Select the correct choices to complete the sentence.
In the figure, line m is parallel to line n. Classify the relationship between ∠2 and ∠7 as alternate interior, alternate exterior, or corresponding.

(a) The number of washers that can be cut from a sheet of steel is 12,732 washers.

(b) No additional washers could be cut from the metal left over after it was remelted and cast into a sheet of the same thickness and width (1 m).

First, we need to calculate the area of the washer, which can be done as follows:

Area = π (de/2)² - π (di/2)²

= π(0.02 m/2)² - π (0.01 m/2)²

= 0.000236 m²

Now, we can calculate the number of washers that can be cut from a 3m x 1m sheet of steel:

Number of washers = (Area of the sheet) / (Area of the washer)

= (3 m x  1 m) / 0.000236 m²

= 12,732 washers

Next, we need to find the area of the metal left over after cutting the 12,732 washers. This can be calculated as follows:

Area of the metal left over = (3 m²) - (12,732  x 0.000236 m²)

= 3 - 3.05

= -0.05 m²

Since the metal left over is negative, it means that not enough metal was available to cut 12,732washers. Hence, 12,732 is the maximum number of washers that can be cut from a 3m x 1m sheet of steel.

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Answer:

Step-by-step explanation:

The perimeter of the rectangle: We know that the frame is equal to 2(L+B)

therefore, the edge of a rectangle is 2[5a^2b^4 + 3ab^2]

                        = 2[ab^2(5ab^2 + 3)]

The area of a rectangle is L * B

                       =  (5a^2b^4) * (3ab^2)

                       =  15a^3b^6

The value of m is 40 degrees, the value of x is 6 and value of y is 9.

Parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

To find the value of variable m.

Forming an equation:

3m = 120°

m = 120/3

m = 40

Therefore the value of m is 40.

Finding x:

x is opposite to the side of measure 6.

As per the first property.

x = 6

So, x = 6

Therefore the value of x is 6.

Finding y.

5y is opposite the angle measuring 45°.

Forming an equation.

5y = 45°

y = 45/5

y = 9

Therefore the value of y is 9.

Hence, the value of m is 40 degrees, the value of x is 6 and value of y is 9.

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The complete question is given below and in attachment

Find the value of each variable in the parallelogram. explain step by step

variety of statistics for 1057 inernet users are  = (0.9180, 0.8998)  solve by given question .

population proportion is the share of a population that belongs to a particular category. Confidence intervals are used to estimate population proportions.

Let p be the population proportion of respondents who say the Internet has been a good thing for them personally.

=p +- z*[tex]\sqrt{p*(1-p)/n}[/tex]

where z* = Critical value p = Sample proportion,n = sample size.

As per given , we have

n= 1057 By z-table , Critical value for 95% confidence interval : z*= 1.96

Then, the 95% confidence interval for the proportion of respondents who say the Internet has been a good thing for them personally. will be :

=p +- z*[tex]\sqrt{p*(1-p)/n}[/tex]

=0.9+-1.96[tex]\sqrt{.9*(1-.9)/1057}[/tex]

=0.9180, .8998

Hence, the required 95% confidence interval for the proportion of respondents who say the Internet has been a good thing for them personally = (=0.918, .881)

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Answer:

B. (-7, -1)

C. (5, 12)

Step-by-step explanation:

A function can only have one output for a specific input

In math terminology that means if y = f(x) is a function of x then the mapping from x to y is 1:1

Or,

For a specific value of x, there can be one and only one value for y

This is often referred to as a vertical line test; if a vertical line parallel to the y-axis is drawn for any x value it should intersect the function graph at one and only one point

g(x) includes all the ordered pairs of f(x) therefore the ordered pairs of g(x) are:
{ ( -18, -31), (-9, -23), (4, 2), (11, 5), (14, 12) }

Looking at the answer choices:
A. (-9, 11) will violate the 1:1 correspondence between x and y since (-9, -23) is already a pair

B. (-7, -1) is OK. There is no other entry with x = -7

C. (5, 12) is OK. There is no other entry with x = 5

D. (4, 15) will violate; there is already an entry for x = 4: (4, 2)

E.  (14,20). This will also violate the properties of a function since there exists an entry for x = 14, namely (14, 20)

The equation which is used to find the number of chocolates candy in the jar is given by 18 + 24 + 19 + n = 82 , the number of chocolate candy in the jar is equal to 21.

Number of strawberry candy in the jar = 18

Number of cherry candy in the jar = 24

Number of lime flavored candies = 19

Let 'n' be the number of chocolate candy in the jar

Total number of candy in the jar = 82

Equation used to represent the given condition is :

18 + 24 + 19 + n = 82

⇒ 61 + n = 82

⇒ n = 82 - 61

⇒ n = 21

Therefore, the equation required to represent the number of chocolate candy is 18 + 24 + 19 + n = 82 and the value of n is equal to 21.

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If there are 15 boys and 17 girls in a math class then, the ratio of boys to girls is Option A. 15:17

The ratio of boys to girls in the math class is 15:17. This can be found by dividing the number of boys by the number of girls, which gives:

15/17

This ratio cannot be simplified because 15 and 17 do not have any common factors other than 1. Therefore, the ratio of boys to girls is 15:17.

The ratio of boys to girls in a math class is the relationship between the number of boys and the number of girls. The ratio is a way of expressing the comparison between two quantities. In this case, there are 15 boys and 17 girls in the class. To find the ratio of boys to girls, we divide the number of boys by the number of girls, which gives 15/17. This ratio cannot be simplified further because 15 and 17 do not have any common factors other than 1. Therefore, the ratio of boys to girls in the math class is 15:17. This means that for every 15 boys in the class, there are 17 girls.

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The value of x and y in the system of equations, are 10 and 44, therefore, the number of booster pack and premade deck are 10 and 44 respectively.

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given that, a deck contains 266 cards which have 9 booster packs and 4 premade decks, and 10 booster packs and 5 premade decks, which included a total of 320 cards.

Let the number of booster pack and premade deck be x and y,

Establishing the system of equations,

9x + 4y = 266....(i)

10x + 5y = 320

2x + y = 64...(ii)

Multiplying eq(ii) by 4 and subtract eq(ii) from eq(i)

(9x + 4y = 266) - (8x + 4y = 256)

x = 10

Put x = 10 in eq(ii)

20 + y = 64

y = 44

Hence, the value of x and y in the system of equations, are 10 and 44, therefore, the number of booster pack and premade deck are 10 and 44 respectively.

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The total number of students at the school is 1240.

What is Ratio ?

With the dividend or number being divided as the antecedent and the divisor or number that is dividing as the consequent, a ratio compares two quantities by division.

we know that, number of boys : number of girls = 11: 9

Let's assume the number of boys = 11x

and, the number of girls = 9x

similarly, There are 124 more boys than girls

So, number of boys = 124 +  number of girls

           11x = 124 + 9x

          2x = 124

          x = 62

So, number of boys = 11 ×62 = 682

number of girls = 9 × 62 = 558

∴ Total number of students is 1240 i.e.(682+558).

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350 pounds of the meal should be added to the grain to produce a mixture that costs $1.10 per pound.

What is meant by addition?

In mathematics, addition is the process of fusing two or more integers. The numbers being added are known as addends, while the outcome of the addition process, or the final response, is known as the sum. It is one of the fundamental mathematical operations we employ on a daily basis. We add numbers in many different contexts.

Let the amount of meal mixed with the grain be 'x' pounds.

Now, Total price of the mixture = x*0.80 + 350*1.40 = (x+350)*1.10

350*(1.40 - 1.10) = x*(1.10 - 0.80)

350*0.3 = x*0.3

x = 350

Therefore, the amount of meal that should be added to the grain is 350 pounds.

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The correct option is C which is out of 30000 there will be 27000 deaths.

According to its definition, a percentage is any number relative to 100. It is shown with the sign %. "Out of 100" is what the percentage means. Consider dividing any quantity or item into 100 identical bits.

Given, according to the website, 90% of the 30,000 deaths caused by unsafe water and filthy living conditions that occur every week around the world involve children under the age of five. All of the following interpretations of this statistic are accurate.

The percentage of deaths will be calculated as:-

Percentage = 30000 x 90%

Percentage = 30000 x 0.9

Percentage = 27000

Therefore, the number of deaths will be 27000.

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The corresponding graph for the given data is  a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points (0, 27), (1,25), (3,21), (4,19) and (7,13)

What is a linear function?

A linear function is a polynomial function whose degree is utmost zero or one. It is represented as a straight line in the graph.

A Girl scout is selling cookies to raise money for her troop.

She is given a certain number of cookies to sell and is tracking the number of boxes remaining each day.

This result is shown in the table:

       Time(in days)         Number of boxes

                 1                                   25

                 3                                   21                                

                 4                                   19

                 7                                   13

The graph for the given data is attached below.

This forms a straight line.

By critically observing the graph and relationship between the time and number of boxes, we determine a function for the graph.

That is y=-2x+27.

Hence, the corresponding graph for the given data is  a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points (0, 27), (1,25), (3,21), (4,19) and (7,13)

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Answer: Its D.

Step-by-step explanation:

The number of people who are not season ticket holders can be found by subtracting the number of season ticket holders from the total number of attendees:

110801 - 4922 = 105879

Therefore, there are 105879 people who are not season ticket holders.

The equivalent expression to 14^6 is given as follows:

[(14^5)^3]/14^9.

When two terms with the same base and different exponents are divided, we keep the base and subtract the exponents.

The power of power exponential rule states that when a single base is elevated to multiple powers, the powers are multiplied.

Then the expression with the desired value of 14^6 is obtained as follows:

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3 minutes is the cost of the call that is same for both plans

Two or more expressions with an Equal sign is called as Equation.

Let's assume the call duration in minutes is represented by x.

For David, the cost of the call can be represented by the equation: C(d) = 4 + x

For Alec, the cost of the call can be represented by the equation: C(a) = 1 + 2x

Since the cost of the call is the same for both plans, we can set the two equations equal to each other and solve for x:

4 + x = 1 + 2x

Solve for x.

3 = x

Hence, the call duration that costs the same on both plans is 3 minutes.

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Answer:

28 cups of Flower

Ratio Table:

2,4,6,8

7,14,21,28

Step-by-step explanation:

2x4/7x4=8/28

The volume of the pool is 768 cubic feet.

What is the Volume?

In mathematics, volume refers to the amount of space occupied by a three-dimensional object. It is a measure of the total amount of space enclosed within the boundaries of an object. The volume of an object is usually measured in cubic units, such as cubic meters (m³), cubic feet (ft³), or cubic centimeters (cm³).

To find the volume of the pool, we need to multiply its length, width, and depth. Looking at the figure, we see that the length of the pool is 16 ft, the width is 6 ft, and the depth is 8 ft.

So, the volume of the pool is:

V = length x width x depth = 16 ft x 6 ft x 8 ft = 768 cubic feet

Hence, the volume of the pool is 768 cubic feet.

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If LA Galaxy has won 36% of their soccer matches, this means that they have won 36/100 * 50 = 18 matches.

So, they have won 18 matches out of 50.

Step-by-step explanation:

percentage of soccer matches won = 36%

total matches = 50

matches won = 36/100 * 50

=18

The of association represented in the graph is positive linear association.

option C

A positive correlation is a statistical relationship between two variables such that as one variable increases, the other variable also increases, and as one variable decreases, the other variable decreases as well.

In other words, positive correlation means that as the value of one variable goes up, the value of the other variable also goes up, and vice versa. The correlation is said to be positive because both variables move in the same direction.

The strength of the correlation can be measured using a correlation coefficient, which ranges from -1 to 1. A correlation coefficient of 1 indicates a perfect positive correlation, while a correlation coefficient of 0 indicates no correlation.

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The equivalent function to the given one is:

L(t) = 7,920*(3)^t

Here we want to rewrite the function:

L(t) = 880*(3)^(t + 2)

Into the form:

L(t) = a*(b)^t

Remember the rule for exponents:

(x^a)*(x^b) = x^(a + b)

Then we can take our function:

L(t) = 880*(3)^(t + 2)

And rewrite this as:

L(t) = 880*(3^t)*(3^2)

L(t) = 9*880*3^t

L(t) = 7,920*(3)^t

That is the equivalent function.

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The surface area of the net is 108 squate feet

The complete question is added as an attachment

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

A net that has the following shapes

The area of the net is the sum of the individual areas

So, we have

Area = 8 * 12 + 2 * 0.5 * 3 * 4

Evaluate

Area = 108

Hence, teh area is 108 squate feet

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Answer:

If A=30 and B= 70 the first unknown angle Y would be 100. When using the E.A.T  (exterior angle theorem) you add the 2 remote interior angles to get the exterior angle. (Y)

Unknown angle 2 is a interior angle, so we know all 3 of the interior angles must equal 180.

30+70=100

180-100=80

C=80

Step-by-step explanation:

The transformation of the triangle is the orientation changes and moves the triangle into Quadrant III

Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images.

The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

Given data ,

Let the transformation of the triangle be represented as A

Now , the initial coordinates are ( x , y )

And , on transformation , we get ( x , y ) - ( x - 3 , y + 4 )

Now , the triangle is reflected across the y-axis

So , when you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

And , its orientation has changed and it is now in Quadrant III.

Hence , the triangle is now in Quadrant III

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Answer: Just to get your attention (don't mind rating this)

Step-by-step explanation:

I'm sorry, but there's no table or information about the sample provided for me to estimate the mean speed of the sample. Can you please provide more information or clarify your question?

For a diamond having volume 161 mm³, the value for side length is 7 mm.

What is volume?

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

The formula for volume of diamond is given as -

V = 0.47 s³

Here, s represents the side length of each edge.

The value for volume of diamond is given as -

Volume = 161 mm³

Plug in the values in the equation -

Volume = 0.47 s³

161 = 0.47 s³

s³ = 161 / 0.47

s³ = 342.553

s = ∛342.553

s = ∛342.553

s = 6.996 mm

Therefore, the side length measures 6.996 ≈ 7 mm.

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r as a percent is a) a = 79, b = 1.002, and r = 0.2%.

The formula given, q = abt = a(1+r)t, represents exponential growth, where a is the starting value, b is the growth factor, r is the growth rate, t is the time period, and q is the final value after t periods.

Given q = 79(1.002)^t, we can see that:

a = 79 (the starting value)

b = 1.002 (the growth factor)

r = 0.2% or 0.002 (the growth rate, expressed as a decimal)

So, the correct answer is a) a = 79, b = 1.002, and r = 0.2%.

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Answer:

[tex]\mbox{\large $0.5 + 0.16 \bar {3}$ = \boxed{\dfrac{199}{300}}}[/tex]

Step-by-step explanation:

[tex]0.16\bar{3} = 0.16333333333\\[/tex]

the 3 repeats until infinity

Let's multiply this by 100 to move the non-repeating part to the left of the decimal point

0.1633333333...... x 100 = 16.333333333333333...

.333333 = 1/3

Therefore the recurring number multiplied by 100 is
[tex]16 + \dfrac{1}{3} = \dfrac{16 \times 3 + 1}{3}=\dfrac{49}{3}[/tex]

Since this fraction was arrived at by multiplying by 100, divide this fraction by 100 to get back the fraction in its original decimal value of 0.163333

[tex]\dfrac{49}{3} \div 100[/tex]

To divide by a number, multiply by the reciprocal of that number

Reciprocal of 100 is 1/100:

[tex]\dfrac{49}{3} \div 100 = \dfrac{49}{3} \times \dfrac{1}{100} = \dfrac{49}{300}[/tex]

(You can verify this by dividing 49 by 300 in a calculator and seeing that the result is 0.163333333333333333333 i.e. 0.16333 recurring

We want to add 0.5 to this.

0.5 = [tex]\dfrac{1}{2}[/tex]

so
0.5 + 0.16333333 = 0.6633333

[tex]= \dfrac{1}{2} + \dfrac{49}{300}[/tex]

We can write [tex]\dfrac{1}{2}[/tex] as [tex]\dfrac{150}{300}[/tex]  by multiplying numerator and denominator by 150

So we get

[tex]0.5 + 0.1633333 = \dfrac{150}{300} + \dfrac{49}{300} = \dfrac{150+49}{300} = \dfrac{199}{300}[/tex]

If you perform this division on a calculator you will get the answer as 0.663333 = [tex]0.66\bar{3}[/tex] which is what you get when you add 0.5 and [tex]0.16\bar{3}[/tex]

The value of the angle 'x' in the right-angle triangle will be 42.99°.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The value of the variable 'x' is given by the sine of the angle 'x'. Then we have

sin x = 15 / 22

sin x = 0.6818

sin x = sin 42.99°

x = 42.99°

The value of the angle 'x' in the right-angle triangle will be 42.99°.

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The values of a, b and c based on the information will be 2, 3, 4.

The square root of c which is 4 will be 2.

From the information, it was stated that the sum of the three consecutive integers, a, b and c, is 9.

This can be Illustrated as:

a + a + 1 + a + 2 = 9

3a + 3 = 9

3a = 9 - 3

a = 6 / 3

a = 2

b will be 2 + 1 = 3

c will be 2 + 2 = 4

The square root of c which is 4 will be:

= ✓4

= 2

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The sum of three consecutive integers, a, b and c, is 9.

(a) What is the greatest possible value of b?

(b) Find the square root of the largest possible value of c.