(3,b) is the midpoint of (a,1) and (b,-a) find a and b​

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

Answer: 20

Step-by-step explanation:

To find the original number when you know that 120% of it is equal to 24, you can use the following steps:

So, 120% of the number is 24, the original number is 20.

Answer: 20

Step-by-step explanation:

Let the unknown number be x.

Then, according to the percentage formula,

x * 120/100 = 24.

By carrying over the numbers from LHS to RHS,

x = 24 * 100/120

x = 24 * 10/12

x = 2 * 10

∴ x = 20.

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:

B. [tex]11x^2[/tex]

Step-by-step explanation:

Monomials are expressions that only have one term. In A, [tex]\frac{9}{x}[/tex], can actually be rewritten as 9 ÷ [tex]x[/tex], which is also two terms. Therefore, B is the only other option.

Answer:

10.4, 6.4

Step-by-step explanation:

The change ratio is -4

Hope this helps

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.

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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The coordinates of the point P along the directed line segment AB are (3, -2).

In this scenario, line ratio would be used to determine the coordinates of the point P on the directed line segment that partitions the segment into a ratio of 5 to 3.

Mathematically, line ratio can be used to determine the coordinates of P and this is modeled by this mathematical expression:

P(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

Substituting the given parameters into the line ratio formula, we have the following;

P(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

P(x, y) = [(5(6) + 3(2))/(5 + 3)],  [(5(1) + 3(7))/(5 + 3)]

P(x, y) = [(30 - 6)/(8)],  [(5 - 21)/8]

P(x, y) = [24/8],  [(-16)/(8)]

P(x, y) = [3, -2]

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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?

The probability that a plain pencil was chosen from the first box and a color pencil was chosen from the second box is given as follows:

5/24.

A probability is calculated by the division of the number of desired outcomes by the number of total outcomes.

For each box, the probabilities are given as follows:

The pencils selected from each box are independent, hence the probability of both events is obtained multiplying the probabilities of each event, as follows:

p = 1/2 x 5/12

p = 5/24.

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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 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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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:

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:

Answer:

Step-by-step explanation:

To represent the unknowns, let x be the amount of money deposited into the first account paying 0.61% simple annual interest and y be the amount of money deposited into the second account paying 0.70% simple annual interest.

The first situation is that the total deposit into the first account is x and the interest earned on that account is (0.61/100)x. The second situation is that the total deposit into the second account is y and the interest earned on that account is (0.70/100)y.

The equation representing the first situation is: (0.61/100)x = (75/12000)x

The equation representing the second situation is: (0.70/100)y = (75/12000)y

The sum of the deposit in both accounts must be equal to $12,000, so we can write the third equation: x + y = 12,000

The system of equations is:

(0.61/100)x = (75/12000)x

(0.70/100)y = (75/12000)y

x + y = 12,000

You can use systems of equation methods like substitution, elimination or graphing to find the solution.

To find the solution, we can use the substitution method. We can start by isolating x or y in one of the equations, then substitute it into the other equation.

Let's start with the equation x + y = 12,000. We'll solve for x:

x = 12,000 - y

Now we can substitute this value of x into the first equation:

(0.61/100)(12,000 - y) = (75/12000)(12,000 - y)

Solving for y, we get:

y = $7,200

Now we can substitute this value of y back into the equation x + y = 12,000 to find x:

x = 12,000 - y = 12,000 - $7,200 = $4,800

So the solution is:

x = $4,800 and y = $7,200

This means you deposited $4,800 in the first account and $7,200 in the second account.

Update It is 1/4 sorry about that

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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-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:5.39

Step-by-step explanation:

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

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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Answer:29122

Step-by-step explanation:

(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 ________?

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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1. To obtain the graph of g(x) = 2x + 7 from the graph of f(x), we need to perform a translation of the graph of f(x).

Graph is a type of visual representation of data that is used to show the relationship between two or more variables. It is a pictorial representation of data that is used to identify trends, patterns, and correlations. Graphs can be used to compare different sets of data or to show the change in data over a period of time. Graphs can be used to represent data in various forms, including bar graphs, line graphs, scatter plots, histograms, and pie charts. Graphs are a powerful tool for understanding complex data and can be used to make predictions about future trends and behavior.

2. A translation of a graph is a transformation that moves the graph left, right, up, or down without changing its shape.

3. To translate the graph of f(x) up 7 units, we need to add 7 to the y-coordinates of the points on the graph of f(x).

4. This will move the graph of f(x) up 7 units, and the resulting graph will be the graph of g(x) = 2x + 7.

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Answer:

To find the equation of a line that is perpendicular to another line and passes through a given point, we can use the slope-point form of the line equation.

The first step is to find the slope of the given line. To do this, we can rearrange the equation 5x - 3y = 2 into slope-intercept form:

y = (5/3)x + 2/3

So the slope of the given line is 5/3.

Next, we need to find the slope of the line that is perpendicular to this line. The slope of a perpendicular line is the negative reciprocal of the original line's slope.

The negative reciprocal of 5/3 is -3/5.

Now that we have the slope, we can use the point-slope form of a line to find the equation of the line that is perpendicular to 5x - 3y = 2 and passes through the point (-1/4, 3/5):

y - 3/5 = -3/5 (x + 1/4)

Expanding the right side:

y - 3/5 = -3/5x - 3/20

Adding 3/5 to both sides:

y = -3/5x + 3/4

So the equation of the line that is perpendicular to 5x - 3y = 2 and passes through the point (-1/4, 3/5) is y = -3/5x + 3/4.

The solution to the system of inequalities 4x + y > 8 and x - y < 5

is (2.6, - 2.4).

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, 4x + y is less than 8, x - y is greater than 5.

Therefore, 4x + y > 8 and x - y < 5.

The solution to the system is (2.6, - 2.4).

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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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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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