Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS.

p(3,0,1), Q(-1,2,5), R(5,1,-1), S(0,4,2)

The equation that has 2 as its root is 2x² - 7x + 6 = 0 (option c)

Suppose we are given a quadratic function f(x) = ax² + bx + c, then x = q is a root if f(q) = 0.

Let's check for the given functions:

a.  x² - 4x + 5 = 0

f(2) =  2² - 4(2) + 5

f(2) = 4 - 8 + 5 = 1

Since f(2) ≠ 0, hence 2 is not its root.

b. x² + 3x - 12 = 0

f(2) = 2² + 3(2) - 12

f(2) = 4 + 6 - 12 = -2

Since f(2) ≠ 0, hence 2 is not its root.

c. 2x² - 7x + 6 = 0

f(2) = 2(2)² - 7(2)+ 6

f(2) = 2(4) - 14 + 6 = 0

Hence, x = 2 is its root.

d. 3x² - 6x - 2 = 0

f(2) = 3(2)² - 6(2) - 2

f(2) = 12 - 12 - 2 = -2

Since f(2) ≠ 0, hence 2 is not its root.

Hence, the correct option is   2x² - 7x + 6 = 0 (option c)

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To calculate the amount of liquid added, the scientist multiplies 6 drops by 0.14 ml, which results in 0.84 ml. Since 0.84 ml falls between 0 ml and 5 ml, it is the exact position of the liquid in the test tube.

6 × 0.14 ml = 0.84 ml

0.84 ml falls between the 0 ml and 5 ml marks on the test tube.

1. Calculate the amount of liquid added: 6 drops × 0.14 ml = 0.84 ml

2. Determine which marks the liquid will be between: 0 ml and 5 ml

3. Determine the exact position of the liquid in the test tube: 0.84 ml falls between the 0 ml and 5 ml marks on the test tube.

The scientist adds 6 drops of liquid to a test tube that has markings every 5 ml. Each drop has 0.14 ml. To calculate the amount of liquid added, the scientist multiplies 6 drops by 0.14 ml, which results in 0.84 ml. Since 0.84 ml falls between 0 ml and 5 ml, it is the exact position of the liquid in the test tube.

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The linearization of the function at a is L(x) = 1/2 + √3/2(x - π/6).

Linearization is a method of taking the gradient of a nonlinear function with respect to all variables. It is used to approximate the output of a function based on the value and slope of the function, at a given point.

The Linearization of function f(x,y) at (a,b) is L(x,y) = f(a,b) + (x−a)fx(a,b) +(y−b)fy(a,b)

Now we take a look at the given function, and the value of point a:

f(x) = sin (x)

a = π/6

Then we differentiate the function, with respect to x:

f(x) = sin (x)

f’(x) = cos (x)

We input the value of a = π/6 into the function:

y = f(π/6)

  = sin (π/6)

  = 1/2

f’(π/6) = cos (π/6)

          = √3/2

Now we input the value of f(a) and f'(a) into the linearization formulas:

L(x) = f(a) + f'(a)(x - a)

      = 1/2 + √3/2 (x - π/6)

Thus the linearization of the function at a is L(x) = 1/2 + √3/2(x - π/6).

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Answer:

he spent about 14 dallors and 49 cent

well, the better bargain for Rita is the bigger savings so, we know "B" gives $14 flat right off the 75 bucks, how about "A"? is the 15% more than 14 bucks?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{15\% of 75}}{\left( \cfrac{15}{100} \right)75}\implies 11.25[/tex]

woopsie, no dice, so she's better off taking the $14 rebate.

The total area of both the circles as calculated from the data given is found out to be as 246.64 cm² .

The formula to calculate the area of a circle is,  (pi)r² where r = radius.

Therefore, the area of the first circle is found out to be as ,

22/ 7 x 7.8 x 7.8

=191.2 cm²

and the area of second circle will be ,

22/7 x 4.2 x 4.2

= 55.44 cm²

Therefore, the sum of the areas of the circle will be ,

191.2 + 55.44

= 246.64 cm² .

The area of a shape is known as the space occupied by it in tw dimensional space.

Every figure has a specific area and can be found by using unique formulas. The formula to calculate the area of a circle is  (pi)r².

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According to the information, it can be inferred that the fraction that is equivalent to the height that differentiates silver A and silver B is 1/2.

To calculate the difference in height between the two floors, we must identify the height of each of the floors. According to the above, we must solve the fractions, that is, do the division as shown below:

Plant A:

Plant B:

Subsequently, we need to identify the difference between these two results as shown below:

Finally, we must identify which fractional is equal to 0.5, in this case it would be 1/2 (option D).

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jj is a transformation of f and the significance of those places in your neighbourhood which are named after famous personalities and prepare a

Answer:

Step-by-step explanation:

yes I can help ok ok ok

The parameter refers to the entire population and the statistics refers to a sample, only a sample will be inspected, no, only 99.7%, a student t distribution with spread σ/√n, The mean is less variable than single observations from the population, The distribution of the mean call length x becomes approximately normal distributed.

The parameter refers to numbers that summarize the data of the entire population while; Statistics refers to the numbers that summarize the data for a subset of the population or of a sample

No, he expects 99.7% to function within three standard deviations of the mean

The distribution of the sample average will be the student t distribution curve with spread = σ/√n

The mean includes a collection of variables from the sample, hence it is less variable than single observations from the population

As per the Central Limit Theorem, the distribution of the mean call length x from large samples of calls becomes more and more approximately normal as the size of the sample approaches that of the population.

--The given question is incomplete, the complete question is

"What is the difference between parameters and statistics? 2. Does statistical process control inspect all the items produced after they are finished? 3. The inspector samples five circuit boards at regular intervals and finds the mean solder quality score of x for these five boards. Do we expect x to be exactly 100 if the soldering process is functioning properly? 4. If the quality of individual boards varies according to a normal distribution with mean µ = 100 and standard deviation σ = 4, what will be the distribution of the sample averages, x? (Recall the sample size is n = 5.) 5. In general, is the mean of several observations more or less variable than single observations from a population? Explain. 6. The distribution of call lengths to a call centre is strongly skewed. What does the Central Limit Theorem say about the distribution of the mean call length x from large samples of calls?"--

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The solution of the inequality is x < -15/2x.

What is the linear equation?

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line. An example of a linear equation is y=mx + b.

We can start solving the inequality by first isolating x on one side of the inequality.

x(2x-1)>15

Divide both sides by x(2x-1)

1>15/(x(2x-1))

To get rid of the fraction, we can invert the inequality and multiply both sides by x(2x-1)

x(2x-1)<15

Now we can simplify the inequality by factoring the left side:

x(2x-1)<15

2x-1 < 15/x

2x < 15/x + 1

2x < (15 + x) / x

Now we can multiply both sides by x

2x*x < 15 + x

2x^2 < 15 + x

Now we can subtract x from both sides

2x^2 - x < 15

Now we can factor the left side

(x-5)(2x+3) < 0

Now we can find the solution of the inequality by finding the values of x that make the inequality true

x = 5, 2x +3 < 0

x < -15/2x

Hence, the solution of the inequality is x < -15/2x.

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Answer:

degree is 7

leading coefficient:-20

Step-by-step explanation:

degree is the highest exponent

leading coefficient is the coefficent with the highest degree

hope this helps :)

Answer:

The difference between constant and variable is that, while the first, as we have already said, remains fixed within a formula, the variable can assume different values.

Step-by-step explanation:

A constant term in an expression is a term that has a fixed value and does not change, while a variable term is a term that can take on different values. For example, in the expression 5x + 2, the 2 is a constant term because it is always 2, while x is a variable term that can take on different values.

In a real-world situation, a constant term represents a quantity that does not change. For example, if we were to write an expression to represent the cost of a product, the constant term would be the fixed cost of the product that does not change. On the other hand, a variable term represents a quantity that is subject to change. For example, in the same scenario, the variable term would represent the quantity of the product being bought, which can change.

In summary, a constant term represents a fixed value that does not change, while a variable term represents a value that is subject to change in a real-world situation.

On solving the provided question we can say that the equation h(x) = 3x / x^2 +5x +7 => [tex]h(x^2) =[/tex] [tex]3x^2 / x^4 + 5x^2 + 7[/tex]

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

here,

given h(x) = 3x / x^2 +5x +7

[tex]h(x^2) =[/tex] [tex]3x^2 / x^4 + 5x^2 + 7[/tex]

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all the missing Angles in the triangles are:

A = 60°

B = 60°

C = 60°

D = 42°

E = 35°

F = 35°

G = 55°

H = 45°

I = 45°

J = 15°

K = 15°

L = 75°

M = 120°

N = 21°

O = 69°

P = 21°

Q = 55°

R = 55°

S = 42°

T = 42°

U = 69°

An equilateral triangle is a triangle whose three sides are all the same length, commonly referred to as a "regular" triangle. Since all three sides of an isosceles triangle are equal, an equilateral triangle is a specific case of such an isosceles triangle.

An equilateral triangle in geometry is a triangle whose sides are all of the same length. The three angles opposing the three equal sides are equal in measure since the three sides are all equal. As a result, it is also known as an equiangular triangle since each angle is 60 degrees.

A = 60°

B = 60°

C = 60°

D = 42°

E = 35°

F = 35°

G = 55°

H = 45°

I = 45°

J = 15°

K = 15°

L = 75°

M = 120°

N = 21°

O = 69°

P = 21°

Q = 55°

R = 55°

S = 42°

T = 42°

U = 69°

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The complete question is as follows:

Answer:

I don't see all the answer choices, but it should be a graph with the slope of -1/2 and intersects y at -2.

Step-by-step explanation:

This equation will help you figure out what a graphed line will look like --> y=mx+b
In this equation, m represents the slope of the line, while b represents the y intercept. Since "m" is negative in the given equation, the line's slope is decreasing. Since "b" is also negative, the point the line intercepts at y will be (0,-2). I hoped this helped.

The measures of the angles.

Generally, In a space defined by Euclidean geometry, the sum of the angles of a triangle is equal to the angle that is straight.

A triangle is characterized by the presence of three angles, one at each vertex, and is defined by a set of sides that are next to one another. For a very long time, it was not known for certain whether or not there are alternative geometries for which this sum is different.

The measures of the angles in a triangle add up to 180 degrees. So, to find the measure of each angle in the triangle, we can set up the equation:

14x + 5x + 11x = 180

where

x represents the number of degrees in each angle.

Simplifying this equation, we get:

30x = 180

Dividing both sides by 30, we get:

x = 6

So, each angle in the triangle measures 6 degrees. To find the measure of each angle, we can simply multiply the ratio by 6.

14x6 = 84 (angle 1)

5x6 = 30 (angle 2)

11x6 = 66 (angle 3)

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The emails would you expect the principal to receive each day is 2.45.

X = 0; P(X) = 0.05

X = 1; P(X) = 0.15

X = 2; P(X) = 0.35

X = 3; P(X) = 0.25

X = 4; P(X) = 0.15

X = 5; P(X) = 0.05

Now the number of emails should be

= 0 × 0.05 + 1 × 0.15 + 2 × 0.35 + 3 × 0.25 + 4 × 0.15 + 5 × 0.05

= 0 + 0.15 + 0.70 + 0.75 + 0.60 + 0.25

= 2.45.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

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The table of a function is a visual table with columns and rows that displays the function with regards to the input and output.

The relationship between an input and an output is expressed mathematically as a function. There are several ways to express a function, such as through a function table, math, graphics, or spoken language. Function machines are another name for these function tables. The output of the table is created by applying a certain rule to the input value. The rule applicable to any one input has to be consistent with the other inputs as well. There are three components: input, function, and output. It is a common practice to design function tables with one of the three components unknown and the other two acting as solving cues.

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(a) On writing 299790000 in scientific notation , the value of a is 2.9979 and value of k is 8  .

(b) On writing 0.51 in scientific notation , the value of a is 5.1 and value of k is -1 .

What is Scientific Notation ?

The general form of writing a number in scientific notation is ⇒ [tex]a\times 10^{k}[/tex] ;

Part (a) ;

the number is given to be : 299790000 ;

For writing it in scientific notation, decimal point will be placed after 2 ;

So , the scientific notation of the number is ⇒ [tex]2.9979 \times 10^{8}[/tex] ,

On comparing it with the general form of scientific notation,

we get , a = 2.9979 and k = 8 .

Part (b) ;

the number is given to be : 0.51 ;

For writing it in scientific notation, decimal point will be placed after 5 ;

So , the scientific notation of the number is ⇒ [tex]5.1 \times 10^{-1}[/tex] ,

On comparing it with general form of scientific notation,

we get , a = 5.1 and k = -1 .

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The contrapositive of the statement "If the lines are skew, then they are not coplanar" is "If the lines are coplanar, then they are not skew."

The contrapositive of a statement is formed by negating both the hypothesis and the conclusion and switching their positions. The contrapositive of "If P then Q" is "If not Q, then not P."

So, the contrapositive of the original statement "If the lines are skew, then they are not coplanar" is "If the lines are coplanar, then they are not skew" (c).

It is important to note that the contrapositive and the original statement are logically equivalent, meaning that if one statement is true, then the other is also true, and vice versa. This is a useful property in mathematical reasoning and proof writing.

Skew lines are lines that do not lie in the same plane and do not intersect. In other words, they are lines that are not parallel and not coincident. Skew lines have different directions and they can have a 3-dimensional relationship with each other.

In geometry, skew lines are important because they help define the concepts of parallel lines, coplanar lines, and intersecting lines. Skew lines are used to describe the relationship between lines in space, and they are also used in applications such as computer graphics, engineering, and architecture.

Skew lines can also be used to demonstrate the concept of non-Euclidean geometry, which is a type of geometry that does not follow the traditional rules of Euclidean geometry, where parallel lines are equidistant from each other and never meet. In non-Euclidean geometry, parallel lines can diverge from each other and can have a more complex relationship with each other in space.

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The vertices of the dilated figure is S'(-20, 4), T'(-12, 20), U'(-4, 4), V'(-12, -4)

Transformation is the movement of a point in the coordinate plane. Types of transformation are reflection, rotation, translation and dilation.

Dilation is the enlargement or reduction in the size of a figure by a scale factor.

Given the coordinates of polygon S(-5, 2), T(-3, 5), U(-1, 1), V(-3, -1). For a dilation with a scale factor of 4, the new coordinates are:

S'(-20, 4), T'(-12, 20), U'(-4, 4), V'(-12, -4)

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a power boat takes 30 minutes to travel 10 miles downstream. the return trip takes 50 minutes then the speed of the current is 4mph

distance = speed × time

In this instance, the distance going downstream and upstream is equal. All we need to do is express speed to solve:

Find the speed going upstream and downstream:

10 / 30 = 1/3 mi / min * 60 min / 1 hour  = 20 mph

10 / 50 = 1/5 mi / min * 60 min / 1 hour = 12 mph

Find the speed of the current by expressing a downstream current as + c and upstream current as -c. The speed of the boat (s), without current, would be the same.

s + c = 20

s - c = 12

We can isolate s to solve for c:

s = 20 - c

s = 12 + c

Set the two equations equal to each other:

20 - c = 12 + c

Add c to both sides:

20 = 12+ 2c

Subtract 20 from both sides:

8= 2c

Divide both sides by 2:

c = 4 mph.

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Answer:

r = 5

Step-by-step explanation:

calculate the slope m of the 2 given points and equate to - 2

using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (3, 2 ) and (x₂, y₂ ) = (r, - 2 )

m = [tex]\frac{-2-2}{r-3}[/tex] = [tex]\frac{-4}{r-3}[/tex]

equating to - 2 gives

[tex]\frac{-4}{r-3}[/tex] = - 2 ( multiply both sides by r - 3 to clear the fraction )

- 4 = - 2(r - 3) ← divide both sides by - 2 )

2 = r - 3 ( add 3 to both sides )

5 = r

Equation for a line given a slope of 2/3 through the pt (-6,10) is y =  [tex]\frac{2}{3}[/tex] x + 16.

Given data :

The equation of a line in point slope form is

y - y1 = m ( x - x1 )

where m represents the slope and ( x1, y1 ) a point on the line here

m = 2 / 3 and  ( x1, y1 ) = ( -6, 10)

y - 10 = [tex]\frac{2}{3}[/tex] ( x - - 6 )

y - 10 = [tex]\frac{2}{3}[/tex] ( x + 6 )

y =  [tex]\frac{2}{3}[/tex] ( x + 6 ) + 10

y =  [tex]\frac{2}{3}[/tex] x + 16

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A correlation is a statistical measure of the relationship between two variables and is expressed as a numerical value between -1 and 1.

A correlation is a measure of the relationship between two variables that is expressed as a numerical value between -1 and 1. To calculate a correlation, start by collecting data on the two variables. Then, calculate the covariance, which is the sum of the product of the differences between the two variables, divided by the number of data points. Finally, calculate the correlation by dividing the covariance by the product of the standard deviations of the two variables. The correlation can range from -1, which signifies a perfect negative correlation, to 1, which signifies a perfect positive correlation. A correlation of 0 indicates that there is no correlation between the two variables.

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The mixed number would be [tex]10\frac{31}{100}[/tex].

What is a mixed number?

A mixed number is a number that is made up of a whole number and a fraction. It is a combination of a whole number and a fraction that represents a value between two whole numbers. For example, 3 1/2 is a mixed number, with 3 as the whole number and 1/2 as the fraction.

To express 10.31 as a mixed number:

The whole number part is 10.

To find the fractional part, subtract the whole number from the decimal: 0.31

To express the fractional part as a fraction, we will have to divide it by 1 and write the decimal as a fraction, in this case 0.31= 31/100

Now we can express 10.31 as a mixed number, that is 10 31/100

Hence, the mixed number would be [tex]10\frac{31}{100}[/tex].

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Therefore , the solution of the given problem of mean comes out to be value of the mean is 600.

A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean). Often referred to as the "mean," this is the most often used measure of central tendency. Simply dividing the dataset's total number of values by the sum of all of those values yields this result. Both raw data and data that have been combined into frequency tables can be used for calculations. Average refers to a number's average. It is straightforward to calculate: Divide by how many digits there are after adding up all the digits. the total divided by the count.

Here,

Given :The sum is 600.

The average arithmetic mean of x, y and z is 50.

=>(x + y + z)/350, sox + y + z = 150

=>4x + y + 3y+z+32

=>4x+4y+4z 4x+4y+4z4(x+y+ z) 4(x+y+2)

=> 4*150 = 600

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The gradient vector field of function f(x,y) is given as follows:

grad(f(x,y)) = (1 + 3xy)e^(3xy) i + 3x²e^(3xy) j.

Suppose that we have a function defined as follows:

f(x,y).

The gradient function is defined considering the partial derivatives of function f(x,y), as follows:

grad(f(x,y)) = fx(x,y) i + fy(x,y) j.

In which:

fx(x,y) is the partial derivative of f relative to variable x.

fy(x,y) is the partial derivative of f relative to variable y.

The function in this problem is defined as follows:

f(x,y) = xe^(3xy).

Applying the product rule, the partial derivative relative to x is given as follows:

fx(x,y) = e^(3xy) + 3xye^(3xy) = (1 + 3xy)e^(3xy).

Applying the chain rule, the partial derivative relative to y is given as follows:

fy(x,y) = 3x²e^(3xy).

Hence the gradient vector field of the function is defined as follows:

grad(f(x,y)) = (1 + 3xy)e^(3xy) i + 3x²e^(3xy) j.

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