Given the rule what is the new coordinate? Show all of your work.
Rule: (x, y) → (x - 7.5, y + 6.8)
Original coordinate: (5, 3)

Answer:

C and D give rational numbers, as the square root of 49 is ±7 and the square root of 100 is ±10.

Answer:

y = 4x

Step-by-step explanation:

formula is y=kx, where k is factor of proportionality

Looking at the graph where y and x meet...

2/0.5 = 4 so 2 = 4(0.5)

Therefore, 4 is k (constant)

4=4(1)

6=4(1.5)

10=4(2.5)

and so on...

Answer:

In explanation below.

Step-by-step explanation:

Presumably, the proof you have in mind is to use a=b=2–√a=b=2 if 2–√2√22 is rational, and otherwise use a=2–√2√a=22 and b=2–√b=2. The non-constructivity here is that, unless you know some deeper number theory than just irrationality of 2–√2, you won't know which of the two cases in the proof actually occurs, so you won't be able to give aa explicitly, say by writing a decimal approximation.

Answer: 45 divided by 3 equals 15

he has 15 dollars

Step-by-step explanation: 45= 3 times 15

Answer: 45=3a   a=15

Step-by-step explanation:

We know that Molly has $45 or 3 times the amount of money her brother has, and a represents the amount of money her brother has. So we would multiply a by 3. In order to find a we just divide 45 by 3.

Looking up the z-value in a standard normal distribution table, we find the p-value to be 0.1473. Since this is greater than the common significance level of 0.05, we fail to reject the null hypothesis. Therefore, the answer to the given question cannot be determined as we do not know what we need to estimate the difference between.

The question seems to be incomplete as it does not mention what we need to estimate the difference between. However, based on the given information, we can calculate the sample proportions for both populations. The sample proportion for population 1 is 35/70 = 0.5, and the sample proportion for population 2 is 35/100 = 0.35.
Assuming we want to estimate the difference between the population proportions, we can use the two-sample z-test. The null hypothesis would be that the difference between the population proportions is 0, while the alternative hypothesis would be that the difference is not 0.
Using the formula for the test statistic, we can calculate the z-value as follows:
z = (p1 - p2) / sqrt(p(1-p)(1/n1 + 1/n2))
where p is the pooled sample proportion, calculated as (x1 + x2) / (n1 + n2) = 70/170 = 0.4118.
Substituting the values, we get:
z = (0.5 - 0.35) / sqrt(0.4118*(1-0.4118)*(1/70 + 1/100)) = 1.449

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Answer:

maximum : \( ϵ -29 \) a number infinitesimally larger than -29, or -28 if you prefer integers

minimum : \( -\infin \)

negative infinity

Explanation:

if t + 31 < 2

than t + 31 - 31 < 2 - 31

t < -29

\( -\infin < t \:< - 29\)

any number less than -29

ϵ just means infinitesimal small quantity denoted as \( \pm \frac{1}{\infin} \)

Answer:

6mm

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

You would make 1/4 into 4/1 and then you would multiply 1/2 by 4/1 to get 4/2 which is equal to 2

1/2 * 4/1 = 4/2 = 2

1 * 4 = 4

2 * 1 = 2

Ratio compares two things. The length of the trail, in reality, is 6.75 km.

A scaling ratio helps us to compare two things.

Given to us

The scale on the map states that 2 centimeters represent 3 kilometers.

Length of the trail on the map, L = 4.5 cm = 0.045 m

As we know that 2 centimeters represent 3 kilometers. therefore,

\(\rm \dfrac{Map}{Real} = \dfrac{0.02\ m}{3000\ m}\)

We know that the Length of the trail on the map is 0.045 m,

\(\rm \dfrac{L}{L'} = \dfrac{0.02\ m}{3000\ m}\)

Substitute the value,

\(\rm \dfrac{0.045}{L'} = \dfrac{0.02\ m}{3000\ m}\\\\L' = 6750\ m\\\\L' = 6.750\ km\)

Hence, the length of the trail, in reality, is 6.75 km.

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The ordered pairs for the given equation are (0, 4), (1, 11/3), (2, 10/3), (3, 3) and (4, 8/3).

The given equation is y = - 1/3 x + 4.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Put x=0, 1, 2, 3, 4, 5,....in the given equation, that is

When x=0, y=4

When x=1, y=-1/3 +4

= 11/3

When x=2, y=-2/3 +4

= 10/3

When x=3, y=-1+4

=3

When x=4, y=-4/3 +4

= 8/3

So, ordered pairs are (0, 4), (1, 11/3), (2, 10/3), (3, 3) and (4, 8/3).

Therefore, the ordered pairs for the given equation are (0, 4), (1, 11/3), (2, 10/3), (3, 3) and (4, 8/3).

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Answer:

8000000 grams

Step-by-step explanation:

8,000kg=8,000,000kg

Answer:

6 hours

Step-by-step explanation:

m= money in dollars earned

h= number of hours worked

you would replace m with the 51 since that is how much he earned in dollars and then solve the equations as such

51= 6h+15 (subtract 15 from both sides)

36=6h (then divide both sides by 6)

6=h

Answer:

a. The expression for the area of the gym is 15·x

b. The expression for the area of the cafeteria is 15·x + 45

c. The expression for the total area of the gym and the cafeteria is 30·x + 45

d. The expression for the total perimeter of the gym and the cafeteria is 36 + 4·x

Step-by-step explanation:

The parameters of the given figures are;

The width of the figure, w = 15

The breadth of the gym, \(b_{gym}\) = x

The breadth of the cafeteria, \(b_{cafeteria}\) = x + 3

The shape of the area of the gym = A rectangle

The shape of the area of the cafeteria = A rectangle

a. The expression for the area, 'A₁', of the gym is given by the area of a rectangle which is Width × Breadth

The area of the gym, A₁ = The width of the figure × The breadth of the gym

Therefore, we have; The area of the gym, A₁ = w × \(b_{gym}\)

A₁ = 15 × x

The area of the gym, A₁ = 15·x

b. The area of the cafeteria, A₂ = The width of the figure × The breadth of the cafeteria

The area of the cafeteria, A₂ = w × \(b_{cafeteria}\)

∴ A₂ = 15 × (x + 3) = 15·x + 45

The expression for the area of the cafeteria, A₂ = 15·x + 45

c. The expression for the total area of the gym and the cafeteria, 'A', is given as follows;

A = A₁ + A₂

∴ A = 15·x + 15·x + 45 = 30·x + 45

The expression for the total area of the gym and the cafeteria = 30·x + 45

d. The expression for the total perimeter of the gym and the cafeteria, 'P', is given as follows;

P = The perimeter of the rectangular area of the gym plus the area of the cafeteria

∴ P = 2 × 15 + 2 × (x + x + 3)

P = 30 + 4·x + 6

P = 36 + 4·x

The expression for the total perimeter of the gym and the cafeteria P = 36 + 4·x.

When a store advertises sales on different combinations of goods, they are engaging in price discrimination. In this case, the holiday store is practicing second-degree price discrimination because it has different prices for different quantities of bows and wrapping paper.

According to the signs in the store, there are two different deals on bows and rolls of wrapping paper. One sign says that one bow and one roll of wrapping paper can be purchased for $6.00. This means that the store is offering a bundle deal that gives a discount if you purchase both items together. The second sign offers five bows and one roll of wrapping paper for $10.00.

This means that the store is offering an even larger discount for customers who purchase a larger quantity of bows.The fact that the store is offering different prices based on the quantity of goods purchased is an example of price discrimination. Specifically, the store is practicing second-degree price discrimination because it is offering different prices for different quantities of goods.

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The solution set for the equation log(x + 2) + log(x + 3) = 1 is {x = -4, x = 1}.To solve the equation algebraically, let's go through the steps:

Start with the given equation: log(x + 2) + log(x + 3) = 1. Combine the logarithm terms using the logarithmic property: log(a) + log(b) = log(ab). Applying this property, the equation becomes: log((x + 2)(x + 3)) = 1. Rewrite the equation in exponential form: 10^1 = (x + 2)(x + 3). Simplifying, we have: 10 = (x + 2)(x + 3). Expand the right side of the equation: 10 = x^2 + 5x + 6.

Rearrange the equation to form a quadratic equation: x^2 + 5x + 6 - 10 = 0. Simplifying, we get: x^2 + 5x - 4 = 0. Solve the quadratic equation using factoring or the quadratic formula. By factoring, we can rewrite the equation as: (x + 4)(x - 1) = 0. Setting each factor to zero, we have: x + 4 = 0 or x - 1 = 0. Solving these linear equations: For x + 4 = 0, we get: x = -4. For x - 1 = 0, we get: x = 1. Therefore, the solution set for the equation is: {x = -4, x = 1}. To summarize, the solution set for the equation log(x + 2) + log(x + 3) = 1 is {x = -4, x = 1}.

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The solution to the system of equation {x + y = 1, 3x - y = 7 } using augmented matrices is ( 2,-1 ).

Given the system of equation in the question;

x + y = 1

3x - y = 7

First, we write the system of equation in matrix form.

\(\left[\begin{array}{ccc}1&1&1\\3&-1&7\\\end{array}\right]\)

Next, we find the reduced row echelon form

Row operation R₂ = R₂ - 3R₁ to make the entry at 2, 1 a 0.

\(\left[\begin{array}{ccc}1&1&1\\3-3*1&-1-3*1&7-3*1\\\end{array}\right] \\\\\left[\begin{array}{ccc}1&1&1\\0&-1\4&4\\\end{array}\right]\)

Next, multiply each element of R₂ by -1/4 to make the entry at 2, 2 a 1.

\(\left[\begin{array}{ccc}1&1&1\\-\frac{1}{4}*0 &-\frac{1}{4}*-4 &-\frac{1}{4}*4 \\\end{array}\right] \\\\\left[\begin{array}{ccc}1&1&1\\0&1&-1\\\end{array}\right]\)

Now, perform the operation, R₁ = R₁ - R₂, to make the entry at 1,2 a 0.

\(\left[\begin{array}{ccc}1-0&1-1&1+1\\0&1&-1\\\end{array}\right] \\\\\left[\begin{array}{ccc}1&0&2\\0&1&-1\\\end{array}\right]\)

Using the result from the matrix, x = 2 and y = -1.

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Answer:

im sorry i need points

Step-by-step explanation:

Answer: z=5

Step-by-step explanation:

The range of horn lengths for the middle 95% of Texas Longhorn cattle is (51 inches, 69 inches)

What is a normal distribution?

A continuous probability distribution for a real-valued random variable is called a normal distribution or a Gaussian distribution.

Here, we have

Given:

Horn lengths of texas longhorn cattle are normally distributed

The mean horn spread:  μ = 60 inches

With a standard deviation:  σ = 4.5 inches

According to the normal distribution, the range for the middle 95% of the values is: (μ  - 2σ,  μ + 2σ)

Replacing the given values:

(60 inches  - 2(4.5 inches), 60 inches + 2(4.5 inches))

(60 inches  - 9 inches, 60 inches + 9 inches)

(51 inches, 69 inches)

Hence, the range of horn lengths for the middle 95% of Texas Longhorn cattle is (51 inches, 69 inches)

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Based on the information presented, the ratio represents 8th-grade baseball players to total athletes.

A ratio is a mathematical expression that shows the proportion or the number of a specific element in a category compared to the number of another element in the same category. For example, if you count the animals on a farm the ratio of cows to chickens can be 5:7, which means that for every 5 cows there are 7 chickens.

5 : This is the number of baseball players who are in 8th-grade

73: This is the total of players. You get this number if you add all the numbers given.

Based on this, this ratio is comparing the number of baseball players and total players, which means the meaning of this ratio is " the ratio of 8th grade baseball players to total athletes".

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Answer:

x = -8

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I

I

I

I

That is the correct answer

Answer:

They travel 5/18 in one hour

Step-by-step explanation:

Answer:

In an hour the car can cover 5/18 of the distance

Answer:

To convert 2 Bigha into Kattha:

If 1 Bigha = 20 Kattha:

2 Bigha = 2 * 20 Kattha = 40 Kattha

If 1 Bigha = 16 Kattha:

2 Bigha = 2 * 16 Kattha = 32 Kattha

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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Rounding to three decimal places, the critical value is ±2.109.

The critical value for a 95% confidence interval, we need to look up the t-distribution with degrees of freedom given by:

df = [(s1²/n1 + s2²/n2)²] / [((s1²/n1)²/(n1-1)) + ((s2²/n2)²/(n2-1))]

s1 and s2 are the sample standard deviations, n1 and n2 are the sample sizes.

Plugging in the values given in the problem:

df = [((24.75)²/19 + (26.75)²/11)²] / [(((24.75)²/19)²/18) + (((26.75)²/11)²/10)]

≈ 17.517

Using a t-distribution table or a calculator, we can find the critical value for a 95% confidence interval with 17 degrees of freedom:

\(t_c\) = ±2.109We must get the crucial value for a 95% confidence interval using the degrees of freedom provided by the following t-distribution:

(S12/n1 + S22/n2)2 = df ((s22/n2)2/(n2-1)) + ((s12/n1)2/(n1-1))))

The sample standard deviations are s1 and s2, and the sample sizes are n1 and n2.

Inserting the values from the problem:

df = [((24.75)²/19 + (26.75)²/11)²] / [(((24.75)²/19)²/18) + (((26.75)²/11)²/10)]

≈ 17.517

We may get the crucial value for a 95% confidence interval with 17 degrees of freedom using a t-distribution table or a calculator:

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Answer: Option 4 - 1440

Step-by-step explanation:

2 Square Sides : Take 12 times 12 and times by two for both sides.

12 x 12 = 144     144 x 2 = 288

4 rectangular sides : The multiplication of 12 times 24

12 x 24 = 288    288 x 4 = 1152

Added All Together : 288 + 1152 = 1440

The answer closest to the number of ways of tiling the rectangle with the given tiles would be 20.000, which is option E, 100.000

We are to determine the number of ways of tiling a 4 x 14 rectangle with 1 x 3 tiles.

We know that each tile measures 1 by 3, therefore we can visualize a 4 x 14 rectangle as containing 4*14 = 56 squares of 1 by 1. Now, each 1 x 3 tile will cover three squares, so the total number of tiles will be 56/3 = 18.666 (recurring).The number of ways to arrange 18.666 tiles is not a whole number. However, since the answer choices are all integers, we must choose the closest one.

Thus, the answer closest to the number of ways of tiling the rectangle with the given tiles is 20.000, which is option E, 100.000.

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Being a listed company on the Jamaica Stock Exchange has three consequences for Derrimon Trading Limited. Firstly, it provides access to additional capital for expansion and growth. Secondly, it increases transparency and accountability to shareholders and the general public. Lastly, it enhances the company's reputation and credibility in the market.

A. Consequences of Derrimon Trading Limited being a listed company on the Jamaica Stock Exchange:

B. Reasons that could have motivated Derrimon Trading Company to list on the exchange:

It's important to note that these are hypothetical reasons and the actual motivations for Derrimon Trading Limited's listing may vary based on their specific circumstances and strategic objectives.

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