Find an integer $x$ such that $\frac{2}{3} < \frac{x}{5} < \frac{6}{7}$.

y = 7/2x represents the relation that is shown in the graph.

Here the line goes through points (0, 0), (1, 3.5), (2, 7).

This means that these points must satisfy the equation of the line.

Let us, check each equation one by one

A. y = x + 2/7

Here if we take x = 0,

y = 0 + 2/7

y = 2/7

Thus, (0,0) does not satisfy and hence, we eliminate this option.

B. y = x + 7/2

Here if x = 0

y = 7/2

Thus, again (0,0) does not satisfy and hence, we eliminate this option.

C. y = 2/7 x

Here, if x = 0

y = 0

Hence, (0,0) satisfies.

if x = 1

y = 2/7

or y = 0.28

Thus, (1, 1.35) does not satisfy and hence, we eliminate this option.

D. y = 7/2x

Here, if x = 0

y = 0

Hence, (0,0) satisfies.

if x = 1

y = 7/2

or y = 3.5

Hence, (1, 1.35) satisfies.

if x = 2

y = (7/2)(2)

y = 7

Hence, (2, 7) also satisfies.

Thus, y = 7/2x represents the relation that is shown in the graph.

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Which equation represents the relation that is shown in the graph?

Cost of Buying Comic Books. On a coordinate plane, a graph titled Cost of Buying Comic Books has number of issues on the x-axis and total cost on the y-axis. A line goes through points (0, 0), (1, 3.5), (2, 7).

y = x + 2/7

y = x + 7/2

y = 2/7 x

y = 7/2x

Answer:

you need to multiply something

Answer:

Yes

Step-by-step explanation:

Substitute:

Calculate the product or quotient:

Calculate the sum or difference:

Obtain a simplified relation:

Determine true or false: True

Answer: True

Answer:

2(x - 2) = 8

x = 6

Step-by-step explanation:

2(x - 2) = 8

2(x - 2) = 8

2x - 4 = 8

     +4   +4

-----------------

2x = 12

÷2   ÷2

----------

x = 6

I hope this helps!

Answer:

Vertex: (2,-2)

Axis of symmetry: x=2

Step-by-step explanation:

The vertex is the maximum or minimum point of a quadratic, which we can see on the graph is (2,-2).

The axis of symmetry is the line about which the graph of the parabola is symmetric, which is the line x=2.

Part A

Given

Solution

We ask to double the time i.e

Part B

Given

Solution

The half-life would be 5

A square piece of cardboard with side length of 34 inches is needed to make the box.

Let the side of the square piece of cardboard be x inches.

After cutting out 7 inch squares from each corner, the dimensions of the base of the box will be (x-14) inches by (x-14) inches, and the height of the box will be 7 inches.

The volume of the box can be expressed as:

V = (x-14\()^2\)\(\times\)7

We know that the box is to hold 2800 in3, so we can set up an equation:

(x-14\()^2\)\(\times\) 7 = 2800

Simplifying and solving for x, we get:

(x-14\()^2\) = 400

x-14 = ±20

x = 34 or x = 6

Since the cardboard cannot have a side length of less than 7+7=14 inches, the only valid solution is x=34 inches.

Therefore, a square piece of cardboard with side length of 34 inches is needed to make the box.

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Using line tangent, the approximation for f(2.1) is 3.95

Given,

The point (a, f(a)) is on the line tangent to the graph of y = f(x) at x = a, which has a slope of f'(a).

The equation be like;

y - f(a) / (x - a) = f'(a)

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

Using the provided data and a = 2, we can determine that the tangent line to the graph of y = f(x) at x = 2 has equation

y = f'(2) (x - 2) + f(2)

y = -1/2 (x - 2) + 4

To compute a "approximation of f(2.1) using the line tangent to the graph of f at x = 2," one must substitute x = 2.1 for f in the equation for the tangent line (2.1). You get 2.1 when you plug this in.

y = -1/2 (x - 2) + 4

y = -1/2 (2.1 - 2) + 4

y = -1/2 x 0.1 + 4

y = 3.95

That is,

The approximation for f(2.1) using line tangent is 3.95

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The equation of the table in slope intercept form is y = - 5 / 2x - 1

Linear equation can be represented in various form, such as standard form, point slope form and slope intercept form.

But the equation of the table below will be represented in slope intercept form.

The equation in slope intercept form can be represented as follows:

y = mx + b

where

Therefore, using (-4, 9)(-2, 4)

m = 4 - 9 / -2 + 4

m = - 5 / 2

Hence, let's find the y-intercept using (0, -1)

y = - 5 / 2x + b

-1  = - 5 / 2(0) + b

b = -1

Therefore, the equation is y = - 5 / 2x - 1

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Answer:

y = 0x + 16

Step-by-step explanation:

Slope of line m = 0

\( (6,\:16)=(x_1,\:y_1) \)

Equation of line in slope point slope form is given as:

\( y-y_1 = m(x-x_1) \\\\

\therefore y - 16 = 0(x - 6)\\\\

\therefore y - 16 = 0x - 0\\\\

\therefore y = 0x + 16\\\\\)

This is the required equation in slope intercept form.

Therefore, the integral of |cos(s)| from 0 to π is 2.

To evaluate the integral of |cos(s)| from 0 to π, we first need to split the integral into two parts because the absolute value function affects the cosine function differently in the given interval.
1. Determine the intervals: From 0 to π/2, cos(s) is positive, so |cos(s)| = cos(s). From π/2 to π, cos(s) is negative, so |cos(s)| = -cos(s).
2. Split the integral: ∫₀ᵖᶦ |cos(s)| ds = ∫₀^(π/2) cos(s) ds + ∫(π/2)ᵖᶦ -cos(s) ds.
3. Integrate both parts: ∫₀^(π/2) cos(s) ds = [sin(s)]₀^(π/2), and ∫(π/2)ᵖᶦ -cos(s) ds = [-sin(s)](π/2)ᵖᶦ.
4. Evaluate the results: [sin(s)]₀^(π/2) = sin(π/2) - sin(0) = 1, and [-sin(s)](π/2)ᵖᶦ = -sin(π) + sin(π/2) = 1.
5. Add the two results: 1 + 1 = 2.

Therefore, the integral of |cos(s)| from 0 to π is 2.

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Answer:

cos A = 7/25

Step-by-step explanation:

Since we are given a right triangle, we can use trig functions

cos A = adj side/ hypotenuse

cos A = 7/25

Answer:

\(\boxed{\sf cos\ A =\frac{7}{25}}\)

Step-by-step explanation:

We need to find out the value of cos A using the given triangle . Here we can see that the sides of the triangle are 7 , 25 and 24 .

We know that the ratio of sine is base to hypontenuse .

\(\sf\longrightarrow cos\theta =\dfrac{ base}{hypontenuse}\)

Here we can see that the side along the angle A is 7 , therefore the base of the triangle is 7. And the side opposite to 90° angle is 25 . So it's the hypontenuse . On using the ratio of sine ,

\(\sf\longrightarrow cos \ A =\dfrac{ b}{h}=\dfrac{AB}{AC}\)

Substitute the respective values ,

\(\sf\longrightarrow \boxed{\blue{\sf cos \ A =\dfrac{7}{25}}}\)

Hence the required answer is 7/25.

The radius of circle F is equal to: C. 12.

In Mathematics and Geometry, Pythagorean's theorem is modeled or represented by the following mathematical equation (formula):

a² + b² = c²

Where:

a, b, and c represents the length of sides or side lengths of any right-angled triangle.

By substituting the given side lengths into the formula for Pythagorean's theorem, we have the following;

a² + b² = c²

a² + 9² = 15²

a² = 225 - 81

a = √144

a = 12 units.

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Given:

The above series is an arithemetic series.

The first term of the series is: a=2

The second term of the series is: b=10

The common difference of the series is,

The expression to calculate the n th term of the series is,

Substitute n=13 in the above expression to calculate the 13 th term.

Thus, the 13th term of the sequence is 98.

To find the probability of a randomly chosen value between -1.341 and 2.602 for a t-distribution with 15 degrees of freedom, we need to calculate the cumulative probability using the t-distribution table or a statistical software.

The cumulative probability represents the area under the t-distribution curve between the given values.

Using a statistical software or t-distribution table, we can find the cumulative probabilities for the lower and upper values and then subtract the lower cumulative probability from the upper cumulative probability to get the desired probability.

For example, let's assume the cumulative probability for -1.341 is P1 and the cumulative probability for 2.602 is P2. Then, the desired probability is P2 - P1.

Since the exact values for P1 and P2 may not be readily available here, I'm unable to provide the specific probability without using a t-distribution table or statistical software. However, you can calculate it using appropriate tools or software by finding the cumulative probabilities for the given values.

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Best investment amounts are $2,000 in high-risk account, $1,000 in bank certificates of deposit, and $7,000 in municipal bonds and remaining $4,000 placed in municipal bonds to optimize return while lowering risk.

We must adhere to two criteria in order to find the best investment amounts: reducing risk and satisfying tax obligations.

Let's think about the high-risk account first. We will only put $2,000 in this account because that is the most we are ready to risk because we want to keep the risk to a minimum.

Let's go on to the tax regulations. We must invest at least $3,000 in municipal bonds to reach the three times minimum investment requirement in municipal bonds compared to bank CDs. We will therefore put $1,000 into bank CDs and $3,000 into municipal bonds.

We currently have $2,000 set aside for the high-risk account, $1,000 for bank CDs, and $3,000 set aside for municipal bonds. We are now left with $4,000 to invest.

This $4,000 can be invested in a way that strikes a compromise between the need to reduce risk and the desire for great returns. We have the choice of investing the final $4,000 in either municipal bonds or CDs from a nearby bank, depending on our investment alternatives.

Our total investment would be $5,000 in bank CDs, $3,000 in municipal bonds, and $2,000 in the high-risk account if we choose to invest the additional $4,000 in the local bank CDs. The expected return from this is:

($5,000 x 8%) + ($3,000 x 7%) + ($2,000 x 12%) = $400 + $210 + $240 = $850.

If we choose to invest the $4,000 in municipal bonds, our overall investment will consist of $2,000 in the high-risk account, $1,000 in bank CDs, and $7,000 in municipal bonds. The expected return from this is:

($1,000 x 8%) + ($7,000 x 7%) + ($2,000 x 12%) = $80 + $490 + $240 = $810.

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This is a contradiction, which means that there is no solution for the given equation. Therefore, the correct answer is option C, "No solution".

There is only one solution for the given equation.

5 - 3x = 4 + x + 2 - 4x

Simplifying the equation, we get:

5 - 3x = 6 - 3x

Subtracting 6 from both sides, we get:

-1 - 3x = -3x

Adding 3x to both sides, we get:

-1 = 0

A linear equation is an equation that can be written in the form y = mx + b, where y and x are variables, m is the slope, and b is the y-intercept. It represents a straight line on a graph. Linear equations can be used to model a variety of real-world situations, such as the relationship between temperature and time, or the cost of producing a certain quantity of goods.

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We can see that both sides are equal, which means that the equation has infinitely many solutions.

Therefore, the answer is: D. Infinitely many solutions is correct.

To solve for the number of solutions of 5 - 3x = 4 + x + 2 -4x,

we first simplify the equation by combining like terms:

Combine like terms on both sides of the equation:

5 - 3x = 6 - 3x

Compare the coefficients of the x terms:

-3x = -3x

Since both sides of the equation have the same coefficients for the x terms, there are infinitely many solutions.

Therefore, the answer is: D. Infinitely many solutions is correct.

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Answer:

A. area of larger rectangle: 18x^2

area of smaller rectangle: 8x^2

B. area of shaded region: 10x^2

Step-by-step explanation:

Larger rectangle: A = lw = (6x)(3x) = 18x^2

Smaller rectangle: A = lw = (4x)(2x) = 8x^2

The shaded region = larger rectangle - smaller rectangle

=> 18x^2 - 8x^2 = 10x^2

Z is 52 and the difference between the values 65 and 52 is 13.

Given,

Two numbers : 65 and Z

Greatest common factor of the above numbers = 13

Z is a positive integer.

Possible values of Z is between 30 and 60.

Now,

13 x 5 = 65

So other number must be a multiple of 13 and a number below 5.

That is, 13 x 4 = 52 and 13 x 3 = 39. These are the two numbers between 30 and 60.

Now consider the difference.

65 – 52 = 13

65 – 39 = 26

In the given options we have 13 and 26 is not given in the option.

So the value of Z is 52 and the difference between 65 and 52 is 13.

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Answer:

Use brainly. or pay better attention in class.

Step-by-step explanation:

Answer:

I speak englush

Step-by-step explanation:

I speak English

To argue why the liberal arts are so important in education and leisure, one must discuss its Greek origin and how it is received today.

The term "liberal arts" comes from the Latin word "liberalis," which means free. It was used in the Middle Ages to refer to topics that should be studied by free people. Liberal arts refers to courses of study that provide a general education rather than specialized training. It encompasses a wide range of topics, including literature, philosophy, history, language, art, and science.The liberal arts curriculum is based on the idea that a broad education is necessary for individuals to become productive members of society. In ancient Greece, education was focused on developing the mind, body, and spirit.  

The study of the liberal arts is necessary to create well-rounded individuals who can contribute to society in meaningful ways. While the importance of the liberal arts has been debated, it is clear that they are more important now than ever before. The study of the liberal arts is necessary to develop the skills that are required in a rapidly advancing technological world.

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9514 1404 393

Answer:

  126°

Step-by-step explanation:

To find the exterior angle, we need to know one of the acute angles. Those are found using the fact that they are complementary.

  (5x -6) +(3x) = 90

  8x = 96 . . . . . . . . . . . add 6, collect terms

  x = 12 . . . . . . . . . . . . . divide by 8

  3x° = 3·12° = 36° . . . . . . find the "remote" acute angle

  exterior angle = 90° +36°

  exterior angle = 126°

__

The exterior angle is the supplement of the one marked (5x-6)°. It is also the sum of the two remote interior angles, 90° and 3x°. Being lazy, we figure that 90 +3·12 is easier to compute than 180 - (5·12 -6). Either way, the exterior angle is 126°.

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:

0.45

Step-by-step explanation:

You divided 2.25 by 5

Answer:

x = 5, y = -2

Step-by-step explanation:

Given equations:

From the first equation we get:

Substitute x in the second equation, find y:

Find x:

Answer:

\(approxmatly \: = 6\)

Answer:

√ [37]

Step-by-step explanation:

I'll be calling the first point, A,

being A(-4,1) ; B(2,0)

For the distance: d(A,B) = √(xB - xA)² + (yB - yA)² ⇔

⇔ d(A,B) = √(2+4)² + (0-1)² = √6² + 1² = √36 + 1 = √37

Answer:

$23780

Step-by-step explanation:

Given data

Let the original price be x

discount= 20%

price= $19,024

so that

20/100*x=x-19,024

0.2x= x-19,024

19,024=x-0.2x

19,024=0.8x

x= 19,024/0.8

x=23780

Hence the original price is $23780

Answer:

1=5/5, 2=10/5, etc. (See if you can figure the rest out yourself)

Step-by-step explanation:

As you can see, between each whole number are four fractions, which means each of them are 1/5 of the whole number. Therefore, 1=5/5, 2=10/5, etc.