For rational functions and functions with square roots, the domain can be all real numbers except (1) anything that will make the

Answer:

B

Step-by-step explanation:

We know that it costs 37 cents to mail a letter that weighs 1 oz or less. This would mean that for x ≤ 1, P(x) should equal 37. Already, we can eliminate A and D.

We also know that it costs an additional 26 cents for at most another ounce added to the original 1 ounce. This means that for 1 < x ≤ 2, P(x) = 26 + 37 = 63. This is shown by B.

Thus, the answer is B.

~ an aesthetics lover

The vertical distance between (2, 11/3) and (2, -4/3) is -5 units.

The distance formula is a mathematical equation used to find the distance between two points in a plane. It is derived from the Pythagorean theorem and is expressed as:

d = √((x₂- x₁)²+ (y₂ - y₁)²)

The distance formula can also be extended to three-dimensional space by adding an additional term to the equation.

The two points (2, 11/3) and (2, -4/3) have the same x-coordinate, which means they lie on a vertical line. To find the vertical distance between these two points, we simply subtract their y-coordinates:

Vertical distance = (y-coordinate of second point) - (y-coordinate of first point)

= (-4/3) - (11/3)

= -15/3

= -5

Therefore, the vertical distance between (2, 11/3) and (2, -4/3) is -5 units. Since this is a negative value, it means that the second point is located 5 units below the first point.

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Answer: Ellie borrowed $150.

Step-by-step explanation:

I = PRT

39 = P x 0.065 x 4

39 = P x 0.26

Divide both sides by 0.26

150 = P

The money Ellie borrows is 150.

percentage, a relative value indicating hundredth parts of any quantity.

Given Ellie borrows money at a year simple rate of \(6\frac{1}{2}\)%.

After 4 years ellie owes 39 interest

We need to find how much money did ellie borrow.

Let us convert  \(6\frac{1}{2}\)% to decimal value by dividing with 100

\(6\frac{1}{2}\)/100=6.5/100=0.065

Now we have formula for interest

I=PRT

Where I is the interest=39

P is the principle amount which we need to calculate

R is rate of interest=0.065

T is the time in years=4

Plug in these values.

39 = P x 0.065 x 4

39 = P x 0.26

Divide both sides by 0.26

150 = P

Hence, the money Ellie borrows is 150.

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62/100 is the fraction

31/50 is the simplest form

explanation:

62%

= 62/100

= (62/2) / (100/2)

= 31/50

The final answer is 31/50~

62%

to get rid of the percentage sign  and change to a fraction divide by 100

62/100

divide both numbers by to to change to simplest form

= 31/50

31/50 by the way I love how some people realize so many people answered this question already and decide they should add something that is totally not necessary.

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2/3 of cookies were she saved.

A fraction represents a part of a whole.

The first batch consisted of 120 gingerbread cookies

Second batch consisted of 150 shortbread cookies.

And, the same fractions of cookies from each batch were saved.

Let x parts of each of cookies were saved.

Then The number of the saved gingerbread cookies = 120 x

While, The number of the saved shortbread cookies = 150 x

150x-120x=20

30x=20

x=20/30

x=2/3

Hence 2/3 of cookies were she saved.

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Part A:  There are nine minors in total.

Part B: The cofactor matrix C is obtained by multiplying each minor by \((-1)^{i+j}\). The entry \(C_i_j\) in the cofactor matrix is equal to \((-1)^{i+j}\)times the corresponding minor.

Part C: The adjugate of A, denoted as Adj(A), is obtained by taking the transpose of the cofactor matrix C.

Part A: To calculate the minors of matrix A, we need to compute the determinants of each matrix obtained by deleting the ith row and jth column,i.e.,we need to delete the ith row and jth column of A and compute the determinants of the resulting 2x2 matrices.

In this case, we need to calculate the determinants of three 2x2 matrices.

Part B: The cofactor matrix C is obtained by multiplying each minor by (-1)^(i+j), where i and j represent the row and column indices of the entry. For each entry in the minors matrix, we multiply it by (-1)^(i+j) to obtain the corresponding entry in the cofactor matrix C.

Part C: The adjugate of matrix A, denoted as Adj(A), is obtained by taking the transpose of the cofactor matrix C.

This means that the entry in the ith row and jth column of Adj(A) is equal to the entry in the jth row and ith column of C.

By calculating the minors, cofactor matrix, and adjugate of matrix A, you can obtain the desired results for Part C.

However, the specific calculation and entries of the adjugate matrix cannot be determined without completing the row-reduction process on matrix A.

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Answer:

£9000

Step-by-step explanation:

= £10 000× 5 ×2

100

= 1000

= £10 000-1000

= £9000

Answer (there are two solutions):

I hope this helps!

Answer:

(1/4)n - 3

Step-by-step explanation:

In math, "of" means times so the first part of the expression is 1/4 times n. Then add minus 3 because it says she subtracted 3.

Answer:

ST = 2.6

Step-by-step explanation:

since the triangles are similar then the ratios of corresponding sides are in proportion, that is

\(\frac{ST}{PQ}\) = \(\frac{SU}{PR}\) ( substitute values )

\(\frac{ST}{18}\) = \(\frac{5.2}{36}\) ( cross- multiply )

36 × ST = 18 × 5.2 = 93.6 ( divide both sides by 36 )

ST = 2.6

Answer:

4/15

Step-by-step explanation:

3/5-1/3

9-5/15

=4/15

I ain't really sure

The BMI of an 118-lb adult who is 5 feet 4 inches tall is approximately 20.25.

BMI stands for Body Mass Index.

It's a measure of body fat based on height and weight that applies to both adult men and women.

BMI is an easy-to-perform screening tool for body fat levels that can help identify individuals who have health risks linked with excess body fatness.

It's important to keep in mind that the BMI measurement should not be used as a diagnostic tool for health conditions and is only one component in an overall evaluation of a person's health status.

Using the formula below, we can calculate the BMI of an 118-lb adult who is 5 feet 4 inches tall: BMI = (weight in pounds / (height in inches x height in inches)) x 703

First, we need to convert the height into inches:5 feet 4 inches = 64 inches

Next, we plug the values into the formula and solve for the BMI:

BMI = (118 / (64 x 64)) x 703BMI = (118 / 4,096) x 703BMI = 0.0288 x 703BMI = 20.2464

Therefore, the BMI of an 118-lb adult who is 5 feet 4 inches tall is approximately 20.25.

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Answer: Tom = R10,000
Peter = R4000

John = R6000

Step-by-step explanation:

Let the ratios be 5x,2x and 3x ,

5x+2x+3x = 20000

10x = 20000

x = 2000

Tom = 5x2000 = 10,000

Peter = 2x2000 = 4000

John = 3x2000 = 6000

assuming R20,000 to be a unit of currency, Tom receives R10,000 ; Peter recieves R4000 and John recieves R6000

the money is to be divided among three persons in the respective order of Tom, Peter, and John.

we can write the share of the amount which will be received by them as follows

Tom = 5 times

Peter= 2 times

John = 3 times

let the money received by them be (x)

Tom = 5x

Peter = 2x

john = 3x

The total amount of money is R20,000, therefore we can write the aforementioned data into a simple equation:

20,000= (money received by Tom) + (money recieved by Peter) + (money recieved by John)

20,000 = 5x + 2x+ 3x

20,000= 10x

2000=x

now we can find out the money received by each one of them

Tom= 5 x (2000) = R10,000

Peter= 2 x (2000) = R4000

John = 3 x (2000) = R6000

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According to the figure's surface area, 712 square centimeters,

A prism is indeed a solid form that is enclosed by flat faces on all of its sides. A prism has two different kinds of faces. Bases refer to the identical top and bottom faces. The word "prism" refers to the form of these bases. For instance, a prism is referred to be a triangular prism if its base is triangular.

We must sum up the places of all the faces of a two rectangular prisms in order to determine the contact area of the this L-shaped composite figure.

First, we'll find the area of the faces of the first prism.

It has a length of 20 cm, a width of 4 cm, and a height of 8 cm.

So, the area of the front face is 204 = 80 sq cm.

The area of the back face is also 80 sq cm.

The area of the top face is 48 = 32 sq cm.

The area of the bottom face is also 32 sq cm.

The area of the right face is 8*20 = 160 sq cm.

The area of the left face is also 160 sq cm.

Now, we'll find the area of the faces of the second prism.

It has a length of 20 cm, a width of 10 cm, and a height of 2 cm.

So, the area of the front face is 2010 = 200 sq cm.

The area of the back face is also 200 sq cm.

The area of the top face is 102 = 20 sq cm.

The area of the bottom face is also 20 sq cm.

The area of the right face is 2*20 = 40 sq cm.

The area of the left face is also 40 sq cm.

Now, we need to subtract the area of the shared face from both prisms. The shared face is 20*2 = 40 sq cm. So, we need to subtract 40 sq cm from both prisms.

So, the total surface area of the figure is (80+80+32+32+160+160) + (200+200+20+20+40+40) - (40+40) = 712 sq cm.

Therefore, the surface area of the figure is 712 square centimeters.

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Answer:

160 feet³

Step-by-step explanation:

Volume of a rectangular prism = length x breadth x height

8 feet x 4 feet x 5 feet = 160 feet³

Answer:

they equal the same i used a ruler and checked the measurments.

Step-by-step explanation:

Producing rDNA involves isolating and cleaving DNA, inserting fragments into a vector, and transforming host cells. rDNA can be introduced via transformation, transfection, or viral vectors. Clinical applications include protein production, gene therapy, vaccines, and diagnostics.

Producing a recombinant DNA (rDNA) vector involves several general steps. Here are the three main steps involved in the process:

Isolation and Cleavage of DNA:

The first step is to isolate the desired DNA fragments from the source organism. This can be done using various techniques such as PCR (Polymerase Chain Reaction) or restriction enzyme digestion. Restriction enzymes are enzymes that cut DNA at specific recognition sites. By using the appropriate restriction enzymes, the desired DNA fragment and a vector DNA can be cut at specific sites. The vector is usually a plasmid, which is a small circular DNA molecule.

Insertion of DNA Fragments into the Vector:

Once the DNA fragments and vector have been cut, they are mixed together and joined through a process called ligation. DNA ligase is used to catalyze the formation of covalent bonds between the ends of the DNA fragments and the vector. This creates a recombinant DNA molecule containing the desired DNA fragment within the vector. The recombinant DNA molecule is then introduced into host cells for replication.

Transformation of Host Cells:

The recombinant DNA molecules need to be introduced into host cells to produce multiple copies of the recombinant DNA. This is typically done using a process called transformation. Host cells, such as bacteria or yeast, are treated in a way that makes them more receptive to taking up the recombinant DNA. Methods for transformation include heat shock, electroporation, or using chemical agents. Once the host cells have taken up the recombinant DNA, they can be grown in culture to produce large quantities of the desired DNA fragment.

Introduction of rDNA into Cells:

Recombinant DNA can be introduced into cells using various methods, depending on the type of cells being targeted. Some common techniques include:

Transformation: As mentioned earlier, host cells, such as bacteria or yeast, can be treated to make them receptive to taking up the recombinant DNA. This can be achieved by exposing the cells to heat shock, electroporation, or using chemical agents.

Transfection: This method is used for introducing rDNA into eukaryotic cells, including animal cells. It involves the use of techniques such as calcium phosphate precipitation, liposome-mediated transfection, or electroporation.

Viral Vectors: Certain viruses, such as retroviruses, adenoviruses, or lentiviruses, can be modified to carry the recombinant DNA. These viral vectors can then infect target cells and deliver the rDNA into the host genome.

Clinical Applications of rDNA:

Recombinant DNA technology has revolutionized biomedical research and has led to numerous clinical applications. Some important applications include:

Production of Therapeutic Proteins: rDNA technology allows for the production of large quantities of therapeutic proteins, such as insulin, growth factors, clotting factors, and monoclonal antibodies. These proteins can be used to treat various diseases, including diabetes, cancer, and genetic disorders.

Gene Therapy: rDNA vectors can be used to deliver functional copies of genes into target cells to correct genetic defects. This holds promise for the treatment of inherited diseases caused by single gene mutations, such as cystic fibrosis and muscular dystrophy.

Vaccine Development: Recombinant DNA technology has been instrumental in the development of vaccines. By expressing specific antigens from pathogens, recombinant vaccines can be created to stimulate an immune response without causing disease.

Diagnostic Tools: Recombinant DNA techniques are used to produce specific DNA or RNA probes for diagnostic purposes. These probes can detect the presence of specific genes or mutations associated with diseases, aiding in early detection and personalized medicine.

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Answer:

\(T(2,4) and U(11,13)\)

Step-by-step explanation:

Answer:

x^2(x+1)

Plz let me know if im wrong!!!

The expression sin(x) cot(x) can be simplified by expressing cot(x) in terms of sine and cosine. The simplified form of the expression sin(x) cot(x) is cos(x).

To simplify the expression sin(x) cot(x), we can rewrite cot(x) as cos(x) / sin(x) since cot(x) is the reciprocal of tan(x).

Therefore, sin(x) cot(x) becomes sin(x) * (cos(x) / sin(x)).

Canceling out sin(x) in the numerator and denominator, we get:

sin(x) * (cos(x) / sin(x)) = cos(x).

Hence, the simplified form of the expression sin(x) cot(x) is cos(x).


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Answer:

Below

Step-by-step explanation:

To complete the square, the leading x^2 coefficient needs to be = 1 , so factor out a 3 to get

y = 3 ( x^2 + 5/3x )   +3                (I assumed it was a + sign between the terms)

 Then take 1/2 of the 5/3   ( 5/6 )  , square it  (25/36) , add it to the parentheses.... then subtract the amount you added (3 * 25/36) by doing this.....  to have this :

y = 3 ( x^2 + 5/3 x + 25/36)  -   3 * 25/36   +3      then simplify to

y = 3 ( x + 5/6)^2  + 11/12               Done.

The new coordinate of A' will be (-1, -5)

And, The correct statement is,

⇒ (x, y) → (−y, x); A′ is at (- 1, -5)

What is Translation?

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Given that;

The rule of translation is 90 degree clockwise rotation.

Now,

Since, We know that;

The rule of translation 90 degree clockwise rotation is,

(x , y) = (- y, x)

Here, The coordinate of A = (- 5, 1)

So, The new coordinate of A' = (- 1, - 5)

Thus, The new coordinate of A' will be (-1, -5)

And, The correct statement is,

⇒ (x, y) → (−y, x); A′ is at (- 1, -5)

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Answer:

the shaded part is 60% of the thing

Step-by-step explanation:

3/5 = 60%

The value of y is 3 if the value of x is 4 in the linear equation with two variables.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have:

Two linear equations in two variables x and y

x + y = 7

x = 4

Plug x = 4 in the equation x + y = 7, we get:

4 + y = 7

y = 7 - 4

y = 3

Thus, the value of y is 3 if the value of x is 4 in the linear equation with two variables.

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Answer:

The value of y is 3 if the value of x is 4 in the linear equation with two variables.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have:

Two linear equations in two variables x and y

x + y = 7

x = 4

Plug x = 4 in the equation x + y = 7, we get:

4 + y = 7

y = 7 - 4

y = 3

Step-by-step explanation:

As per the mathematical operation both Jillian and Samuel are correct.

Given expression = 30+40+70,

The methodology by Jillian = added 30 and 40 and then 70

The methodology by Samuel = added 30 and 70 and then 40.

Determining the result of the given equation:

30 + 40 + 70

= 140

Reviewing the operations of both Jillian and Samuel

Jillian

He added 30 and 40 and then 70:

30 + 40 = 70

70 + 70 = 140

Samuel

He added 30 and 70 and then 40

30 + 70 = 100

100 + 40 = 140

The result of both mathematical operations is 140. Thus, it can be stated that both are correct.

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To solve the problem, define the system of equation and solve it.

The first step to do it is to find the equation of the line drawn. Find the slope using the given points (-2,0) and (2,2).

Use one of the points (-2,0) and the slope to find the equation of the line using the point slope formula:

Once found the equation of the line drawn, it is not even necessary to solve the system to answer the problem.

As both equations have the same slope, they are parallel lines, which means they will not intercept each other at any point. In other words, the system does not have a solution.

The correct answer is C. There is no solution.

We can be 90% confident that the true proportion of newborns born at a healthy weight lies between 0.653 and 0.747.

The maximal margin of error (e) at 90% confidence is 0.055. To construct a 90% confidence interval for the true proportion of interest, we can use the formula:

where the z-score for a 90% confidence level is 1.645.

The standard error can be calculated using the formula:

where n is the sample size.

Substituting the values, we get:

Therefore, we can be 90% confident that the true proportion of newborns born at a healthy weight lies between 0.653 and 0.747.

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Heron's formula makes use of s, which is described as the semi-perimeter of the triangle. Before we can use Heron's formula, let us solve first for the value of s via the equation

The lengths of the triangle are given in the problem. Just plug it in on the equation above and compute.

Now, let's move on using Heron's formula to solve the area of the triangle. We have

Therefore, the area of the triangle is 5.3 square units.