Combine √2 -3√2 5√2 to write one single simplified radical

Answer: y = (1/4)x^2 + 1

Step-by-step explanation:

The equation of a parabola in vertex form is given by:

y = a(x-h)^2 + k

Where (h,k) is the vertex of the parabola and "a" is a coefficient that determines the shape of the parabola.

In this case, the vertex is given as (0,1), so h=0 and k=1. Also, the parabola passes through the point (8,17), which means that when x=8, y=17. We can use this information to solve for "a".

Substituting the values of h, k, x, and y in the equation, we get:

17 = a(8-0)^2 + 1

Simplifying this equation, we get:

17 - 1 = 64a

16 = 64a

a = 16/64

a = 1/4

Now that we know the value of "a", we can substitute it in the vertex form equation to get the final equation of the parabola:

y = (1/4)(x-0)^2 + 1

Simplifying this equation, we get:

y = (1/4)x^2 + 1

Therefore, the equation of the parabola in vertex form is y = (1/4)x^2 + 1.

Explanation:

We start with the general equation of a parabola in vertex form and substitute the given values of the vertex and the point that the parabola passes through. Then, we solve for the coefficient "a" by simplifying the resulting equation. Once we have the value of "a", we substitute it in the vertex form equation to obtain the final equation of the parabola.

The statement "25 = 14" is clearly false, so Kermit's solution of x = 5 is not correct. Therefore, Kermit made a mistake in solving the equation.

What is the equivalent expression?

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

To check if Kermit's solution is correct, we can substitute x = 5 back into the original equation and see if it makes a true statement:

5(x - 4) + 20 = 14

5(5 - 4) + 20 = 14

5(1) + 20 = 14

25 ≠ 14

Hence, The statement "25 = 14" is clearly false, so Kermit's solution of x = 5 is not correct. Therefore, Kermit made a mistake in solving the equation.

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Answer: (a) John spent 2/5 of the remainder of his money on a toy. Let's first find the remainder of his money after he spent 20% on food. If he spent 20% on food, then he has 80% of his money remaining. So, if he had $x initially, he has $0.8x remaining.

John spent 2/5 of the remainder on a toy, so we can set up the equation:

(2/5)(0.8x) = 12

Simplifying, we get:

0.32x = 12

Dividing both sides by 0.32, we get:

x = 37.5

So, John initially had $37.5.

To find the percentage of his money he spent on the toy, we can use the following formula:

Percentage = (amount spent on toy / initial amount) * 100%

The amount John spent on the toy is $12, and his initial amount is $37.5, so we get:

Percentage = (12 / 37.5) * 100% = 32%

Therefore, John spent 32% of his money on the toy.

(b) John initially had $37.5.

Step-by-step explanation:

Therefore, the cost price is $1113.64 if the selling price is $980 and the loss is 12%.

Cost price (also known as CP) is the amount of money that is required to produce or purchase a particular product or service. It includes all the expenses incurred in the production or purchase of a product, such as the cost of raw materials, labor, transportation, rent, and other overhead expenses. The cost price is an important factor in determining the profit margin of a business, as it is used to calculate the selling price of a product or service. In general, the cost price is the amount that a seller pays to acquire a product, while the selling price is the amount that a buyer pays to purchase the same product.

Let's assume that the cost price is "C".

We know that the selling price (S) is $980, and the loss percentage is 12%.

We can use the formula for calculating the cost price:

C = S / (1 - Loss%)

where Loss% is expressed as a decimal (i.e., 12% = 0.12).

Substituting the values, we have:

C = $980 / (1 - 0.12)

C = $980 / 0.88

C = $1113.64

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The experimental probability that the card selected was a K or 6 is option B.

What is Probability?

PrοbabiIity is the study οf the chances οf οccurrence οf a resuIt, which are οbtained by the ratiο between favοrabIe cases and pοssibIe cases.

Frοm the tabIe, we can see that the frequency οf drawing a K οr 6 is:

Frequency(K οr 6) = Frequency(K) + Frequency(6) = 4 + 10 = 14

The tοtaI number οf draws is 100.

The experimentaI prοbabiIity οf drawing a K οr 6 can be caIcuIated as:

ExperimentaI PrοbabiIity(K οr 6) = Frequency(K οr 6) / TοtaI number οf draws

ExperimentaI PrοbabiIity(K οr 6) = 14 / 100

ExperimentaI PrοbabiIity(K οr 6) = 0.14

Therefοre, the experimental prοbabiIity that the card seIected was a K οr 6 is 0.14 οr 14%. Optiοn b is the cοrrect answer.

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The volume of the sphere is 32/3 cubic feet.

What is Volume ?

Volume is a measure of the amount of space that a three-dimensional object takes up. It is typically measured in cubic units such as cubic meters, cubic centimeters, cubic feet, or cubic inches.

To find the volume of a sphere, we use the formula:

V = (4/3) * pi * [tex]r^{3}[/tex]

where V is the volume of the sphere, pi is the constant pi (3.14...), and r is the radius of the sphere.

In this case, the radius of the sphere is given as 2ft. So, substituting this value into the formula, we get:

V = (4/3) * 3 * [tex](2ft)^3[/tex]

= (4/3) * 3 * 8[tex]ft ^ 3[/tex]

= 32/3 [tex]ft ^ 3[/tex]

Therefore, the volume of the sphere is 32/3 cubic feet.

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Answer:

X=18.88

Step-by-step explanation:

This is a 90 degree triangle which means that you can use Sin, Cos, Or Tan. In this case you have to use Tan as you don't know the hypotenuse length. Which means you would set up an equation that looks like Tan(42°)=17/x as tangent is opposite over adjacent. Then if you were to solve for X eventually you'll get X= 17/Tan(42°) and if you plug it in a calculator you would get that X= 18.88 or 19 if you round to a whole number.

Answer:

  A)sin(100°) >0 and tan (100°) < 0

Step-by-step explanation:

You want to know the signs of sin(100°) and tan(100°).

100° is an angle in the 2nd quadrant, where angles between 90° and 180° lie.

In that quadrant, the sine function is positive, and the cosine function is negative. The tangent is the ratio of sine to cosine, so the tangent is negative in the 2nd quadrant.

__

Additional comment

Of course, your calculator can help you figure this out. Be sure it is in degrees mode.

The second attachment shows you sine is positive above the x-axis; cosine is positive to the right of the y-axis. Everything else derives from this.

We can expect her to pick about 70 blue marbles in the next 200 rounds.

We must divide the number of blue marbles by the total number of marbles to determine the likelihood of selecting a blue marble in a single round:

P(blue) = 14/40 = 7/20

Since the experiment has been conducted 50 times, we may anticipate that the proportion of blue marbles will eventually be around 7/20. This suggests that in the subsequent 200 rounds, Zendaya will likely choose to focus on:

70 blue marbles result from P(blue) 200 = (7/20) 200.

So, in the following 200 rounds, we can anticipate her choosing roughly 70 blue marbles.

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Answer:

The answer would 81, LOLOLOLOL

Step-by-step explanation:

Answer:

Step-by-step explanation:

1 quarter = 25 cents

1 dime = 10 cents

Let

q = the number of quarters, q>=0, q is integer

d = the number of dimes, d>=0, d is integ

30 coins totaling $4.80 = 480 cents:

q + d = 30

25q + 10d = 480

q = 12 quarters

d = 18 dimes

12 quarters and 18 dimes.

Answer:

Let x be the number of dimes in the jar.

Then the number of quarters in the jar would be 30 - x.

The total value of the dimes in the jar would be 0.10x, and the total value of the quarters would be 0.25(30 - x) = 7.50 - 0.25x.

We know that the total value of the coins is $4.80, so we can set up the equation:

0.10x + 7.50 - 0.25x = 4.80

Simplifying and solving for x, we get:

0.15x = 2.70

x = 18

Therefore, there are 18 dimes and 30 - 18 = 12 quarters in the jar.

Step-by-step explanation:

To create a confidence range for the population standard deviation, we can use the chi-square distribution. Finding the chi-square values that correlate to 10% and 90% in the right tail of the distribution is necessary given that we have 94 samples and want an 80% confidence range.

The chi-square value for the 10th percentile is 71.47, and the chi-square value for the 90th percentile is 112.31, according to a chi-square distribution chart with 93 degrees of freedom (n-1).

The confidence interval's calculation is:

((n-1)*s2)/sqrt(X), (n-1)*s2)/sqrt(Y))

Where:

The group number is n.

The sample's standard variation is s.

X represents the bottom limit of the confidence interval's chi-square value.

Y is the chi-square value for the upper bound of the confidence interval

Substituting the values we have:

(sqrt((94-1)*4.11^2)/sqrt(112.31)) = 5.63

(sqrt((94-1)*4.11^2)/sqrt(71.47)) = 4.81

Therefore, the 80% confidence interval for the population standard deviation of the widths of all doors in this factory is (4.81, 5.63).

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Answer:

C. Camille used the subtraction property of equality in step 5.

Step-by-step explanation:

In step 2, Camille subtracted 80 from both sides of the equation. In step 3, she simplified the equation by combining like terms. In step 4, Camille divided both sides of the equation by 70 to isolate the variable x. In step 5, she subtracted y-80 from both sides of the equation to isolate x. In step 6, Camille simplified the equation by dividing both sides by -1/70. Finally, in step 7, she calculated the value of x.

Therefore, option C is the correct answer.

The answer of the given question based on the histogram that shows battery life is, (A). The distribution of the data is approximately symmetric. (B).  The mean battery life is around 125 hours.

Data distribution refers to pattern or shape of how data is spread out or distributed over range of values. It is important to understand  distribution of data because it can provide insights into nature of the data and inform statistical analysis.

There are several ways to describe  distribution of data, including measures of center (like mean, median, and mode) and measures of spread (like range, variance, and standard deviation)

A. The distribution of the data is approximately symmetric.

B. The mean battery life can be estimated by finding the center of the histogram, which appears to be around 125 hours. However, without knowing the exact bin widths or the midpoint of each bin, it is difficult to estimate the mean precisely.

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Based on the histogram that displays energy life, the following is the response to the question:

a). The data are distributed in a roughly symmetrical manner.

b). An average charge lasts for about 125 hours.

Data distribution describes the way that data is dispersed or distributed across a variety of values. Understanding data distribution is crucial because it can shed light on the character of the data and help with statistical analysis.

Measures of the center (like mean, median, and mode) and measures of spread are two methods to describe data distribution. (like range, variance, and standard deviation).

A). The facts are distributed in a roughly symmetrical manner.

B). You can determine the average battery life by locating the histogram's center, which looks to be 125 hours.

It is challenging to calculate the mean exactly without knowing the precise bin widths or the midpoint of each bin, though.

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The image of the question attached below,

The equation of the parabola is

[tex]y = \frac{1}{32} {x}^{2} [/tex]

What is the vertex form of the equation of a parabola?

[tex]y = a {(x - h)}^{2} + k[/tex]

where (h, k) is the vertex and 'a' is a constant that determines the shape of the parabola. For a parabola with a horizontal axis of symmetry (opening to the right or left), the focus is (h + c, k), where c is the distance from the vertex to the focus, and the directrix is the line x = h - c.

Given,the vertex of a parabola is (0, 0) and the focus is(1/8,0).

We want to find equation of the parabola.

Given by In this problem, the vertex is at (0,0) which means h=0 and k=0. Also, the focus is at (1/8,0) which means c=1/8. So, the directrix is the line x = -1/8.

Since the parabola opens to the right, the equation of the parabola can be written as:[tex]y = {(x - 0)}^{2} + 0[/tex]

or simply: [tex]y = a {x}^{2} [/tex]

To find the value of 'a', we need to use the distances formula between the vertex and the focus:

[tex]c = \frac{1}{8} = \sqrt{ \frac{4a}{2} } \\ a = \frac{1}{32} [/tex]

Therefore, the equation of the parabola is:

[tex]y = \frac{1}{32} {x}^{2} [/tex]

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Part A:

First, we need to find the dimensions of the print by multiplying the dimensions of the original painting by the scale factor of 3.

The width of the print is 14 inches x 3 = 42 inches

The length of the print is 24 inches x 3 = 72 inches

To convert these dimensions into feet, we need to divide by 12 (since there are 12 inches in a foot):

Width of print = 42 inches / 12 = 3.5 feet

Length of print = 72 inches / 12 = 6 feet

Therefore, the dimensions of the print are 3.5 feet by 6 feet.

Part B:

To find the area of the print, we need to multiply the width by the length:

Area of print = (3.5 feet) x (6 feet) = 21 square feet

Therefore, the area of the print is 21 square feet

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Answer:

The scale factor to dilate ABCD to WXYZ is 1/sqrt(2) or (sqrt(2))/2.

The scale factor to dilate ABCD to WXYZ is k = 2.

Given data:

To find the scale factor between two similar figures,  compare the corresponding side lengths.

The perimeter of triangle BCD is 16 and the perimeter of triangle XYZ is 32. Since corresponding sides of similar triangles are proportional, the ratio of their perimeters to determine the scale factor.

The scale factor is calculated by dividing the perimeter of triangle XYZ by the perimeter of triangle BCD:

Scale factor = Perimeter of XYZ / Perimeter of BCD

Scale factor = 32 / 16 = 2

Hence, the scale factor to dilate pyramid ABCD to WXYZ is 2.

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B. Lin can make 2 batches of blueberry muffins.

C. Lin needs to make 2/3 of a batch of blueberry muffins to use all of the blueberries.

What is mixed fraction?

A mixed number is one that contains both a whole number and a fraction. The fraction is written after the whole number, with a space or plus sign placed between them. The mixed number 2 1/4 serves as an explanation for how the numbers 2 and 1/4 were added. Objects that aren't whole numbers but are close to them, such length or time measurements, are typically represented by mixed numbers.

a) Diagram

   4 cups of blueberries

    __ __ __ __

    |    |     |    |    |

    |__|__|__|__|

Each batch uses 3/2 cups of blueberries

B) To find the number of batches Lin can make, we need to divide the total amount of blueberries by the amount of blueberries per batch:

4 cups of blueberries ÷ (3/2 cups of blueberries per batch)

= (4 cups of blueberries) × (2/3 batches per cup of blueberries)

= 8/3 batches

Therefore, Lin can make 8/3 or approximately 2.67 batches of blueberry muffins using all of the blueberries.

C) To find the fraction of a batch Lin will need to make in order to use all of the blueberries, we need to subtract the number of whole batches from the total number of batches:

8/3 batches - 2 batches = 2/3 of a batch

Therefore, Lin will need to make 2/3 of a batch in order to use all of the blueberries.

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   The diagram shows two intersecting lines, labeled line m and line n. Line m intersects line n at a point labeled point P. There are several angles labeled in the diagram:

Note that angles 1, 3, 5 are all alternate interior angles formed by the intersection of line m and line n.

Answer:

If the scale factor is -5, it means that the new image will be a reflection across the origin (negative scale factor means reflection) and enlarged by a factor of 5.If the scale factor is 1/2, it means that the new image will be half the size of the original image.If the scale factor is 0.4, it means that the new image will be 40% of the size of the original image.If the scale factor is 3/2, it means that the new image will be enlarged by a factor of 3/2 or 1.5 times the size of the original image.If the scale factor is 1, it means that the new image will be the same size as the original image.II.   The diagram shows two intersecting lines, labeled line m and line n. Line m intersects line n at a point labeled point P. There are several angles labeled in the diagram:Angle 1 is an acute angle that is adjacent to angle 2.Angle 2 is a right angle formed by the intersection of lines m and n.Angle 3 is an obtuse angle that is adjacent to angle 2.Angle 4 is a vertical angle to angle 2 and is congruent to angle 2.Angle 5 is an acute angle that is adjacent to angle 4.Angle 6 is a straight angle formed by the collinear extension of lines m and n.Note that angles 1, 3, 5 are all alternate interior angles formed by the intersection of line m and line n.

Step-by-step explanation:

The point (2, 2) would end up at the point (1, 1) after the transformations.

Functions can be represented in different ways, including graphs, tables, and equations. A graph of a function is a visual representation of the relation between the inputs and outputs, usually plotted on a coordinate plane. A table of values lists the inputs and corresponding outputs of a function. An equation of a function expresses the rule for calculating the output in terms of the input variable.

To sketch the graph of the new function h(x), we can start by considering the effect of each transformation on the original function f(x).

First, we have a horizontal shift of 1 unit to the left, since we are subtracting 1 from the argument of f(x). This means that the graph of f(x+1) will be shifted 1 unit to the left compared to the graph of f(x).

Next, we have a vertical stretch by a factor of 2, since we are multiplying the output of f(x+1) by 2. This means that the graph of 2f(x+1) will be twice as tall as the graph of f(x+1).

Finally, we have a vertical shift downwards by 3 units, since we are subtracting 3 from the output of 2f(x+1). This means that the graph of h(x) will be shifted 3 units downwards compared to the graph of 2f(x+1).

To find where the point (2, 2) ends up after these transformations, we can first apply the horizontal shift of 1 unit to the left, which gives us the point (1, 2). Next, we apply the vertical stretch by a factor of 2, which gives us the point (1, 4). Finally, we apply the vertical shift downwards by 3 units, which gives us the point (1, 1).

Therefore, the point (2, 2) would end up at the point (1, 1) after the transformations.

To sketch the graph of h(x), we can start with the graph of f(x) and shift it 1 unit to the left, stretch it vertically by a factor of 2, and shift it 3 units downwards. The resulting graph will have the same shape as the graph of f(x), but will be shifted and scaled as described above. The point (1, 1) will be on this graph as well.

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A. Regardless of the values of b and c, the point (-2,2) is included in the curve of g(x).

B. On the graph of h(x), the point (2,2) would be changed into the point (2,1).

A graph is a graphical representation of data, functions, or variable connections. It is a method of displaying information that is simple to analyse and comprehend.

Graphs are widely used in a variety of disciplines, including science, economics, business, engineering, and others. They make it simpler for researchers and analysts to visualise data and identify trends or patterns, allowing them to draw conclusions and make educated choices based on the data.

A. To include the spot (-2,2), we must shift the f(x) graph two units to the right and two units up. So far, we have:

g(x) = a f(x - (-2)) + 2

g(x) = a f(x + 2) + 2

We must now determine the worth of "a." Because the point (3,4) on the f(x) graph is transferred to the point (2,2) on the g(x) graph, we have:

g(3) = a f(3 + 2) + 2 = 2

4a + 2 = 2

4a = 0

a = 0

Therefore, the function g(x) is:

g(x) = 0 f(x + 2) + 2

g(x) = 2

As a result, independent of the values of b and c, the point (-2,2) is included in the graph of g(x).

B. The function h(x) has a slope of 2 and a y-intercept of -1. We plug x=2 into h(x) to determine where the point (2,2) would end up after the transformations and get:

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

As a result, the point (2,2) on the graph of h(x) would be changed to the point (2,1).

The transformations applied to f(x) to produce h(x) are a one-unit horizontal shift to the left (x+1), a two-unit vertical stretch (2(x+1)), and a three-unit vertical shift downwards (-3).

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Complete question and graph attached below,

Answer: x>-18

Step-by-step explanation:

simplify

9x-24-12x<30

-3x-24<30

-3x>54

-x>18

x>-18

The value of y when x is equal to 10 is 60.

Value in math is the numerical representation of a given quantity. It can be a literal number, a variable, or an expression. Values are used to solve equations, calculate statistics, and determine patterns. They can be used to measure physical quantities such as length, area, volume, and force. Values are also used to measure abstract concepts such as money, probability, and time. Values help us understand and make sense of the world around us.

The value of y when x is equal to 10 can be calculated by using y = mx + c, where m is the gradient and c is the y-intercept of the line. Using the given values, we can calculate the equation of the line to be y = 5x + 10.

Therefore, when x = 10, y = 5(10) + 10 = 60.

Therefore, the value of y when x is equal to 10 is 60.

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Answer:

2/7 is the right answer

14 and 21 are both divisible by 7, their GCF, so if you divide the numerator and the denominator by 7, you get the fraction 2/7

To calculate the probability of Gretchen getting a roast beef sandwich on wheat bread and popcorn in her boxed lunch, we need to know the total number of possible boxed lunch combinations and the number of boxed lunches that contain roast beef on wheat bread and popcorn.

Let's assume there are 4 different types of sandwiches available: roast beef on wheat bread, turkey on white bread, ham on rye bread, and vegetarian on whole wheat bread. Also, let's assume there are 3 different snack options available: popcorn, chips, and fruit.

If each boxed lunch contains one sandwich and one snack, then there are 4 x 3 = 12 possible boxed lunch combinations.

Out of these 12 combinations, we need to determine how many contain roast beef on wheat bread and popcorn. Let's say there are 2 boxed lunches that contain roast beef on wheat bread and popcorn.

Therefore, the probability of Gretchen randomly choosing a boxed lunch with roast beef on wheat bread and popcorn is 2/12, which simplifies to 1/6, or approximately 0.1667.

So, there is a 16.67% chance that Gretchen will get a roast beef sandwich on wheat bread and popcorn in her box.

The surface area of the toy box is 846 [tex]cm^2[/tex].

What is surface area?

A three-dimensional object's surface area is the space it takes up when viewed from the outside.

Here the given toy is form of rectangular prism.

Length = 15 cm , width w = 9 cm and height h = 12 cm

Surface area of the rectangular prism is,

=> A = 2( lw+ wh+ lh) square unit.

=> A = 2( 15*9+9*12+12*15)

=> A = 2(135+108+180)

=> A = 2(423)

=> A= 846 [tex]cm^2[/tex].

Hence surface area of the rectangular prism is 846 [tex]cm^2[/tex].

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Answer:

205:275

300:

Find the answer

After answering the provided question, we can conclude that Following expression the completion of the necessary journal entries, the T-account for Cash would show an adjusted balance of $2,575.

An expression in mathematics is a collection of representations, octal, and huge corporations that resemble a clear association or regimen. A real number, a mutable, or a combination of the two can be used as an expression. Mathematical operators include inclusion, subtraction, rapid spread, division, and exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.

Starting Balance: $4,000

Addition: $900 EFT deposit from tenant

Less: ($65) service charges

Less: ($460) NSF check

$4,375 in adjusted bank balance

Book Balance according to Company Records:

Starting Balance: $3,200

Addition: $350 deposit not yet recorded

($525) in outstanding checks [$205 + $320]

Less: Erroneous $500 check recorded: ($450) [$500 - $50]

$2,575 in Adjusted Book Balance

Bank Reconciliation: Modified $4,375 in bank balance

$2,575 in Adjusted Book Balance

The difference is $1,800. (overdraft)

a. Not yet recorded deposit:

Debit: $350 in cash

Credit: $350 in earnings

b. Uncollected checks:

Debit: $525 Accounts Payable

Credit: $525 in cash

c. Incorrectly recorded $500 check:

Debit: $450 Accounts Payable

Credit: $450 in cash

Following the completion of the necessary journal entries, the T-account for Cash would show an adjusted balance of $2,575.

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complete question

the following data  gathered the latest details for Synchronic, Inc.:

A. The bank amount as of July 31 was $4,000.

a. There have been $65 in service fees on the bank statement.

c. The bank statement showed an EFT deposit of $900 for the tenant's monthly rent.

d. The cancelled checks that were included with the statement were not checks #541 and #543, which were for amounts of $205 and $320, respectively.

g. The $350 deposit made on July 31 did not show up on the bank statement.

f. A $50 cheque was mistakenly reported as $500 by the bookkeeper. A seller received the check as payment for a debt.

g. A check from Synchronize Corporation for $200 that was taken out of Synchronic' account was included with the cancelled checks.

h . An NSF check for a $460 payment to an account that was written by Multimedia, Inc. was also included in the bank statement.

i. As of July 31, the bank had a $3,200 balance in the cash account.

1. Complete the bank reconciliation for Synchronic, Inc. on July 31.

2. Modify the company's cash position.