1. find the square roots of (a) 2i; (b) 1−√3i and express them in rectangular coordinates.

The simplified form of the expression x² - 8x +16 is (x - 8)²

Expressions are mathematical statements that involve operations, such as addition, subtraction, multiplication, and division. In this problem, we are given the expression x² - 8x + 16 and asked to simplify it.

The expression can be simplified by using factoring techniques. We can factor the expression as (x - 8)(x - 8), which can be further simplified as (x - 8)2. The simplified expression is (x - 8)²

Therefore, the simplified expression for x² - 8x + 16 is (x - 8)². This shows that the expression is a perfect square, which can be written as (x - 8)², where (x - 8) is the square root of the expression

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Complete Question:

Simplify the expression x² - 8x + 16

Answer: Here is the answers to your previous question that was deleted. As for this question, I believe the answer is the first one.

1) [tex]200\pi[/tex]
2) [tex]3\sqrt{3}[/tex]  
3) [tex]-1[/tex]  
4) 9  
5) 0.151

Step-by-step explanation:

#1

[tex]=\frac{dV}{dt} =\frac{4}{3} \pi .3r^3\frac{dr}{dt}[/tex]

[tex]=\frac{dV}{dt} =4\pi r^2\frac{dr}{dt}[/tex]

[tex]=\frac{dV}{dt} =4\pi r^2*2...[\frac{dr}{dt} =2][/tex]

[tex]=\frac{dV}{dt} = 8\pi r^2~~~ in^3/min[/tex]

         [tex]r=5[/tex]

[tex]=\frac{dV}{dt} =8\pi (5)^2[/tex]

[tex]=200\pi ~~~in^3/min[/tex]

#2

[tex]\frac{d}{dt} (x^2+y^2)=\frac{d}{dt} (16)[/tex]

[tex]2x(\frac{dx}{dt} )+2y(\frac{dy}{dt})=0[/tex]

[tex]2x(\frac{dx}{dt} )+-2y(\frac{dy}{dt})=0[/tex]
Divide both sides by 2.

[tex]x(\frac{dx}{dt})=-y(\frac{dy}{dt})[/tex]

[tex]\frac{dx}{dt}=\frac{-y(\frac{dy}{dt}) }{x}[/tex]

As the particle is passing through the point [tex](2,2\sqrt{3})[/tex] , So, the point will satisfy the equation. Substituting the value of [tex]x=2[/tex] , [tex]y=2\sqrt{3}[/tex] and [tex]\frac{dy}{dt} -3[/tex],

we get ,

[tex]\frac{dx}{dt} =\frac{((-2\sqrt{3})*(-3))}{2}[/tex]

[tex]=\frac{6\sqrt{3} }{2}[/tex]

[tex]=3\sqrt{3}[/tex]

#3

Go on to Desmos and put in [tex]x+3y=6[/tex] and look at x=0 and x=1 and use those two as your points.

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]=\frac{1-3}{2-0}[/tex]

[tex]=\frac{-2}{2}[/tex]

[tex]=-1[/tex]

#4

[tex]y=3x^2-4x-6[/tex]

[tex]\frac{dy}{dt} =5x-6[/tex]

[tex]\frac{dy}{dt}=5(3)-6[/tex]

[tex]\frac{dy}{dt} =9[/tex]

#5

[tex]V=s^3[/tex]

[tex]\frac{dV}{dt} =3*s^2(\frac{ds}{dt})[/tex]

[tex]-2=3*s^2(\frac{ds}{dt} )~~~~~~~~~~~~~Equation 1[/tex]

[tex]\frac{ds}{dt} =\frac{1.33}{s^2}[/tex]

[tex]V=s^3[/tex]

[tex](27)^0^.^3^3=(s^3)^0^.^3^3[/tex]

[tex]s[/tex] ≈ [tex]2.97 ~~~~~~~~~~~~~~~~~~~~~~Equation2[/tex]

Substitute equation2 to equation1, we get

[tex]\frac{ds}{dt} =\frac{1.33}{(2.97)^2} =0.151[/tex]

I hope this helps you! Cheers! ^^

Rhonda's claim that 8th graders performed better than 7th graders on the state English test seems to be supported, as the median and mode for the 8th graders are both higher than those for the 7th graders.

The 7th graders mode: 0 (since it appears twice in the sample)

The 7th graders median: 3.5 (since the scores are already sorted, the median is the average of the two middle scores, which are 3 and 4)

The 8th graders mode: 3 (since it appears twice in the sample)

The 8th graders median: 8.5 (since the scores are already sorted, the median is the average of the two middle scores, which are 7 and 10)

Based on these measures of center, Rhonda's claim that 8th graders performed better than 7th graders on the state English test seems to be supported, as the median and mode for the 8th graders are both higher than those for the 7th graders.

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From the given information provided, the probability of event F given that event E has occurred is 0.5.

Conditional probability is probability of an event A occurring with given that event B has occurred. It is denoted as P(A|B) and is calculated as follows:

P(A|B) = P(A and B) / P(B)

To find P(F/E), we use the conditional probability formula:

P(F/E) = P(E and F) / P(E)

We are given that P(E and F) = 0.1 and P(E) = 0.2. Substituting the given values in the formula, we get:

P(F/E) = 0.1 / 0.2

Simplifying this expression, we get:

P(F/E) = 0.5

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500 grams is equivalent to approximately 17.637 ounces.

Gram is a metric unit of weight equal to one thousandth of a kilogram.

Ounce is a unit of weight equal to one sixteenth of a pound or 16 drams or 28.349 grams.

Ounce is defined as exactly 28.349523125 grams and is equivalent to one sixteenth of an avoirdupois pound.

To convert 500 grams to ounces,

We can use the conversion factor that 1 ounce is equal to 28.3495 grams.

So, we can write:

500 grams = (500 ÷ 28.3495) ounces

500 grams = 17.637 ounces (rounded to three decimal places)

Therefore, 500 grams is equivalent to approximately 17.637 ounces.

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Answer:

[tex]\text{Area of larger $\triangle$} = 81 \:cm^2[/tex]

Step-by-step explanation:

Given.

Ratio of corresponding sides of two similar triangles = 2:3 or [tex]\dfrac{2}{3}[/tex]
Area of smaller triangle = 36 cm²

By the property of area of two similar triangle,
Ratio of area of both triangles = (Ratio of their corresponding sides)²

[tex]\dfrac{\text{Area of smaller $\triangle$ }}{\text{Area of larger $\triangle$ }} = \left(\dfrac{2}{3}\right)^2}[/tex]
[tex]\dfrac{36}{{\text{Area of larger $\triangle$ }}} = \dfrac{4}{9}[/tex]

Cross-multiplying we get
[tex]36 \times \dfrac{9}{4} = \text{Area of larger $\triangle$}\\\\81 = \text{Area of larger $\triangle$}\\\\\text{Area of larger $\triangle$} = 81 \:cm^2[/tex]

The coordinate of point C which is 7 / 8 of the distance from M to J is 16 .

The first step is to find the distance between M and J to be :

= Coordinate of J - Coordinate of M

= 18 - 2

= 16

The distance that is 7 / 8 between M and J is :

= 16 x 7 / 8

= 14

The coordinate of C would be :

= Coordinate of M + 7 / 8 distance

= 2 + 14

= 16

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Labro overlooks the Rieti Valley, which was frequently visited by which saint: Francis of Assisi.

Francis of Assisi spent a great deal of time in the Rieti Valley, where he established four sanctuaries that are stopping points for pilgrims following the Cammino di Francesco pathway. Francis is also said to have made the first live nativity scene during a visit to the valley in 1223.

Francis of Assisi, one of the Catholic Church's most loved and darling saints. St. Francis is known for his ministry to poor people and oppressed, his consideration for nature and animals, and establishing the Franciscan request.

His life and message were uncompromising and simple: voracity causes suffering for both the victims and the perpetrators.

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Knowing the absolute prices of goods X, Y and Z, we obtain their relative prices:

The relative price of a good is the price of that good in terms of another good. It is calculated by dividing the absolute price of one good by the absolute price of another good.

The relative price of X in terms of Y is calculated by dividing the absolute price of X by the absolute price of Y:

Relative price of X in terms of Y = Absolute price of X / Absolute price of Y

X/Y = $23 / $42

X/Y = 0.55

The relative price of Y in terms of Z is calculated by dividing the absolute price of Y by the absolute price of Z:

Relative price of Y in terms of Z = Absolute price of Y / Absolute price of Z

Y/Z = $42 / $56

Y/Z = 0.75

The relative price of Z in terms of X is calculated by dividing the absolute price of Z by the absolute price of X:

Relative price of Z in terms of X = Absolute price of Z / Absolute price of X

Z/X = $56 / $23

Z/X = 2.43

In conclusion, the relative price of X in terms of Y is 0.55, the relative price of Y in terms of Z is 0.75, and the relative price of Z in terms of X is 2.43.

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Linda can choose any combination of three events that adds up to more than a kilometer but less than 1.5 kilometers

In order to find the best combination of events for Linda to sign up for to run a total of more than a kilometer but less than 1.5 kilometers, we must first determine the total distances of the individual events.

Depending on the events offered, Linda can choose three events that add up to more than a kilometer but less than 1.5 kilometers.

If Linda has the option of running the 100m, 200m, and 800m, she can satisfy her requirement of running more than a kilometer but less than 1.5 kilometers by choosing the 100m, 200m, and 800m.

This would add up to 1100m, which is slightly over a kilometer but below 1.5 kilometers.

Another option for Linda is to run the 100m, 400m, and 600m, which would add up to 1100m, once again satisfying her requirement.

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Answer:

A) 210 B) 0.18

Step-by-step explanation:

got it right

For converting fractions to decimals, we need to divide numerator with denominator,

So, the value of 51/16 as a decimal is equal to 3.1875.

In mathematics, the ratio of two integers is how a fraction is defined in mathematics.

The fraction indicates that it is the numerator value to denominator value ratio.

A decimal number is one in which the decimal point separates the whole number component from the decimal component.

From the question,

As we need to convert the given fractional value to decimal.

So, for determining the equivalent decimal value, we will simply divide the value given in the numerator to the value given in the denominator.

So, dividing 51 by 16

We will get it as:

51/16: 51 16 = 3.1875

As a result, 51/16 is equivalent to 3.1875 in decimal form.

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The statements required for the prove are given in the explanation.

Vertical angles are two opposite angles which have equal values because they are formed by two straight lines intersecting at a point.

And a midpoint is a point which divides a line segment into two equal parts.

The required statements to prove that ΔTPR ≅ΔQPS are given below;

                 STATEMENT                                 REASON

1. P is the midpoint of TQ and RS                  Given

2. TP = QP, RP = SP                                        Definition of midpoint

3. <SPQ ≅ <RPT                                              Vertical angle theorem

4. ΔTPR ≅ΔQPS                                             Side-Angle-Side theorem

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Answer:

The value of x can be 10

The value of y can be -4

Step-by-step explanation:

Assume the function is linear of the form
y = mx

When x = 5, y = -2

Simply multiply x by 2 and equivalently multiply -2 by 2

x = 5 x 2= 10

y = -2 x 2 = -4

Answer:

The solutions to the equation cos(x + 3π/2) = √2/2 on the interval [0, 2π] are x = π/4 + 2kπ, k ∈ {0, 1, 2, 3}.

Answer:

[tex] \sf \: a) \: 27 = 9p \: ; p = 3[/tex]

Step-by-step explanation:

Given information,

→ Simon have 27 pieces of candy.

→ Each person will get 9 pieces.

Now we have to,

→ Find the required equation.

The equation will be,

→ 27 = 9p

→ 9p = 27

=> As each person (p) gets 9 pieces.

Then the value of p will be,

→ 9p = 27

→ p = 27 ÷ 9

→ [ p = 3 ]

Hence, option (a) is correct.

The economic life cycle analysis does not take into account factors such as technological advancements or changes in regulatory requirements, which can affect the optimal replacement interval.

Yet, it is important to review and update the analysis periodically to ensure that the replacement interval remains optimal.

There are the normal steps for calculating the optimum replacement interval using the economic life cycle analysis:

1. Estimate the annual maintenance and repair costs for the item, based on historical data or industry standards.

2. Estimate the annual operating costs for the item, such as energy or fuel costs.

3. Compare the total cost of ownership for the item over its expected useful life to the cost of replacing the item with a newer or more efficient model.

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The volume of the solid generated when the region bounded by y = 9x and y = 27x/x is revolved around the x-axis is given by V = 27lnx - 9x + c

To calculate this volume, we need to calculate the area of the cross-section of a shell at x.

The cross-section is found by taking the difference of the two curves, y = 9x and y = 27x/x, at that particular x in the form of a rectangle.

The height of the rectangle is y₂ - y₁ and the width is the interval dx. Therefore, the area of the cross-section is given by

A(x) = (y₂ - y₁)dx = [(27x/x - 9x)dx].

The volume of the solid is then given by the formula

=> V = ∫A(x)dx.

Substituting in the expression for A(x), we have

=>  V = ∫(27x/x - 9x)dx.

Integrating this expression, we get V = 27lnx - 9x + c, where c is an arbitrary constant.

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Rana has 1 and 5/12 cups of chocolate chips left. Answer: $\boxed{\text{one and five-twelfths cups}}$.

How to find?

To find out how many cups of chocolate chips Rana has left, we need to subtract the amount she used in the cookie recipe from the amount she bought.

First, we need to convert both mixed numbers to improper fractions, so we can subtract them.

Three and three-fourths cups can be written as:

3\frac{3}{4} = \frac{(3 \times 4) + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4}

Two and one-third cups can be written as:

2\frac{1}{3} = \frac{(2 \times 3) + 1}{3} = \frac{7}{3}

Now, we can subtract:

\frac{15}{4} - \frac{7}{3} = \frac{45}{12} - \frac{28}{12} = \frac{17}{12}

Therefore, Rana has 1 and 5/12 cups of chocolate chips left. Answer: $\boxed{\text{one and five-twelfths cups}}$.

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The total number of possible selections is 18,643,560. This is calculated using the combination formula nCr.

In nCr, n is the total number of objects (50) and r is the number of objects to be selected (7). This is equal to 50C7, which can be written as

To explain this further, the combination formula is used to find the total number of combinations when selecting a certain number of objects from a larger set. In this case, we are selecting 7 numbers from a set of 50, so the total number of combinations is 18,643,560.

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Answer:

81°

Step-by-step explanation:

the sum of the interior angles of a triangle is 180°.

The base of the 10 triangles make a straight line.  180/10 = 18°

The small angle along the base is 18°

180-18 = 162

The other two angles of the triangle must add up to 162. Since this is a isosceles triangle.  The other 2 angles have the same measurements.

162/2 = 81.  The measurement of the angle we are looking for is 81°

In reference to the article “Climate Change and Ecosystems,” the EPA  explains how the Earth's ecosystems are being impacted by climate change, resulting in negative consequences for both natural resources and human well-being.

In response to widespread public environmental concerns that grew in strength in the 1950s and 1960s, the Environmental Protection Agency was established. By examining the effects of pollutants and setting usage restrictions, the EPA has worked to preserve and protect the environment while also enhancing human health.

The EPA controls the production, transformation, use, and disposal of chemicals and other pollutants. The EPA is also tasked with figuring out the acceptable levels of chemicals and other pollutants in water, animal feed, and food.

In general, the Environmental Protection Agency develops and implements environmental regulations, sponsors and conducts research, and guards against serious health risks to people and the environment and also maintain a favorable climate for all.

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The density of air in lb/ft³ based on the conversion using the formula is 0.08 lb/ft³.

We know that the density of air is 1.29 grams per litre. Now, to perform the conversion, we need to find the relation between grams and pounds and litre and feet.

So, we know that 1 gram is equal to 0.0022 pound and 1 litre is equal to 0.0353 cubic foot.

Therefore, keeping these values in the actual formula for conversion.

Density of air = 1.29 × 0.0022/0.0353

Performing division and multiplication on Right Hand Side of the equation

Density of air = 0.08 lb/ft³

Therefore, the density of air is 0.08 lb/ft³.

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The coordinates of point bbb are \left(\dfrac{2a+7c}{9}, 0\right)left( 9 2a+7c ​ , 0 right).

To find the coordinates of point bbb on \overline{ac}ac start overline, a, c, end overline, we need to use the formula for the division of a line segment in a given ratio. The formula is:

\begin{aligned} x &= \dfrac{x_1m+x_2n}{m+n} \\ y &= \dfrac{y_1m+y_2n}{m+n} \end{aligned}
Where m and n are the given ratio, and (x1, y1) and (x2, y2) are the coordinates of the two endpoints of the line segment.

In this case, the given ratio is \dfrac{2}{7}7 2 ​ start fraction, 2, divided by, 7, end fraction, and the coordinates of the two endpoints are (x1, y1) = (a, 0) and (x2, y2) = (c, 0).

Plugging in the values into the formula, we get:
\begin{aligned} x &= \dfrac{a \cdot 2 + c \cdot 7}{2+7} \\ y &= \dfrac{0 \cdot 2 + 0 \cdot 7}{2+7} \end{aligned}

Simplifying the equations, we get:
\begin{aligned} x &= \dfrac{2a+7c}{9} \\ y &= 0 \end{aligned}

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The ratios are equivalent by simplifying is shown below.

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

We have first ratio 3:1

and, second 6:2 on simplifying we get 3:1.

and, third 9: 3 on simplifying we get 3:1.

and, Fourth 12:4 on simplifying we get 3:1.

So, all the ratio gave same value on Simplification which shows the ratios are Equivalent.

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The correct way to measure the zone of inhibition is to place a known amount of an antimicrobial agent on a solid medium.

Area is a quantity that measures the size of a two-dimensional surface or shape. It is expressed in square units such as square centimetres (cm2), square metres (m2) or square kilometres (km2). Area is used to describe the size of a garden, a house, a room, a city and much more. It can also be used to calculate the amount of material required for a project, such as paint, carpet or tiles. Knowing the area of a shape can help to calculate costs, and to make sure that enough materials are ordered.

The zone of inhibition is then measured as the area surrounding the antimicrobial agent where microbial growth has been inhibited. This area is typically measured in millimeters. To accurately measure the zone of inhibition, it is important to ensure that the size of the inoculum and the amount of antimicrobial agent used remain constant. Additionally, it is important to consider the type of organism being studied, as different organisms can have different levels of susceptibility to the antimicrobial agent. Finally, the medium used should be appropriate for the organism being studied, as different media can produce different results.

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The given set of points {(-7, 20), (3, 5), (0, 5), (-2, 0), (6, -4), (-6, -9), (4, 4)} is a function since each x-value has a unique y-value.

To determine whether the given set of points is a function or not, we need to check if each input (x-value) corresponds to exactly one output (y-value).

Let's first list the x-values in the set: -7, 3, 0, -2, 6, and -6.

Now, we need to check if each of these x-values has a unique y-value. We can see that:

The point (-7, 20) has an x-value of -7 and a y-value of 20.

The point (3, 5) has an x-value of 3 and a y-value of 5.

The point (0, 5) has an x-value of 0 and a y-value of 5.

The point (-2, 0) has an x-value of -2 and a y-value of 0.

The point (6, -4) has an x-value of 6 and a y-value of -4.

The point (-6, -9) has an x-value of -6 and a y-value of -9.

The point (4, 4) has an x-value of 4 and a y-value of 4.

We can see that each of the x-values has a unique y-value. Therefore, this set of points is a function.

In fact, we can even represent this function using set-builder notation as:

{ (x, y) | x ∈ {-7, 3, 0, -2, 6, -6, 4}, y is the corresponding y-value for x }

or using a mapping notation as:

f = { (-7, 20), (3, 5), (0, 5), (-2, 0), (6, -4), (-6, -9), (4, 4) }

where f(x) is the corresponding y-value for x.

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As a result, if the two angles' measurements are (3y+11) and (11y+15) and they are congruent, then y must equal -1/2.

An angle is a geometric figure formed by two rays that have a common endpoint, called the vertex. The rays are also known as the sides or legs of the angle. Angles are typically measured in degrees, with a full circle measuring 360 degrees. Angles can also be measured in radians, which are another unit of angular measurement used in mathematics and physics. One radian is equal to the angle subtended by an arc of a circle that has a length equal to the radius of the circle. The size of an angle is determined by the amount of rotation that occurs between the two rays. This is typically measured relative to the positive x-axis, with counterclockwise rotations being considered positive and clockwise rotations being considered negative. Angles are used in a wide range of mathematical and scientific applications, including geometry, trigonometry, physics, engineering, and architecture. They are also used in many everyday situations, such as measuring the size of an opening or the angle of incidence of sunlight on a surface.

Here,

If the two angles are congruent, then they must have the same measure.

So we can set the expressions for the measures of the two angles equal to each other and solve for y:

3y + 11 = 11y + 15

Subtracting 3y from both sides:

11 = 8y + 15

Subtracting 15 from both sides:

-4 = 8y

Dividing both sides by 8:

y = -1/2

Therefore, if the measure of the two angles is (3y+11) and (11y+15) and they are congruent, then y must equal -1/2.

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The required value of h(t)=-20+11t at t=11 is , h(11)=101.

The word PEMDAS is primarily used in the US, although we refer to it as BODMAS in India and the UK. Yet, there is no distinction between them. For both the rule and brackets, addition, subtraction, multiplication, and division are performed in the same order.

The following is the full form of PEMDAS:

P – Parentheses  [{()}]

E – Exponents (Powers and Roots)

MD- Multiplication and Division (left to right) (× and ÷)

AS –A= Addition  and S= Subtraction (left to right) (+ and -)

whereas the full form of BODMAS is – Brackets Order Division Multiplication Addition and Subtraction.

If h(t)=-20+11t and you wish to evaluate h(11):

h(11)=-20+11(11)

h(11)=-20+121

h(11)=101

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The correct answer is (c) Understate change in the cost of living because consumers substitute toward goods whose relative prices are declining.

consumers do substitute toward goods whose relative prices are declining. This means that they are able to maintain their standard of living even if the overall cost of living increases. Therefore, the CPI tends to understate changes in the cost of living because it does not fully account for consumer substitution.  

The other options are not correct because:

a. The CPI does take into account quality changes by adjusting prices for changes in quality.

b. The CPI adjusts for changes in relative prices, so it does not overstate changes in the cost of living due to substitution effects.

d. The CPI includes services, but it may understate changes in the cost of living if the prices of services are increasing faster than the prices of goods.

e. The CPI includes a wide range of items, including volatile items such as fruit, vegetables, and petrol. However, the weights assigned to these items may change over time to reflect changes in consumer spending patterns.

The correct answer is (c) Understate change in the cost of living because consumers substitute toward goods whose relative prices are declining.

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