(i) Express 2x² +8x-10 in the form a(x+b)² + c

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Based on the table of values, the slope and y-intercept are as follows:

Slope = -1/2.

y-intercept = -1/2.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-1/2 - (-1))/(0 - 1)

Slope (m) = (-1/2 + 1)/(0 - 1)

Slope (m) = -1/2

In Mathematics, the y-intercept is sometimes referred to as an initial value and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

This ultimately implies that, the y-intercept is equal to -1/2.

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Answer:

x > 11

Step-by-step explanation:

9x - 4 > 95

Add 4 to both sides.

9x - 4 + 4 > 95 + 4

9x + 99

Divide both sides by 9.

9x/9 > 99/9

x > 11

Answer:

[tex] \sf \: x > 11[/tex]

Step-by-step explanation:

Given inequation,

→ 9x - 4 > 95

Now the value of x will be,

→ 9x - 4 > 95

→ 9x > 95 + 4

→ 9x > 99

→ x > 99 ÷ 9

→ [ x > 11 ]

Hence, the value of x is 11.

The value of the equation is A = 56x + 21

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = ( -7 ) ( -8x - 3 )   be equation (1)

On simplifying the equation , we get

A = ( -7 ) ( -8x ) - ( 7 ) ( -3 )

On further simplification , we get

A = 56x + 21

Hence , the equation is A = 56x + 21

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Answer:

47

Step-by-step explanation:

We know, that the angle at the vertex of a rectangle is 90 degree
So, if a line drawn divides it into two angles, then one of them is complementary to the other.
Hence, ADB = 90 - EDC
= 90 - 43
= 47

The x-axis of the graph is the upper limits of each class, while the y-axis is the cumulative frequency or cumulative relative frequency. The cumulative relative frequency for the last class is always equal to 1.

An ogive graph is a type of line graph that is used to show the cumulative frequency or cumulative relative frequency of a given set of data. To start, the data must be organized into classes with upper and lower limits. Once the data is organized, the ogive graph can be constructed. The x-axis of the graph is the upper limits of each class, while the y-axis is the cumulative frequency or cumulative relative frequency. Each plotted point on the graph will have an x-coordinate that is equal to the upper limit of the class. The cumulative relative frequency for the last class must always be 1, since all observations are less than or equal to the last class. To plot the points on the graph, start by finding the cumulative frequency or relative frequency for the first class. Then, for each subsequent class, add the cumulative frequency or relative frequency to the cumulative frequency or relative frequency of the previous class. Once all the points are plotted, draw a line connecting the points to form an ogive graph.

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An equation of the line that passes through the point (-8, -4) and (0, 5) in slope-intercept form is y = 9x/8 + 5.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

From the information provided above, we have the following data points on the line:

Points on the x-axis = (-8, 0).

Points on the y-axis = (-4, 5).

Therefore, a linear equation in slope-intercept form of this line can be calculated by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 5 = (5 + 4)/(0 + 8)(x - 0)

y - 5 = 9x/8

y = 9x/8 + 5

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Answer:

Multiply each term in the first expression by each term in the second expression and combine like terms. x³-3x² - 4x + 12

Step-by-step explanation:

In Cartesian or rectangular coordinate system we represent any point using the ordered pair (x,y) . Similarly in polar coordinate system we represent any point using the ordered pair (r,θ), where r is the distance from origin and θ is the angle made by the line joining origin and the point with x-axis measured in anti-clockwise direction.

Answer:

No solutions

Step-by-step explanation:

y - 1/2x = -1

y = 1/2x + 4

Move 1/2x over to other side for 2nd equation

y - 1/2x = 4

You can tell that if you plot the lines on a graph, there would be no intersecting points because the line is parallel, meaning there are no solutions.

(a) the critical value of t at P = 10% and 16 degrees of freedom is 1.337.

(b) the critical value of t at P = 10% and 11 degrees of freedom is 1.363.

(c) the critical value of t at P = 1% and 23 degrees of freedom is 2.500.

(d) the critical value of t at P = 10% and 22 degrees of freedom is 1.321.

(e) the critical value of t at P = 20% and 12 degrees of freedom is 0.8726.

(f) the critical value of t at P = 5% and 8 degrees of freedom is 1.860.

We need to find the critical t value for every one of the accompanying confidence levels and test sizes given underneath.

As we realize that in the t table there are two segments. The flat section is addressed by the image P which addresses the level of importance and the upward segment is addressed by the image '' which addresses the degrees of freedom.

(a) In this way, here the level of importance = 1 - confidence level

                                                           = 1 - 0.90 = 0.10

What's more, the degrees of freedom = n - 1

                                               = 17 - 1 = 16

Presently, in the t table, the critical value of t at P = 10% and 16 degrees of freedom is 1.337.

(b) Thus, here the level of importance = 1 - confidence level

                                                           = 1 - 0.90 = 0.10

Furthermore, the degrees of freedom = n - 1

                                               = 12 - 1 = 11

Presently, in the t table, the critical value of t at P = 10% and 11 degrees of freedom is 1.363.

(c) Thus, here the level of importance = 1 - confidence level

                                                           = 1 - 0.99 = 0.01

Furthermore, the degrees of freedom = n - 1

                                               = 24 - 1 = 23

Presently, in the t table, the critical value of t at P = 1% and 23 degrees of freedom is 2.500.

(d) In this way, here the level of importance = 1 - confidence level

                                                           = 1 - 0.90 = 0.10

Furthermore, the degrees of freedom = n - 1

                                               = 23 - 1 = 22

Presently, in the t table, the critical value of t at P = 10% and 22 degrees of freedom is 1.321.

(e) Thus, here the level of importance = 1 - confidence level

                                                           = 1 - 0.80 = 0.20

Furthermore, the degrees of freedom = n - 1

                                               = 13 - 1 = 12

Presently, in the t table, the critical value of t at P = 20% and 12 degrees of freedom is 0.8726.

(f) In this way, here the level of importance = 1 - confidence level

                                                           = 1 - 0.95 = 0.05

Furthermore, the degrees of freedom = n - 1

                                               = 9 - 1 = 8

Presently, in the t table, the critical value of t at P = 5% and 8 degrees of freedom is 1.860.

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The complete question is:

What is the appropriate t critical value for each of the following confidence levels and sample sizes? (Round your answers to two decimal places.)

(a) 90% confidence, n = 17

(b) 90% confidence, n = 12

(c) 99% confidence, n = 24

(d) 90% confidence, n = 23

(e) 80% confidence, n = 13

(f) 95% confidence, n = 9

Answer:

12.5 cm

Step-by-step explanation:

Diameter of circle = 25 cm

Radius of circle = Diameter/2 = 25/2 = 12.5 cm

Answer:

The radius of the circle would be 12.5 cm.

Step-by-step explanation:

The reason it is 12.5 cm is because r=d/2. So it would be r=25/2, and that equals 12.5 cm.

The time taken by the planes when they are 2000 miles apart is 2 hours.

We all know that formula of distance, speed and time is given by  distance = speed*time or time = distance/speed

Let x be the number of hours that the two planes will be 2000 miles apart.

Let 430x be the distance traveled by the first plane at 430 miles per hour

and 570x be the distance traveled by the second plane at 570 miles per hour.

here, 430x +570x =2000 is the total distance travelled by the first plane and the second plane

Solving yields the following steps:

1000x = 2000

Dividing 1000 to both sides of the above equation, we get

1000x/1000=2000/1000

So the value of x will be equivalent to 2

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The coordinates of the other endpoint include the following: C. (32.5, 47.7).

In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and then divide by two (2):

Midpoint BC = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Next, we would determine the coordinate of B with midpoint AB at (25.4, 60.1) as follows;

25.4 = (18.3 + x₂)/2

50.8 = 18.3 + x₂

x₂ = 50.8 - 18.3

x₂ = 32.5.

For the other co-ordinate of B on line segment BC, we have:

60.1 = (72.5 + y₂)/2

120.2 = 72.5 + y₂

y₂ = 120.2 - 72.5

y₂ = 47.7.

Therefore, the coordinate of B is (32.5, 47.7).

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The total number of samples in the sample space is 15,504.

The total number of samples in the sample space can be calculated by using the formula for combinations, which is the number of ways to select r items from n distinct objects. The formula is written as nCr and is calculated as n!/(r!(n-r)!). In this case, n is equal to 60, and r is equal to 4.

To calculate the total number of samples in the sample space, we will first calculate n!, which is 60! = 60*59*58*57*...*2*1. Then, we will calculate r! which is 4!, which is 4*3*2*1. Finally, we will calculate (n-r)!, which is (60-4)!, which is [tex]56! = 56*55*54*53*...*2*1.[/tex]

Using the formula, the total number of samples in the sample space is calculated as 60!/(4!(60-4)!) = 60!/(4!*56!) = 15,504. Therefore, the total number of samples in the sample space is 15,504.

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The weighted average of the numbers 1 and 6 is 2 2/3

The weighted average of 1 and 6 in this instance, means the sum of the two numbers multiplied by their weights which are four-fifths and one-fourth respectively.

weighted average = (first number * weight of first number) + (second number * weight of second number)

first number = 1

weight of the first number = 2/3

second number = 6

weight of the second number = 1/3

weighted average = (1 * 2/3) + (6 * 1/3)

weighted average = 2/3 + 2

weighted average = 8/3 = 2 2/3

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The distance between point A and point B is 214.807 km.

To find the distance between point A and point B, we can use the formula: distance = speed * time.Let's call the total distance between point A and point B "d".

For the first part of the journey, when the car was traveling at a constant speed of 78 km/hr, the distance traveled was 63% of the total distance, or 0.63d. The time taken for this part of the journey was 3.3 hours * 63% = 2.099 hours. Therefore, the distance traveled in this part of the journey was 78 km/hr * 2.099 hours = 160.862 km.

For the second part of the journey, when the car was traveling at a constant speed of 45 km/hr, the distance traveled was the remaining 37% of the total distance, or 0.37d. The time taken for this part of the journey was 3.3 hours - 2.099 hours = 1.201 hours. Therefore, the distance traveled in this part of the journey was 45 km/hr * 1.201 hours = 53.945 km.

Adding up the distance traveled in both parts of the journey gives us a total distance of 160.862 km + 53.945 km = 214.807 km.

So, the distance between point A and point B is 214.807 km.

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We need -1.94 gallons of 18%-salt solution to be mixed with 7 gallons of 30%-salt solution to obtain a 25%-salt solution.

The formula used to calculate the number of gallons of 18%-salt solution needed to be mixed with 7 gallons of 30%-salt solution to obtain a 25%-salt solution is:

V1C1 + V2C2 = V3C3

Where:

V1 = Volume of 18%-salt solution

C1 = Concentration of 18%-salt solution

V2 = Volume of 30%-salt solution

C2 = Concentration of 30%-salt solution

V3 = Volume of 25%-salt solution

C3 = Concentration of 25%-salt solution

Plugging in the given values, we get:

V1C1 + 7(0.30) = V3(0.25)

Simplifying the equation, we get:

V1(0.18) + 2.1 = 0.25V3

Subtracting 2.1 from both sides, we get:

V1(0.18) = 0.25V3 - 2.1

Dividing both sides by 0.18, we get:

V1 = (0.25V3 - 2.1) / 0.18

Substituting V3 with 7, we get:

V1 = (1.75 - 2.1) / 0.18

Simplifying, we get:

V1 = -0.35 / 0.18

Therefore,

V1 = -1.94 gallons

Hence, we need -1.94 gallons of 18%-salt solution to be mixed with 7 gallons of 30%-salt solution to obtain a 25%-salt solution.

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The system of equation  y = 4x - 1 and 12x - 3y = - 1 has no solution.

If a system of equations only contains two linear equations with two variables, the system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.

There are only three matching forms of solution for a given system of equations because there are only three different ways that two straight lines in the plane can graph.

The given system of equation is y = 4x - 1 and 12x - 3y = - 1.

Multiplying equation (i) by 3 and adding it to equation (ii) we have,

 3y =   12x - 3

- 3y = - 12x - 1

____________

  0 =     0 -  4

But 0 ≠ - 4 so, The system of the equations has no solution.

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Answer:

104

Step-by-step explanation:

it says it in the question

Answer:

In this scenario, the school wants to use an AI system to classify fans at sporting events and direct them to either the home or away side of the stadium. This system could potentially use various AI technologies, such as image recognition, facial recognition, or even crowd analysis, to determine the affiliation of the fans and direct them to the appropriate side. This could help to improve the overall experience of the fans by reducing congestion and ensuring that they are able to sit with other fans that share their loyalty. However, it is important to note that implementing such a system also raises privacy and ethical concerns, such as the potential for bias or misuse of personal data. It is important for the school to carefully consider these issues before implementing such a system.

Darren's salary will be $102,724.24 in 9 years.

Annual salary can be defined as the amount of money a company pays you in exchange for the job you do during the year.

We can calculate Darren's salary in 9 years by multiplying his current salary by (1 + 5.5%) raised to the power of 9.

The formula would look like this:

Salary in 9 years = $66,648 * (1 + 0.055)^9

Plugging in the numbers and using a calculator, we get:

Salary in 9 years = $66,648 * 1.55946429

Salary in 9 years = $102,724.24

So, Darren's salary will be $102,724.24 in 9 years.

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The coordinate point of f(x + 1) will shift 1 unit to the left along the x-axis.

(x , y) ⇒ (x - 1, y).

Suppose we have a function f(x).

f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).

f(x ± c) = Horizontal left/right shift by c units (x - + c, y).

(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).

f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).

f(-x) = Reflection over y-axis, (-x, y).

-f(x) = Reflection over x-axis, (x, -y).

Let, y = f(x) = 3x.

Now, After the transformation f(x + 1) = g(x),

g(x) = 3(x + 1).

This is a horizontal transformation by 1 unit to the left.

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Answer:

5

Step-by-step explanation:

23 x + 977 y = 2023

977 x + 23 y = 2977

add the 2 together

1000x+1000y =5000

so x+y =5

x=5-y

plug this into first equation

23(5-y) +977y =2023

solve for y =2

so x=3

x² -y² =(x+y)*(x-y) =5*1 =5

Seating arrangement would best suit a family restaurant is c) a space with all booths.

This restaurant with a comfortable atmosphere usually serves food in large quantities by placing it in the middle of the table.

So, each family member can take food from the middle and enjoy it on their respective plates. This concept is exactly the same as how to eat at home with the family.

Apart from that, the characteristics of this restaurant are almost the same as a casual dining restaurant, the difference is the absence of alcoholic beverages in family restaurants.

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The equation and the slope of the line that passes through (6, –4) and is parallel to the x-axis are; Slope = 0 and equation: y = -4

The general form of the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Now, when a line is parallel to the x-axis, it means that the slope will be zero as there will be no intersection point with the x-axis. Thus, from y = mx + c, we can say that;

y = 0(x) + c

y = c

Now, from the given point, we can tell that the y-intercept will be constant and as such we have;

y = -4

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An equation and the slope of the line that passes through (6, –4) and is parallel to the x-axis:

C. Equation: y = –4

D. Slope: 0

In Mathematics, the y-intercept is also referred to as an initial value and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

Since the given line is parallel to the x-axis (x-coordinate), the value on the y-coordinate would remain constant and forms a horizontal line.

In this context, we can reasonably infer and logically deduce that the slope of this line would be equal to zero (0).

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The probability that at least one of them has received immunizations is 97.5611%.

Probability, in its simplest form, gauges the likelihood that something will happen. When we are unsure of how an event will turn out, we might talk about the likelihood of different outcomes. The study of events susceptible to probability is known as statistics. Probability is a mathematical representation of the likelihood or potential that an event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%. Probability, in its simplest form, gauges the likelihood that something will happen. When we are unsure of how an event will turn out, we might talk about the likelihood of different outcomes. The study of events susceptible to probability is known as statistics.

1 - P( no one was vaccinated).

1-71%=0.29

If you pick one person at random from the population, there is a [tex]29[/tex]% chance they are not immunized. There is therefore no chance that any of the three people you choose will be an unvaccinated person [tex]0.29 X 0.29 X 0.29 = 0.024389.[/tex] Your solution, calculated as a percentage by deducting from [tex]1[/tex], is [tex]97.5611[/tex]%.

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The proportion that could be used to find the average number of shepherd mixes at any given time is given as follows:

4. 7/9 = x/50

The proportion is obtained as the ratio between two amounts, dividing the amount a by the amount b.

The number of Sheperd Mix in each sample is given as follows:

7 and 9.

Hence the first part of the ratio is of 50, hence:

7/9.

As the total number is of 50, the second part is given as follows:

x/50.

Hence the proportional equation is given as follows:

7/9 = x/50.

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Answer:

Step-by-step explanation:

The expression 191 divided by 3 equals 63.66666666666667 (approximately 64)

Y = (1/6)*e^5t  is  differential equation .

What exactly does differential equation mean?

An equation that connects one or more unknown functions and their derivatives is known as a differential equation in mathematics.  

                                     Applications typically use functions to describe physical quantities, derivatives to indicate the rates at which those quantities change, and differential equations to define a relationship between the two.

y′′−9y′+26y=e^(5t)

The characteristice equation of the differential equation is : r^2 -9r +26 =0

On solving we get the values of r=4.5 + 2.34i (z1) ,  4.5 - 2.4i(z2)--- (complex roots)

homogeneous solution is: yh = c1e^z1t + c2e^z2t

Plug  Y = Ae^5t in the ODE:

=   25Ae^5t -9*5Ae^5t +26Ae^5t =e^(5t)

25A -45A +26A =1 ;  6A = 1; A =1/6

Y = c1e^z1t + c2e^z2t  is a general solution but we wnata particular solution

So, simply Y = (1/6)*e^5t

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