What is substitution reaction explain with two examples?

Answers

Answer 1

The reaction in which one (or more) hydrogen atoms of a hydrocarbon are replaced by some other atoms (like chlorine), is called a substitution reaction.

Substitution reaction is a type of chemical reaction in which an atom, ion, or group of atoms or ions in a molecule is replaced by another atom, ion, or group.

The examples of substitution reactions are as follows:
1. Reaction of copper with zinc sulphate gives zinc with copper sulphate by replacing the zinc with copper.

[tex]Cu + ZnSO_{4}[/tex] → [tex]CuSO_{4} + Zn[/tex]

2. Reaction of magnesium with copper sulphate gives magnesium sulphate with copper by replacing copper with magnesium.

[tex]Mg + CuS0_{4}[/tex] → [tex]MgSO_{4} + Cu[/tex]

To know more about hydrocarbon, here

https://brainly.com/question/17578846

#SPJ4


Related Questions

How do you dilate from 2cm to 10cm?

Answers

Drawing 2 cm 5 times in a straight line will give us a 10 cm line segment after dilation.

What is Dilation ?

Dilation is the process of increasing an object's size without altering its form. Depending on the scale factor, the object's size may rise or shrink. A square of side 5 units can be widened to a square of side 15 units using dilation math, but the square's form doesn't change.

A dilation is a function f from a metric space M into itself that, for any locations x, y in M, fulfills the identity d=rd, where d is the distance between x and y and r is a positive real integer. Such a dilatation is a resemblance of the space in Euclidean space.

Meaning of Dilation in Math. Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. However, there is a variation in the shape's size.

To dilate 2 cm to 10 cm we need to scale 2 cm 5 times

so drawing 2 cm 5 times in a straight line will give us a 10 cm line segment.

To learn more about Dilation refer to :

https://brainly.com/question/29811168

#SPJ4

To get from one side of the pond to the other you must walk 34 meters south and 41 meters east to the nearest meter how many less meters would it take if it were possible to go directly across the pond

Answers

it would take 53.38 meters to go directly across the pond.
To know how many less meters it would take you need to substract 53.38 by 34 + 41 = 75
so 75 - 53.38 = 21.62 meters less

A jet plane has 160,000 pounds of fuel after the first hour of flight. The four engines consume a total of 14,000 pounds per hour at its cruising altitude. How many pounds of fuel remain after the 9th hour?.

Answers

The fuel remain after the 9th hour is 48,000 pounds. The result is obtained by subtracting the amount of fuel consumed by four engines for 8 hours from the amount of fuel after the first hour.

How to count the fuel remain?

A simple way to count the fuel remain is subtracting the amount of fuel consumed from the amount of initial fuel.

We have

160,000 pounds of fuel after the 1st hour of flight.Fuel consumed for 4 engines = 14,000 pounds per hour.

Find the fuel remain after the 9th hour of flight!

From 1st hour to 9th hour of flight, the time duration is

= 9 - 1

= 8 hours

The fuel remain would be

= 160,000 pounds - (14,000 pounds /hour × 8 hours)

= 160,000 pounds - 112,000 pounds

= 48,000 pounds

Hence, after the 9th hour of flight, the fuel is 48,000 pounds.

Learn more about fuel, time, and speed here:

brainly.com/question/17605858

#SPJ4

find the total surface area of this cuboid measurements are 5cm 4cm 6cm the answer measurements must be cm squared

Answers

This cuboid's total surface area measured 5cm, 4cm, and 6cm is 120 cm³.

What is total surface area?

The surface area of a solid item is a measurement of the entire area occupied by the object's surface. The total surface area includes the base(s) and the curving portion. It is the whole area covered by the object's surface. The total area of a form with a curved surface and base is the sum of the two areas. The total surface area is obtained by summing all the areas on the surface: the areas of the object's base, top, and lateral surfaces (sides).

Here,

total surface area of cuboid,

=l*b*h

=5*4*6

=120 cm³

The total surface area of this cuboid measured 5cm, 4cm and 6cm is 120 cm³.

To know more total surface area,

https://brainly.com/question/8419462

#SPJ1

What is the possible factors of the given number or expression of 8?

Answers

So on solving the provided question we can say  that factors 8 = 1,2,4,8; factor 50 = 1,2,5,10,5,25,50

what is prime factor?

Any natural number other than 1 with just itself and the number 1 as its divisors is considered a prime factor. Actually, 2, 3, 5, 7, 11, and so on are some of the first prime numbers. an amount that has been multiplied to produce another amount. By dividing 15 by 3 and 5, for instance, we get 3 5 = 15. main elements: Prime factors include all factors that are prime but are not composite. A few prime factors of 30 are 2, 3, and 5. Only 2 and 3 are prime factors of 12, so listing 2 twice as 2 2 3 (or 22 3) is necessary to factorize 12. The sum of 2 + 3 is not 12.

factors 8 = 1,2,4,8

factor 50 = 1,2,5,10,5,25,50

To know more about prime factor visit:

https://brainly.com/question/29775157

#SPJ4

please help me solve this urgently.

Answers

Answer:

  2.5 or 3.5

Step-by-step explanation:

You have an x-cm square and a rectangle ℓ cm by 3 cm. Together, they have a total perimeter of 32 cm. You want the length ℓ and the area S in terms of x, and you want to know the values of x that make the area be 30.25 cm².

(i) Wire length

The length of the wire is 32 cm. This is the sum of the perimeters of the square and the rectangle.

  P = 4s +2(l+w)

  32 = 4x + 2(ℓ +3) . . . . . . . . substitute given values

(ii) Rectangle length

Solving the equation for ℓ, we have ...

  16 = 2x +ℓ +3 . . . . . . . . . divide by 2

  ℓ = 13 -2x . . . . . . . . . . . subtract 3+2x

(iii) Total area

The total area of the two figures is the sum of the area of the square and that of the rectangle:

  S = x² +3ℓ

  S = x² +3(13 -2x) . . . . . . substitute for ℓ

  S = x² -6x +39 . . . . . . . simplify

(iv) Value of x

For an area of 30.25 cm, we require ...

  30.25 = x² -6x +39

  -8.75 = x² -6x . . . . . . . . . . subtract 39

  0.25 = x² -6x +9 . . . . . . . complete the square

  ±0.5 = x -3 . . . . . . . . . . . . take the square root

  x = 3 ± 0.5 = {2.5, 3.5}

The total area is 30.25 cm² for x = 2.5 or x = 3.5.

<95141404393>

Lori works as a cartoonist for a teen magazine. The time she spends sketching is given by the equation m = 12s, where m is the number of minutes and s is the number of sketches.
If Lori made
3
4
of a sketch

Answers

If Lori made a fraction of 3/4 of a sketch, she spent 9 minutes sketching.

What is fraction?

A portion of something is called a fraction. When the numerator and denominator are divided, a number is represented mathematically as a quotient. In a simple fraction, both are integers. A complex fraction contains a fraction in either the numerator or denominator. In a proper fraction, the numerator is smaller than the denominator.

Given the equation

m = 12s,

where

m is the number of minutes, and

s is the number of sketches.

Lori made 3/4 of a sketch i.e.

m = 12(3/4)

m = 9 mins

Thus, If Lori made 3/4 of a sketch, she spent 9 minutes sketching.

Learn more about fraction

https://brainly.com/question/12220774

#SPJ1

Full question:-

Lori works as a cartoonist for a teen magazine. The time she spends sketching is given by the equation m = 12s, where m is the number of minutes and s is the number of sketches.

If Lori made 3/4 of a sketch, she spent ____ minutes sketching.

HELP PLEASE ASAP!!!!

Answers

Answer: H

Step-by-step explanation:

x<19


how do i solve this? they dont make it clear on here

Answers

Since opposite sides of equal angles in a triangle are equal, segment AP is segment PE.

Explain circle theorems?

Circle theorems are a set of results in geometry that relate to properties of circles. There are several important circle theorems, including:

The Angle in a Semi-Circle is a Right Angle: The angle formed by a chord and a tangent to a circle at the point of tangency is a right angle.The Angle at the Centre is Twice the Angle at the Circumference: If two lines from a point on the circumference of a circle to the center of the circle are extended to intersect, the angle at the center is twice the angle at the circumference.Equal Chords are Equidistant from the Centre: If two chords of a circle are equal in length, they are equidistant from the center of the circle.Cyclic Quadrilaterals: If a quadrilateral can be inscribed in a circle, then its opposite angles add up to 180 degrees.Chord-Chord Angle: If two chords in a circle intersect, then the measure of the angle formed by the chords is half the measure of the arcs intercepted by the angle.

According to question it has been established that a tangent PA exists between the points P and O.

When given, EAF BAE a°

A plus B Equals mPAE

AEP = BAE + ABE = a + b°

An outside view of ABE is [AEP].

In ΔPAE,

When given, EAF BAE a°

A plus B Equals mPAE

AEP = BAE + ABE = a + b°

An outside view of ABE is [AEP].

In ΔPAE,

(a + b)° PAE PEA

Since opposite sides of equal angles in a triangle are equal, segment AP is segment PE.

so proved.

To know more about circle theorems visit:

brainly.com/question/26594685

#SPJ1

If f(x) = 5x, what is f¹(x)?

f¹(x) = -5x
ƒ¹(x) = -1/5 x
f¹(x) = 1/5x
f¹(x) = 5x

Answers

Answer:

[tex]\displaystyle f^{-1}(x)=\frac{1}{5}x[/tex]

Step-by-step explanation:

[tex]f(x)=5x\\\displaystyle y=5x\\x=5y\\\frac{1}{5}x=y\\ f^{-1}(x)=\frac{1}{5}x[/tex]

The inverse of the given function f(x) will be x/5.

What is the function?

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

To find the inverse function f⁻¹(x) for f(x) = 5x, we can use the following steps:

Replace f(x) with y: y = 5xSwap x and y: x = 5ySolve for y: y = x/5

Therefore, the inverse function of f(x) = 5x is f⁻¹(x) = x/5.

Note that f⁻¹(x) is not equal to -5x, 1/5x, or 5x.

Learn more about function here:

https://brainly.com/question/29633660

#SPJ5

How do you enlarge a shape by scale factor 3 centre?

Answers

Enlarge the shape by scale factor 3.

How can you increase a form by scaling it by 3?

To expand a form, multiply all of its lengths by the scaling factor. The scale factor indicates how much larger the shape will be. For example, increasing a form by a scale factor of two means that all of its sides will be twice as long. This rectangle measures one square broad by two squares long.

To employ a center of enlargement, we must draw lines from the center of enlargement to the original shape’s vertices. These are known as ray lines. E.g. Triangle ABC has been expanded by a scale factor of 2 around an expansion point O.

To learn more about Scale factor to refer:

https://brainly.com/question/22644306

#SPJ4

What word from algebra refers to the steepness of a line or segment?

Answers

Answer: Slope

Step-by-step explanation:

Answer:

slope

Step-by-step explanation:

HELP PLSS!! Find cos (A) given the triangle!!

Answers

2.25/10.25 (put that in a calculator)

To find this understand SOH CAH TOA

S stands for sin and the OH means you do the opposite side of the angle divided by the hypotenuse

C stands for cos and the AH means you do the adjacent side divided by the hypotenuse or 2.25/10.25

T stands for tan and the OA means you do the opposite side divided by the adjacent side.

Hope this helps

What is length of scale formula?

Answers

The length of a scale formula refers to the mathematical relationship used to determine the length of a scaled representation of an object or image.

What is length of scale formula?

We’ll use the formula Scale factor = Dimension of the new shape Dimension of the old shape. Dimension of the new form = Scale factor Dimension of the original shape is how this is expressed. We obtain Dimension of the new form = 7 after inserting the specified numbers.

In dimensional analysis, length scales are generally the operative scale (or at least one of the scales). In scattering theory, for example, the most frequent number to compute is a cross section, which has length squared units and is measured in barns. Typically, the cross section of a particular process equals the square of the length scale.

To learn more about length of scale visit:

brainly.com/question/30234391

#SPJ4

What is the value of x in the triangle? a 45-45-90 triangle with leg length 7 and hypotenuse length x a. B. C. D.

Answers

The value of x in the given 45-45-90 triangle is 9.89.

The given triangle is a right-angled triangle which can be solved using the Pythagoras theorem. The Pythagoras theorem states that the square of the hypotenuse is equal to the sum of the square of the base and the square of the perpendicular. This theorem can be applied to all right-angled triangles.

In the given triangle, we have been told that the length of both legs is 7. Now, after applying the theorem -

= 7²+7² = H²

= 49 + 49 = H²

= 98 = H²

= √98 = H

= 9.89 = H

Hence, this is the value of x.

Learn more about the Pythagoras Theorem on

https://brainly.com/question/21926466?referrer=searchResults

#SPJ4

HELP ME SOMEONE QUICK

Answers

Answer:

<abc is 30*

<fde is 60*

Step-by-step explanation:

Hope this helps!

In a computer catalog,the diagonal distance of computer monitor screen is labeled as 21 inches.if the screen measures 14 inches in height, waht us the width of the screen?

Answers

The width of the screen  is 15.65 inches

What is the width?

The diagonal , the width and the height form a right angle. A right triangle is a triangle that has three sides known as the opposite, adjacent and hypotenuse. The hypotenuse is the longest sides of the triangle.

The width  can be determined using Pythagoras theorem

The Pythagoras theorem: a² + b² = c²

where:

a = lengthb = basec = hypotenuse

14² + b = 21²

b = 21² - 14²

b² = 441 - 196

b² = 245

b = √245

b = 15.65 inches

To learn more about right angled triangle, please check: https://brainly.com/question/20694080

#SPJ1

What is a loop describe its function and importance?

Answers

A loop is a programming construct that allows a set of instructions to be repeated until a certain condition is met.

What is function?

Function is a relation between input and output values, where each input is related to exactly one output. A function is a mathematical rule that assigns a unique output to each input. It is a process that produces a specific result from given inputs. Functions are used in many areas of mathematics, including algebra, calculus and geometry.

The loop can be used to execute a set of instructions multiple times, or it can be used to iterate over a collection of items such as an array. Loops are an important part of programming, as they allow for efficient and concise code.

Loops are especially useful when it comes to dealing with large datasets. For example, if you wanted to loop through an array of 100 elements, you could do so by writing a single loop statement. This allows you to quickly and easily process large amounts of data without having to write separate instructions for each element. Similarly, loops can be used to iterate over a collection of items such as a linked list or a hash table, making it easier to deal with complex data structures.

To know more about function click-
https://brainly.com/question/2456547

#SPJ4

End behavior of equation

Answers

The x-axis "ends" of a function's graph are referred to as the function's "end behavior" in mathematical terms.

what is equation ?

Its simplest form is thought to be the number's smallest equivalent fraction. How to determine the simplest form. Look for shared factors in the denominator and numerator. A fractional number can be checked to discover if it is a prime number. A statement having two equal sides and an equal sign in the middle is referred to as a mathematical equation. Every variable's degrees are listed in descending order in the general form of any equation. The formula for a linear equation is x + b = 0. The general form of a two-variable linear equation is an x + b y + c = 0. (or something similar). Either conditional equations or identities are categories for equations. An identity holds true for whatever value of the variables.

given

The x-axis "ends" of a function's graph are referred to as the function's "end behavior" in mathematical terms.

In other words, if we look at the graph's trend from the right end of the x-axis (as x approaches +) and the left end (as x approaches ), the end behavior of a function describes both.

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

The complete question is :-

What do you mean by end behavior of equation ?

A. The slope of m is −25.
B. The slope of q is −52.
C. The slope of n is 25.
D. The slope of p is −52. Which statements are true?

Answers

The answer is A: the slope of m is -2/5

f\left(x\right)=2\left(x\right)^{2}+5\sqrt{\left(x+2\right)}

Answers

The graph of the function is attached. The given function has no solution.

What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the function as -

[tex]f\left(x\right)=2\left(x\right)^{2}+5\sqrt{\left(x+2\right)}[/tex]

The given function is -

[tex]f\left(x\right)=2\left(x\right)^{2}+5\sqrt{\left(x+2\right)}[/tex]

The graph of the function is attached. The given equation has no solution.

Therefore, the graph of the function is attached. The given function has no solution.

To solve more questions on graphs, visit the link below-

brainly.com/question/1041084

#SPJ1

I need help with this problem. I've never been good at math.

Answers

Perimeter: 27.5m
Area: 60.64m^2
if you want to explain how I found it lmk!! Have a great day :))

Write the expression using only positive exponents. Assume no denominator equals zero.

Answers

Answer:

[tex]\cfrac{x^{13}}{y^3}[/tex]

-------------------------------------

Given expression:

[tex]\cfrac{(x^5y^2)^2}{x^{-3}y^7}[/tex]

Rewrite it as follows, to get only positive exponents:

[tex]\cfrac{(x^5y^2)^2}{x^{-3}y^7}=\cfrac{x^{10}y^4}{x^{-3}y^7}=\cfrac{x^{10+3}}{y^{7-4}}=\cfrac{x^{13}}{y^3}[/tex]

find the gradient and intercept of the following equation of line y= -2x - 5​

Answers

Answers

We know this equation is in slope intercept form
y = mx + b
So
m = slope
b = y intercept

Gradient is the same as slope. Slope is “m” the coefficient next to the x, so your slope is -2.
Your y intercept is “b” so it is -5, where your line crosses the y axis.

You are given the line, y=-2x-5. This line is in slope-intercept form, y=mx+b, where m is the slope (or gradient) and b is the y-intercept.

The gradient of the given line is -2 and the y-intercept is -5.

write in simplest form
8 5/12 + 11 1/4

Answers

Answer:

19 2/3

Step-by-step explanation:

8+11=19, & 5/12+1/4=8/12

What are the two 2 coordinate system in AutoCAD?

Answers

AutoCAD uses two different coordinate systems. Your working plane's angle is determined by the World Coordinate System (WCS) and User Coordinate System (UCS).

In order to guarantee that everything lines up with the center of a file in a real-world location, the WCS should always be utilized as the geometry reference. The screen can be oriented to a location using the UCS. The file originated from the WCS. The WCS can't be moved from its current location.

Drawing elements will use the rotating coordinate system if a user coordinate system is set, however, the WCS can always be changed. A "User Coordinate System" (UCS) specifies the angle of the XY plane in which you are operating. The XY plane is rotated when a user coordinate system is defined, making it easier to work with alternative orientations.

To learn more about AutoCAD, visit the link below:

brainly.com/question/26979679

#SPJ4

neena is listening to a song. It has a consistent beat. She counts 11 beats in 5 sec. what is the C.O.P for the realtionships of beats to minute.

Answers

Answer:

Step-by-step explanation:

The proportional relation is y= 2.2x

What is proportion?

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

According to the concept of proportion, two ratios are in proportion when they are equal.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

Neena counts 11 beats in 5 seconds

So, x=11 and y=5

Using the proportionality

y = k x

k= y/x

k= 11/5

k= 2.2

Hence, the proportional relation is y= 2.2x

Answer:

2.2

Step-by-step explanation:

1. COP= constant of proportionality

What does that mean? This is how much of something you need for the variables to be proportional no matter their value. For example, if you pay 1.99 for 1 gallon of gas but then 30 dollars for 2 gallons at the same gas station, it doesn't make sense. You need to pay $3 for 2 gallons, and so on.

2. How do we find COP?

K is going to represent the constant of proportionality (COP), what we are solving for. Your equation should be k=b/a.

3. B is what comes first in the ratio, and is second. They said "beats to minutes" so beats= b and minutes= a

3. Solve: 11/5= 2.2

Find the sum of the first 47 terms of the following series, to the nearest integer. 13, 18,23,...

Answers

The sum of the first 47 terms of the following series is 6016

What type of series is this?

The series of numbers is an arithmetic progression.  In an arithmetic progression, the subsequent terms are gotten by the addition of a common difference to the terms.

The series is 13, 18,23,...

The first term is = 13.

The common difference is = 18-13 = 5

The nth term is 47

the formula for sum of nth term is given by

Sn = n/2{2a + (n-1)d}

S₄₇ = 47/2{2*13 + (47-1)5}

Simplifying the expression we have

S₄₇ = 23.5 [26 + (46*5)]

S₄₇ = 23.5 [26 +230]

S₄₇ = 23.5 * 256

This shows that the S₄₇ = 6016

Learn more about sequences on https://brainly.com/question/30262438

#SPJ1

Rafa has $6,450 in his savings account. if the bank pays 3.7% interest per year on savings, how much interest does he need to earn in one year

Answers

The amount of interest that Rafa earns in one year, given the amount in the savings account and the interest is $ 238. 65 .

How to find the amount earned ?

The amount earned by Rafa in one year can be found by the formula :

= Amount in savings account x Interest per year

Amount in savings account = $ 6, 450

Interest per year = 3. 7 %

The amount earned by Rafa for the year is therefore :

= 6, 450 x 3. 7 %

= $ 238. 65

Find out more on interest earned at https://brainly.com/question/19852297

#SPJ1

((16526+828929)÷82727)×0

need step by step explanation​

Answers

The value of the equation A = ( ( 16526 + 828929 ) ÷ 82727 ) × 0 is A = 0

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

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

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = ( ( 16526 + 828929 ) ÷ 82727 ) × 0   be equation (1)

On simplifying the equation , we get

A = ( 8,45,455 ÷ 82727 ) × 0

On further simplification , we get

A = 10.219819405 x 0

Any number multiplied by the number 0 will result in 0

Therefore , the value of A = 0

Hence , the equation is A = 0

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ1

Other Questions
A right triangle has legs 2m and 3m in length. What is thelength of its hypotenuse? If micheal invests $2000 in the bank at a rate of 5.5% for 6 years how much interest will he make?help me plz Carol bought bananas for $0.50 per pound and 1 pint of strawberries for $2.25. If Carol paid $4.10, how many pounds, p , of bananas did she buy?Which equation can be used to find p ? A. .50p+2=4.10B. .50p+2.25=4.10C .50+2.25p=3.85D. 2.75+.25p=4.10 En un paralelogramo de tiene ? The article lists numerous sports in which an individual can compete. In a few sentences, select an activity from the list you think would be the most strenuous to play and explain your choice. Round 0.9271 to the nearest whole number. please help me I will mark you brainliest PLEASEEE HELPPP me!!!!! pouvez vous faire c'est exercices svp les questions 1.2.3.4.5 Plzzzz help me only have ten minutes left help it's due todayyyyy Triangle ABCis rotated 90 clockwise around the origin to gettriangle A'B'C. Find the length of the line segment, AC A. 2.23OB. 4.47O c. 2.44D.2 What would make someone feel very connected to school? Thesis Writing Activity:Topic: Change is needed in schools across the United States Great! I scored two goals. We 1_______ the match 60. The team we 2_______ weren't very good, though. They've 3_______ every 4_______ they've played this year. Most of the 5_______ on their team couldn't even 6_______ the ball properly! por cada persona que tiene gripe,hay 6 personas que solamente tienen sintomas de gripe. si un medico ve a 40 pacientes, calcula aproximadamente cuntos pacientes esperas que tengan solamente sintomas de gripe. Answer and solution plse :) An example of a career thesis topic pls on computer careers like here's an example of nursing: Nursing is a career that has a demanding job description, requires rigorous training in health care, but has a very positive outlook for jobs. So like that but in the computer career range, ya dig? Which evidence is provided by fossil record I REALLY NEED AN ANSWER FAST! Which statement about the diagram is true? A. m1 m3 + m4 B. m1 + m2 m2 + m3 + m4 C. m2 = m3 + m4 D. m1 m4Pick one of the answers