a certain positive integer has exactly 8 factors. two of these factors are 15 and 21. what is the sum of all eight factors?

Therefore, the table showing the original points and their corresponding dilated points is:

Original Point     Dilated Point

(0,1)                  (0,1/2)

(4, -3)                (2, -3/2)

(-6,1)                 (-3,1/2)

I believe you might have meant "dilated point", which is a term commonly used in geometry. A dilated point is a point that has been enlarged or reduced in size with respect to a fixed center of dilation.

To dilate a point, you need to multiply its coordinates by a scale factor, which is a constant value greater than zero. If the scale factor is greater than one, the point will be enlarged, and if it is less than one, the point will be reduced in size. The fixed center of dilation is the point about which the dilated point is enlarged or reduced.

given by the question.

To apply the dilation rule of (1/2x, 1/2y) to a given point (x,y), we need to multiply the x-coordinate and y-coordinate of the original point by 1/2.

Using this rule, we can find the dilated points for the given set of points as follows:

For the point (0,1), we have:

1/2x = 1/2 * 0 = 0

1/2y = 1/2 * 1 = 1/2

So, the dilated point is (0, 1/2).

For the point (4, -3), we have:

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

1/2y = 1/2 * (-3) = -3/2

So, the dilated point is (2, -3/2).

For the point (-6,1), we have:

1/2x = 1/2 * (-6) = -3

1/2y = 1/2 * 1 = 1/2

So, the dilated point is (-3,1).

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The area of the given shape is 22 square tiles. The given shape consists of two rectangles and a square.

To find the area of the shape, we need to find the area of each of these three shapes and then add them up.

First, we can see that the length of the longer rectangle is 6 tiles and the width is 2 tiles. Therefore, the area of this rectangle is 6 × 2 = 12 tiles.

Next, the length of the shorter rectangle is 3 tiles and the width is 2 tiles. Thus, the area of this rectangle is 3 × 2 = 6 tiles.

Finally, the square has a side length of 2 tiles, so its area is 2 × 2 = 4 tiles.

Adding up the areas of the three shapes, we get 12 + 6 + 4 = 22 tiles.

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The expense of 1.5 lbs of bananas and 1 gallon of apple juice, according to the provided statement, is $7.45.

Multiplication is one of the four basic operations in mathematics, along with adding, subtracting, and division. Multiply in mathematics refers to the continual adding of sets of identical size.

The cost of 1.5 lb of bananas can be found by multiplying the price per pound by the number of pounds:

Cost of 1.5 lb of bananas = 1.5 x $1.97 = $2.96 (rounded to the nearest cent)

The cost of 1 gallon of apple juice is $4.49.

So, the total cost of 1.5 lb of bananas and 1 gallon of apple juice is:

Total cost = Cost of bananas + Cost of apple juice

Total cost = $2.96 + $4.49

Total cost = $7.45

Therefore, the cost of 1.5 lb of bananas and 1 gallon of apple juice is $7.45.

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Answer: x is equal to 1

Step-by-step explanation:

The nurse should administer 3.5 mL of Lanoxin elixir 0.05 mg/mL to the patient to achieve the desired dose of 0.175 mg.

First, we need to convert the prescribed dose of 0.175 mg to milligrams per milliliter (mg/mL) using the concentration of the Lanoxin elixir, which is 0.05 mg/mL.

To determine how many milliliters of Lanoxin elixir 0.05 mg/mL the nurse should administer to the patient, we need to use a simple formula:

Dose = Desired dose / Stock strength

Where:

Desired dose is 0.175 mg

Stock strength is 0.05 mg/mL

So, substituting the values into the formula:

Dose = 0.175 mg / 0.05 mg/mL

Dose = 3.5 mL

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Answer:

Step-by-step explanation:

To find g(4), we substitute x = 4 into the expression for g(x):

g(4) = -3(4) - 4 = -12 - 4 = -16

To find g(4) + 8, we add 8 to the value we just found for g(4):

g(4) + 8 = -16 + 8 = -8

Therefore, g(4) + 8 = -8.

Answer: 3.9b−2.6

Step-by-step explanation: Hope this helps

Answer:

1.3b

Step-by-step explanation:

The equation is -2.6+3.9b. A negative number acts like subtraction, so we would subtract 2.6 from 3.9 to get 1.3. The b is still there, and we don't know what it is, so we simplify the equation to 1.3b.

Sorry, this explanation isn't the best. Hope it helped! :)

the %Cr in the complex is 26.294%.

To determine the % Cr in the chromium-complex Legna synthesized, she massed out a 1.0240 g sample of the Cr complex. She dissolved the sample in a volumetric flask and made 100.0 mL of solution. From the standard curve of Absorbance versus concentration Legna obtained [Cr3+]=0.03933 M. Calculate the %Cr in the complex.

To determine the % Cr in the chromium-complex synthesized by Legna, we can use the following formula:% Cr = (mass of Cr/mass of sample) x 100We have the mass of the sample, which is 1.0240 g. We need to find the mass of Cr in the sample. To do this, we need to find the number of moles of Cr in the solution, and then use the molar mass of Cr to convert this to mass.

The concentration of Cr3+ in the solution is given as 0.03933 M. We know that the complex is made up of Cr and some other ligands, and the concentration of Cr3+ is not the same as the concentration of Cr in the complex. To find the concentration of Cr in the complex, we need to use the formula:[Cr] = [Cr3+] x (1/x), where x is the number of moles of Cr3+ in the complex.

Let's assume that there is one mole of Cr3+ in the complex, then x = 1. If there are n moles of Cr3+ in the complex, then x = n. We can find x by using the formula:x = (mass of sample/Mr of Cr3+) x [Cr3+]/volume of solutionWe know that the mass of the sample is 1.0240 g, and the volume of the solution is 100.0 mL = 0.1000 L. The molar mass of Cr3+ is 52.00 g/mol. Substituting these values into the formula, we get:x = (1.0240/52.00) x 0.03933/0.1000x = 0.000761 moles of Cr3+ in the complex

Now we can use the formula [Cr] = [Cr3+] x (1/x) to find the concentration of Cr in the complex:[Cr] = 0.03933/0.000761[Cr] = 51.69 M

Finally, we can use the formula:% Cr = (mass of Cr/mass of sample) x 100The molar mass of Cr is 52.00 g/mol. The mass of Cr in the complex is 51.69 x 52.00 = 2689.88 g/mol. Substituting this value and the mass of the sample (1.0240 g) into the formula, we get:% Cr = (2689.88/1.0240) x 100% Cr = 262944.53% Cr = 26.294%

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The sum to infinity of the series 1 + 2x + 3x² + 4x³ + ... is 1/[(1-x)²] when |x| < 1.

The formula for the sum of an infinite geometric series when |x| < 1 is given as:

S = a/(1-r)

We have a = 1 and r = x/1.

S = 1/(1-x) + 2x/(1-x)² + 3x²/(1-x)³ + 4x³/(1-x)⁴ + ...

we multiply both sides of this equation by (1-x)²,

S(1-x)² = (1-x) + 2x + 3x²(1-x) + 4x³(1-x)² + ...

S(1-x)² = 1 + x + x² + x³ + ...    eqn (1)

Using the formula for the sum of an infinite geometric series when |x| < 1, we have:

1/(1-x) = 1 + x + x² + x³ + ...

Substituting this into equation (1), we get:

S(1-x)² = 1/(1-x)

S = 1/[(1-x)²]

In conclusion, the sum to infinity of the series 1 + 2x + 3x² + 4x³ + ... is 1/[(1-x)²] when |x| < 1

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The risk of owning a home in Randolph County based on the given sample can be calculated as:

Risk of owning a home = Number of residents who own a home / Total number of residents in the sample

Risk of owning a home = 59 / 90

Therefore, the risk of owning a home in Randolph County based on the given sample is approximately 0.656 or 65.6%.

Hope has 6 nickels (x) and 10 quarters (x + 4).

How many of each coin Hope has if she has 4 more quarters than nickels and they have a combined value of 280 cents. To solve this problem, we can use algebraic equations.

Let's assume the number of nickels Hope has is x. Then, the number of quarters she has would be x + 4.

Now, we need to find the total value of the coins. Each nickel is worth 5 cents, so the total value of nickels is 5x cents. Similarly, each quarter is worth 25 cents, so the total value of quarters is 25(x + 4) cents. The combined value of the coins is 280 cents, so we can set up an equation:

5x + 25(x + 4) = 280

Simplify and solve for x:

5x + 25x + 100 = 280
30x = 180
x = 6

Therefore, Hope has 6 nickels (x) and 10 quarters (x + 4).

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Answer:

Step-by-step explanation:

We know that

To now how many pounds will be in each bag, we have to divide

[tex]3 \ lb \div12 \ bags =0.25 \ lb/bag[/tex]

This means that May will have 0.25 pounds per bag, that is, a quarter pound of raisin in each bag.

If we divide this using the long method, we would have to add a zero to "3", because 3 is less than 12, so we have to transform it from "3" to "30". To be able to do that, we have to add a decimal point to the quotient, and then continue with the division.

The required medians of the triangle intersect at the point [tex]\left(4,\frac{10}{3}\right)$[/tex].

The medians of a triangle intersect at a point known as the centroid. To find the centroid of a triangle, we need to find the average of the x-coordinates and the average of the y-coordinates of its vertices.

Let the vertices of the triangle be A(0,0), B(5,0), and C(7,5). Then the midpoint of AB is

[tex]\left(\frac{0+5}{2},\frac{0+0}{2}\right) = (2.5,0)$[/tex],

the midpoint of BC is [tex]\left(\frac{5+7}{2},\frac{0+5}{2}\right) = (6,2.5)$[/tex], and the midpoint of CA is

[tex]\left(\frac{0+7}{2},\frac{0+5}{2}\right) = (3.5,2.5)$[/tex]

Therefore, the centroid of the triangle is:

[tex]$\begin{align*}\left(\frac{0+5+7}{3},\frac{0+5+5}{3}\right) &= \left(\frac{12}{3},\frac{10}{3}\right) \&= \left(4,\frac{10}{3}\right)\end{align*}[/tex]

So the medians of the triangle intersect at the point [tex]\left(4,\frac{10}{3}\right)$[/tex].

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A group of observations measured at successive time intervals is known as a(n) time series. So, correct option is C.

A time series is a collection of observations or measurements that are taken at regular intervals over time. These observations can be of any variable that changes over time, such as stock prices, weather patterns, or population growth. Time series analysis is a statistical technique used to understand and interpret the patterns and trends in such data.

The data in a time series can be analyzed to identify trends, seasonal variations, and other patterns that may exist over time. These patterns can be used to develop forecasts and make predictions about future values of the variable being measured.

On the other hand, an additive time series model is a specific type of model used to analyze time series data. It involves decomposing a time series into its underlying components, such as trend, seasonality, and random fluctuations, and modeling each component separately.

This approach can help to improve the accuracy of forecasts and predictions based on the time series data.

In summary, a time series is a collection of observations measured at successive time intervals, while an additive time series model is a specific type of statistical model used to analyze and forecast time series data.

Therefore, Option C is correct answer.

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We know that the temperature was 56°F at midnight, so we can plot the point (24, 56)

What is graph ?

Graph can be defined as visual representation of given data using the ordered pairs.

To graph Elroy's data, we can use the x-axis to represent the time of day in hours and the y-axis to represent the temperature in degrees Fahrenheit.

First, we can plot the point (6, 50) to represent the temperature at 6am.

Next, we can use the information that the temperature rose 3° per hour for the next 4 hours. This means that at 10am, the temperature would be 50 + 3(4) = 62°F. We can plot this point at (10, 62). Similarly, we can find the temperature at 7am, 8am, and 9am using the same formula and plot those points as well.

Then, we can use the information that the temperature rose 2° per hour for the next 6 hours. This means that at 4pm, the temperature would be 62 + 2(6) = 74°F. We can plot this point at (16, 74). Similarly, we can find the temperature at 11am, 12pm, 1pm, 2pm, and 3pm using the same formula and plot those points as well.

The temperature then stayed steady until 6pm, so we can draw a horizontal line at y = 74 from 4pm to 6pm.

For the next 2 hours, the temperature dropped 1° per hour. This means that at 8pm, the temperature would be 74 - 2 = 72°F. We can plot this point at (20, 72). Similarly, we can find the temperature at 7pm using the same formula and plot that point as well.

Therefore,  we know that the temperature was 56°F at midnight, so we can plot the point (24, 56).

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Answer:

4,320

Step-by-step explanation:

answer is 4,320

9x2x3x8x2x5

Answer:

66 km²

Step-by-step explanation:

To solve this, you should find the area of the rectangle as if it were complete and then subtract the area of the missing section.

Step one: Finding the area of the big rectangle

A =  length x width

A = 9 x 8

A = 72 km²

Step two: Find the area of the smaller rectangle

A = 2 x 3 = 6 km²

Step three: Subtract the area of the small rectangle from the area of the big rectangle

72 - 6 = 66

In Circuit B, the ammeter is connected in series with resistor R1 and the voltmeter is connected in parallel with resistor R2.

Therefore, the circuit is correctly setup to measure the desired quantities.

The correct circuit for measuring the current through resistor R1 and the potential difference across R2 is Circuit B. Circuit B is formatted with an ammeter measuring the current through R1 and a voltmeter measuring the potential difference across R2.

An ammeter is used to measure current and should be connected in series with the component it is measuring; whereas a voltmeter is used to measure potential difference and should be connected in parallel with the component it is measuring.

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There are 25 feet in 300.0 inches.

Conversion is a numerical quantity that enables you to convert one unit to another. There are various units for measurements such as length, weight, mass, and so on.

The conversion factor between inches and feet is important to understand when performing this type of calculation. As I mentioned earlier, there are 12 inches in one foot, which can be expressed as:

1 foot = 12 inches

This means that to convert a measurement in inches to feet, we need to divide the number of inches by 12.

300.0/12 = 25

Therefore, 300.0 inches is equivalent to 25 feet.

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Answer:

Step-by-step explanation:

To find the percentage of the original amount that Dylan has remaining on his gift card, we can divide the remaining amount by the original amount and then multiply by 100 to express it as a percentage.

The original amount on the gift card was $20.00, and the remaining amount is $0.06, so the percentage of the original amount that Dylan has remaining on his gift card is:

($0.06 ÷ $20.00) x 100% =

0.003 x 100% =

0.3%

Therefore, Dylan has 0.3% of the original amount remaining on his gift card.

answer: 10

step by step explanation:

this is not a textbook way but

4:5 means 4/5 and we know that the numbers will be equal to this number so we can multiply the number 4/5*2/2 so we will get 8/10

8/10=4/5

and 8*10=80

so 1st no. is 8 and 2nd is 10

10>8

Answer:

greater number is 10

Step-by-step explanation:

the ratio of the 2 numbers = 4 : 5 = 4x : 5x ( x is a multiplier )

their product is 80 , that is

4x × 5x = 80

20x² = 80 ( divide both sides by 20 )

x² = 4 ( take square root of both sides )

x = [tex]\sqrt{4}[/tex] = 2

then greater number = 5x = 5 × 2 = 10

The probability that a student chosen randomly from the class is an only child is 0.23 or 23%.

What is the probability?

To find the probability that a student chosen randomly from the class is an only child, we need to add up the number of students who do not have a brother and do not have a sister, and then divide by the total number of students in the class.

From the table, we can see that there are 6 students who do not have a sister and do not have a brother. Therefore, the probability that a student chosen randomly from the class is an only child is:

P(only child) = number of only children / total number of students

= 6 / (2 + 13 + 5 + 6)

= 6 / 26

= 0.23 (rounded to two decimal places)

Therefore, the probability that a student chosen randomly from the class is an only child is 0.23 or 23%.

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The total sales for a one-night concert with all seats taken will be $2,024,000.

To solve this problem, we need to find the total number of seats in the concert hall. We know that the first row has 25 seats, the second row has 27 seats, and the third row has 29 seats.

We can represent the number of seats in each row using an arithmetic sequence with a first term of 25 and a common difference of 2. The nth term of this sequence can be found using the formula:

a_n = a_1 + (n - 1)d

where a_1 is the first term (25), d is the common difference (2), and n is the number of the row.

Using this formula, we can find the number of seats in the 20th row

a_20 = 25 + (20 - 1)2

a_20 = 25 + 38

a_20 = 63

Therefore, the total number of seats in the concert hall is the sum of the seats in all 20 rows:

total seats = 25 + 27 + 29 + ... + 63

To find this sum, we can use the formula for the sum of an arithmetic sequence

S_n = (n/2)(a_1 + a_n)

where S_n is the sum of the first n terms of the sequence. In this case, n = 20, a_1 = 25, and a_n = 63.

S_20 = (20/2)(25 + 63)

S_20 = 10(88)

S_20 = 880

Therefore, there are a total of 880 seats in the concert hall. If all seats are taken, the total sales for the one-night concert will be

total sales = number of seats x price per ticket

total sales = 880 x $2,300

total sales = $2,024,000

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Equations are collections of two or more statements with equal signs.

I must locate the solution that the hanger diagram matches. [tex]3x=4[/tex] is the equation that fits the hanger diagram. Thus, option C is correct.

The hanger shows a total weight of 7 units on one side that is balanced with 3 equal, unknown weights and a 1-unit weight on the other.

Two or more expressions containing equal signs are called equations. I need to find the equation that corresponds to the hanger diagram. The hanger model is a visual representation of the equation.

Both sides must have the same weight to keep the hanger balanced. Like scales and barbells. There are 3 x on the left side of the hanger and 4 x on the right side.

So [tex]3x=4[/tex]  is an equation that satisfies the given trailer diagram.

So option C is correct.   [tex]3x=4[/tex] is the equation that fits the hanger diagram.

From the diagram we have,

Left=x+x+x

Right [tex]=1+1+1+1[/tex]

This gives

Left=[tex]3x[/tex]

Right [tex]=4[/tex]

Therefore, the equation [tex]3x =4[/tex]

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Answer: 81 ham subs

Step-by-step explanation:

4 times 9 is 36. That means you have to multiply 9 by 9, to get 81 ham subs. The ratio is 81:36. :)

The statement "A global firm is a firm that operates in more than one country and captures R&D, production, logistical, marketing, and financial advantages not available to purely domestic competitors." is the correct .

Therefore option C is correct.

What is a global firm?

A global firm is a company that operates in more than one country and has access to research and development, production, logistical, marketing, and financial advantages that are not available to purely domestic rivals.

Global companies have expanded beyond their home country's boundaries to capitalize on the advantages of global sourcing and production.

Global companies have a variety of advantages that pure domestic companies do not have.

The following are some of the benefits of global businesses:

In conclusion, a global firm is a firm that operates in more than one country and captures R&D, production, logistical, marketing, and financial advantages not available to purely domestic competitors.

Therefore option C is correct.

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The answer of the given question based on the greatest value is One such number is 3,043,728.

A number system is a system of representing and expressing numbers in a clear, concise, and organized way. The most commonly used number system is the decimal system, which is based on the numbers 0 through 9. However, there are many other number systems, including binary, octal, hexadecimal, and more.

Each number system has a set of rules and conventions for representing numbers. For example, in the decimal system, each digit can represent a value from 0 to 9, and the position of each digit determines its value.

The digit 3 in 143,728 has a value of 3 x 1000 = 3000. To find a number in which the digit 3 has a value that is 10 times as great as this, we need to find a number in which the digit 3 has a value of 10 x 3000 = 30,000.

One such number is 3,043,728. In this number, the digit 3 appears in the hundred thousands place, which means its value is 3 x 100,000 = 300,000. This is indeed 10 times as great as the value of the digit 3 in 143,728.

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The number 137 has the same relationship to the number 143 as the numbers 398,389,392, which have a digit 3 that is 10 times greater than the number 137.

A number's face value is the digit itself, while its place value is determined by its placement.

In order to answer the question, we must determine which of the following integers has a value for the digit 3 that is 10 times greater:

If we pay close attention, we can see that the number 137 has a third digit in its tens place while the number 143 has a third digit in its unit place. Additionally, there are 398,389,392, which has a digit 3 and is ten times bigger than the number 137.

These numbers will be written as follows if we now express their location and value in words:

143 = 1 × 100 + 4 × 10 + 3 × 1.

137 = 1 × 100 + 3 × 10 + 7 × 1.

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The complete question is:

In which number does the digit 3 have a value that is 10 times as great as the value of the digit 3 in 143,728? 137,982 142,398 292,389 392,097.

There can be any angles  like vertical, linear pair, supplemenatry which can be shown in the following figure.

(a) One pair of vertical angles:

Vertical angles are formed by the intersection of two lines. They are opposite to each other and are congruent. For example, in the following diagram, ∠1 and ∠6 are a pair of vertical angles, and ∠3 and ∠8 are another pair of vertical angles.

b) one pair of angles that form a linear pair:

A linear pair is formed by  pair of adjacent angles whose non-adjacent sides form a line.

In the figure the linear pair will be ∠4 and ∠8.Beacause they are adjacent angles whose non adjacent sides form a line.

c)one pair of angles that are supplementary:

Two are said to be supplementary if they add up to be 180 degrees.

So in the figure ∠4 and ∠8 can be supplementary and also ∠1 and ∠5 can be supplementary.

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On his journey to his room, Eugene first found a few pieces of paper before discovering three more. Let's assume that he began with x bits of paper. Eugene started with  [tex]3[/tex] pieces of paper.

Eugene started with some pieces of paper, and then he found 3 more on his way to his room. So, let's say he started with x pieces of paper.

After finding the 3 more pieces, he had a total of   [tex]x + 3[/tex] pieces of paper.

He then cut each piece of paper in half, which means he doubled the number of pieces of paper. So, he ended up with  [tex]2 \times (x + 3) = 2x + 6[/tex]  half-pieces of paper.

We're given that he had 12 half-pieces of paper in the end, so we can set up the equation:

[tex]2x + 6 = 12[/tex]

Solving for x, we get:

[tex]2x = 6[/tex]

[tex]x = 3[/tex]

Therefore, Eugene started with 3 pieces of paper.

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