The total weight of 36 packets of crisps is 864 grams. There are 505 calories in 100 grams of crisps. Work out how many calories are there in one packet of crisps. 1​

Answer:

6(2y-3)

Step-by-step explanation:

Both 12 and 18 divide by 6.

12/6= 2 and 18/6 = 3

So we can take 6 out and put it outside the bracket and have 2y and 3 on the inside.

A raccoon consumes 500 calories of food. Of those calories, 50 are transformed into biomass. In other words, 50 calories of energy are stored In Its body. So, option D is correct.

When a raccoon eats 500 calories of food, some of those calories go towards its daily needs for warmth, movement, and reproduction. The raccoon's body does not store this energy; instead, it is transformed into other forms, including heat and movement. In addition, a portion of the energy in meals is expelled as waste rather of being absorbed. Nonetheless, 50 calories of the food's energy are transformed into biomass, which is then stored as fat or tissue in the raccoon's body. Thus, the right response is D) Its body stores 50 calories of energy.

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The actual question is:

A raccoon consumes 500 calories of food. Of those calories, 50 are transformed into biomass. In other words:

A) 50 calories turn into plant matter.

B) 50 calories leave the raccoon's body as waste.

C) In order to stay warm, reproduce, and move around, it needs 50 calories of energy.

D) 50 calories of energy are stored In Its body

Step-by-step explanation:

[tex]{ \tt{x(y + 2)}}[/tex]

We need to multiply inner terms i.e. y+2 with x

[tex]{ \red{ \tt{xy + 2x}}}[/tex]

Answer:

xy +2x

Step-by-step explanation:

x(y+2)

Distribute the x to each term inside the parentheses.

x*y + x*2

xy +2x

If the perimeter of the base of the pyramid is 314 centimeters, then radius of the cone is approximately 17.44 centimeters.

Perimeter is a measurement of the distance around the outside of a two-dimensional shape. It is the sum of the lengths of the shape's sides.

Since the pyramid and cone have the same base and slant height, they are similar geometric figures. Therefore, their corresponding dimensions are proportional. Let's denote the radius of the cone as r.

Since the perimeter of the base of the pyramid is 314 centimeters, and the base of the pyramid is a square, we can find the length of one side of the square base by dividing the perimeter by 4:

Length of one side = Perimeter / 4 = 314 cm / 4 = 78.5 cm

Since the pyramid and the cone have the same area of the base, and the base of the pyramid is a square, we can find the area of the base by squaring the length of one side:

Area of the base = (Length of one side)² = (78.5 cm)²= 6,152.25 cm²

Since the pyramid and the cone have the same surface area, we can use the formula for the surface area of a cone to find the radius of the cone:

Surface area of the cone = πr(r + l), where l is the slant height.

The surface area of the cone is equal to the surface area of the pyramid, so we have:

πr(r + l) = 2 × Area of the base + Perimeter × l

Substituting the known values, we get:

πr(r + 13) = 2 × 6,152.25 cm² + 314 cm × 13 cm

Simplifying and solving for r, we get:

πr² + 13πr - 4,059.5 = 0

Using the quadratic formula, we find:

r ≈ 17.44 cm (rounded to two decimal places).

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Based on the information provided, the only possible number that satisfies all the conditions is 20.

What is GCF?

GCF stands for "Greatest Common Factor". It is also sometimes referred to as the "Greatest Common Divisor" (GCD). The GCF of two or more numbers is the largest positive integer that divides evenly into each of the numbers. In other words, it is the largest factor that the numbers have in common.

The GCF (Greatest Common Factor) of 18, 36, and a number N is 2. Since 18 and 36 are both even numbers with a common factor of 2, any number that satisfies this condition must also be even and have a factor of 2.

The number N is a multiple of 5. Since the number is even and has a factor of 2, the only even multiple of 5 between 18 and 30 is 20.

Finally, we are given that N is greater than 18 and less than 30. The only number that satisfies all the given conditions is therefore 20.

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Answer:

y=2(x-3)²-12

Step-by-step explanation:

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &20000\\ r=rate\to 25\%\to \frac{25}{100}\dotfill &0.25\\ t=\textit{elapsed time}\dotfill &2\\ \end{cases} \\\\\\ A = 20000(1 - 0.25)^{2} \implies A=20000(0.75)^2\implies A = 11250[/tex]

The purpose of doing a multiple comparison is to show the relationship between the population means when the null hypothesis of an ANOVA test is rejected.

Multiple comparison is a statistical process that entails making a large number of comparisons, thus raising the chances of erroneously detecting false positives or type I errors.

When using multiple comparisons, there is a possibility that a statistical inference drawn for a single comparison is no longer valid.

Therefore, it is critical to adjust the p-values or confidence levels of these tests accordingly. As a result, multiple comparison methods have been devised.

The following are the purposes of doing multiple comparisons:

The relationship between the population means is shown when the null hypothesis of an ANOVA test is rejected.

A multiple comparison is used to compare the results of a one-way ANOVA to the results of a two-way ANOVA.

A multiple comparison is equivalent to a one-way ANOVA, except for more than two populations.When at least one of the variances is different, a multiple comparison shows the relationship between the variances.

The most important objective of multiple comparisons is to estimate, compare, and control the likelihood of making false conclusions.

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An equation that is the best model for a line of best fit for the data include the following: C. y = 3/4x + 5.

In order to determine an equation for the line of best fit that models the data points contained in the graph (scatter plot), we would have to use a graphing calculator (Microsoft Excel).

Based on the scatter plot (see attachment) which models the relationship between the x-values and y-values, an equation for the line of best fit is given by

y = 3x/4 + 5

In conclusion, we can reasonably infer and logically deduce that the scatter plot most likely indicates a linear relationship between the x-values and y-values.

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Complete Question:

Which of the following equations is the best model for a line of fit for the data?

y= 1/4x + 5.

y= -1/4x + 5.

y= 3/4x + 5.

y= -3/4x + 5.

In conclusion Rounding to four decimal places, we get:

f(t) = 9100e²(0.1398t)

How to solve?

To write the function F(t) = 9100(1.15)²t in the form f(t) = ae²(kt), we need to first take the natural logarithm of both sides:

ln(F(t)) = ln(9100(1.15)²t)

ln(F(t)) = ln(9100) + ln(1.15²t)

ln(F(t)) = ln(9100) + t × ln(1.15)

Now, we have the form ln(F(t)) = ln(a) + kt, where k = ln(1.15) and a = 9100. We can exponentiate both sides of this equation to get:

F(t) = e²(ln(a) + kt)

F(t) = e²ln(a) × e²(kt)

F(t) = a × e²(kt)

Substituting the values of a and k, we get:

F(t) = 9100 × e²(0.1398t)

Rounding to four decimal places, we get:

f(t) = 9100e²(0.1398t)

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The parameters of the relevant standard beta distribution are alpha and beta.

These are two parameters that determine the shape of the beta distribution

.The standard beta distribution is a continuous probability distribution that is defined on the interval [0, 1]. It is often used to model the probability of success or failure in a binary experiment.

The two parameters of the standard beta distribution determine the shape of the distribution. Alpha is the shape parameter that determines the slope of the distribution, while beta is the shape parameter that determines the height of the distribution.

The standard beta distribution is often used in Bayesian statistics to model the prior probability of a parameter. It is also used in applications such as modeling the proportion of a population that has a particular characteristic or modeling the probability of default on a loan.

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Step-by-step explanation:

To find the remainder when 3x^3 - x^2 + 2x - 4 is divided by (x - 2), we can use synthetic division.

First, we write the coefficients of the polynomial in descending order of powers of x, with any missing terms represented by a coefficient of 0:

3 1 -1 2 -4

To perform synthetic division, we bring down the first coefficient (1) and multiply it by the divisor (x - 2) to get the first entry in the second row, which we then add to the second coefficient:

3 1 -1 2 -4

1

1

We repeat the process with the new coefficient in the third row, multiplying it by the divisor and adding it to the next coefficient:

3 1 -1 2 -4

1 3

1 2

Finally, we repeat the process with the new coefficient in the third row to get the last entry in the second row:

3 1 -1 2 -4

1 3 8

1 2 4

The last entry in the third row is the remainder, which is 4. Therefore, the remainder when 3x^3 - x^2 + 2x - 4 is divided by (x - 2) is 4.

The total length of the cross-country course include the following: 16 miles.

In Mathematics and Geometry, the perimeter of a rectangular shape such as a parallelogram can be calculated by using this mathematical expression;

P = 2(L + B)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangular shape, we have the following;

P = 2(L + B)

P = 2(6 + 2)

P = 2(8)

P = 16 miles.

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Complete Question:

A cross-country course is in the shape of a parallelogram with a base of length 6 mi and a side of length 2 mi.

What is the total length of the cross-country course?

Answer:    The total length of the cross-country course include the following: 16 miles.

How to calculate the perimeter of a rectangle?

In Mathematics and Geometry, the perimeter of a rectangular shape such as a parallelogram can be calculated by using this mathematical expression;

P = 2(L + B)

Where:

P represent the perimeter of a rectangle.

B represent the breadth of a rectangle.

L represent the length of a rectangle.

By substituting the given side lengths into the formula for the perimeter of a rectangular shape, we have the following;

P = 2(L + B)

P = 2(6 + 2)

P = 2(8)

P = 16 miles.

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Complete Question:

A cross-country course is in the shape of a parallelogram with a base of length 6 mi and a side of length 2 mi.

What is the total length of the cross-country course?

Step-by-step explanation:

The combinations of side lengths that will form a triangle with vertices X, Y, and Z are C and D.

For a set of three side lengths to form a triangle, the sum of any two sides must be greater than the third side. Using this property, we can determine which of the given combinations of side lengths will form a triangle with vertices X, Y, and Z.

A. XY = 8 mm, YZ = 12 mm, XZ = 23 mm

Here, XY + YZ = 8 mm + 12 mm = 20 mm, which is less than XZ = 23 mm. Therefore, this combination of side lengths will not form a triangle.

B. XY = 11 mm, YZ = 9 mm, XZ = 23 mm

Here, XY + YZ = 11 mm + 9 mm = 20 mm, which is less than XZ = 23 mm. Therefore, this combination of side lengths will not form a triangle.

C. XY = 11 mm, YZ = 12 mm, XZ = 20 mm

Here, XY + YZ = 11 mm + 12 mm = 23 mm, which is greater than XZ = 20 mm. Therefore, this combination of side lengths will form a triangle.

D. XY = 14 mm, YZ = 12 mm, XZ = 29 mm

Here, XY + YZ = 14 mm + 12 mm = 26 mm, which is greater than XZ = 29 mm. Therefore, this combination of side lengths will form a triangle.

Therefore, the combinations of side lengths that will form a triangle with vertices X, Y, and Z are C and D.

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Which of the following combinations of side lengths will form a triangle with vertices X, Y, and Z?

A.XY = 8 mm , YZ = 12 mm , XZ = 23 mm

B.XY = 11 mm , YZ = 9 mm , XZ = 23 mm

C.XY = 11 mm , YZ = 12 mm , XZ = 20 mm

D.XY = 14 mm , YZ = 12 mm , XZ = 29 mm

Answer:

equalateral

Step-by-step explanation:

each side is equal to the next

Answer:

2. Equilateral

Step-by-step explanation:

Step 1: Process Of Elimination-

1. Right: No

This triangle is not a right triangle because it does not have a right triangle indicator nor does it equal 90°.

2. Equilateral: Yes

This triangle is an equilateral triangle because all 3 sides are equal and they add up to 180° meaning each side equal 60°.

3. Acute: No

A acute triangle is a triangle that is less then 90° but this triangle equals 180°.

4. Scalene: No

A scalene triangle is a triangle that has different side angles but they all add up to 180° but here we can see that the sides are equal.

The two sided confidence interval on mean is 3.56 and 4.80.

What is confidence interval?

The proportion of probability, or certainty, that the confidence interval would include the real population parameter when a random sample is drawn numerous times is referred to as the confidence level.

The given data is  3.7, 4.5, 4.1, 4.7, 3.9.  Here n = 5

=> σ = 1- 95% = 5% = 0.05

We know that the confidence interval is

=> CI = [tex]\overline x {\displaystyle \pm }\frac{z(\sigma)}{\sqrt n}[/tex]

Here 95% confidence level so z= 1.96

Mean [tex]\overline x = \frac{3.7+4.5+4.1+3.9+4.7}{5} = 4.18[/tex] and σ = 0.5

Here  n<30 so we can use t instead of z then t-value = 2.776.

Now confidence level CI = [tex]\ 4.18 {\displaystyle \pm }\frac{2.776\times0.5}{\sqrt 5}[/tex]

=> CI = 4.18 [tex]\display \pm[/tex] 0.62 = ( 3.56 , 4.80)

Hence the two sided confidence interval on mean is 3.56 and 4.80.

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Answer: 7

Step-by-step explanation:

Step 1: 6^9 * 6^x = 6^2

Step 2: 9 + x = 2

Step 3: x = 2 - 9

Step 4: x = -7

Step 5: Since the power of a number cannot be negative, x must be 7.

So, the measure of angle B is 90 degrees.

An angle is a geometric figure formed by two rays or line segments that share a common endpoint, called the vertex. The two rays or line segments are called the sides or arms of the angle. Angles are typically measured in degrees or radians, and they are used to measure the amount of rotation between two lines or planes. A full rotation is 360 degrees or 2π radians, while a half rotation is 180 degrees or π radians. Angles play an important role in geometry, trigonometry, physics, engineering, and many other fields of science and mathematics.

by the question.

To find the measure of angle B, you need to use the fact that angle DB bisects angle ADC. This means that angle ADB and angle CDB are congruent, or have the same measure. So you can set the measure of angle ADB equal to the measure of angle CDB and solve for x.

Once you have found the value of x, you can substitute it into either equation for angle ADB or angle DBC to find the measure of that angle. Finally, since angle B is an exterior angle of triangle ADB, its measure is equal to the sum of the measures of angles ADB and DBC.

So, the steps to find the measure of angle B are:

Set the measure of angle ADB equal to the measure of angle CDB:

(3x - 12) = (2x + 6)

Solve for x:

x = 18

Substitute x = 18 into either equation for angle ADB or angle DBC to find the measure of that angle:

angle ADB = (3x - 12) = (318 - 12) = 48 degrees

angle DBC = (2x + 6) = (218 + 6) = 42 degrees

Find the measure of angle B as the sum of the measures of angles ADB and DBC:

angle B = angle ADB + angle DBC = 48 + 42 = 90 degrees.

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The person who has the fastest speed is given as follows:

Aubri and Tyler(tied).

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other. This means that if one quantity is multiplied by a certain factor, the other quantity will also be multiplied by the same factor.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

The constant for each person, representing the velocity, is given as follows:

The problem asks for the person who has the fastest speed.

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Carlos needs to score 29 points in the next game to have an average of 24 points per game.

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

Let x be the number of points Carlos needs to score in the next game to have an average of 24 points per game.

To find the solution, we can use the formula for the mean of a set of numbers:

(mean) = (sum of numbers) / (number of numbers)

In this case, we want the mean to be 24, and we have 5 numbers (4 previous game scores and the score in the next game), so:

24 = (24 + 19 + 20 + 28 + x) / 5

Multiplying both sides by 5, we get:

120 = 91 + x

Subtracting 91 from both sides, we get:

x = 29

Therefore, Carlos needs to score 29 points in the next game to have an average of 24 points per game.

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Answer:

The answer to your problem is:

m +14.3 =43.6

m =29.3

Step-by-step explanation:

Miles to travel: 43.6

Miles left to travel: 14.3

To find the amount of miles that the train has already traveled (m), we know that the sum of that value (m) and the miles left to travel (14.3) is equal to the total miles (43.6)

m +14.3 = 43.6

m = 43.6-14.3= 29.9

Thus the answer to your problem is,

m +14.3 =43.6

m =29.3

The area of the rectangle is 220.5 square inches when the perimeter of the rectangle is 242/4 inch and  one side of the rectangle is 49/4 inch.

Perimeter = [tex]60 \frac{2}{4}[/tex] inch = 242/4 inch

one side of rectangle = [tex]12\frac{1}{4}[/tex] inch = 49/4

The perimeter of a rectangle is the sum of all its sides. In this case, we know that the perimeter of the rectangle is 242/4 inch, which simplifies to 60.5 inch. We also know that one side of the rectangle is 49/4 inch.

Let's call the other side of the rectangle "n". Then, we can write the equation:

2(49/4 + n) = 60.5

Simplifying this equation, we get:

98/4 + 2n = 60.5

24.5 + 2n = 60.5

2n = 36

n = 18

Therefore, the other side of the rectangle is 18 inch.

To find the area of the rectangle, we can use the formula:

Area = length * width

In this case, the length is 49/4 inch and the width is 18 inch. So, we have:

Area = (49/4) * 18 = 220.5 square inches

Therefore, the area of the rectangle is 220.5 square inches.

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The complete question is :

Find n. Then find the area. Perimeter = [tex]60 \frac{2}{4}[/tex] inch . If one side of rectangle = [tex]12\frac{1}{4}[/tex] inch and other n inch.

The answer is positive 15 because the final result is 15 units to the right of zero on the number line.  

To solve this problem, we simply need to add the three integers together.

Starting with 209, we add -142 to get 67. Then, we add -52 to get a final result of 15. Therefore, the answer is 15.

To understand why the answer is positive, negative, or zero, we can think of integers on a number line. Positive integers are to the right of zero, negative integers are to the left of zero, and zero is at the center.

Starting with 209, we move 209 units to the right of zero on the number line. Then, adding -142 means moving 142 units to the left of zero, resulting in a position of 67 units to the right of zero. Finally, adding -52 means moving 52 units to the left of 67, resulting in a position of 15 units to the right of zero.

Therefore, the answer is positive 15 because the final result is 15 units to the right of zero on the number line.

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The coordinate matrix TB,B of a linear transformation T with respect to bases B and C is found to be [2 5 4; 1 1 2; -1 -1 -1].

To find the coordinate matrix TB,B of T with respect to B, we can use the formula:

TB,B = Ic,B * Tc,c * Ib,c

where Ib,c is the change of basis matrix from basis B to basis C.

To find Ib,c, we can use the inverse of Ic,B:

Ib,c = (Ic,B)^(-1)

We can use a calculator to find the inverse of Ic,B:

Ib,c = [1/4 1/4 -1/4]

[ 0 1 1 ]

[-1/4 -3/4 3/4]

Now, we need to calculate Ic,B * Tc,c:

Ic,B * Tc,c = [ 1 -3 -1 ] [-2 -2 -27 ] [ 1/4 1/4 -1/4 ] = [ 23 29 68 ]

[-1 2 -1 ] [-1 -3 -1 ] [ 0 1 1 ] [-15 -23 -48]

[-1 -3 -2 ] [ 2 0 -1 ] [-1/4 -3/4 3/4 ] [ 3 11 25]

Finally, we can calculate TB,B:

TB,B = (Ic,B * Tc,c * Ib,c)^(-1)

We can use a calculator to find the inverse of Ic,B * Tc,c * Ib,c:

TB,B = [ 2 5 4 ]

[ 1 1 2 ]

[-1 -1 -1 ]

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Answer:

Step-by-step explanation:

the answer will be 2

Answer:

2 people

Step-by-step explanation:

6/3 = 2

Helping in the name of Jesus.

Let's order them from most likely to least likely to occur:

To calculate the probability of selecting each type of ball, we need to find the total number of balls in the bin first.

Then, we will divide the number of each type of ball by the total number of balls.

Total number of balls = 15 baseballs + 12 basketballs + 8 soccer balls + 5 footballs + 10 volleyballs

Total number of balls = 50 balls

Now, let's calculate the probability of selecting each type of ball:

Baseballs: P(Baseballs) = (Number of baseballs) / (Total number of balls) = 15/50 = 0.3

Basketballs: P(Basketballs) = (Number of basketballs) / (Total number of balls) = 12/50 = 0.24

Soccer balls: P(Soccer balls) = (Number of soccer balls) / (Total number of balls) = 8/50 = 0.16

Footballs: P(Footballs) = (Number of footballs) / (Total number of balls) = 5/50 = 0.1

Volleyballs: P(Volleyballs) = (Number of volleyballs) / (Total number of balls) = 10/50 = 0.2

Now, let's order them from most likely to least likely to occur:

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We can see here:

4. Given: 6x + 7 = 8x - 17. Prove: x = 12

Statements                         Reasons

1. 6x + 7 = 8x - 17                     Given

2. 7 = 2x - 17               Subtracted 6x from both sides    

3. 24 = 2x                    Added 17 to both sides

4. 12 = x                       Divided both sides by 2

5. x = 12                       Final answer proven

An algebraic expression is a mathematical phrase that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. It can represent a value, an equation, or a formula.

5. Given: -7(x + 2) + 4x = 6(2x - 4): Prove: x = 2/3

Statements                               Reasons

1. -7(x + 2) + 4x = 6(2x - 4)   Given

2. -7x - 14 + 4x = 12x - 24     Opened the brackets by multiplying all

3. -3x - 14 = 12x - 24          Added -7x and 4x at LHS      

4. -15x - 14 = -24               Subtracted 12x from both sides

5. -15x = -10                      Added 14 to both sides          

6. x = 2/3                          Divided both sides by -5 to arrive to the result.

6. Given: 3x + 1 = -14: Prove: x = -5

Statements                        Reasons

1. 3x + 1 = -14                   Given

2. 3x = -15                       Subtracted 1 from both sides

3.  x = -5                        Divided both sides by 3. Final answer proven.

7. Given: 2(x - 9) = -10; Prove: x = 4

Statements                           Reasons

1. 2(x - 9) = -10                 Given

2. 2x - 18 = -10                Opened the brackets.

3. 2x = 8                         Added 18 to both sides

4. x = 4                          Divided both sides by 2. Final answer proven.

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Answer:6n-5

Step-by-step explanation:

1,7,13,19,25

It goes up in 6 each time, so you will need to go back 6 back on the number one, so it will be -5 so the answer will be 6n-5.

6(2)-5 = 7
6(3)-5 =13

If a company understates its ending balance of inventory in year 1 and states its inventory correctly in year 2, then the correct statement is option (c) Net income is understated in year 2

Understating the ending balance of inventory in year 1 would result in the cost of goods sold (COGS) being overstated and net income being understated in that year. This is because the COGS is calculated as the beginning inventory plus purchases minus ending inventory. By understating the ending inventory balance, the COGS for year 1 would be overstated, which would result in a lower net income for year 1.

In year 2, if the inventory is stated correctly, it would not have an impact on the COGS for that year. However, if the net income for year 1 was understated due to the understated ending inventory balance, the cumulative effect would be an understated net income for both years. This means that the correct answer is c. Net income is understated in year 2.

Therefore, the correct option is (c) Net income is understated in year 2

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