346.41

The standard deviation of the monthly amount charged is 346.41

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It is possible to multiply or divide an equation by the same number on each side of the equation without changing the answer, according to the "multiplication property" of the equation.

How can you use the properties of operations to multiply linear expressions?

According to the equation's "multiplication property," it is possible to multiply or divide an equation by the same number on each side of the equation without changing the equation's outcome. The result of multiplying two terms with two different signs will be negative, while the product of two factors with the same sign will be positive. If a and b are positive integers and x is a variable, then (xa * xb) = x(m + n). The identity, commutative, associative, and distributive properties of multiplications are four properties that can facilitate the process. They offer guidelines for solving multiplication problems quickly using properties that always hold true for particular equations.

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