The answer and steps

A person pays $1 to play a certain game by rolling a single die once. if a 1 or 2 comes up, the person wins nothing. if, however, the player rolls a 3, 4, 5, or 6 he or she wins the difference between the number rolled and $1, this means that the game is not fair, based on the expected value

We can see that the expected value of the game can be found by multiplying each payout by its probability of occurring and then summing up the results:Expected value = (0.2)($1) + (0.2)($1) + (0.2)($2) + (0.2)($3) + (0.2)($4) + (0.2)($0) + (0.2)($0)Expected value = $0.40 Since the expected value of the game is positive, it means that, over the long run, players are expected to make money on average. This means that the game is not fair.

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The system has infinitely many solutions, which can be written as (x, y, z) = (1 - 60s, -10 + 600s, s) where s is a parameter.

To solve the system of equations:

1x + 0y + 60z = 1

1x + 10y + 0z = 0

0x + 0y + 0z = 0

The third equation is an identity, implying that it does not give us any new information. The first two equations can be used to solve for x, y, and z:

From the first equation, we get x = 1 - 60z

From the second equation, we get y = 0 - 10x = -10(1 - 60z) = -10 + 600z

Therefore, the solution to the system can be written as a point in terms of z as:

(x, y, z) = (1 - 60z, -10 + 600z, z)

Since z can take on any value, there are infinitely many solutions to the system, which can be parameterized as:

(x, y, z) = (1 - 60s, -10 + 600s, s) where s is a parameter.

he system has infinitely many solutions, which can be written as (x, y, z) = (1 - 60s, -10 + 600s, s) where s is a parameter.

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The option a. S-(red,red), (red,black), (black,red), (black,black) is the most appropriate sample space S for the possible outcomes of selecting two cards from a deck of 52 cards

The most appropriate sample space S for the possible outcomes of selecting two cards from a deck of 52 cards and observing the color of each (26 cards in the deck are red and 26 are black) is given by option a. S-(red,red), (red,black), (black,red), (black,black).

Sample space S in probability theory denotes the set of all possible outcomes of an experiment.

In other words, the sample space S represents all possible outcomes of an experiment under consideration. For instance, in the current scenario,

These four possible outcomes are independent and equally likely events, and the sample space S for the possible outcomes is given by option a. S-(red,red), (red,black), (black,red), (black,black).

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the sine and cosine of the two non-right angles in a right triangle are related to each other by their complementary nature.

How to find middle angle?

In a right triangle, the middle angle is the angle opposite the hypotenuse. To find this angle using trigonometry, you can use either the sine, cosine, or tangent ratio. Let's say that the two legs of the right triangle are a and b, and the hypotenuse is c. Then, you can use the following trig ratios to find the middle angle:

Sine ratio: sin(theta) = a/c

Cosine ratio: cos(theta) = b/c

Tangent ratio: tan(theta) = a/b

To find the middle angle, you would use the inverse sine, cosine, or tangent function, depending on which ratio you used. For example, if you used the sine ratio, you would take the inverse sine of a/c to find the angle: theta = sin²-1(a/c).

What is the relationship between the sine and cosine of the two non-right angles in a right triangle, and how do they define the ratios sine, cosine, and tangent?

In a right triangle, the two non-right angles are complementary, which means that their sum is 90 degrees. Let's call these angles alpha and beta. The sine and cosine of these angles are defined as follows:

Sine of alpha: sin(alpha) = opposite leg / hypotenuse

Cosine of alpha: cos(alpha) = adjacent leg / hypotenuse

Sine of beta: sin(beta) = adjacent leg / hypotenuse

Cosine of beta: cos(beta) = opposite leg / hypotenuse

Note that the opposite and adjacent legs are relative to the angle being considered. The ratios sine, cosine, and tangent are defined in terms of these ratios:

Sine ratio: sin(theta) = opposite leg / hypotenuse

Cosine ratio: cos(theta) = adjacent leg / hypotenuse

Tangent ratio: tan(theta) = opposite leg / adjacent leg

Therefore, the sine and cosine of the two non-right angles in a right triangle are related to each other by their complementary nature. If you know the value of one of these ratios, you can use it to find the value of the other using the fact that sin(alpha) = cos(beta) and cos(alpha) = sin(beta). This relationship is known as the complementary angle identities.

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If the parametric equations for x and y are both non-constant linear functions of t, then curve must be a line.

A curve (sometimes known as a curved line in ancient texts) is a mathematical entity that is similar to a line but does not have to be straight.

A curve may be conceived of intuitively as the trace left by a moving point. "The [curved] line[a] is [...] the first species of quantity, which has only one dimension, namely length, without any width nor depth, and is nothing else than the flow or run of the point which [...] will leave from its imaginary moving some vestige in length, exempt of any width," Euclid wrote more than 2000 years ago.

Let x = at+b and y = ct+d

Then,

[tex]\frac{x-b}{a}=\frac{y-d}{c}=t xc-bc=ay-adxc-ay+ad-bc=0[/tex]

Which is linear equation in x and y.

Therefore, curve is always a line.

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Answer:

Starting with the left side of the equation:

cosθ(1+tanθ) = cosθ(1+sinθ/cosθ) (since tanθ = sinθ/cosθ)

= cosθ + sinθ

Therefore, the left side of the equation is equal to the right side of the equation, which means that cosθ(1+tanθ) = cosθ+sinθ is true.

The temperature in Buffalo when it is 23 degrees Fahrenheit is equivalent to -5 degrees Celsius.

Fahrenheit is a temperature scale that was created by Gabriel Fahrenheit in 1724. Fahrenheit is used primarily in the United States and a few other countries. The boiling point of water on this scale is 212 degrees Fahrenheit, while the freezing point is 32 degrees Fahrenheit.

The Celsius scale, on the other hand, is a temperature scale that is used throughout the world. It was created in 1742 by Swedish astronomer Anders Celsius. On this scale, the boiling point of water is 100 degrees Celsius, and the freezing point is 0 degrees Celsius.

The formula for converting degrees Fahrenheit to degrees Celsius is: C=5/9(F-32). C is the equivalent Celsius temperature, while F is the equivalent Fahrenheit temperature.

Let's put the formula into practice to answer the question, "If the temperature in Buffalo is 23 degrees Fahrenheit,

We can simply plug in the given value for Fahrenheit temperature, which is 23 degrees Fahrenheit.

C = (5/9) (23 - 32)C = (5/9) (-9)C = -5

Therefore, -5 degrees Celsius is equivalent to 23 degrees Fahrenheit when the temperature is in Buffalo.

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Answer:f(-2)=6+10

So f(-2) =16

Step-by-step explanation:

Let θ be equal to 855∘. Sketch θ in standard position. θ = 855∘ is in the fourth quadrant of the coordinate plane θ = 855∘

Hence, we sketch θ in the standard position with its initial side along the positive x-axis.

Find an angle between 0∘ and 360∘ that is coterminal with θ.

The angle between 0∘ and 360∘ that is coterminal with θ is given by:

θ1 = θ - n × 360∘θ1 = 855∘ - 2 × 360∘θ1 = 855∘ - 720∘θ1 = 135∘

Find an angle between −360∘ and 0∘ that is coterminal with θ.

The angle between −360∘ and 0∘ that is coterminal with θ is given by:

θ2 = θ + n × 360∘θ2 = 855∘ + 2 × 360∘θ2 = 855∘ + 720∘θ2 = 1575∘

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When the radius of circle 2 is twice the radius of circle 1, the size of circle 2 is larger than circle 1.

In geometry, a triangle is a polygon with three sides and three angles. The sum of the angles in a triangle is always 180 degrees. Triangles are one of the most basic and fundamental shapes in geometry and are used in many mathematical and real-world applications, such as in architecture, engineering, and physics. There are different types of triangles based on the length of their sides and the measures of their angles, such as equilateral triangles, isosceles triangles, scalene triangles, acute triangles, obtuse triangles, and right triangles.

Here,

2. This is because the circumference and area of a circle are directly proportional to the radius.

3. To determine if triangles ABC and DEF are similar, we need to check if their corresponding angles are congruent and if their corresponding sides are in proportion. From the diagram, we can see that angle A is congruent to angle D, angle B is congruent to angle E, and angle C is congruent to angle F. This satisfies the angle-angle (AA) similarity criterion. Additionally, we can use the side-side-side (SSS) similarity criterion to determine if the corresponding sides are in proportion. From the diagram, we can see that side AB is parallel to side DE, side AC is parallel to side DF, and side BC is parallel to side EF. Therefore, we can conclude that triangles ABC and DEF are similar.

4. To find the coordinates of D using the coordinates of A, we need to determine the translation from A to D. From the diagram, we can see that A is translated two units to the right and three units down to get to D. Therefore, we can find the coordinates of D by adding two to the x-coordinate of A and subtracting three from the y-coordinate of A. If the coordinates of A are (x1, y1), then the coordinates of D would be (x1 + 2, y1 - 3).

A= (-0.87,0.5)

D=(-0.87 + 2, 0.5 - 3)

D=(1.13,-2.5)

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The person must leave the money in the bank for approximately 13.6 years to reach 13300 dollars.

Using the formula A=P(1+r/n)⁽ⁿᵗ⁾, where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years, we can solve for t.

We have P = 4500, A = 13300, r = 0.0625, n = 2. Plugging these values into the formula and solving for t, we get t ≈ 13.6 years. Therefore, the person must leave the money in the bank for approximately 13.6 years to reach 13300 dollars.

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the temperature at 8:00 am is 9°C  This means that every hour from midnight to 8:00 am, the temperature increased by 1.5°C, resulting in a total increase of 12°C over the 8 hour period.

To solve this problem, we need to use the formula for calculating the final temperature based on the initial temperature and the rate of change per hour.

The formula for this is:

Final Temperature = Initial Temperature + (Rate of Change per Hour x Number of Hours)

In this case, the initial temperature is -3°C, the rate of change per hour is 1.5°C, and the number of hours is 8.

Plugging these values into the formula, we get:

Final Temperature = -3 + (1.5 x 8)

Final Temperature = -3 + 12

Final Temperature = 9°C

Therefore, the temperature at 8:00 am is 9°C.

This means that every hour from midnight to 8:00 am, the temperature increased by 1.5°C, resulting in a total increase of 12°C over the 8 hour period.

It's important to note that this problem assumes that the rate of change per hour remains constant throughout the 8 hour period. In reality, the temperature may fluctuate based on various factors, such as wind, cloud cover, and humidity. However, for the purposes of this problem, we can assume that the rate of change per hour remains constant.

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A. In this instance, the research hypothesis may be that the new workout is successful in lowering the incidence of heart attacks.

A p-value is a statistical indicator that, under the null hypothesis, shows the likelihood of receiving a test statistic that is as extreme to or more extreme than the one seen in the sample data. Depending on the degree of statistical significance the researcher selects, it is employed in hypothesis testing to determine whether to reject or fail to reject the null hypothesis. The null hypothesis is rejected in favour of the alternative hypothesis if the p-value is less than or equal to the selected level of significance (typically 0.05). The null hypothesis is not rejected if the p-value is higher than the selected level of significance.

A. In this instance, the research hypothesis may be that the new workout is successful in lowering the incidence of heart attacks.

B. The alternative hypothesis may be that the additional exercise has no impact on the frequency of heart attacks.

C. Depending on the study's specific design and the outcome measure used to gauge the prevalence of heart attacks, the comparison distribution would vary.

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Answer:

Step-by-step explanation:

xs nxqxm,nswjnej,cebxhjme2ckjwadbcweckslnvc

First, we need to find the value of g(pi/2):

g(pi/2) = cos(pi/2) = 0

Now we can substitute this value into f(x):

f(g(pi/2)) = f(0) = sin(0) = 0

Therefore, f(g(pi/2)) = 0.

Answer:

  11/168  

Step-by-step explanation:

You want the decimal value 0.06547619047 represented as a fraction.

The obvious choice is ...

  [tex]\dfrac{6547619047}{100000000000}[/tex]

However, we see that this might be a truncation of the repeating decimal fraction ...

  [tex]0.065\overline{476190}[/tex]

This value can be represented  by the fraction 11/168.

  [tex]0.065\overline{476190}=\boxed{\dfrac{11}{168}}[/tex]

__

Additional comment

You can arrive at this several ways. The attached calculator display shows one way.

Another is to write it as the sum 0.065 +(1/1000)(476190/999999). Reducing the fraction here may require a bit of trial and error.

You can also write it as a continued fraction and then evaluate the result.

  0.06547619047 = 1/(15 +1/(3 +1/(1 +1/2))) = 11/168

where the last 2 is a rounding of 1.999999825...

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The percentage of customers who do not purchase clubs or balls is 0.66 or 66%.

Ten percent of customers who walk into a golf store purchase a golf club and 30% of customers purchase golf balls. Six percent of customers purchase both clubs and balls. The percentage of customers who do not purchase clubs or balls is 0.66.

Given that, The percentage of customers who purchase golf clubs = 10%The percentage of customers who purchase golf balls = 30%The percentage of customers who purchase both clubs and balls = 6%To find out the percentage of customers who do not purchase clubs or balls, we have to subtract the percentage of customers who purchase either clubs or balls or both from 100%.

Percentage of customers who purchase either clubs or balls or both = 10% + 30% - 6% = 34% Percentage of customers who do not purchase clubs or balls = 100% - 34% = 66%.

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The resulting double-line graph should show the sales data for desktop and laptop computers over the five days, with a line for each type of computer.

A double-line graph is a graph that displays two sets of data on the same graph, using two lines to show how each set of data changes over time or some other variable.

To create a double-line graph of the sales data for desktop and laptop computers over five days, follow these steps:

Draw a graph with two perpendicular axes, the horizontal axis (x-axis) representing the days, and the vertical axis (y-axis) representing the number of computers sold.

Label the horizontal axis with the days from Day 1 to Day 5.

Label the vertical axis with the heading "Number of Computers Sold".

Plot the data points for desktop computer sales. For Day 1, plot a point at (1, 4), for Day 2 plot a point at (2, 1), for Day 3 plot a point at (3, 2), for Day 4 plot a point at (4, 5), and for Day 5 plot a point at (5, 1).

Connect the data points for desktop computer sales with a line.

Plot the data points for laptop computer sales. For Day 1, plot a point at (1, 5), for Day 2 plot a point at (2, 2), for Day 3 plot a point at (3, 3), for Day 4 plot a point at (4, 7), and for Day 5 plot a point at (5, 3).

Connect the data points for laptop computer sales with a line.

Use a different color or style for the line representing desktop sales and the line representing laptop sales.

Add a legend to the graph to indicate which line corresponds to desktop sales and which corresponds to laptop sales.

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Sara’s hair was 25 inches long. Three years later it was 43 inches long. The percentage increase rounded to the nearest hundredth will be 72.

Percentage:

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we need to calculate the percentage of a number, we divide the number by the whole number and multiply by 100. So , percent means one hundredth and the word percent means every 100th. It is represented by the symbol "%".

Calculate the percentage of a total value:

Since percent implies 100, we will split the total portion into 100 parts and then multiply it by b to gather b things per 100 items.

The percentage increase is found as:

   [tex]% increase = \frac{change in value}{original value}[/tex][tex]%increase = \frac{change in value}{original value}[/tex][tex]%[/tex]% increase = Change in value/ Original value

⇒ % increase = [tex]\frac{13-25}{25} * 100[/tex]

⇒ % increase = 72

Hence, the percent increase rounded to the nearest hundredth will be 72.

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The 90% confident sample of size 191 with 23 successes that the true population proportion falls between 0.077 and 0.163 based on the sample data.

To find the 90% confidence interval for a sample proportion, we can use the following formula:

Confidence Interval = sample proportion ± margin of error

where the margin of error is:

Margin of Error = z* (\sqrt{(p*(1-p)/n))}

where z is the z-score corresponding to the level of confidence,

p is the sample proportion, and n is the sample size.

In this case, we have a sample size of n = 191 and 23 successes,

which gives a sample proportion of p = 23/191 ≈ 0.120.

To find the z-score corresponding to a 90% confidence level,

The z-score for a 90% confidence level is approximately 1.645.

Plugging in the values into the formula, we get:

Margin of Error = 1.645 * (\sqrt{(0.120*(1-0.120)/191)}) ≈ 0.043

Therefore, the 90% confidence interval for the population proportion is:

0.120 ± 0.043

which can be expressed as (0.077, 0.163) rounded to three decimal places.

So we are 90% confident that the true population proportion falls between 0.077 and 0.163.

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95 Gigabytes 1/3 Every 10 seconds, files are transmitted that are 10 times larger than the transfer rate as a whole. 2 / 3 The graph's slope is 5, according to the slope-intercept version of the equation for S. The unit rate is 5 gigabytes per second, according to this.

We are given the equation:- S(t)= 5t+45

calculate the value of S in 10s, 20s, 30s, ....... and difference in them.

for t= 10:-

S= 5(10)+45= 50+45= 95

for t= 20:-

S= 5(20)+45= 100+45=145

for t= 30:-

S= 5(30)+45= 150+45= 195

The difference:-

195-145= 50 and 145-95= 50

Hence, the file size is 50 MB per 10 seconds or 5 MB per second.

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Answer:

The observer deck of a ship is located at the origin of a coordinate system. Find the bearing of an object located at the point (5, 5).

Step-by-step explanation:

To find the bearing of an object located at the point (5, 5) relative to the observer deck at the origin of a coordinate system, we need to find the angle between the positive x-axis and the line connecting the observer deck to the object.

First, we calculate the slope of the line connecting the observer deck at (0, 0) to the object at (5, 5):

slope = (change in y) / (change in x)

= (5 - 0) / (5 - 0)

= 1

Next, we use the inverse tangent function to find the angle whose tangent is equal to the slope:

angle = arctan(slope)

= arctan(1)

= 45°

Therefore, the bearing of the object located at (5, 5) relative to the observer deck at the origin is 45 degrees.

Answer:

45° north of east

Step-by-step explanation:

tan⁻¹(y/x) = tan⁻¹(5/5) = tan⁻¹(1) = 45°

There is a significant difference in the mean search times between the two websites, as indicated by the p-value, which is larger than 0.05 but less than 0.10.

It is calculated by adding up all the values in the set and then dividing the sum by the total number of values. The mean is often used as a measure of central tendency, which describes the typical or representative value in a set of data.

This is a two-sample independent means t-test problem.

The null hypothesis is that there is no difference between the mean times needed to access flight information for the two major airlines, and the alternative hypothesis is that there is a difference.

Assuming the conditions for inference are met (random sampling, normality of the population, and independence between the two samples), we can calculate the t-value and the p-value for the test.

The formula for the t-value in a two-sample independent means t-test is:

t = (x1 - x2) / √[ (s1²/n1) + (s2²/n2) ]

Plugging in the given values, we get:

t = (2.5 - 2.1) / √[ (0.8²/20) + (1.1²/20) ]

t = 1.21

Using a t-table with 38 degrees of freedom (df = n1 + n2 - 2), we find that the p-value is between 0.10 and 0.05.

Therefore, the correct answer is c:

There is a significant difference in the mean search times between the two websites, as indicated by the p-value, which is larger than 0.05 but less than 0.10.

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Answer:

9.5 decimal

espero y te ayude

To find:-

Answer:-

To find out the equation of the line , we need to find out the slope first. It can be calculated as ,

[tex]\implies m =\dfrac{\Delta y}{\Delta x }=\dfrac{y_2-y_1}{x_2-x_1} \\[/tex]

And here ,

On substituting the respective values, we have;

[tex]\implies m =\dfrac{25-20}{8-3} \\[/tex]

[tex]\implies m=\dfrac{5}{5}\\[/tex]

[tex]\implies m=\boxed{1} \\[/tex]

Hence the slope of the line is 1 . Now we may use point slope form of the line to find out the equation of the line. Point slope form of the line is,

[tex]\implies y - y_1 = m(x-x_1) \\[/tex]

Take any of the given two points. Here i am taking (3,20) . So here we have;

On substituting the respective values, we have;

[tex]\implies y - 20 = 1(x - 3) \\[/tex]

[tex]\implies y -20 = x - 3 \\[/tex]

[tex]\implies x - 3 - y +20 = 0 \\[/tex]

[tex]\implies \underline{\underline{\green{ x - y +17=0}}}\\[/tex]

Hence the equation of the line in standard form is x - y + 17 = 0 .

and we are done!

Therefore, Thabo will get R18, Patrick will get R24, and Lucas will get R30.

In mathematics, a ratio is a comparison between two quantities or numbers, indicating how many times one quantity is contained within another. Ratios are often expressed in the form of a fraction, with the first quantity as the numerator and the second quantity as the denominator. Ratios can also be simplified by dividing both the numerator and denominator by their greatest common factor. Ratios are used in many areas of mathematics, science, and everyday life, such as in finance, cooking, and sports. They are particularly useful for comparing two quantities of different units or scales, as they provide a standardized way to express the relationship between them.

Here,

To determine how much each person will get, we first need to find the total of the ratios which is:

3 + 4 + 5 = 12

This means that the total amount of money is divided into 12 equal parts.

To find out how much each person gets, we need to multiply their share of the ratio by the total amount of money:

Thabo's share = 3/12 x R72 = R18

Patrick's share = 4/12 x R72 = R24

Lucas's share = 5/12 x R72 = R30

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Answer:

9.5x + 8 = 65

Step-by-step explanation:

Let x = number of sandwiches.

The cost of x sandwiches is 9.5x.

The delivery fee is $8.

The total cost of an order is the price of the sandwiches, 9.5x plus the delivery fee, 8.

In this case, the total cost is $65.

9.5x + 8 = 65

Answer:

$65

Step-by-step explanation:

X=9.50 because you add the $8 delivery fee to equal 65 in total.

In mathematics, a ratio is a comparison of two quantities or numbers expressed in terms of division. The order in which the quantities are expressed in a ratio is also important.

Ratios are used in various mathematical applications such as in finance, geometry, and physics. The units or quantities being compared in a ratio are crucial in determining the meaning and significance of the ratio.

For example, if the ratio is expressed as 2:1, it could mean that the first quantity is twice the size of the second quantity, or it could mean that the second quantity is half the size of the first quantity. Therefore, it is important to clearly define the units or quantities being compared to avoid any ambiguity or misunderstanding.

In the example above, if the ratio was expressed as 1:2 instead of 2:1, the meaning of the ratio would be reversed. Therefore, the order of the quantities in a ratio should be consistent with the context in which it is being used. In summary, the units and the order in which the quantities are expressed in a ratio are important in conveying accurate and meaningful information.

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Complete question:

In mathematics, the units or quantities being compared and the order in which they are expressed in a ratio are both important. The _____ in which ratio is expressed is important  

Solution:

we have been asked to graph [tex]f(x)=2^x+1[/tex] and [tex]g(x)=-x+7[/tex] on the same coordinate plane.

Then we have been asked to find the solution to the equation ?

So we will plot the graph and look for their point of intersection, the x-coordinate of the point of intersection will give the value of x.

So from the graph its clear that the point of intersection is (2,5)

Hence the value of x=2.

The bank statement  that is shown in the question shows a loss of £285.00 and calculated by subtracting the total expenses (money out) from the total revenue (money in).

Profit or loss is a measure of the financial performance of a business, organization, or individual over a given period of time.

Profit refers to the positive difference between the revenue earned by a business or individual and the expenses incurred during a given period.

A loss occurs when the expenses incurred exceed the revenue earned during a given period.

To calculate the profit or loss, you need to subtract the total expenses (money out) from the total revenue (money in).

In this case, the total revenue is £315.00 + £265.00 + £190.00 = £770.00, and the total expenses are £210.00 + £30.00 + £450.00 + £100.00 = £790.00.

So, the calculation would be:

Total revenue - total expenses = profit/loss

£770.00 - £790.00 = -£20.00

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