A Sulfa drug is to be given to a 130-pound patient at the rate of 2.5 mg per pound of body weight.

How many mL are necessary if the concentration of the drug is 200 mg per mL?

Reduced matrix to its reduced echelon form Original Matrix:

[tex]$$ \begin{bmatrix}1 & -1 & 2 & -1 & 3 \\2 & -2 & 3 & 0 & 4 \\0 & 0 & 0 & 1 & -2\end{bmatrix} $$[/tex]

Pivot Positions (Original): (1,1), (2,2), (3,4)

Pivot Columns (Original): 1, 2, 4

Reduced Echelon Form:

[tex]$$ \begin{bmatrix}1 & 0 & \frac{2}{3} & 0 & \frac{11}{3} \\0 & 1 & \frac{1}{3} & 0 & \frac{2}{3} \\0 & 0 & 0 & 1 & -2\end{bmatrix} $$[/tex]

Pivot Positions (Reduced): (1,1), (2,2), (3,4)

Pivot Columns (Reduced): 1, 2, 4

To reduce this matrix to its reduced echelon form, I used the following series of elementary row operations:

1. Divide row 1 by 1 to get the leading 1 in the first column

2. Subtract two times row 1 from row 2 to get the leading 1 in the second column

3. Subtract three times row 1 from row 3 to get the leading 1 in the fourth column

4. Divide row 2 by 3 to get the coefficient 2/3 in the third column

5. Subtract row 2 from row 1 to get the coefficient 11/3 in the fifth column

6. Subtract row 2 from row 3 to get the coefficient 2/3 in the fifth column

Exercise 4:

Original Matrix:

[tex]$$ \begin{bmatrix}1 & 2 & -3 & 1 & 5 \\2 & 4 & -6 & 2 & 8 \\-1 & -2 & 3 & -1 & -4\end{bmatrix} $$[/tex]

Pivot Positions (Original): (1,1), (2,2), (3,3)

Pivot Columns (Original): 1, 2, 3

Reduced Echelon Form:

[tex]$$ \begin{bmatrix}1 & 0 & 0 & \frac{2}{3} & \frac{11}{3} \\0 & 1 & 0 & \frac{-1}{3} & \frac{1}{3} \\0 & 0 & 1 & \frac{2}{3} & \frac{5}{3}\end{bmatrix} $$[/tex]

Pivot Positions (Reduced): (1,1), (2,2), (3,3)

Pivot Columns (Reduced): 1, 2, 3

To reduce this matrix to its reduced echelon form, I used the following series of elementary row operations:

1. Divide row 1 by 1 to get the leading 1 in the first column

2. Subtract two times row 1 from row 2 to get the leading 1 in the second column

3. Subtract row 1 from row 3 to get the leading 1 in the third column

4. Divide row 2 by 3 to get the coefficient -1/3 in the fourth column

5. Add row 2 to row 1 to get the coefficient 2/3 in the fourth column

6. Divide row 3 by 3 to get the coefficients 2/3 and 5/3 in the fourth and fifth columns respectively

7. Add row 3 to row 1 to get the coefficient 11/3 in the fifth column

8. Add row 3 to row 2 to get the coefficient 1/3 in the fifth column

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Answer:

No, there is no value of a that makes the statement |a| = -2 true.

Step-by-step explanation:

The absolute value of a number is the distance of that number from zero on the number line. It is always non-negative, so it can't be -2. The absolute value of a number is denoted by two vertical lines on either side of the number like this |a|.

For example, the absolute value of -5 is 5 and the absolute value of 5 is 5. In both cases, the distance from zero is 5.

In the statement |a| = -2, the absolute value of a is -2, which is impossible as the absolute value can't be negative. Therefore, there is no value of a that makes the statement true.

Answer:

  no

Step-by-step explanation:

You want to know if there's any value of the variable 'a' that would make its absolute value be -2.

The absolute value of a number is always positive. There is no such thing as a number whose absolute value is negative, not -2 or any other negative number.

  such a value of 'a' Does Not Exist (DNE)

Answer: 2343.8 meters

Step-by-step explanation: If 3.8 meters is walked in 1/2 hours then another 4680 meters per hour is ran for a half hour is 2340 meters add those 2 together

Answer:

There are 10,000 four-digit decimal numbers that have an estimated value of 10 when rounded off to the nearest tenths place. This is because each decimal number from 0.0001 to 0.9999 will have an estimated value of 10 when rounded off to the nearest tenths place.

If you divide 11 by 2.5 you will end up with 4.4. Answer = 4.4

In order to factor your quadratic polynomials, the box method, as its name suggests, uses a box. You can divide your quadratic into its factors by using the box, which is essentially a square divided into four equal parts.

Employing the Box Method

For our first quadratic, 6x2 - x - 12, let's utilize the box approach to solve it.

The first step is to create a two by two grid, as shown here:

using a box

Following that, we place the first term in the upper left box and the last term in the lower right box.

The Complete Question.

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The lower and upper bounds of the temperature at noon in Valletta are 10.9° C and 27.8° C.

The upper bound of Valletta = Upper bound of Leeds - Copenhagen +23

upper bound of Valletta  = 16.8 -12+23

upper bound of Valletta = 27.8 °C

Lower bound of Valletta = 0.1 -12+23

Lower bound of Valletta = 10.9 °C

Hence, The lower and upper bounds of the temperature at noon in Valletta are 10.9° C and 27.8° C.

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The amount of sugar present in the milk chocolate bar is, 12000   milligrams.

Given,

Amount of milk chocolate bar = 20.00 grams

Amount of sugar = 12.00 grams

The conversion used for grams to milligram is :

1 gram = 1000 milligram

As per question we are given that, 12 grams of sugar

As, 1 gram of sugar = 1000 milligram of sugar

So, 12.00 grams of sugar = (12/1) x 1000

                                          = 12000 milligrams of sugar

Therefore, the amount of sugar present in the milk chocolate bar is, 12000 milligrams.

(b) THe reduced size is 3 g

3 g bar has 12x3/20 g of sugar

i.e 7.2 g

hence , he amount of sugar in milligrams if the size of the milk chocolate bar is reduced from 20.00 g to 3.000 g is 7200mg.

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The distance that Tonya walk on Saturday more than on Sunday would be = 8/15 miles

Distance is defined as the quantity that describes the space that exists between two locations in a field.

The number of miles Tonya covered on Saturday = 3 ⅓ miles

The number of miles that Tonya covered on Sunday = 2 ⅘

Therefore the distance that Tonya walk on Saturday more than on Sunday would be the difference between the distance covered in Saturday and Sunday.

That is; 3⅓ - 2⅘ ( change to single fraction form)

= 10/3 - 14/5

= 50-42/15

= 8/15

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Slope between the points (1,7) and (-5, -11) is m = 18/6 as a decimal m = 3

The slope of a hill describes its steepness. The steepness of a line follows a similar pattern. The rise between two points, which is the vertical change, is divided by the run, which is the horizontal change between those same two points, to determine the slope.

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

step1:

calculate the slope m using the slope formula

slope m=y2-y1/x2-x1

with (x₁, y₁ )=(1,-5) and (x₂, y₂ ) =(-5,-11)

step2:

m=-11-7/-5-1=-18/-6=18/6

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Answer:

Step-by-step explanation:

You want the number of lines of symmetry of the 4-leaved rose shown in the figure.

The figure is symmetrical about a line through opposite petals. It is also symmetrical about a line through the space between petals. The attachment shows the 4 lines of symmetry.

The petals have the same geometry, but are rotated 90° from each other. That means any rotation that is a multiple of 90° will map the figure to itself. (180° is a multiple of 90°)

The figure maps to itself when rotated 90° or 180°.

La tarjeta de crédito tiene una tasa efectiva de interés anual de 21,375 %.

En este problema tenemos que Merle obtiene una tarjeta de crédito bajo la siguientes condiciones: 0 % E.A. para los primeros 60 días, 23,19 % E.A. para los 365 restantes.

Debemos determinar la tasa de interés efectiva anual equivalente, esto es posiblemente mediante una aplicación consecutiva del concepto de interés, descrito abajo:

I = (1 + r / 36500)ⁿ

Donde:

La situación es descrita por la siguiente expresión matemática:

1 + R / 100 = (1 + 0 / 36500)⁶⁰ + (1 + 23,19 / 36500)³⁰⁵

Donde R es la tasa efectiva de interés anual.

Finalmente, despejamos la variable correspondiente:

R = 21,375

La tasa efectiva de interés anual a sufragar por Merle por el uso de tarjeta de crédito es 21,375 %.

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Answer: 22 vaccines

Step-by-step explanation:

first, reduce the amount that doctors leave out from the total amount of a vial

6 - 0.5 = 5.5

next divide 5.5 by the amount that is given to each person, which will give you the number of vaccinations the doctor can give

5.5/ 0.25 = 22 vaccines

Answer:

0.750

Step-by-step explanation:

Yellow sections: section 2 and section 3

Number of yellow sections: 2

Number of non yellow sections: 6

Total sections: 8

p(not yellow) = 6/8 = 0.75

Answer:

0.750

Step-by-step explanation:

you take a quarter and then you divide and think  

By adding (81.7-23.456)+(78.44+2.72), we get 139.404

Use the three rules below to calculate the number of significant figures in a number:

Non-zero digits are always meaningful.

Any zero between the first and second significant digits is significant.

Only the last zero or trailing zeros in the decimal section are important.

Numbers Have Rules INCLUDING a Decimal Point

START COUNTING FOR SIGNIFICANT FIGURES. On the very first non-zero digit.

STOP COUNTING FOR SIGNIFICANT FIGURES.

Non-zero numbers are ALWAYS meaningful.

After the first non-zero digit, any zero is still relevant. The zeroes preceding the first non-zero digit are unimportant.

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The product of the binomial factors is x² + 16x + 64

from the question, we have the following parameters that can be used in our computation:

(x+8)2

Express properly

So, we have

(x+8)²

Using the square of a binomial sum, we have

(x+8)² = x² + 2 * x * 8 + 8²

Evaluate

(x+8)² = x² + 16x + 64

Hence, the solution is x² + 16x + 64

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The domain of each expression is given as follows:

1. All real values except y = 0 and y = 2.

2. All real values.

3. All real values except y = 0 and y = -7.

The domain of an expression is composed by the set of all the possible input values that the expression can assume.

For an expression that is a fraction, the denominator cannot be zero, hence:

For item 2, the function is a multiplication, which has no restrictions on the domain, and thus the domain is composed by all real values.

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For function f(x)= x² + 7 and g(x)= x² + 2,

a) f(x) + g(x) = 2x² + 9

b) f(x) - g(x) = 5

c) f(x) . g(x) = x⁴ + 9x² + 14

d) [tex]\frac{f(x)}{g(x)} =\frac{x^2 + 7 }{ x^2+2}[/tex]

Consider given functions  f(x)= x² + 7 and g(x)= x² + 2

a) To find addition of functions: f(x) + g(x)

f(x) + g(x)

= (x² + 7) + (x² + 2)

= x² + x² + 7 + 2             .............(associative property of addition)

= 2x² + 9                       ................(combine like terms)

b) to find subtraction of functions : f(x) - g(x)

f(x) - g(x)

= ( x² + 7 ) - (x² + 2)

= 7 - 2

= 5

c) To find multiplication of functions: f(x).g(x)

f(x) . g(x)

= ( x² + 7 ).(x² + 2)

= x² (x² + 2) + 7(x² + 2)

= x⁴ + 2x² + 7x² + 14

= x⁴ + 9x² + 14              ................(combine like terms)

d) To find division of functions: f(x)/g(x)

[tex]\frac{f(x)}{g(x)}\\\\ =\frac{x^2 + 7 }{ x^2+2}[/tex]

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Answer:

1

Step-by-step explanation:

We have g(f(2))

Working from the inside out, we start with f(2)

So we go to the f(x) graph and find where X is 2. We get to the point (2, -2). f(2) is pretty much asking for the Y value at 2. On this graph the y value is -2

Now that we know f(2) is -2, we can plug that into g(f(2)), giving us g(-2)

Now we can go to the other graph, g(x) and find where X is -2.

That's where we find the point (-2,1)

Like last time, g(2) is asking for that Y value at that point of -2. On this graph, it's 1

Now we can conclude g(f(2)) = 1

Using the graph of g, we can see that g(4) is approximately 3. So, g(f(2)) = 3.

What is the graph?

A graph is a visual representation of data or information, often used in mathematics and science to depict relationships between variables. Graphs can take many forms, including line graphs, bar graphs, scatter plots, and pie charts.

To evaluate g(f(2)), we need to first find the value of f(2) using the graph of f. From the graph, we can see that f(2) is approximately 4. So, g(f(2)) = g(4).

Then, using the graph of g, we can see that g(4) is approximately 3. So, g(f(2)) = 3.

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IIn a case whereby Transistors are used to build computer chips and the size of the earliest transistors was about 1 x 10* micrometers and today, transistors can measure smaller than 1 × 10-2 micrometer the numbert of times the old is as great as the size of transistors today is 1 × 10^6.

The concept that will be use here is division. One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping. In this post, let's study more about the division operation in math.

We were told that the side of the earliest form of transistors for computer was 1 × 10⁴.

In another sentence, we were told that the size of the transistor today  is expressed as  1 × 10^-2

We can then know the difference in size will  which will be

= 1 × 10^4 / 1 × 10^-2

= 1 × 10^6

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complete question:

Transistors are used to build computer chips. The size of the earliest transistors was about 1 x 10^4 micrometers. Today, transistors can measure smaller than 1 × 10-2 micrometer. The size of the earliest transistors is about how many times as great as the size of transistors today?

The height of the building that cast the shadow 98 feet will be 61.25 feet.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

Laurie, who is 5 feet tall, notices that she casts an 8-foot shadow. If Laurie is standing 90 feet away from the base of a building.

Let 'h' be the height of the building. Then the equation is given as,

h / (90 + 8) = 5 / 8

h / 98 = 5 / 8

h = 98 x 5 / 8

h = 12.25 x 5

h = 61.25 feet

The height of the building that cast the shadow 98 feet will be 61.25 feet.

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The denominator could be any real value

From the question, we have the following parameters that can be used in our computation:

Fraction = same denominator

Such that the numerators are 5 and 7

This means that the fractions can be represented as

Fractions = 5/x and 7/x

There is no restriction on the possible value of x

hence, the denominator is any value

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The centroid of the given triangle is =(5.3 , 7.3)

The centroid is the term for the object's geometric centre. We apply the centroid formula to find the triangle's centroid's coordinates. The intersection of a triangle's three medians yields the centroid, or centre, of the triangle. All of the medians are divided by the centroid of a triangle in a 2:1 ratio.

The centroid formula of a given triangle can be expressed as,

C = ((x1+x2+x3)/3 , (y1+y2+y3)3/3)

where,

C denotes the centroid of a triangle

x1,x2,x3  are the x-coordinates of the 3 vertices.

y1,y2,y3  are the y-coordinates of the 3 vertices

To find: Centroid of a triangle.

We are taking the Cordinates of the traiangle XYZ

as x1,y1,x1,y2,x3,andy3

so,Given parameters are,

(x1,y1)=(-2,6)

(x2,y2)=(4,10)

(x3,y3)=(14,6)

Using centroid formula,

The centroid of a triangle = ,

 =-2+4+14/3  6+10+6/3

 =5.3 7.3

The centroid of a triangle is ==(5.3 and 7.3)

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The values of  (f + g) (x),  (f - g) (x),  (fg) (x) and  (f /g) (x) for the functions are x/(x + 9) + x³, x/(x + 9) - x³, x³/(x³ + 9) and  1/ [x² (x + 9)] respectively

A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input

Since f(x) = x/(x + 9), g(x) = x³

(a) (f + g) (x) will be the addition of f(x) and g(x). That is:

(f + g) (x) = x/(x + 9) + x³  or  x³ +  x/(x + 9)

(b) (f - g) (x) will be the subtraction of f(x) and g(x). That is:

(f - g) (x) = x/(x + 9) - x³

(c) (fg)(x) substitute x = x³ into f(x). That is:

f(x)= x/(x + 9), g(x) = x³

(fg)(x)  = x³/(x³ + 9)

(d) (f/g)(x) will be the division of f(x) by g(x). That is:

(f/g)(x) = [x/(x + 9)] / x³ =  x/ [x³ (x + 9)] = 1/ [x² (x + 9)]

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Trigonometric expressions are mathematical functions that use the ratios of the sides of a right triangle to calculate angles. Non-trigonometric functions are mathematical functions that do not use the sides of a triangle to calculate angles, but rather use other mathematical operations such as exponentials, logarithms, and polynomials.

Trigonometric expressions are mathematical functions that use the ratios of the sides of a right triangle to calculate angles. These functions are often used in applications such as navigation and surveying, as they allow us to calculate angles and distances in the real world. Examples of trigonometric functions include sine, cosine, tangent, cotangent, secant, and cosecant. Non-trigonometric functions are mathematical functions that do not use the sides of a triangle to calculate angles, but rather use other mathematical operations such as exponentials, logarithms, and polynomials. These functions are often used in engineering and scientific applications, as they allow for more precise calculations than trigonometric functions. Examples of non-trigonometric functions include polynomial functions, exponential functions, logarithmic functions, and hyperbolic functions. In each case, the function being used must be appropriate for the type of problem being solved. By understanding the differences between trigonometric and non-trigonometric functions, it is possible to choose the right function for the right problem.

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The unit vector perpendicular to the plane of given vectors P =i−2j+ k and Q =2i + j − k is ( i + 3j + 5k )/√35

The vector that perpendicular to the plane is equal to the cross product of:

P ⨉ Q

Remember the properties of cross product of two vectors:

i ⨉ i = j ⨉ j = k⨉ k = 0

i ⨉ j = k

j ⨉ i = - k

j ⨉ k = i

k⨉ i = j

i⨉ k = -j

Hence,

P ⨉ Q = (i−2j+ k) ⨉ (2i+j−k)

          = k + j +4k + 2i +2j - i

          = i + 3j + 5k

The magnitude of P ⨉ Q is:

|| P ⨉ Q || = √(1² + 3² + 5²)

               = √35

Therefore, the unit vector = ( i + 3j + 5k )/√35

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The number of scarves in 4 hours is 9.6

From the question, we have the following parameters that can be used in our computation:

Rate = 3 scarves in 75 minutes

Time = 4 hours

The number of scarves is then calculated as

Scarves = Rate * Time

substitute the known values in the above equation, so, we have the following representation

Scarves = (3/75 minutes) * 4 hours

Evaluate the product

Scarves = 9.6

Hence, the number of scarves is 9.6

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The slope of the given lines are representing that these lines are perpendicular.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given, the pair of the equation are parallel, perpendicular, or neither y=-7/8x-1, 32x-28y=-36

Slope intercept form of both equations of a line

1)  y = -7/8x - 1

it is already in a slope intercept form

2) 32x - 28y = -36

-28y = -32x -36

y = 8/7x + 9/7

Since their slope is inverse and had a negative constant.

The slope of a perpendicular line from the slope of a given line is obtained by taking the negative reciprocal of the slope of the given line. If the slope of the given line is m1 and the slope of a perpendicular line is m2 then we have m2 = -1/m1.

Therefore, The slope of the given lines are representing that these lines are perpendicular.

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