23.From the following information, prepare trading account for the year ended 31st March, 2013 Cash purchases Rs. 4,50,000; credit purchases Rs. 27,00,000; returns inward Rs. 60,000; cash sales Rs. 4,80,000; credit sales Rs. 33,00,000; returns outward Rs. 30,000; freight inwards Rs. 9,000; carriage inwards Rs. 9,000; wages and salaries Rs. 12,000; opening stock Rs. 4,50,000; closing stock Rs. 2,64,000 but its market value is Rs.2,52,000​

Now, when a system has at least one solution, it's called consistent. When it has only one solution, it's called independent. otherwise inconsistent

The classification which best describes the system of equations is; Consistent and dependent

A linear or nonlinear system of equations as the case may be is termed consistent if there is at least one set of values for the unknowns that satisfies each equation in the system. In essence, when substituted into each of the equations, they make each equation hold true.

Additionally, the system of equations is dependent because the value of each variable is dependent on the others.

Now, when a system has at least one solution, it's called consistent. When it has only one solution, it's called independent.

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Tommy and Zach will be 16 miles apart after 2.90 hours.

Let the time taken for Tommy and Zach to run until they are 16 miles apart be t hours.

Tommy runs North at a speed of 5 miles per hour.

Therefore, the distance covered by Tommy in t hours is 5 multiplied by t hours:

=5t miles

Zach runs East at a speed of 8 miles per hour.

Zach started running 2 hours later so that he would run for (t - 2) hours.

Distance covered by Zach in (t - 2) hours running at a speed of 8 miles per hour :

=8(t - 2) miles

Since they are now 16 miles apart, Pythagoras's theorem, a²+ b² = c², is applied.

[8(t - 2)]²+ (5t)² = 16²

64(t - 2)² + 25t² = 256

64(t² + 4 - 4t) + 25t² = 256

64t² + 256 - 256t + 25t² = 256

89t² -256t + 256 - 256 = 0

89t² - 256t = 0

t( 89t - 256) = 0

(89t - 256) = 0

9t = 256

= 256÷9

t = 2.90 hours

Therefore, for 2.90 hours, Zach and Tommy will be 16 miles apart.

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Answer:

1. has ordered both a gown and a yearbook: 54%

2. has ordered a yearbook or a gown: 58% + 54% = 112%

3. has ordered neither a yearbook nor a gown: 100% - (58% + 54%) = 88%

4. has ordered a yearbook but not a gown: 54% - 15% = 39%

Step-by-step explanation:

The circumference of the circle with a radius of 4 inches is 8π inches.

The circumference is the perimeter of a circle or ellipse in geometry. That is, the circumference would be the circle's arc length if it were opened up and straightened out to a line segment. In general, the perimeter is the length of the curve around any closed figure.

Given that the radius of the circle is 4 inches. The circumference of the circle will be calculated by the formula,

Circumference = 2πr

Circumference = 2 x π x 4

Circumference = 8π inches

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Answer:

31

Step-by-step explanation:

What is the median of 35 27 51 31 28 19 33?

Median: center most value when values are arranged in numerical order so:

19 , 27 , 28 , 31 , 33 , 35 , 51

(a) The distribution of X is binomial with parameters n = 20 and p = 600/3000 = 1/5 since we are randomly selecting 20 clients without replacement and interested in the proportion of happy consumers. Given below is the probability density function for this binomial distribution.

f(x) is equal to (n pick x) * p * x * (1-p) (n-x)

Where p and 1-p are the probability of success and failure, respectively, and n pick x is the binomial coefficient, which is equal to n!/(x! * (n-x)!).

(b) The formula for the anticipated value of X, or E[X], is

E[X] = np = 20 * (1/5) = 4

Var X, the variance of X, is defined as follows:

Var X = np(1-p) = 20*1/5*4/5=3.2

(c) The cumulative distribution function of the binomial distribution's formula can be used to get P[X >= 3]:

Sum(i=3 to n) f for P[X >= 3] (i)

Summarizing from I = 3 to 20 and substituting the values from the density function, we obtain:

Sum(i=3 to 20) = P[X >= 3] [(20 pick I (1/5)*i*4/5*(20-i)]

(d) We must determine the value of the cumulative distribution function at x = 3, which is equivalent to the likelihood of receiving three or fewer successes out of 20 trials, in order to approximate P[X >= 3] using the binomial table. By using n = 20 and p = 1/5 to calculate the value of the cumulative distribution function at x = 3 in the binomial table, it is possible to determine this probability. P[X >= 3]'s estimated value is 0.586.

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The mean number who have immunity in samples of size 17  is 13.6

Sample Size =17

Immunity to a Particular disease=0.8

=17*0.8

=13.6

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Answer: The answer is option 1

Step-by-step explanation

The given equation is [tex](p^{2} r^{3} /pr^{4} )^{2}[/tex]

 [tex](p^{2} r^{3} /pr^{4})^{2}[/tex]  =  [tex]p^{4} r^{6} /p^{2}r^{8}[/tex]  (the given equation whole square is applied)

[tex]p^{4} r^{6} /p^{2} r^{8}[/tex]  =  [tex]p^{2} /r^{2}[/tex]   (the p and r are canceled out )

Therefore the correct answer is  [tex]p^{2} /r^{2}[/tex]

Answer:

145

Step-by-step explanation:

Cuánto es means what is the answer

35 - (-110)

Two negative signs equal a positive sign

35 + 110 = 145

The value of b2 - 4ac for the equation 2x2 + 2x - 1 = 0 is 12.

The equation 2x2 + 2x - 1 = 0 can be written in the form ax2 + bx + c = 0, where a = 2, b = 2 and c = -1. The formula for calculating b2 - 4ac for this equation is

[tex]b2 - 4ac = (b2) - (4)(a)(c)= (2)2 - (4)(2)(-1)= 4 - (-8)= 12[/tex]

Therefore, the value of b2 - 4ac for the equation 2x2 + 2x - 1 = 0 is 12.

To calculate this value, the formula first finds the value of b2, which is the square of the coefficient of the x-term (2). Then it multiplies the coefficient of the x2-term (2) by the constant term (-1), and multiplies the result by 4. Finally, it subtracts the result of this multiplication from the value of b2.

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Answer:

f(x) and G(x)

Step-by-step explanation:

When you want to write a function of something, you can write it as the letter followed by "(x)"

Using the linear function y = -5/3x + 3000, the boulder will touch the ground at 1800m

A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.

A model of a linear function is given as y = mx + c

where m is the slope or rate of change of the function and c is the constant value or y - intercept

In this function;

The slope is - 5/3 and the constant is 3000

The linear function can be written as

y = -5/3x + 3000

The height at which the boulder will strike the ground, the value of y = 0

0 = -5/3x + 3000

5/3x = 3000

x = 1800

The point is at 1800m

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The total cost for Bob's ride is C = x + m and no. of minutes of the ride is

m = C - x.

A mathematical statement expressed as a string of numbers and unknowable variables is known as a numerical expression. Statements can be used to create numerical expressions.

Given,  A ride on a rental scooter, bob paid a fee to start the scooter plus cents per minute of the ride.

Let, 'x' be the fee in cents to start the scooter and 'm' be the no. of minutes of riding.

Therefore, The total bill(C) for Bob's ride is,

C = x + m.

The no. of minutes Bob ride the scooter is simply,

m = C - x.

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Y- intercept for the line y = 5x is 0. This can be get from the standard equation for a line.

For the The standard equation for a line is,

     y = ax + b

y is called the dependent variable because its value depends on the value of x

a is the slope of the line

x is called the independent variable because it can be any value

b is the y-intercept

Here y is a function of x. You could simply write it as y = 5x.  Thus if we compare to the standard form equation y = ax + b, a=5 and b=0.  Thus the y-intercept is zero.  The reason that this is the case is that when you set x=0 the value is plotted on the y axis because the equation for the y axis is the line defined by x=0.  Any value in the x, y plane where x is equal to zero plots on the vertical line going through (0,0) or in other words the y axis.

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Answer:

43.1

Step-by-step explanation:

2.5 % = .025    look for this value on the z-score table to find this corresponds to z = - 1.96   Standard Deviations

72.5      - 1.96 * 15    = 43.1  

Answer: $2.70

Step-by-step explanation:

10% = 0.1

Take 27 times 0.1 = $2.70

The graph of y=3x-1 will be a straight line that does not passes through origin.

A line is a geometry object that extends on both sides and is defined by zero width. Simply put, a straight line is a line devoid of bends. A straight line is one that has no curves and continues to infinity on both sides.

ax+by=c is the standard form of straight line.

A straight line serves as the visual representation of a linear function's graph.

The given function is as follows:

y=3x-1

A linear function looks like this:

y=mx+c

Where:

m=3:  the slope

c=-1: the y-intercept

So given function has a different y-intercept than 0.

So, the resulting graph o does not cross through the origin.

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Answer:

it means multiply like the × symbol

Step-by-step explanation:

Answer:

4.9 miles

Step-by-step explanation:

(.01)(490)=4.9

A prime number is a positive integer greater than one that has no positive integer divisors other than one and itself. To find if a number is prime or not, if a number is divide by any other positive number other than 1 and itself it is not a prime number.

A whole number higher than one that cannot be divided exactly by any other whole number than itself and one is a prime number.

Complete numbers, the range of numbers that includes zero and natural numbers and not a decimal or fraction.

8 is not a prime number because 8 is divided by 2 and 4 other than 1 and itself.

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y = 3/x equation is an example of inverse variation between the variables x and y .

Now, According to the question:

The equation with the inverse variation between the variables 'x' and 'y' .

Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value.

y = 3/x is an example of inverse variation.

Hence, y = 3/x equation is an example of inverse variation between the variables x and y .

Let's know:

What is an Inverse variation equation?

Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value. It states if the value of one quantity increases, then the value of the other quantity decreases.

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A function is continuous if it is defined for all values of the independent variable and there are no breaks, jumps, or gaps in its graph. In other words, a function is continuous if you can draw its graph without lifting your pen from the paper.

To check whether a function is continuous at a particular point, you can use the following methods:

The two-part definition of continuity: A function is continuous at a point if the following two conditions are met:

The limit of the function as it approaches the point from the left and the right exists and is equal to the function's value at that point.

The function is defined at the point.

The Epsilon-Delta definition of continuity: A function is continuous at a point if, for every epsilon (a small positive number) there exists a delta (also a small positive number) such that, for all points x within delta units of the point in question, the function's value at x is within epsilon units of the function's value at the point.

The graph of the function: You can also check the continuity of a function by looking at its graph. If the graph is a continuous curve with no breaks or jumps, then the function is continuous. If the graph has breaks or jumps, then the function is discontinuous.

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The Epsilon-Delta definition of continuity states that a function is continuous at a point if there is an epsilon (a small positive number) and a delta (also a small positive number) such that the value of the function at x is within epsilon units of the value of the function at the point for all points x within delta units of the point in question.

The function's graph: Additionally, you can examine a function's graph to see whether it is continuous. The function is continuous if the graph displays a continuous curve without any interruptions or leaps. The function is discontinuous if the graph has breaks or jumps.

The average change in the volume of water per day is obtained as 0.625  litres.

The rate change of volume is the change of volume with respect to time.

For instantaneous change the derivative of the expression of volume can be taken.

The average change in the volume of water can be obtained as follows,

Average change = Volume of water ÷ Number of days

                            = 2.5 ÷ 4 = 0.625

Hence, the average change in water volume is given as  0.625 liters per day.

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The probability of getting an ace from a well-shuffled deck of 52 cards is  1/13 and the probability of not getting an ace is 12/13

We can calculate the probability by the following method:

Total number of cards in a pack of cards= 52

Number of ace cards in a pack of cards= 4

Probability of an event= Number of possibilities of that event / Total number of possibilities

(i) If drawing an ace card is considered an event, suppose E, then:

P(E)= Number of ace cards/ Total number of cards

= 4/52

(ii) Probability of any event other than E= 1- Probability of the event E=

If the drawing of a non-ace card is considered an event, suppose E', then

P(E')= 1- the probability of drawing an ace card

= 1- P(E)

= 1-1/13

= (13-1)/ 13

= 12/13

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The equation that represents a proportional relationship is y/X = 2.5. That is option D.

A proportional relationship is the type of relationship that exist when between two variables which can be represented as y and x where a constant of proportionality exists between the two variables as k.

The relationship between these two variables can either be directly proportional or indirectly proportional.

The relationship that exists between X and y is a direct proportional relationship with a constant of proportionality of 2.5.

y = 2.5 X

= y/X = 2.5. Where 2.5 is the constant.

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The value of angle x is 70° and angle y is 60° in the given figure with exterior angle = 120°

From the given figure, we know that the Exterior angle = 120°

To find the values of x and y we will follow the following steps.

We know that the sum of interior opposite angles is equal to the exterior angle of the triangle.

The exterior angle of the triangle=120°

The interior angles are x and 50°

50° + x = 120°

x = 120°- 50°

x = 70°

Also, we know that the sum of the y and the exterior angle is 180° because they are forming a linear pair.

Hence we have,

y + 120° = 180°

y = 180° - 120°

y = 60°

Therefore, the value of angle x is 70° and angle y is 60°.

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To simplify this expression, we can start by simplifying the square roots:

2√12 + 3√48 - 75

= 2√(12) + 3√(48) - 75

= 2√(43) + 3√(412) - 75

= 2√4 * √3 + 3√4 * √12 - 75

= 2 * √3 + 3 * √12 - 75

We can then combine like terms:

= 2 * √3 + 3 * √12 - 75

= (2 * √3 + 3 * √12) - 75

= 5 * √12 - 75

Finally, we can simplify the expression to get our final answer:

= 5 * √12 - 75

= 5 * 2√3 - 75

= 10√3 - 75

= -75 + 10√3

= -75 + 10√3

So the simplified expression is -75 + 10√3.

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By using the the application of ASA we can determine the two angles are congruent by AAS.

AAS stands for Angle-Angle-Side. When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent.

AAS congruence can be proved in easy steps.

Suppose we have two triangles ABC and DEF, where,

Diagram attaches at the end of the solution.

∠B = ∠E [Corresponding angles]

∠C = ∠F [Corresponding angles]

AC = DF [Adjacent sides]

By angle sum property of triangle, we know that;

∠A + ∠B + ∠C = 180 ………(1)

∠D + ∠E + ∠F = 180 ……….(2)

From equation 1 and 2 we can say;

∠A + ∠B + ∠C = ∠D + ∠E + ∠F

∠A + ∠E + ∠F = ∠D + ∠E + ∠F [Since, ∠B = ∠E and ∠C = ∠F] ∠A = ∠D

Hence, in triangle ABC and DEF,

∠A = ∠D

AC = DF

∠C = ∠F

Hence, by ASA congruency, (AAS: the application of ASA)

Δ ABC ≅ Δ DEF

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The z-scores are (-1.85, 1.85)

An illustration of a standardised score is the z-score. A z-score calculates how far a data point deviates from the distribution's mean by standard deviation.

If a Z-score is 0, it indicates that the data point's score is identical to the mean score

Given:

If we look at the z score table we will get the value of z- score.

The value 0.0322 lies in horizontal row 1.8 and column 0.05.

Then, for left value 0.0322 is -1.85

and, for right value 0.0322 is 1.85.

Hence, the z-scores are (-1.85, 1.85)

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Take the function y = f(x), with the independent variable x as well as the dependent variable y, to determine the domain of a. If a value for x successfully enables the creation of a single value y using another value for x, it is said to be in the domain of the function f.

The collection of all potential inputs for a function is its domain.

For instance, the domain of f(x)=x2 and g(x)=1/x are all real integers with the exception of x=0.

The set of numbers x for which a function is defined in a valid manner is known as the domain of the function.

A function's domain is referred to as a closed interval if it is specified across the interval a ≤ x ≤ b.

So, to find the domain of a, consider the function y = f(x), which has the independent variable x and the dependent variable y.

A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.

Therefore, take the function y = f(x), with the independent variable x as well as the dependent variable y, to determine the domain of a. If a value for x successfully enables the creation of a single value y using another value for x, it is said to be in the domain of the function f.

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