Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. X = t2 + 63 , y = ln(t2 + 63), z = t; (8, ln(64), 1).

The solution is y will increase by 2 units with every unit increase in x1

A single dependent variable and several independent variables can be analyzed using the statistical technique known as multiple regression. In order to predict the value of the single dependent value, multiple regression analysis uses independent variables whose values are known.

X and Y variables are the sole ones in simple linear regression. Two or more x variables and one y variable make up multiple linear regression. For instance, basic linear regression is used when we forecast rent using only square footage.

In the above question:-

Interpretation of b1=2

it means that y will increase every 2 units for every unit increase in x1

holding x2 constant.

Hence option B is the correct answer.

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The angle ACB would be 80 degrees.

What is tangent to a circle?

The tangent always makes a single-point contact with the circle. It never intersects the circle twice. Tangents from an external point to a circle have the same length.

In the given figure,

angle AOB = 40.

So angle OBA = 40.

Then the angle AOB = 180 - 40 -40

                          AOB = 100.

By the theorem of circles,

          AOB + ACB = 180

          100 + ACB = 180

              ACB = 80.

Hence, the angle ACB would be 80 degrees.

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The zeroes of the function f(x) = 28x² - 7 will be 1/2 and negative 1/2.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.

The function is given below.

f(x) = 28x² - 7

For the zeroes of the function, put f(x) = 0, then we have

f(x) = 0

28x² - 7 = 0

x² = 1/4

x = ± 1/2

The zeroes of the function f(x) = 28x² - 7 will be 1/2 and negative 1/2.

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Answer: C

Step-by-step explanation: The slope of Function A is 6 and the slope of Function B is 5.

The matrix form of the given equation is:

[tex]\left[\begin{array}{ccc}0&2&7\\-3&-3&0\\7&0&-8\end{array}\right] * \left[\begin{array}{ccc}x&\\y&\\z \end{array}\right] = \left[\begin{array}{ccc}-3&\\3&\\3\end{array}\right][/tex]

How do you write a system of linear equations in matrix form?

A coefficient matrix, a variable matrix, and a constant matrix can all be used to describe a system of linear equations in matrix form. Take into account the equation 2x+3y=85x+y=2. The coefficients of the variables in each equation can be arranged in a row to create the coefficient matrix.

We have,

2y + 7z = -3

-3x - 3y = 3

7x - 8z = 3

Hence, the matrix form of the given equation is:

[tex]\left[\begin{array}{ccc}0&2&7\\-3&-3&0\\7&0&-8\end{array}\right] * \left[\begin{array}{ccc}x&\\y&\\z \end{array}\right] = \left[\begin{array}{ccc}-3&\\3&\\3\end{array}\right][/tex]

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If original question was you are debating about two different computers. The number of hours  you have to work to pay for the new computer is: 89 hours.

Before determining the number of hours we have to first of all find the FICA ,Federal tax withholding and state tax rate per hour.

FICA = $10 per hour × 0.0765

FICA= $0.77 per hr

Federal  tax withholding = $10 per hr × 0.12

Federal  tax withholding = $1.2 per hr

State tax= $10 per hr × 0.08

State tax = $0.8 per hr

Number of hours = $640 / ($10 -$0.77 - $1.2-$0.8)

Number of hours = $640 / $7.23 per hr

Number of hours = 88.5 hours

Number of hours = 89 hours (Approximately)

Therefore the number of hours is 89 hours.

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The equation of a line is y = 4x +10

What is an equation of a line?

A line's equation is a unified representation of all of the line's points. Any point on a line will satisfy the equation in its general version, which is of the type ax + by + c = 0. The slope of the line and a point on the line are the two essential elements needed to create the equation of a line.

Here, we have

Given

m = 4

x = -3

y = -2

By applying slope intercept formula, we get

Equation of line is y = 4x + c

There is one unknown term here which is c.

So to find it we will put (-2,-3) in the line.

-2 = (4)(-3) + c

c = 10

Hence the equation of a line is y = 4x +10

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If in the school of 1970 pupils, there are 799 boys, there are 372 girls more than the boys.

A linear equation is an equation with the maximum degree of one. No variable in a linear equation, thus, has an exponent greater than 1. The graph of a linear equation is always a straight line.

Both linear equations with one variable and those with two variables exist. This is already taught in schools. Let's use the examples below to understand how to distinguish between linear and non-linear equations.

y = 8x - 9 Linear

y = x2 - 7 Non-Linear, the power of the variable x is 2

√y + x = 6 Non-Linear, the power of the variable y is 1/2

y + 3x - 1 = 0 Linear

How to solve?

total number of pupils = 1970

number of boys = 799

number of girls = 1970 - 799 = 1171

number of girls more than the boys = 1171 - 799 = 372

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Answer:   4/3 is not irrational, it is rational

Explanation:

A rational number is a ratio, or fraction, of two integers. The denominator cannot be zero.

4/3 is rational since it's the ratio of the integers 4 over 3.

Since it is rational, it is not irrational. The term "irrational" literally means "not rational". Therefore, a real number is either of those options, but not both simultaneously.

A famous example of an irrational number is [tex]\pi \approx 3.14...[/tex] because it cannot be written as a fraction of two integers. We can get approximations like 22/7, but never manage to capture the full value of [tex]\pi[/tex] with a single fraction.

Another example of an irrational number is [tex]\sqrt{2}[/tex]

[tex]\displaystyle\\Answer: \ \frac{4}{3} \ isn`t\ an\ irrational\ number[/tex]

Step-by-step explanation:

An irrational number is an infinite non-periodic fraction

[tex]\displaystyle\\\frac{4}{3}=1\frac{1}{3} \\\\\frac{4}{3} =1.333333...\\\\\frac{4}{3}=1.(3)[/tex]

1.(3) - is an infinite periodic fraction

[tex]\displaystyle\\Hence,\ \frac{4}{3} \ isn`t\ an\ irrational\ number[/tex]

5) <OSL

Vertical pair angles are equal angles formed by intersecting lines

6) <MSN (or <LOS)

Supplementary angles are angles that add up to 180 degrees

Answer:

12 miles

Step-by-step explanation:

72 x [tex]\frac{10}{60}[/tex] = 12

By using the concept of direct proportion, it can be calculated that

The equation which represents the given relationship is

[tex]p = \frac{2}{3}m[/tex]

What is direct proportion?

Suppose there are two quantities. Proportionality indicates that if there is a change in the value of one quantity, the value of other quantity also changes but maintaining a constant ratio

Direct proportion

Two quantities are said to be in direct proportion if on increasing the value of one quantity, the value of other quantity also increases and vice versa.

For example cost of a commodity and quantity of a commodity are in direct proportion

The number of pages read, p, varies directly as the number of minutes spent reading, m.

So the equation is

p = km, where k is the constant of proportionality

After 15 minutes, Zoe had read 10 pages.

Putting m = 15 and p = 10

10 = k [tex]\times[/tex] 15

k = [tex]\frac{10}{15}[/tex]

k = [tex]\frac{2}{3}[/tex]

So the equation which represents the given relationship is

[tex]p = \frac{2}{3}m[/tex]

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The equation of the line with a slope of 6 and a y-intercept of -3, is  y = 6x - 3

From the question, we are to determine the equation of the line that has the given slope and y-intercept

From the slope-intercept form of the equation of a straight line, we have that

y = mx + b

Where m is the slope

and b is the y-intercept

From the given information,

The slope of the line is 6

and

The y-intercept is -3

That is,

m = 6

b = -3

Substitute the values into the equation

y = mx + b

y = 6(x) + (-3)

Simplify

y = 6x - 3

Hence, the equation is y = 6x - 3

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The area of the triangle as the function of x is [tex]x^2[/tex] / 2x - 4 and the domain of the function is  x∈(2, ∞)

The point on the line = (2, 1)

The give three points are (0, y), (2, 1) and (x, 0)

The slope of the line is the change in y coordinates with respect to the change in x coordinates of the line

Consider the point (0, y) and (2, 1)

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

= (1-y) /2

Consider the point (2, 1) and (x, 0)

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

= -1/x-2

Both slopes are equal

(1-y) /2 = -1/x-2

(1-y) = -2 / (x-2)

y = 1 + (2/(x-2))

y = x / (x-2)

The area of the triangle = (1/2)bh

Where b is the base

h is the height

The area of the triangle = (1/2) × x × (x / (x-2))

= [tex]x^2[/tex] / 2x - 4

The domain is x∈(2, ∞)

Hence, the area of the triangle is  [tex]x^2[/tex] / 2x - 4 and the domain of the function is x∈(2, ∞)

The complete question is

A right triangle is formed in the first quadrant by the x- and y-axes and a line through the point (2,1). Write the area of the triangle as a function of x, and determine the domain of the function.

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The statement that best describes the relationship in the graph is Jane earns $8 for every hour she babysits

In the graph, the x directions shows the number of hours. while the y directions show the amount earned

At point 1, in the x directions trace up to meet the line, then at the point of intersection with the line, trace to the left to meet the y directions

Following the description shows that at 1 hour (in x direction) the corresponding value in the y direction is $8

Therefore we say that Jane earns $8 per hour

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Measures of dispersion are used to indicate the spread or variability of the data.

Measures of dispersion are crucial for representing the spread of the data, or its fluctuation around a central value, whereas measures of central tendency are used to assess a dataset's "normal" values.

The four main measure of dispersion include

The range in statistics refers to the distribution of data between the lowest and greatest value in the distribution. It is a widely used indicator of variation.

The standard deviation deals with how much the data is away from the mean

The variance is standard deviation squared

These measures the spread, variability or distribution of data

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The number of text messages sent by carla in a month is 34.

What is an algebric equation ?

An algebraic equation is a mathematical statement that sets two expressions equal to each other. An algebraic equation is typically made up of a variable, coefficients, and constants.

For given question,

Phone service = $35

For each text message = $0.50

Total bill = $52

Let x be the no. of total text messages.

Equation:  52 = 35 + 0.50x

Solving for x,

52 - 35 = 0.50x

17 / 0.50 = x

34 = x

The number of text messages sent by carla in a month is 34.

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Answer:11/25

Step-by-step explanation:

Rosie's statement about expecting a total of about 175 points over 100 turns is accurate.

Based on the expected value, Rosie's statement is correct.

The expected value, denoted as E(X), represents the average or mean value of a random variable, in this case, the sum of points in a given turn when rolling the five dice.

Tom's statement, "A player will most likely get 17.5 points in any given roll," is not accurate. The expected value of 17.5 points does not necessarily mean that a player is most likely to get exactly 17.5 points in any single roll. Instead, it indicates that over many rolls, the average value of points earned in a turn is 17.5 points.

On the other hand, Rosie's statement, "Over 100 turns, we can expect a total of about 175 points," is correct. Since the expected value is 17.5 points per turn, over 100 turns, we can expect the total sum of points to be approximately 100 turns × 17.5 points/turn = 1750 points.

In summary, the expected value of 17.5 points represents the average outcome over multiple rolls, and based on this value, Rosie's statement about expecting a total of about 175 points over 100 turns is accurate.

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The complete question:

Tom and Rosie are designing a game. In each turn, a player rolls five 6-sided dice and adds the numbers showing on each face to determine how many points they get that turn. For example, the lowest number of points in a given turn is 1+1+1+1+1=5 points, and the highest is 6+6+6+6+6=30 points.

They let X represent the sum in a given turn, and they find the expected value of X is E(X) = 17.5 points.

Tom says, "A player will most likely get 17.5 points in any given roll."

Rosie says, "Over 100 turns, we can expect a total of about 175 points."

Whose statement is correct based on the expected value?

Answer:

3.50 × 6 = $21.004.50 × 4 = $18.00

But to Add These Two Numbers up The Cost Would $39.00 All Together :D

And pp+ dd+ =$39.00

Step-by-step explanation:

The population of the next year will be, 108,864.

What is population?

The term "population" refers to all citizens who are either permanently residing in a nation or are just temporarily absent from it. This indicator displays the population of a given area on a regular basis. Growth rates are the yearly changes in population brought on by births, deaths, and net migration.

Given:

The population of a city increases by 0. 8% per year.

This year's population is 108,000.

0.8% of 108,000 is,

108,000 x 0.008 = 864

The population increased by 864 people.

So, the next year's population will be,

108,000 + 864 = 108,864.

Hence, the next year's population will be 108,864.

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The second derivative, inflation point and slope of differential equation are explained below.

differential equation states how a pace of progress (a "differential") in one variable is connected with different factors. For example, when the position is zero (ie. the spring is neither extended nor compacted) then the  velocity isn't evolving.

We have,

dy/dx = 2x-y

Suppose f'(x) = 2x - y

d^2y/dx^2 = d(2x - y)/dx

⇒ 2

(b) To find the inflection points, equate f(x) to zero and solve for x.

f"(0) =0

f" (x)=2

So, the function defined on the interval (- ∞, 2) (2,  ∞)

In the interval (- ∞, 2), when x-1

f"(1)=2>0

So, the concave up wards on this interval.

In the interval (2,∞) when x=2

f"(2)=2>0

the concave up wards on this interval

Now, the slope of the function,

f(2)=3

here x-2y=3

Then, x = 2, y = 3

[tex]\frac{dy}{dx}|_{2, 3}[/tex] = 2(2) - 3 = 1

Thus, the slope of the function is 1.

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T statistics are more unpredictable than z scores since they employ sample variance rather than population variance.

Thus, because the t statistic employs the sample variance rather than the population variance, it is more volatile than z scores.

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Answer: No solution

Step-by-step explanation:

3y - x = (3 * 2 - 18) = 6 - 18 = -12

3y - x = -12

x - 3y = 12

since parallel lines, by definition, have NO point of intersection, there is no solution.

Answer:

connect with a tour

Step-by-step explanation:

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