Complete each comparison by entering the correct inequality symbol, < or >, in the box .

The shape drawn on a square grid is not an equilateral triangle, the shape is an isosceles triangle.

Having three edges and three vertices, a triangle is a three-sided polygon. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.

Given a square grid and a triangle is drawn between the grid,

let the distance of the grid be 1 unit,

so the base of the triangle is 1 unit.

for the equilateral triangle, the other two sides should be equal to 1 unit

the portion which is not shaded forms a right triangle, and the side of the triangle is hypotenuse if triangle,

using the Pythagorean theorem,

the side of the triangle be x,

height of triangle = 1 unit, base = 0.5 unit

x = √(1² + 0.5²)

x = 1.118 units

only two sides of a triangle are equal so the triangle is an isosceles triangle.

Hence the shape is not an equilateral triangle.

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The school's profit for selling 120 lunches is $210.

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.

From the graph, we have (50, 0) and (65, 45).

Here, slope(m)= (45-0)/(65-50)

= 45/15

= 3

Substitute m=3 and (x, y)=(50, 0) in y=mx+c, we get

0=3(50)+c

c=-150

Substitute m=3 and c=-150 in y=mx+c, we get

y=3x-150

Put x=120 in y=3x-150, we get

y=3(120)-150

y=210

Therefore, the school's profit for selling 120 lunches is $210.

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"Your question is incomplete, probably the complete question/missing part is:"

The graph shows a school's profit P for selling x lunches on one day.

PART A: What is the school's profit for selling 120 lunches?

Answer:
I believe the answer is 11 units

Step-by-step explanation:

as point P and Q are 11 horizontal units apart from each other.

Update It is 1/4 sorry about that

The control limits can then be used to analyze future data, with any points outside of the control limits indicating that the process is out of control.

Control limits for P chart and NP chart are used to analyze future data. The upper control limit (UCL) and lower control limit (LCL) for P chart are calculated by applying statistical formulas to the sample data. For P chart, the UCL is equal to the average of the sample data plus 3 times the standard deviation of the sample data, while the LCL is equal to the average of the sample data minus 3 times the standard deviation of the sample data. For NP chart, the UCL is equal to the average of the sample data plus 3.267 times the standard deviation of the sample data, while the LCL is equal to the average of the sample data minus 3.267 times the standard deviation of the sample data. The control limits can then be used to analyze future data, with any points outside of the control limits indicating that the process is out of control.

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Answer: The interior angles of the Pentagon are 80° , 100° , 120° , 140° and 100°.

Step-by-step explanation:

Let the angles of the Pentagon be 4x, 5x, 6x, 7x and 5x.

Let 'n' be the number of sides.

In a regular Pentagon, sum of interior angles = (2n - 4) × 90°

= ( 2 × 5 - 4) × 90°

= 6 × 90°

= 540°

Acc. to the ques.

=> 4x + 5x + 6x + 7x + 5x = 540°

=> 27x = 540°

=> x = 540° / 27

=> x = 20°

The interior angles of the given Pentagon -

1) 4x = 4 × 20° = 80°

2) 5x = 5 × 20° = 100°

3) 6x = 6 × 20° = 120°

4) 7x = 7 × 20° = 140°

5) 5x = 5 × 20° = 100°

I hope it helps

The length of the diagonal of the table is 11.312 ft. We can round it to the nearest hundredth of a foot as 11.31 ft.

The length of the side of the square table in the cafeteria is: 8 ft

As the diagonal is like the hypotenuse of the right triangle formed by dividing the square by the diagonal, we can find its length by using the Pythagoras' theorem:

hypotenuse = sqrt ((side)^2 +(side)^2)

Therefore, the length of the diagonal is:

sqrt ( (8)^2 + (8)^2) = sqrt (128) = 8[tex]\sqrt{2\\}[/tex] = 8 x 1.414 = 11.312 ft.

Rounding off the length of the diagonal to the nearest hundredth:

11.312 ft. ≈ 11.31 ft.

The given question is incomplete, the complete question is:

a square table in cafeteria has the dimensions shown. what is the length of the diagonal of the table? round to the nearest hundredth of a foot

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From the table of number digits, 400 unique random numbers need to be selected.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Aeronautical researchers have developed three different processes to pack a parachute.

They want to compare the different processes in terms of time to deploy and reliability.

There are 1,200 objects that they can drop with a parachute from a plane. Using a table of random digits, the researchers will randomly place the 1,200 items into three equally sized treatment groups suitable for comparison.

That means,

1200/3 = 400.

Therefore, 400 unique numbers.

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Answer: 115°

Step-by-step explanation:

180° - 65°  (angles on a straight line)

= 115° (alternate angle to z)

z = 115°

The precision of the measurements can change based on the number of data points and the variability of the data.

The mean absolute deviation (MAD) is a measure of the precision of a set of data. It represents the average difference between each value in the set and the mean of the set.

In this scenario, you and two other groups measured the same glassware, and you want to recalculate the MAD using the combined data from all three groups.

To find the new MAD, you need to first find the mean of the combined data set and then find the absolute difference between each value and the mean.

This will give you a set of values representing the deviation from the mean. To find the MAD, you then take the average of these deviation values.

Comparing the new MAD with your original measurement will give you an idea of the precision difference between your measurements and the combined measurements of the three groups.

If the new MAD is smaller than your original MAD, this means the combined measurements are more precise and have a smaller deviation from the mean.

The more data points and the less variability, the more precise the measurements will be. In this scenario, combining the data from three groups has likely improved the precision of the measurements.

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Answer:5.39

Step-by-step explanation:

30+21=51+52=103+21=124/23=5.39

Answer:

0.04860

Step-by-step explanation:

10^2=100

4.860/100

There are 2 zeroes, and in division, you move the decimal point left, so you move the decimal point 2 places to the left.

one place to the left: 0.4860

two places to the left: 0.04860

When writing a number in expanded form, the value of each digit's sum must be multiplied.

The expanded form of the number 35713 is 30,000+ 5000+700+10+3.

When writing a number in expanded form, the value of each digit's sum must be multiplied. A place value chart can be used to determine the value of a number's digits. In its expanded form, a number is written as a sum, where each digit stands in for a distinct term that has been multiplied by its place value.

When we expand a number to include the values of each digit, we say that the number is written in expanded form. Simply stating the importance of each digit when writing numbers in expanded form is sufficient. Except for zeroes, a number's extended form gets longer as it gets bigger.

The entry for the number 35713 in the place value table. As a result, the number 2 is in the lakhs position, the number 7 is in the ten thousand, the number 9 is in the thousand, the number 4 is in the hundred, the number 0 is in the tens, and the number 4 is finally in the one position.

Last but not least, the enlarged form of 35713 is 30,000+ 5000+ 700+ 10+ 3.

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(1) The slope of line X between (-7,6) and (-4,4) is -2/3 .

(2) The slope of line X between (-1,2) and (5,-2) is -2/3 .

(1) The points are (-7,6) and (-4,4).

The formula of the slope of line is

m = [y(2) - y(1)]/[x(2) - x(1)]

From the points; x(1) = -7, y(1) = 6, x(2) = -4 and y(2) = 4.

Now putting the value

m = (4 - 6)/(-4 - (-7))

m = -2/(-4 + 7)

m = -2/3

(2) The points are (-1,2) and (5,-2).

The formula of the slope of line is

m = [y(2) - y(1)]/[x(2) - x(1)]

From the points; x(1) = -1, y(1) = 2, x(2) = 5 and y(2) = -2.

Now putting the value

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

m = -4/(5 + 1)

m = -4/6

m = -2/3

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The complete question is:

(1) What is the slope of line X between (-7,6) and (-4,4) is ________?

(2) What is the slope of line X between (-1,2) and (5,-2) is ________?

Answer:

Socrates was paradigmatically a philosopher whose thought, however taken up with logic and abstract argument, is inseparable from the search for self-understanding and from a deeply felt attachment to the concerns of human life.

Step-by-step explanation:

-Ben earns $6/h

-Ben is saving to reach $360

360=total money/goal

6=money per hour

x=total number of hours

360=6x

x=60

Ben needs to work for 60 hours babysitting to earn $360 to but an MP3 player.

Answer:

( a ) What is the smallest number of people that could have attended ?
34, 650

( b ) What is the greatest number of people that could have attended​?
34, 749.

Step-by-step explanation:

The estimate of the crowd to the nearest hundred is 34,700

Since we are rounding to the nearest hundred, the tens place determines whether the number is rounded up or down. So 34, 650 will round up to 34,700 but 34, 649 will round down to 34, 600

The smallest number that will be rounded to 34, 700 is 34, 650
(if it was one lower, 34, 649, that would be rounded down to 34, 600)

The largest number that can be rounded down to 34, 700 is 34, 749.
(If it was 1 more larger, i.e. 34, 750 it would be rounded up to 34, 800 )

In short, if rounding to the nearest 100,  the smallest number  will be the number - 50. Here it is 34, 700 - 50 = 34, 650

The largest number is found by adding 49 to the number so it will be
34, 749

To find the percentages of U.S. presidents who were lawyers, we can divide the number of presidents by the total number of presidents and then multiply by 100 to get the answer as a percentage.

Given the information, we have:

Number of presidents who were lawyers = 29

Total number of presidents = 42

So, the percentages of presidents who were lawyers is:

(29 / 42) * 100 = 69%

Therefore, 69% of the first 42 U.S. presidents were lawyers.

A percentage is a number or ratio expressed as a fraction of 100. It represents a portion of a whole and is often used to describe parts of a larger quantity in terms of 100. For example, if a student scored 80 out of 100 on a test, their score can be expressed as 80%, which means they answered 80 out of 100 questions correctly. The symbol for percentage is "%". To convert a fraction or decimal to a percentage, it is multiplied by 100.

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The two column proof that shows that ΔPMK ~ ΔLMQ is as shown below by AA Similarity

A two-column proof is defined as a geometric proof that consists of a list of statements, and the reasons that we know those statements are true.

Now, the two column proof is completed as follows;

Statement 1: PM:MQ and KM:ML

Reason 1: Given

Statement 2: KM/MQ = PM/ML

Reason 2: Property of cross multiplication

Statement 3: ∠PMK ≅ ∠LMQ

Reason 3: Vertical angles are congruent

Statement 4: ΔPMK ~ ΔLMQ

Reason 4: AA similarity

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The side lengths of the rectangle for the least perimeter of fencing are 12.49 yards and 20.49 yards.

What is a rectangle?

A rectangle is a type of quadrilateral with four 90-degree-distance vertices and parallel sides that are equal to one another. It is also referred to as an equiangular quadrilateral because of this.

We are given that the area of the rectangle is 256 square yards.

We know that area = length * width

Let the width be 'x'

So, as per the question,

Length = x+8

So,

⇒Area = (x+8)(x)

⇒256 = x^2+8x

⇒x^2+8x-256 = 0

Using quadratic formula, we get

x = [-b ± √(b^2 - 4ac)]/(2a)

= [-8 ± √(8^2 + 4*256)]/2

= (-8 ± √1088)/2

= [-8 ± √(64*17)]/2

= (-8 ± 8√17)/2

= -4 ± 4√17

x = -4 + 4√17 ≈ 12.49

x + 8 = 20.49

Hence, the side lengths of the rectangle for the least perimeter of fencing are 12.49 yards and 20.49 yards.

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Answer:

20

Step-by-step explanation:

[tex]20^{2} = 400[/tex]

[tex]\sqrt{400} = 20[/tex]

Answer: The square root of 400 is 20.

Step-by-step explanation:

The square root of a number is the value that, when multiplied by itself, gives the original number. To find the square root of 400, you can use the long division method or an electronic calculator.

Alternatively, you can approximate the square root of 400 by finding the nearest perfect square (a number whose square root is a whole number). In this case, the perfect squares closest to 400 are 361 and 441. Since the square root of 361 is 19 and the square root of 441 is 21, you can estimate that the square root of 400 is between 19 and 21. Since 20 is halfway between 19 and 21, you can approximate the square root of 400 to be 20.

There are 9 questions on the test.

Let, the number of multiple-choice questions on the test = m

the number of essay questions on the test = s

m + s = 26  .......(1)

So, We are also told that multiple choice is worth 3 points each, so the total number of points for m questions will be 3m.

As essays are worth 8 points each, so the total number of points for s questions will be 8s.

3m + 8s = 123 .......(2)

Now we will use the substitution method to solve a system of linear equations.

From equation (1) we will get,

m = 26 -s

Substituting this value in equation (2) we will get,

3 * (26- s) + 8s =123

78 - 3s + 8s = 123

5s = 123 -78

5s = 45

s = 45/5 = 9

So, there are 9 questions on the test.

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The complete question is:

Ada’s history teacher wrote a test for the class.

The test is 26 questions long and is worth 123 points.

Ada wrote two equations, where m represents the

number of multiple choice questions on the test, and

s represents the number of essay questions on the test.

m+s= 26

3m + 8s = 123

How many essay questions are on the test?

The gross earnings of a worker who produced 87 items, based on the unit rates, are $172.20.

The unit rate is the average rate.

We can also think of the unit rate as the variable rate per unit.

The unit rate can be multiplied by the number of units to obtain the gross earnings.

Graduated Earnings:

1-30 items produced: $1.50           = $45.00 (30 x $1.50)

31-60 items produced: $1.99         = $59.70 (30 x $1.99)

61-90 items produced: $2.50        = $67.50 (27 x $2.50)

91 or more items produced: $2.75 = $0.00 (0 x $2.75)

Gross earnings =                            $172.20

Thus, the worker's gross earnings are $172.20 based on the various unit rates.

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The distance between the boat and Johnstown is changing at a rate of 27.73 miles per hour.

This is calculated by taking the speed of the boat (30 miles per hour) and subtracting the rate of change in the boat's displacement in a southward direction, which is 2.27 miles per hour (calculated by taking the distance travelled (126 miles) and dividing it by the time taken (126/30 = 4.2 hours)).

Distance is a measure of how far something is from a given point, while velocity is a measure of the rate at which something changes its position or moves. Distance is a scalar quantity, meaning it has only magnitude and no direction, while velocity is a vector quantity, meaning it has both magnitude and direction.

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Answer:29122

Step-by-step explanation:

The solution of a system of equations by elimination method is at x = -4 and y = 12.

The points where the lines representing the intersection of two linear equations intersect are referred to as the solution of a linear equation. In other words, the set of all possible values for the variables that satisfy the specified linear equation constitutes the solution set of the system of linear equations.

Given equations,

4x + 3y = 20........(1)

3x + 2y = 12........(2)

using the elimination method,

in elimination, we need to eliminate one of the variables from equations,

eliminating x,

multiply by 3 in equation 1

(4x + 3y)3 = 20 * 3

12x + 9y = 60.........(3)

and multiply by 4 in equation 2

(3x + 2y)4 = 12*4

12x + 8y = 48.........(4)

subtraction equations 3 and 4

12x + 9y - (12x + 8y) = 60 - 48

12x - 12x + 9y - 8y = 12

y = 12

substitute the value of y in the equation

3x + 2y = 12

3x + 12 *2 = 12

3x = 12 - 24

3x = -12

x = -4

Hence the solution is at x = -4 and y = 12.

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The computations are then repeated for drawing blue first, with probabilities of 6/10 and 4/9. To calculate the likelihood of choosing blue over red, we multiply by one more, and the outcome is the same.

Getting a red ball has a 4/10 chance of happening, followed by a 6/9 chance of picking a blue ball. Multiplying these yields the likelihood of selecting a red card before a blue one.

P1 = 24/90

We then perform the identical calculations for drawing blue first, where the odds are 6/10 and 4/9. We multiply one more to obtain the likelihood of selecting blue over red, and the result is the same.

P2 = 24/90

P1 and P2 are added to obtain the overall probability.

P = P1 + P2 = 48/90

The complete question is:

A box contains 4 red and 6 blue balls. two balls are picked at random without replacement. What's the probability of drawing balls not of the same color?

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Step-by-step explanation:

what is so difficult for you ?

r - 7 > -10

the only thing that keeps us from a direct answer is the "- 7" on the side of r.

to get rid of it, we have simply to add 7. but to kero the inequality balance unchanged, we need to do this on both sides :

r - 7 + 7 > -10 + 7

r > -3

that's really all.

Answer:

10.4, 6.4

Step-by-step explanation:

The change ratio is -4

Hope this helps