A "Pick 3" lottery game involves drawing
3 numbered balls from separate bins
each containing balls labeled from 0 to 9.
So there are 1,000 possible selections in
total: 000, 001, 002, . . . , 998, 999.
Players can choose to play a "straight"
bet, where the player wins if they choose
all 3 digits in the correct order. Since
there are 1,000 possible selections, the
probability a player wins a straight bet is
1/1,000. The lottery pays $400 on a
successful $1 straight bet, so a player's
net gain if they win this bet is $399.
Let X represent a player's net gain on a
$1 straight bet.
Calculate the expected net gain E(X).

Answer:

write ✍️

Step-by-step explanation:

justification for the following line translation . line 1 3p-

The probability that the duration is at least 4 is 0.0053 (rounded to four decimal places).

Probability is represented by a number between 0 and 1, with 0 denoting an impossibility and 1 denoting a certainty.

(a) Let X be the duration of the contest. Then X can take values from 1 to 6, where 1 indicates that A or B wins the first game, and 6 indicates that the contest ends in a draw after 5 successive draws.

We can find the PMF of X by considering the possible outcomes for each value of X.

P(X = 1) = P(A wins) + P(B wins) = 0.2 + 0.5 = 0.7

P(X = 2) = P(A loses, B loses, A wins or B wins) = 0.3 * 0.3 * (0.2 + 0.5) = 0.054

P(X = 3) = P(A loses, B loses, A loses, B loses, A wins or B wins) = [tex]0.3^4[/tex] * (0.2 + 0.5) = 0.01323

P(X = 4) = P(A loses, B loses, A loses, B loses, A loses, B loses, A wins or B wins) = [tex]0.3^6[/tex] * (0.2 + 0.5) = 0.00243

P(X = 5) = P(A loses, B loses, A loses, B loses, A loses, B loses, A loses, B loses, A wins or B wins) = [tex]0.3^8[/tex] * (0.2 + 0.5) = 0.0004374

P(X = 6) = P(5 successive draws) = [tex]0.3^5[/tex] = 0.00243

Therefore, the PMF of X is:

X 1 2          3          4         5                 6

P(X) 0.7 0.054 0.01323 0.00243 0.0004374 0.00243

(b) To find the probability that the duration is at least 4, we need to add the probabilities of X = 4, X = 5, and X = 6.

P(X >= 4) = P(X = 4) + P(X = 5) + P(X = 6) = 0.00243 + 0.0004374 + 0.00243 = 0.0052974

Therefore, the probability that the duration is at least 4 is 0.0053 (rounded to four decimal places).

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Answer:

hope it helps.

Let's add the fractions first and then we can estimate the sum.

[tex]= \dfrac{2}{3} +\dfrac{3}{4}[/tex]

change to common denominators

[tex]= \dfrac{8}{12} +\dfrac{9}{12}[/tex]

add numerators only

[tex]\dfrac{17}{12}[/tex] or [tex]1\dfrac{5}{12}[/tex] or [tex]1.42[/tex]

ANSWER: 13 is the best estimate of the answer. Normally we round up to 1.4 with a number like 1.42, but since that is not a choice, we can estimate 1 as the answer.

Answer:

2 [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

1 1/9 x 2 2/5 = ?

1 1/9 = 10/9

2 2/5 = 12/5

[tex]\frac{10}{9}[/tex] x [tex]\frac{12}{5}[/tex] = [tex]\frac{120}{45}[/tex] = [tex]\frac{8}{3}[/tex] = 2 [tex]\frac{2}{3}[/tex]

So, the answer is 2 [tex]\frac{2}{3}[/tex]

A)The volume of cat food in the can is 9.62 cubic inches .

B) A ratio to show cubic inches to ounces is 4.83.

What is a cylinder?

A cylinder is a three-dimensional geometric shape that has two congruent circular bases connected by a curved surface.

The volume of a cylinder can be calculated using the formula

=> [tex]V = \pi r^2h,[/tex]

where r is the radius of the circular base, h is the height of the cylinder, and π is the mathematical constant pi (approximately equal to 3.14).

To find the volume of the cat food in the can, we need to use the formula for the volume of a cylinder,

Since the diameter is 3.5 inches, the radius is half of that, which is 1.75 inches. The height is 1 inch.

So,[tex]V=3.14\times(1.75)^2\times1[/tex] = 9.62 cubic inches (rounded to the nearest hundredth).

Therefore, the volume of cat food in the can is approximately 9.62 cubic inches.

Now ,To find the ratio of cubic inches to ounces,

Since the can holds 5.8 ounces of cat food, we can find the volume of cat food in cubic inches by dividing the weight by the density:

=> 5.8 ounces / 1.2 ounces per cubic inch

= 4.83 cubic inches (rounded to the nearest hundredth).

Therefore,  a ratio to show cubic inches to ounces is 4.83.

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The utility company will have to increase its generating capacity by approximately 185.3% to meet the expected increase in electricity consumption over the next decade.

The problem involves the use of the exponential growth formula in mathematics, where we are given the current consumption of electricity in a city and we are asked to find the expected consumption of electricity after a certain period of time, assuming a fixed annual growth rate.

We can use the formula:

Here we have

A utility company in a western city in the United States expects the consumption of electricity to increase by 11%/year during the next decade, due mainly to the expected increase in population.

Let C₀ be the current consumption of electricity in the western city of the United States, and let C₁₀ be the expected consumption of electricity at the end of the decade.

We can use the following formula to calculate C₁₀:

C₁₀ = C₀ × (1 + r)ⁿ

Where r is the annual growth rate, n is the number of years

The amount by which the utility company will have to increase its generating capacity in order to meet the needs of the area at the end of the decade is given by the difference between C₁₀ and C₀

That is:

Amount of increase = C₁₀ - C₀

Substituting the values given in the problem, we get:

C₁₀ = C₀ (1 + 0.11)¹⁰

C₁₀/C₀ = (1.11)¹⁰

C₁₀/C₀ = (1.11)¹⁰

C₁₀ = C₀ × 2.84

Therefore, the amount by which the utility company will have to increase its generating capacity in order to meet the needs of the area at the end of the decade is:

Amount of increase =C₁₀ - C₀ = 2.853 × C₀ - C₀ = 1.853 × C₀

Therefore,

The utility company will have to increase its generating capacity by approximately 185.3% to meet the expected increase in electricity consumption over the next decade.

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We can cοnclude that there is a significant difference between the treatments.

This methοd is abοut determining "likely" οr "unlikely" by determining the prοbability assuming the null hypοthesis were true οf οbserving a mοre extreme test statistic in the directiοn οf the alternative hypοthesis than the οne οbserved.

Using the p-value apprοach, we can calculate the p-value fοr the F-statistic.

we see that F = 7.28. The degrees οf freedοm fοr treatments and errοr are df1 = 2 and df2 = 38, respectively. we can find that the p-value is apprοximately 0.0026.

Using the critical-value apprοach, we can find the critical value οf F fοr a significance level οf 0.05 and degrees οf freedοm df1 = 2 and df2 = 38. Frοm a table οr calculatοr, we find that the critical value is apprοximately 3.18.

Since the p-value (0.0026) is less than the significance level (0.05), we reject the null hypοthesis. Alternatively, since the F-statistic (7.28) is greater than the critical value (3.18), we reject the null hypοthesis.

Therefοre, we can cοnclude that there is a significant difference between the treatments.

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So, the answer in its simplest form is 1/200.a) Here's the completed frequency tree: Drink tea.

So, the number of people who drink at least 3 cups of tea each day is:[tex]10 * 0.2 = 2[/tex]Therefore, the fraction of the 400 people who drink at least 3 cups of tea each day is: 2 / 400This fraction can be simplified by dividing both the numerator and the denominator by their greatest common factor, which is 2:1 / 200So, the answer in its simplest form is 1/200.

A fraction is a numerical quantity representing a part of a whole or a ratio between two quantities. It is expressed as one number (the numerator) divided by another number (the denominator), separated by a horizontal line. The numerator represents the number of parts being considered, while the denominator represents the total number of equal parts that make up the whole. For example, in the fraction 3/4, the numerator is 3, which represents three parts out of a total of four equal parts. Fractions can be used to represent many different types of quantities, such as parts of a whole, ratios, percentages, and probabilities.

b) Out of the 400 people, 10 said yes to drinking tea, and 20% of those (or 0.20*10 = 2) said they drink at least 3 cups each day. Therefore, the fraction of people who drink at least 3 cups of tea each day is 2/400, which simplifies to 1/200.

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Answer:

Area_sector = 9.8 square inches

Step-by-step explanation:

A sector is a piece of a circle. Like a pie slice. We can use the angle given to find out what fraction of the circle we are looking for.

There are 360° in a circle. The sector is 125°. So the fraction of the circle we are looking for is (125/360) Of course this can be reduced, but we should just let the calculator handle it.

Now, the area of the whole circle is:

A = pi•r^2

A = pi • 3^2

The radius is given. r = 3

A = 9pi

They said to use 3.14 for pi

A = 28.26

This is the area of the whole circle, so we need to multiply by that fraction to find the area of the pie slice (sector)

Area_sector =

(125/360)28.26

= (0.3472222)28.26

= 9.8125

Round to the nearest tenth.

~= 9.8

The answer choice which is not a true statement include the following: C. the solution set of |3k + 3| ≤ -9 is {k|-4 ≥ k ≥ 2}.

In Mathematics and Geometry, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;

In order to determine the solution set to the given inequality, we would write out the absolute value function (inequality) as shown below.

|3k + 3| ≤ -9

Since |3k + 3| would always be positive and negative nine (-9) is negative,  |3k + 3| will always be greater than negative nine (-9), and as such, the inequality cannot be true and has no solution set.

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Both the lines are parallel hence, they cannot intersect each other and value of H= (0,0).

A mathematical statement known as an equation consists of two algebraic expressions separated by equal signs (=) on either side.

It demonstrates the equality of the relationship between the printed statements on the left and right.

Left side equals right side in all formulas.

To find the values of unknowable variables, which stand in for unknowable quantities, you can solve equations.

A statement is not an equation if it lacks the equals sign.

When two expressions have the same value, a mathematical statement known as an equation will include the symbol "equal to" between them.

Hence, Both the lines are parallel hence, they cannot intersect each other and value of H= (0,0).

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The width of the garden is 4 feet.

What is Rectangle ?

A rectangle is a quadrilateral with four right angles, opposite sides that are parallel, and equal in length. It is a type of parallelogram where the adjacent sides are equal in length, but the opposite sides are not necessarily equal.

Let's start by using the formula for the perimeter of a rectangle:

Perimeter = 2(length + width)

We know that the perimeter is 34 feet, so we can plug in that value and simplify:

34 = 2(l + w)

17 = l + w

We also know that the length is 5 more than 2 times the width, so we can write an equation for that:

l = 2w + 5

We can substitute this expression for l into the first equation:

17 = (2w + 5) + w

Simplifying, we get:

17 = 3w + 5

12 = 3w

w = 4

Therefore, the width of the garden is 4 feet.

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[tex]yx=5[/tex]

Explanation:

If [tex]y[/tex] varies inversely as [tex]x[/tex] then

         [tex]y\times x=k[/tex] for some constant [tex]k[/tex]

Since [tex]y = \frac{1}{8}[/tex] when [tex]x=40[/tex]

          [tex]\huge \text(\dfrac{1}{8}\huge \text)\times(40)=k[/tex]

          [tex]\longrightarrow k=5[/tex]

Answer:

the correct answer is option B.

Step-by-step explanation:

We can use the formula for the margin of error for a confidence interval for a population mean with a known population standard deviation:

Margin of error = z*σ/√n

where z is the critical value from the standard normal distribution for the desired confidence level (95% in this case), σ is the population standard deviation, and n is the sample size.

We are given that the margin of error is $135 and σ is $538. We need to find the sample size, n. To do this, we first need to find the appropriate value of z for a 95% confidence level. Using a standard normal distribution table or calculator, we can find that z = 1.96.

Substituting the values into the margin of error formula and solving for n, we have:

$135 = 1.96*($538)/√n

Squaring both sides and solving for n, we get:

n = [1.96*($538)/$135]^2 ≈ 62

Therefore, a sample size of 62 business students must be randomly selected to estimate the mean monthly earnings of business students at one college with 95% confidence that the sample mean is within $135 of the population mean, assuming the population standard deviation is known to be $538.

So the correct answer is option B.

The bird covered 34 metres of vertical space overall. Warm-blooded, feathery animals with the ability to fly are known as birds.

The bird soared 15 m above the water, dove 2 m vertically, and descended to a depth of the water that was 15 + 2 = 17 m below its starting height. The bird must fly 17 m vertically upwards in order to cover the same distance in the other direction in order to return to its starting height.

Consequently, the bird travelled a total vertical distance of 34 metres (17 metres when diving and 17 metres while returning to its starting height).

Hence, the bird covered 34 metres of vertical space overall.

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Answer:

6xy^2/(x-y)(x+y)(2x+y)(2x-y)

Step-by-step explanation:

1      - 2          +   1          - 2

x-y     2x+y         x+y        2x-y

= take LCM

Then simplify.

Answer:

-2x+2/x

Step-by-step explanation:

For acute angles A and B it is known that sin A - 28/53 and tan B = 4/3. , , the value of cos(A+B) in simplest form is -15/53.

In geometry, an angle is the measure of the amount of turn between two lines that intersect at a point, called the vertex of the angle. Angles are typically measured in degrees, but can also be measured in radians.

Angles can be classified based on their measures. An angle that measures less than 90 degrees is called an acute angle, while an angle that measures exactly 90 degrees is called a right angle. An angle that measures greater than 90 degrees but less than 180 degrees is called an obtuse angle, while an angle that measures exactly 180 degrees is called a straight angle. Finally, an angle that measures greater than 180 degrees but less than 360 degrees is called a reflex angle.

We can start by using the identity:

cos(A + B) = cos A cos B - sin A sin B

To find cos A and sin A, we can use the identity:

sin² A + cos² A = 1

sin A = √(1 - cos² A)

We are given sin A = 28/53, so we can solve for cos A:

sin² A + cos² A = 1

(28/53)² + cos² A = 1

cos² A = 1 - (28/53)²

cos A = ± √[(53/53)² - (28/53)²]

Since A is acute, we take the positive root:

cos A = √(1 - (28/53)²)

To find sin B and cos B, we can use the identity:

tan B = sin B / cos B

We are given tan B = 4/3, so we can solve for sin B and cos B using the Pythagorean identity:

sin² B + cos² B = 1

sin B = (4/3) cos B

(4/3)² cos² B + cos² B = 1

cos² B = 1 / ((4/3)² + 1)

cos B = √(1 / ((4/3)² + 1))

sin B = (4/3) cos B

Now we can substitute all of these values into the formula for cos(A + B):

cos(A + B) = cos A cos B - sin A sin B

cos(A + B) = √(1 - (28/53)²) √(1 / ((4/3)² + 1)) - (28/53) (4/3) √(1 / ((4/3)² + 1))

cos(A + B) = (√((53² - 28²) / 53²)) (√(9 / (16 + 9))) - (4/3) (28/53) (√(9 / (16 + 9)))

cos(A + B) = (45/53) (√(9/25)) - (112/265) (√(9/25))

cos(A + B) = (9/53) - (24/53)

cos(A + B) = -15/53

Therefore, cos(A + B) = -15/53.

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The correct answer for this would be: Triangles BCA and DAC are congruent according to the Angle-Side-Angle (ASA) Theorem.

A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.

According to the ASA theorem, if the included side of one triangle and its two angles are comparable to the parts of another triangle, then the triangles are said to be congruent.

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Answer: 18 students

Step-by-step explanation: 43+27+48=118 118-100=18

Step-by-step explanation:

It is not clear from the given information which angles and sides are being referred to as "107⁰", "-x-8", "-42-7", and "3y-1". However, we can use some properties of rhombuses to solve for x, y, and z.

Opposite angles in a rhombus are equal. Therefore, if one angle is 107⁰, then the opposite angle is also 107⁰.

The diagonals of a rhombus are perpendicular bisectors of each other. This means that they intersect at a right angle and divide each other into two equal parts.

The diagonals of a rhombus bisect each other's angles. This means that the angles formed by each diagonal with the sides of the rhombus are equal.

Using these properties, we can set up some equations to solve for x, y, and z:

Let's assume that "-x-8" and "-42-7" are the lengths of the diagonals of the rhombus, and that "3y-1" is the length of one of the sides.

Since the diagonals bisect each other's angles, we know that the angles formed by each diagonal with the side of the rhombus are equal. Let's call each of these angles "z":

-z + 107⁰ + z = 180⁰ (sum of angles in a triangle)

107⁰ = 180⁰ - 2z

2z = 73⁰

z = 36.5⁰

Now let's use the fact that the diagonals are perpendicular bisectors of each other:

(-x-8)/2 = (-42-7)/2

-x-8 = -49

-x = -41

x = 41

Finally, let's use the fact that the sides of a rhombus are equal:

-x-8 = 3y-1

41-8 = 3y-1

33 = 3y

y = 11

Therefore, the values of x, y, and z in the rhombus are:

x = 41

y = 11

z = 36.5⁰

The total amount that he will pay for the car will be $17,093.40, assuming a loan amount of $15,000, a down payment of $4,300, a 5-year loan term, and a 5.25% APR.

Assuming that Dean has used the $4,300 as a down payment, his loan amount would be the total cost of the car minus the down payment, which is not given in the question.

However, assuming that the loan amount is $15,000 (which would be the case if the total cost of the car was $19,300), the monthly payment would be $284.89.

To calculate the total amount that Dean pays for the car over the course of the loan, we can multiply the monthly payment by the number of payments (60 payments over 5 years) and add the down payment:

Total amount = (Monthly payment x Number of payments) + Down payment

Total amount = ($284.89 x 60) + $4,300

Total amount = $17,093.40

Therefore, if Dean gets the loan and pays it off as scheduled, the total amount that he will pay for the car will be $17,093.40.

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Answer:

The probability of not getting a blue marble is the probability of getting either a red or a green marble. P(not blue) = P(red or green) P(red or green) = P(red) + P(green) P(red or green) = 8/12 + 1/12 P(red or green) = 9/12 P(not blue) = 3/4 Therefore, the answer is D. three-fourths.

Answer:

The circumcenter of the triangle with vertices A(2,6), B(8,6), and C(8,10) is (8,6).

Step-by-step explanation:

To find the circumcenter of the triangle with vertices A(2,6), B(8,6), and C(8,10), we can use the following steps:

Step 1: Find the midpoint of two sides

We first find the midpoint of two sides of the triangle. Let's take sides AB and BC:

Midpoint of AB: ((2 + 8)/2, (6 + 6)/2) = (5, 6)

Midpoint of BC: ((8 + 8)/2, (6 + 10)/2) = (8, 8)

Step 2: Find the slope of two sides

Next, we find the slope of the two sides AB and BC:

Slope of AB: (6 - 6)/(8 - 2) = 0

Slope of BC: (10 - 6)/(8 - 8) = undefined

Step 3: Find the perpendicular bisectors of two sides

Since the slope of AB is 0, its perpendicular bisector is a horizontal line passing through the midpoint of AB, which is y=6. Since the slope of BC is undefined, its perpendicular bisector is a vertical line passing through the midpoint of BC, which is x=8.

Step 4: Find the intersection of perpendicular bisectors

The circumcenter is the point where the two perpendicular bisectors intersect. The intersection point is (8,6).

Therefore, the circumcenter of the triangle with vertices A(2,6), B(8,6), and C(8,10) is (8,6).

Answer:

145°

Step-by-step explanation:

The exterior angle 3 is equal to the sum of angle 1 and 2.

Using substitution we can say that:

5x + 4x + 10 = 10x -5

9x + 10 = 10x -5

10x-9x=10+5

x= 15

We have just found that the value of x is equal to 15.

By substituting this back to the angle 3 expression, 10x-5, we get

10(15) - 5

150 - 5

145°

So, (f o h)(-3) = 3. This is the value of the composite function (f o h) at -3. Please note that (f o h)(-3) is equivalent to f(h(-3))

An input and an output are connected by a function. It functions similarly to a machine with an input and an output. Additionally, the input and output are somehow connected. The traditional format for writing a function is f(x) "f(x) =... "

To find (f o h)(-3), we need to first evaluate h(-3), and then plug that result into the function f(x).

Given:

f(x) = -2x - 1

h(x) = -x - 5

First, we evaluate h(-3):

h(-3) = -(-3) - 5

h(-3) = 3 - 5

h(-3) = -2

Now, we plug the result of h(-3) into the function f(x):

f(h(-3)) = f(-2)

f(h(-3)) = -2(-2) - 1

f(h(-3)) = 4 - 1

f(h(-3)) = 3

So, (f o h)(-3) = 3. This is the value of the composite function (f o h) at -3. Please note that (f o h)(-3) is equivalent to f(h(-3)), which means we first evaluate h(-3) and then plug that result into f(x). I hope this helps! Let me know if you have any further questions. :)

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The GPA corresponding to the 70th percentile at the college is approximately 3.246 based on standard deviation.

We can use the conventional normal distribution table or a calculator with a normal distribution function to determine the 70th percentile of GPAs at a college, which are normally distributed with a mean of 2.9 and a standard deviation of 0.6.

The inverse normal distribution function with a mean of 2.9, a standard deviation of 0.6, and a percentile of 70 can be used on a calculator. This results in:

[tex]3.246 for invNorm(0.7, 2.9, 0.6).[/tex]

As a result, the GPA that represents the 70th percentile is roughly 3.246.

We can determine the z-score corresponding to the 70th percentile, which is 0.5244, by using a common normal distribution table. Thus, we may apply the equation z = (x - ) /, where x is the GPA that corresponds to the 70%ile, is the mean, and is the standard deviation, and all three variables have values of 2.9. After finding x, we obtain:

0.5244 = (x - 2.9) / 0.6

x = 3.246

Once more, doing so yields the same outcome as using a calculator.

In conclusion, the GPA at the college that represents the 70th percentile is roughly 3.246.

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Tom would bank Ksh 277,272.73 and John would bank Ksh 693,939.39 at the end of the business day with 25% markup.

The markup is the discrepancy between a product's selling price and its cost price. Adding a particular percentage to the cost price to arrive at the selling price of a product is a frequent practise in business. Depending on the sector, the level of competition, and other elements, the markup % may change.

Since it influences a product's or service's profitability, markup is significant in business. If the markup is too low, the company could not have a sufficient profit to pay its bills and continue operating. The product could not be competitive with other similar items on the market if the markup is too high.

Let us suppose the cost price and sales price = x.

Thus,

For Tom:

Cost of 5 A + Cost of 2B = 5x + 2x = 7x

Sale of 10 B = 10(2x) = 20x

Here,

Profit = Sale - Cost = 20x - 7x = 13x

For the given value of profit we have:

Tom's profit = Ksh 230,000

13x = 230,000

x = 17,692.31

Simillarly for Jhon:

or John:

Sale of 3 A = 3(5x) = 15x

Cost of 13 B = 13x

Profit = Sale - Cost = 13x - 15x = -2x

John's profit = Ksh 110,000

-2x = 110,000

x = -55,000

Now, the markup is 25%,:

New cost price for John = 17,692.31

New sale price for John = 17,692.31 + 0.25(17,692.31) = 22,115.39

Actual sale price for John = 22,115.39 - 0.15(22,115.39) = 18,798.08

The new profit is thus:

New cost price for John = 17,692.31

New sale price for John = 17,692.31 + 0.25(17,692.31) = 22,115.39

Actual sale price for John = 22,115.39 - 0.15(22,115.39) = 18,798.08

Hence, Tom would bank Ksh 277,272.73 and John would bank Ksh 693,939.39 at the end of the business day.

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Answer: 63,932

Step-by-step explanation:

September: 11,724

October: 14,380 + 11,724 = 26,104

November: 14,380 + 11,724 = 26,104

Combine all 3 months to get your answer= 63,932