how many litres of a 12 litre concoction containing wine and spirit in the ratio of 2 : 3 be replacedwith pure wine so that the resultant concoction contains wine and spirit in equal proportion?

The second loan option would allow Clarissa to pay the least amount of interest since it has a lower interest rate and a shorter repayment term.

What is simple interest?

Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.

The loan option that would allow Clarissa to pay the least amount of interest would be the one with the lowest interest rate and the shortest repayment term.

If we assume that Clarissa has the option of choosing between two loans, we can compare their interest rates and repayment terms to determine which one would be better for her.

Let's say the first loan has an interest rate of 5% and a repayment term of 5 years, while the second loan has an interest rate of 4% and a repayment term of 4 years.

Using a loan calculator or a financial formula, we can calculate the total amount of interest that Clarissa would pay for each loan. For the first loan, the total interest paid would be:

Total interest = (Loan amount) x (Interest rate) x (Repayment term)

Total interest = 42,500 x 0.05 x 5

Total interest = 10,625

For the second loan, the total interest paid would be:

Total interest = (Loan amount) x (Interest rate) x (Repayment term)

Total interest = 42,500 x 0.04 x 4

Total interest = 6,800

Therefore, the second loan option would allow Clarissa to pay the least amount of interest since it has a lower interest rate and a shorter repayment term.

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Complete Question:

The center of the circle is (-3, -1). The new center of the new circle is (-3, -5). The new equation of the circle is:

(x -3)² + (y - 5)² = 10².

With a circle's center and radius, one may mathematically describe a circle using the equation of a circle. A circle's equation is distinct from the formulae used to determine a circle's area or circumference. Many circles-related coordinate geometry issues employ this equation. We require the circle's equation in order to represent a circle on the Cartesian plane. If we are aware of the radius's length and the circle's centre, we can draw a circle on a sheet of paper. The same is true for drawing circles on a Cartesian plane if we are aware of the center's and radius's coordinates.

The general equation of the circle is given as:

(x - h)² + (y - k)² = r²

Where, h and k are the coordinates of the center.

The given equation is (x -3)² + (y - 1)² = 10²

The center is (-3, -1).

Given that, the circle is shifted 4 up.

The y-coordinate is:

y - (1 + 4) = y - 5

Thus, the new equation of the circle is:

(x -3)² + (y - 5)² = 10²

The new center of the new circle is (-3, -5).

Hence, the center of the circle is (-3, -1). The new center of the new circle is (-3, -5). The new equation of the circle is:

(x -3)² + (y - 5)² = 10²

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The value of x in the equation (x - m)/ (n + m) = (x - n)/ (n - m) when solved is x = n²/m.

A list of the elements that make up an equation includes coefficients, variables, operators, constants, terms, and the equal to sign. An equation must always begin with the "=" sign and have terms on both sides. Each party should be treated equally.

Each side of an equation does not need to have a lot of terms, operators, and variables. Each equation with variables is an algebraic equation.

In the question, equation given:

(x - m)/ (n + m) = (x - n)/ (n - m)

Apply cross multiplication:

⇒ (x - m) (n - m) = (n + m) (x - n)

After opening the brackets, we have:

⇒ xn - xm - mn + n² = xn + xm - n² - mn

Evaluating the like terms in the equation we get:

⇒ 2xm = 2n²

So, we have

⇒ xm = n²

Divide by m on both sides:

x = n²/m

Therefore, the solution of the equation is x = n²/m.

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The calculated value of the price per quart of the laundry detergent is $1.25.

To find the price per quart of the laundry detergent, we need to first convert the volume of the container from gallons to quarts.

Since 1 gallon is equal to 4 quarts,

5 gallons will be equal to 20 quarts.

Next, we can calculate the price per quart by dividing the total cost of the container by the total volume in quarts.

Price per quart = Total cost of container / Total volume in quarts

Price per quart = $25 / 20 quarts

Price per quart = $1.25

Therefore, the price per quart of the laundry detergent is $1.25.

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Answer:

x>5

Step-by-step explanation:

11x+2> 57

11x>55

x>5

Answer:

x>5

Step-by-step explanation:

11x + 2 > 57

      -2     -2

11x > 55

divide both sides by 11, the 11's cancel and

x > 5

y = 26.4

Given: 3y + 7y - 84 = 180

First, we should combine any value that is similar.

3y + 7y - 84 = 180

10y - 84 = 180

Next, we will substitute.

10y - 84 + 84 = 180 = 84

10y = 264

Now we will divide by the value before the variable.

[tex]\frac{10y = 264}{ 10}[/tex] = y = 26. 4

Lastly, we will plug in the values.

3(26.4) + 7(26.4)- 84 = 180

76.2 + 184.8 - 84 = 180

264 - 84 = 180

180 = 180 ✓

The surface area of the given cuboid is 228 cm².

What is surface area of a cuboid?

The surface area of a cuboid is a measure of the total area of its six faces. It is an important concept in geometry and is used in many real-life applications. For example, when calculating the amount of paint needed to cover the walls of a room, you would need to know the surface area of the walls. Similarly, when designing packaging for a product, you would need to know the surface area of the box to determine the amount of material required to make it.

To find the surface area of a cuboid, you need to add up the areas of all six faces.

Given the dimensions of the cuboid as,

Length = 9 cm

Breadth = 4 cm

Height = 6 cm

The surface area of the cuboid can be calculated as follows,

Area of the top face = length × breadth = 9 cm × 4 cm = 36 cm²

Area of the bottom face = length × breadth = 9 cm × 4 cm = 36 cm²

Area of the front face = breadth × height = 4 cm × 6 cm = 24 cm²

Area of the back face = breadth × height = 4 cm × 6 cm = 24 cm²

Area of the left side face = length × height = 9 cm × 6 cm = 54 cm²

Area of the right side face = length × height = 9 cm × 6 cm = 54 cm²

Therefore, the total surface area of the cuboid is the sum of all six faces, which is:

Surface Area = 2 × (length × breadth + breadth × height + length × height)

Surface Area = 2 × (9 cm × 4 cm + 4 cm × 6 cm + 9 cm × 6 cm)

Surface Area = 2 × (36 cm² + 24 cm² + 54 cm²)

Surface Area = 2 × 114 cm²

Surface Area = 228 cm²

Therefore, the surface area of the given cuboid is 228 cm².

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Answer:

Step-by-step explanation:

It's 1/(-x-1) my guy. To find the reciprocal of anything, you put that whole thing as a denominator with 1 as the numerator.

Hope this helps *fire emoji*

The position of the diver in relation to the surface of the water 8 minutes after beginning to rise can be calculated as follows:

The diver was at a depth of 80 feet below the surface initially. After 8 minutes of rising, the diver has come up to the surface by 3 x 8 = 24 feet. So, the diver's position in relation to the surface of the water is:

80 - 24 = 56 feet below the surface.

Therefore, the integer that describes the position of the diver in relation to the surface of the water 8 minutes after beginning to rise is A. -56.

Using multiplication principle of counting, Argyle can make 140 different outfits.

Argyle has 10 T-shirts and 7 pairs of shorts, which he can wear with either sandals or sneakers. To find out how many different outfits he can make, we can use the multiplication principle of counting, which states that the total number of outcomes for a sequence of events is the product of the number of outcomes for each event.

First, we need to determine the number of ways Argyle can choose a T-shirt and a pair of shorts. He can choose one of 10 T-shirts and one of 7 pairs of shorts, giving us:

10 x 7 = 70

Next, we need to determine the number of ways Argyle can choose shoes. For each outfit, he can choose either sandals or sneakers, giving us:

shoes = 2

Finally, we can find the total number of different outfits by multiplying the number of ways to choose a T-shirt and shorts by the number of ways to choose shoes:

70 x 2 = 140

Therefore, Argyle can make 140 different outfits if all the colors and patterns coordinate.

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After answering the provided question, we can conclude that Therefore, the solutions for the equation are b ≈ -1.973 and b ≈ 1.973.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the value "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

Starting with the given equation:

[tex]2b^4 - 13 = 73\\2b^4 = 86\\b^4 = 43\\b = (43)^(1/4)\\b =1.973\\b = -1.973, 1.973\\[/tex]

Therefore, the solutions for the equation are b ≈ -1.973 and b ≈ 1.973.

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Answer: To make one bracelet, Maura needs 25 beads and 20 centimeters of elastic cord.

If Maura bought a pack of 1,000 beads, she can make:

1,000 beads ÷ 25 beads per bracelet = 40 bracelets

To make 40 bracelets, she will need:

40 bracelets × 20 centimeters of elastic cord per bracelet = 800 centimeters of elastic cord

To convert centimeters to meters, we divide by 100:

800 centimeters ÷ 100 centimeters per meter = 8 meters

Therefore, Maura should buy 8 meters of elastic cord to make 40 bracelets with a pack of 1,000 beads.

Step-by-step explanation:

Answer:

suiiiii

Step-by-step explanation:

The solution of p-5>7 can be represented on a number line.We start by adding 5 to both sides of the inequality:p - 5 + 5 > 7 + 5p > 12This means that any value of p that is greater than 12 would satisfy the inequality.On a number line, we would represent this by shading the region to the right of 12, since any number to the right of 12 is greater than 12.

Using a significance level of 0.05, we found a statistically significant difference in the number of rounds played by day of the week.

To determine if the test statistic is significant, we need to compare it to a critical value from an F-distribution table.

The critical value is based on the degrees of freedom, which is calculated as follows: df between = k - 1 (where k is the number of groups being compared, in this case 5) and df within = N - k (where N is the total sample size, in this case 5).

Using these values, we can find the critical value from the F-distribution table to be 2.866.

Comparing this critical value to our calculated test statistic of 3.60, we can see that the test statistic exceeds the critical value.

This means that we can reject the null hypothesis and conclude that there is a statistically significant difference in the number of rounds played by day of the week at the 0.05 significance level.

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Without more information and statistical analysis, it is difficult to determine whether the data provide convincing evidence that the average GRE verbal reasoning score has changed since 2004.

To determine whether the average GRE verbal reasoning score has changed since 2004, we would need to conduct a hypothesis test. We could set up a null hypothesis that the population mean for the verbal reasoning score has not changed since 2004, and an alternative hypothesis that the population mean has increased.

Assuming a normal distribution of scores, we could use a two-sample t-test to compare the means of the two populations (scores from 2004-2007 and scores from 2011). We would need to collect a random sample of scores from both time periods and calculate the sample means and standard deviations.

Without knowing the sample size or standard deviation of the 2011 scores, it is difficult to determine whether the difference in average scores is statistically significant. However, if the sample sizes are large enough and the difference in means is significant, then we could conclude that there is convincing evidence that the average GRE verbal reasoning score has changed since 2004.

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It should be noted that the provided assertion indicates that (A) is 41° (b) is -17.16 (a) is 5.41

Having three sides, three angles, and three points, a triangular is a closed, two-dimensional object.

We know that a right angle is , and we are given another angle that is , so that means that angle  is:

A + 49 +90 = 180

A + 139 = 180

A = 180 - 139

A = 41°

To find side length b, we can use the sin function:

sin(49) = b/18

18 ×-0.53 = b

b = -17.16

To find side length a, we can use the cos function:

cos(49) = a/18

18 × 0.300 = a

a = 5.41

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Answer:

a. {-2, -1, 0, 1, 2, 3, 4}

b. {-2, -1, 0, 1, 2, 3}

The given system of linear equations has infinite solutions. The solution has been obtained by using the elimination method.

What is the elimination method?

The elimination approach involves taking one variable out of the system of linear equations by utilising addition or subtraction together with multiplication or division of the variable coefficients.

We are given a system of linear equations as -x + y = -8 and 2x - 2y = 16.

Now, on dividing the equation 2x - 2y = 16 by 2, we get

x - y = 8.

Now, on adding the first and the third equation, we get

⇒ (-x + y) + (x - y) = -8 + 8

⇒ 0 = 0

Hence, the system has infinetly many solutions.

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Question: What is the solution for the given system of linear equations?

-x + y = -8 and 2x - 2y = 16

The graph of the solution to the system of inequalities is added as an attachment

Given that

x + y ≥ 6

8x + 16y ≤ 160

To graph the solution to a system of inequalities, follow these steps:

See attachment for the system of inequalities

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For given circle, the length of arc ST and RPT are 13.44 ft and 50.8 ft respectively.

What exactly is a circle?

A circle is a geometric object made up of all the points on a plane that are equidistant from the centre. A circle, in other terms, is a collection of points that are all the same distance from a centre point. This distance is known as the circle's radius.

The circumference of a circle is the distance around the outside of the circle, and it can be calculated using the formula C = 2πr, where π (pi) is a mathematical constant and r = radius of the circle.

Now,

For given circle

radius=14 ft

then

circumference=2*π*r=2*22/7*14

=88 ft

angle for the arc ST=180-125

=55°

then length of arc ST=55/360*88

=13.44 ft

and angle of arc RPT=180-97+125

=208°

then length of arc RPT=208/360*88

=50.8 ft

Hence,

             the length of arc ST and RPT are 13.44 ft and 50.8 ft respectively.

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The required average speed of the given train is 42 km/hour.

Speed is what it means. the speed at which an object's location changes in any direction.

The distance traveled in relation to the time it took to travel that distance is how speed is defined.

As speed simply has a direction and no magnitude, it is a scalar quantity.

So, we have:

63/x + 72/6+x = 3

63(x+6)+72x/x(x+6) = 3

63x + 378 + 72x/x²+6x = 3

378 + 135x = 3x² = 18x

3x² - 117x - 378 = 0

x² - 39x - 126 = 0

x² - 42x + 3x - 126 = 0

x(x-42)+3(x-42) = 0

(x+3)(x-42) = 0

x = 42, -3

As speed cannot be zero, the first average speed is 42 km per hour.

Therefore, the required average speed of the given train is 42 km/hour.

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Correct question:

A train travels at a certain average speed for a distance 63 km and then travels a distance of 72 km at an average speed of 6 km/hr more than the original speed. If it takes 3 hours to complete total journey, what is its original average speed?

Answer:

Julianne (she owes 25 more than Rosa)

Step-by-step explanation:

Because Rosa owes -0.25 less than Julianne and because if you subtract the two balances  or do keep change flip method it will give you -0.25 meaning that when Julianne owes nothing Rosa still will owe some money (25 cents).

If one-tower can hold 4.37×10⁶ gallons of water and other tower can hold 3.92×10⁶ gallons of water, then combined water capacity of two towers is 8.29×10⁶ gallons.

In order to find the combined water capacity of the two towers, we simply need to add their individual capacities.

The water capacity of one tower is = 4.37×10⁶ gallons of water, and the water capacity of other tower is = 3.92×10⁶ gallons of water,

So, their combined capacity is:

⇒ 4.37×10⁶ + 3.92×10⁶ = 8.29×10⁶ gallons

Therefore, the combined water capacity of the two towers is 8.29×10⁶ gallons.

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The given question is incomplete, the complete question is

A city has two water towers. one tower holds 4.37×10⁶ gallons of water and the other holds 3.92×10⁶ gallons of water. What is the combined water capacity of the two towers?

The meaning of a 95% confidence interval for a population mean is to select an interval where when the process is repeated for many different samples, approximately 95% of the intervals would contain the sample mean and when the process is repeated for many different samples, approximately 95% of the intervals would contain the population mean. These two are the correct options from the given choices.

A confidence interval is a range of values, constructed from a sample, that is expected to include the value of an unknown population parameter with a specific level of certainty.

Confidence intervals are typically used to indicate the precision and accuracy of an estimate, rather than the probability of an event occurring.

Therefore, in the context of this question, we can say that a 95% confidence interval for a population mean would select an interval where when the process is repeated for many different samples, approximately 95% of the intervals would contain the sample mean and when the process is repeated for many different samples, approximately 95% of the intervals would contain the population mean.

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The area of the floor of the hall is 96 square meters.

A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles.

The volume of a rectangular prism is expressed as;

V = w × h × l

Where w is the width, h is height and l is length.

Given that, the length of a hall is three times and width is two times of its height.

Let the height of the hall be h.

Then the length = 3h and width = 2h

Volume of the hall = Length ×  Width × Height

384 = (3h) × (2h) × (h)

384 = 6h³

6h³ = 384

Divide both sides by 6

h³ = 64

Take the cube roots

h = ∛64

h = 4

Hence;

Length = 3h = 12

Width = 2h = 8

Area of the floor = Length x Width

Area of the floor = 12 × 8

Area of the floor = 96 square meters.

Therefore, the area is 96 square meters.

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Answer:

r = 4.3

Step-by-step explanation:

10r + 6 = 49

subtract 6 from both sides:

10r = 43

divide both sides by 10:

r = 4.3

Answer:

R=4.3 or 43/10

Step-by-step explanation:

10r + 6 - 6 = 49 - 6  subtract 6 from each side of equation

10r = 43

10r/10 = 43/10 divide each side by 10

r = 43/10 or 4.3 or 4 3/10 as mixed number

Answer:

Step-by-step explanation:

Answer:

a) 11:09
b) 31 minutes it should take to arrive at newtown

Step-by-step explanation:

a) you have to read the table
b) you need to know how many minutes are in an hour and for 11:38 to 12 is 22 minutes and you need an extra 9 so add them both together which will give the answer of 31 minutes.

The graph of the given piecewise functions will open towards for all.

What exactly is a piecewise function?

A piecewise function is a mathematical function that is defined by different expressions or formulas over different intervals or "pieces" of the domain. In other words, a piecewise function is defined by multiple "pieces" or "cases," each of which is defined over a different interval of the domain. The domain of the function is partitioned into intervals, and each interval has its own expression or formula that describes the function's behavior over that interval. The different pieces of the function are typically joined together at the boundaries of the intervals to create a continuous function overall.

Now,

Graph of f(x)=|3x| (y=|3x|):

The graph of g(x) = f(x) - 2 (y=|3x|-2) is obtained by shifting the graph of f(x) downward by 2 units. Therefore, the graph of g(x) is:

The graph of h(x) = f(x-4  )(y=|3x|-4) is obtained by shifting the graph of f(x) to the right by 4 units. Therefore, the graph of h(x) is:

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Answer:

[tex] 1\frac{299}{475} [/tex]

Step-by-step explanation:

[tex] \frac{2.58 \times 1.2 \times {10}^{ - 5} }{1.9 \times {10}^{ - 5} } = \frac{2.58 \times 1.2}{1.9} = \frac{3.096}{1.9} = \frac{774}{475} = 1\frac{299}{475} [/tex]

Answer:

Step-by-step explanation:

(2.58) (1.2×10^-5)/1.9×10^-5​;

=(2.58) (1.2×[tex]\frac{1}{10^{5} }[/tex])/1.9×[tex]\frac{1}{10^{5} }[/tex];

=(2.58)([tex]\frac{1.2}{100000}[/tex])/1.9×[tex]\frac{1}{100000}[/tex];

=0.000031/1.9×[tex]\frac{1}{100000}[/tex];

=0.0000163×[tex]\frac{1}{100000}[/tex];

=0.000000000163;

=1.63×10^-10