2. Which of the following statements is correct based on the number line below?
A.
B.
C.
D.
0
√28
√28
A
1 2 3
B
844
t
C
to
5
6 7 8 9
is to the right of Point C because it is less than 5.
D
+
10
is to the right of Point C because it is greater than 5.
11
√28
is between points B and C because it is less than 0 and greater than 5.
√28
is between points B and C because it is greater than 0 and less than 5.

(7) Slope of line AB = -6/5 and Slope of the line CD = -6/5 and line AB and line CD are parallel in nature.

(8)Slope of line AB = 3/4 and the Slope of line CD = 1 and line AB and line CD is neither parallel nor perpendicular.

(9) We have drawn the graph passing through the point P and parallel to line AB.

(10)We have drawn the graph passing through the point P and perpendicular to line AB.

What is the property of slopes of parallel lines and perpendicular lines?

If two lines are given and they are parallel to each other then the slopes are equal and for perpendicular lines, the product of their slopes is equal to -1.

(7) The line AB is passing through the points (-1, 5/2) and (3/2, -1/2).

   Slope = y2 - y2/x2 - x1

              = (-1/2 - 5/2)/(3/2-(-1))

              = -6/5

   As line AB and line CD are parallel in nature so the slope of line CD is also -6/5.

(8) The line AB is passing through the points (1/2, 1) and (5/2, 5/2).

    Slope = y2 - y2/x2 - x1

              = (5/2 - 1)/(5/2-1/2)

              =3/2/2

             = 3/4

    Line CD is passing through points (1, 1) and (2, 3).

    Slope = y2 - y2/x2 - x1

              = (3 - 1)/(2-1)

              =2/2

             = 1

  As the product of their slopes is not equal to -1.

  So lines are neither parallel nor perpendicular.

(9) Slope of AB can be computed as (-2, 1) and (-5, 5)

     Slope = 5 - 1/-5 + 2

                = 4/-3.

  The slope of line passing through the point P = -4/3 as we have to draw the parallel line.

 Point P = (-1, 3)

Equation of the line :

      y - 3 = -4/3(x + 1)

    3y +9 = -4x - 4

   3y = -4x - 13

Now we can draw the line

(10) Slope of line AB = -4/3

    So the slope of the line passing through point P should be 3/4 in order to be perpendicular to line AB.

     Equation of the line passing through point P:

       y - 3 = 3/4(x - (-1))

       y - 3 = 3/4(x+1)

Hence,

(7) Slope of line AB = -6/5 and Slope of the line CD = -6/5 and line AB and line CD are parallel in nature.

(8)Slope of line AB = 3/4 and the Slope of line CD = 1 and line AB and line CD is neither parallel nor perpendicular.

(9) We have drawn the graph passing through the point P and parallel to line AB.

(10)We have drawn the graph passing through the point P and perpendicular to line AB.

To learn more about the slopes of parallel lines and perpendicular lines, visit:

https://brainly.com/question/14687265

#SPJ1

Answer: We can set up the equation 21 stickers/pack + 24 stickers/pack + x stickers/pack = 15 stickers.

We can solve this equation to find that x, the number of stickers in each pack, is equal to 6 stickers/pack. Answer: 6

Answer: 20

Step-by-step explanation:

24 + 21 = 45

45 + 15 = 60

60 / 3 = 20

They must make 18,000 pencils in a month to break even.

Let,      n = number of pencils they sell

           R = revenue

           C = cost

           P = profit

We know that,

          P = R - C

At the break-even point,

              P = 0

            ⇒R - C = 0

            ⇒ R = C

Putting the value,  

            C = [tex]\frac{3500 - 1500}{3000}[/tex] n + 1500

        ⇒ C = 0.667n + 1500

and,       R = 0.75n

When   R = C

           ⇒ 0.75n = 0.667n + 1500

           ⇒  0.0833n = 1500

           ⇒     n   =  18000

 ∴ They must make 18,000 pencils in a month to break even.

Read more about the break-even point :

https://brainly.com/question/20276478

#SPJ4

Error Analysis 1:(x-3)/(x+7)

Error Analysis 2:(x(x-7)(x+3))/2(x+1)(x+9)(x+5)

Error analysis is a procedure that is usually used to identify the cause of the issue when pupils continually make mistakes. The method entails going over a student's work and looking for patterns of misinterpretation. Mathematical errors can occur for a variety of reasons and can be factual, procedural, or conceptual. The study of the kind and quantity of mistake, or uncertainty, that might be present in the solution to a problem is known as error analysis in mathematics. This issue is particularly common in practical disciplines like statistics and numerical analysis. The teacher can examine a student's errors on a worksheet, test, or progress monitoring tool to do an error analysis for mathematics. In order to grade each problem, the teacher should mark each wrong digit in the student's response, starting from the RIGHT, going to the LEFT for addition, subtraction, and multiplication problems.

Error Analysis 1:

(x²-x-6)/(x²+9x+14)

=(x-3)(x+2)/(x+2)(x+7)

=(x-3)/(x+7)

Error Analysis 2:

(x²-6x-27)/(2x²+2x)÷(x²+14x+45)/(x²)

=(x(x-7)(x+3))/2(x+1)(x+9)(x+5)

To know more about error analysis, visit:

https://brainly.com/question/29261280

#SPJ1

A function that will match the given graph is; f(x) = 2(x - 5)²(x + 2)

In polynomial graphs, we know that the roots are the points where the graph crosses or touches the x-axis.

In this given graph, we see that the graph touches the x-axis at x = 5 and then crosses the x-axis at x = -2. Thus;

The roots of the equation are -2 and 5.

However, when the graph changes sign at a point on the x-axis, it means that point represents double roots. Thus, we will now have three roots which are -2, 5 and 5. The factors of the polynomial are;

(x + 2), (x - 5)²

Now, we see that when x = 0, y = 100 from the graph. Thus;

a(0 + 2)(0 - 5)² = 100

a(50) = 100

a = 100/50

a = 2

Thus, the equation would now be;

f(x) = 2(x - 5)²(x + 2)

Read more about Polynomial Graphs at; https://brainly.com/question/14625910

#SPJ1

The volume of the composite solid is 47.2 cubic cm

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

The composite solid

From the composite solid, we have the following shapes

Cube: Side length = 4 cm

Cone = Radius = 2 cm, Height = 4 cm

The volume of a cube is

Cube = Side length³

Substitute the known values in the above equation, so, we have the following representation

Cube Volume = 4³

Cube Volume  = 64

The volume of a cone is

Cone = 1/3 * πr²h

Substitute the known values in the above equation, so, we have the following representation

Cone Volume = 1/3 * 22/7 * 2² * 4

Cone Volume = 16.8

The volume of the composite solid is

Volume = Cube Volume - Cone Volume

So, we have

Volume = 64 - 16.8

Volume = 47.2

Hence, the volume is 47.2 cubic cm

Read more about volume at

https://brainly.com/question/463363

#SPJ1

Answer:

$8 per person

Step-by-step explanation:

32 divided by 4 is 8

32 : 4 = 8 : 1

The hours that it take a pipes to feel the same pool is 120 hours.

Rate demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

In this situation, 5 pipes can fill the pool in 24 hours.

The rate for a pipe will be:

= Number of hours × Number of pipe

= 24 × 5

= 120 hours

The time taken is 120 hours.

Learn more about rate on:

brainly.com/question/25537936

#SPJ1

Answer:

y = -1/2x - 2

Step-by-step explanation:

y = mx+b, m = -1/2, and b (the y-intercept) is -2.

A true average strain in a way that converys information about precision and reliability (24.33, 27.67)

From given information we have:

the sample size n = 20

the mean failure strain x(bar) = 26.0

the standard deviation s = 3.4

Assuming a normal distribution for failure strain, we need to estimate true average strain in a way that converys information about precision and reliability.

A 95% confidence interval is necessary; other confidence intervals can be calculated in a similar way.

c = 0.95 or 95%

In the table with the critical values for t distributions in the appendix, locate the row beginning with degrees of freedom.

Here, the degree of freedom :

df = 20 - 1

df = 19

and  α = (1-c)/2

          = 0.025

To find the t-value:

t_(α/2) = 2.145

Therefore, the error margin is:

E = t_(α/2) × s/√n​

E = 2.145× 3.4/√19

E ≈ 1.67

And the confidence interval would be,

(x{bar} - E, x{bar} + E) = (24.33, 27.67)

Therefore, the confidence interval is: (24.33, 27.67)

Learn more about the confidence interval here:

brainly.com/question/13067956

#SPJ4

Ф {0, [3√3/2(3√3-π)]}

The poster above has good diagrams ; so , I will just go through the calculations .

The region of integration is with in the circle x ^2+y^2=2y but outside the circle   x^2+y^2=1.

I would convert to polar . With polar , we have  x^2+y^2=r^2 ,x=rcosФ and        y=rsinФ
We thus have the first circle becomes x^2+y^2=2y ⇒r^2=2rsinФ Divide through by r,  and you get r=2sinФ(1).  
This is the upper circle in the previous posters diagrams .

The other equation of a circle becomes :
x^2 + y^2 =  1  ⇒ r^2 = 1 ⇒ r =  1   (2)      
These two curves intersect at :
r= 2sinФ =1 ⇒     sinФ=1/2  ⇒Ф= [tex]\alpha[/tex]/6 or 5[tex]\pi[/tex]/6    
From the previous poster's diagrams , we can see that there is as much mass on either side of the positive. y axis or
Ф=[tex]\pi[/tex]/2 axis in polar ; so , the X  coordinate of the center of mass is zero  
X=0 We can also see from his diagrams that the mass and moment of mass is symmetrical about the Ф=[tex]\pi[/tex]/2
we only need to integrate from Ф=[tex]\pi[/tex]/6 to Ф=[tex]\pi[/tex]/2  ( the answers from to are the same and double )
The differential of area in polar coordinates is
d A=rdrdФ  They say the area mass density is inversely proportional to the distance from the origin .

This can be written as : p=k/r. We can thus say the differential of mass is
d M=PDA=

To learn more about center of mass of circle, click here  
  https://brainly.com/question/29142813.

Using the slope, the required value of k is 48.

In mathematics, the steeper direction of a line is overall processed by the slope or gradient of the line.

A line's slope can be used to determine how steep it is.

Theoretically, the gradient is calculated as "rise over run" (change in y divided by change in x).

Given is a line that crosses through the origin:

y = mx

Let,s take x = -12 and y = -2.

y = mx

-2 = -12m

m = -2/12

m = -1/6

m is the slope.

The equation now:

y = mx

y = -1/6x

Now, insert:
x = k and y = 8

y = mx

8 = -1/6x

x = 6*8

x = 48

Therefore, using the slope, the required value of k is 48.

Know more about the slope here:

brainly.com/question/29280886

#SPJ1

A selective industrialization is a phenomenon in which those sectors or elements where it is desired to centralize or focus the industrialization itself are selected.

This has been a type of industrialization where industrialization is projected in sectors that are previously selected and defined.

Some of the characteristics of selective industrialization are:

¡Hope this helped!

Selective industrialization is a strategy that involves focusing on the development of specific industries or sectors in a country's economy.

This approach is often used by developing countries to promote economic growth and development by targeting key industries that have the potential to drive growth and create jobs.

In the context of an Expo, selective industrialization could refer to showcasing and promoting specific industries or sectors that a country or region specializes in or wants to develop further.

This could involve exhibiting products, technologies, and innovations related to those industries, as well as networking with potential investors, partners, and customers to explore opportunities for collaboration and growth.

Answer:

Step-by-step explanation:

To find the percentage increase in the dog's weight, you can use the following formula:

percentage increase = (final value - initial value) / initial value x 100%

In this case, the initial value is 40 pounds and the final value is 48 pounds, so the percentage increase is:

percentage increase = (48 - 40) / 40 x 100% = 8 / 40 x 100% = 20%

Therefore, the dog's weight increased by 20%.

Answer:true, false, false, true

Step-by-step explanation:

The proof that  Δ SVW ≅ Δ UTW is given by ASA congruence criterion.

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure. These triangles can be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with each other.

The symbol of congruence is’ ≅’.

Given:W is the midpoint of SU

⇒ SW = WUTU ⊥ SU and SU ⊥ SV

To prove:Δ SVW ≅ Δ UTW

Proof:In Δ SVW and Δ UTWSW = UW (given)

∠S ≅ ∠U (given)

∠ SVW ≅ ∠ UTW (vertically opposite angle)

Therefore, Δ SVW ≅ Δ UTW (by ASA congruence criterion)

To learn more about the congruence of triangle from the given link. https://brainly.com/question/1675117

#SPJ1

The required answer is the domain is time (t) and the range is a distance (d) i.e. Option 2.

What are domain and range?

The value range that can be plugged into a function is known as its domain. In a function like f, this set represents the x values f(x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.

From the given question, and the above definition of domain and range,

the time (t) acts as an x-values or input value and the distance (d) acts as a y-value or output value

Hence, the domain is time (t) and the range is a distance (d) i.e. Option 2.

To learn more about the domain and range

https://brainly.com/question/2264373

#SPJ1

The margin of error of a confidence interval 0.5432

In statistics, the term margin of error is calculated by multiplying a critical factor with the population standard deviation and then the result is divided by the square root of the number of observations in the sample.

Margin of Error = Z * ơ / √n.

Here we have to calculate the margin of error of a confidence interval for the difference between two population means using the given information.

While we looking into the given question we have given the values,

σ1=5.94

n1=98

σ2=2.87

n2=79

α=0.05

Here we have to calculate the margin of error for the value 1, n1, and α

First, find the critical value: zα2=1.9599

Next, find the standard error of the mean which is

SE = 297√2/√700

Finally, the margin of error is 1.1760

Similarly, the value for the nest set of values is,

First, find the critical value: zα2=1.9599

Next, find the standard error of the mean: SE = 287√79/√7900

Finally, the margin of error is ME = 0.6328

Then the difference between these population is

=> 1.1760 - 0.6328

=> 0.5432

To know more about Margin of error here.

https://brainly.com/question/29101642

#SPJ4

Answer:lol

Step-by-step explanation:lol

The height of the triangular cross section is equal to 2.5 cm.

Mathematically, the volume of a rectangular prism can be calculated by using this formula:

Volume = L × W × H or Volume = base area × length

Where:

Next, we would determine the base area of this rectangular prism by using the formula for the area of a triangle:

Area of triangle = 1/2 × base area × height

Area of triangle = 1/2 × 4 × h

Area of triangle = 2h

Now, we can determine the height of this rectangular prism as follows;

Volume = base area × length

35 = 2h × 7

Height, h = 35/14

Height, h = 2.5 cm.

Read more on prism here: https://brainly.com/question/21012007

#SPJ1

The probability that exactly four complaints will be received during the next eight hours is 15.41%.

A discrete probability distribution called the Poisson distribution provides the likelihood that an event will occur a specific number of times over the course of a given period of time or location. The formula for this distribution is given by [tex]P(X=x)=\frac{e^{-\mu}\times \mu ^x}{x!}[/tex] where x is the number of successes, μ is the mean, and e is Euler's number.

Given n = 8 hours then, μ = 0.7n = 0.7×8 = 5.6.

Then, the probability that exactly four complaints are received is,

[tex]\begin{aligned}P(X=4)&=\frac{e^{-5.6}\times5.6^4}{4!}\\&=0.1541\end{aligned}[/tex]

The required answer is 15.41%.

To know more about Poisson distribution:

https://brainly.com/question/7283210

#SPJ4

stem                            leaf

0                               7, 7, 8, 8

1                                   3 , 3

2                                   5, 2

What is stem and leaf plot ?

A stem and leaf plot, also known as a stem and leaf diagram, arranges data in a way that makes it simple to see how often certain sorts of values occur. It is a graph that displays ordered numerical data. A stem and a leaf are divided into each piece of data.

A stem and leaf plot is shown as a customized table with the first or final digit of each data value divided into a stem and the remaining digit in a leaf. The stem and leaf plot key is the symbol " | " that is used to display stem and leaf values.

For instance, the stem and leaf plot key is used to represent 46 as 4 on the stem and 6 on the leaf.

in 2|5 , 2 is the stem side and 5 is the leaf side

in 0|7 , 0 is the stem side and 7 is the leaf side

in 1|3 , 1 is the stem side and 3 is the leaf side

in 0|8 , 0 is the stem side and 8 is the leaf side

in 2|2 , 2 is the stem side and 2 is the leaf side

in 0|7 , 0 is the stem side and 7 is the leaf side

in 1|3 , 1 is the stem side and 3 is the leaf side

in 0|8 , 0 is the stem side and 8 is the leaf side

Learn more about stem and leaf from the link below

https://brainly.com/question/9798801

#SPJ1

The expressions are x=9°+n.36° and x= -9°+n36°.

So, options C and D are correct.

A finite combination of symbols that are well-formed in accordance with context-dependent rules is referred to as an expression or mathematical expression in mathematics. Mathematical symbols can represent variables, operations, functions, brackets, punctuation, and grouping to help specify the logical syntax and order of operations. Lambda expressions are a new class of expressions that Alonzo Church and Stephen Kleene introduced in the 1930s for formalizing functions and their evaluation. In mathematical logic and the theory of programming languages, they serve as the foundation for the formal system known as lambda calculus.

Given,

4cos(10x)+2=2

4cos(10x)=0

cos(10x)=0

10x=90°+n360°

x=(90°/10°)+n(360°/10)

x=9°+n.36°

(or)

10x= -90°+n360°

x= -9°+n36°

Therefore, the expressions are x=9°+n.36° and x= -9°+n36°

Hence, options C and D are correct.

To know more about expressions, visit:

https://brainly.com/question/1859113

#SPJ1

The fraction in simplest form is  [tex]\frac{8}{125}[/tex].

What is a fraction?

The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection. The denominator is the figure that appears below the line. It displays the total number of identical objects in a collection or the total number of equal sections the whole is divided into.

Given, [tex](\frac{2}{5})^{3}[/tex]

= [tex]\frac{2}{5} *\frac{2}{5} *\frac{2}{5}[/tex]

= [tex]\frac{8}{125}[/tex]

Hence, the fraction in simplest form is  [tex]\frac{8}{125}[/tex].

To learn more about fractions

https://brainly.com/question/78672

#SPJ1

omgggg thats what she said

(a) A vector function, r(t), that represents the cylinder x^2+y^2 = 25 and the surface z = xy.

(b) A vector function, r(t), that represents the paraboloid z = 7x^2 + y^2 and the parabolic cylinder y = 2x^2 is r(t) = <t, 2t^2, 7t^2+4t^4.

(a) We have to find a vector function, r(t), that represents the curve of intersection of the two surfaces.

The cylinder x^2+y^2 = 25 and the surface z = xy.

The given cylinder is x^2+y^2 = 25

We can write it as

x^2+y^2 = 5^2………………(1)

The given surface is z = xy………………..(2)

Let x = 5cost and y = 5sint, then x and y satisfy the equation 1

Now putting x=5cost and y=5sint in equation (2), we get

z = (5cost)(5sint)

z = 25sintcost

Now x=5cost, y=5sint and z=25sintcost

Hence, r(t) = <x(t),y(t),z(t)>

r(t) = <5cost, 5sint, 25sintcost>

(b) We have to find a vector function, r(t), that represents the curve of intersection of the two surfaces.

The paraboloid z = 7x^2 + y^2 and the parabolic cylinder y = 2x^2.

The given paraboloid z = 7x^2+y^2………………………(1)

The parabolic cylinder y = 2x^2……………………….(2)

Let x = t, then from equation 2

y = 2t^2

Now putting the value of x and y in equation (1)

z = 7t^2+(2t^2)^2

z = 7t^2+4t^4

Now x=t, y=2t^2 and z=7t^2+4t^4

Hence, r(t) = <x(t),y(t),z(t)>

r(t) = <t, 2t^2, 7t^2+4t^4>

To learn more about finding vector function link is here

brainly.com/question/29555329

#SPJ4

Answer: Answer is 8.47

Step-by-step explanation:

[(6x2.99)-1] ÷2

16.94 / 2

8.47

Answer:

8.47

Step-by-step explanation:

[(6x2.99)-1] ÷2  16.94 /2 =8.47