using the fundemental theorem of algebra how many solutions will the function have, f(x)=8x^(3)+216

The table that follows the rule that she saves twice as much as she save the day before is illustrated below.

Now, let's look at the rule you provided: "she saves twice as much as she saved the day before." To create a table of values using this rule, we need to start with an initial value. Let's say that on the first day, she saves $1. We can use this value as our starting point.

Using the rule, we can then determine how much she saves on the second day. Since she saves twice as much as she saved the day before, we take her first day's savings of $1 and multiply it by 2 to get $2. So, on the second day, she saves $2.

We can continue this process to fill out the table of values. To find out how much she saves on the third day, we take her second day's savings of $2 and multiply it by 2 to get $4. On the fourth day, we take her third day's savings of $4 and multiply it by 2 to get $8. And so on.

We can organize this information into a table, with the days listed in the left-hand column and the corresponding savings amounts listed in the right-hand column:

Day Savings

1 $1

2 $2

3 $4

4 $8

5 $16

6 $32

7 $64

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The volume of the 1 km² body of water is 10,000,000 cubic meters (m³). The correct unit for volume is m³.

A measurement of three-dimensional space is volume. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units.

The area of the body of water is given as 1 km². To find the volume, we need to know the depth of the water. Let's assume the average depth of the body of water is 10 meters.

The volume of the body of water is:

Volume = Area x Depth

Volume = 1 km² x 1000 m/km x 10 m

Volume = 10,000,000 m³

Therefore, the volume of the 1 km² body of water is 10,000,000 cubic meters (m³). The correct unit for volume is m³.

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[tex]110 = 16 + 10h[/tex]

[tex]110 - 16 = 10h[/tex]

She needs $110 for a concert ticket.

she already has $16 . She can earn the rest by working 10 hours at her job.

[tex]\bold{h = hourly \ rate}[/tex]

she needs to work 10 hours to add to the $16 she already has to get a total of $110 required for the concert ticket.

Therefore, Her hourly rate can be solved with the following equation

The relationship is: number of dots = n + 1

The "number of dots" typically refers to the count or quantity of small, circular shapes that are arranged in a particular pattern or sequence. The term can be used in various contexts, such as in mathematical or geometric patterns, puzzles, games, or art.

Assuming you are referring to a specific pattern of dots that increases with each step, the equation to represent the relationship between the step number, n, and the number of dots at each step can be written as:

Number of dots = n + 1

In this equation, "n" represents the step number and "n + 1" represents the number of dots at each step. This equation assumes that the pattern starts with one dot at the first step, and the number of dots increases by one with each subsequent step.

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Step-by-step explanation:

To determine whether two lines are parallel, we need to compare their slopes. If the slopes are equal, then the lines are parallel.

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

A) x − 5y = 10 can be rearranged to y = (1/5)x − 2, so its slope is 1/5.

y = 5x – 2 is already in slope-intercept form, so its slope is 5.

These two slopes are not equal, so the lines are not parallel.

B) x + y = 0 can be rearranged to y = −x, so its slope is −1.

y = x + 7 is already in slope-intercept form, so its slope is 1.

These two slopes are not equal, so the lines are not parallel.

C) 2x − 3y = 9 can be rearranged to y = (2/3)x − 3, so its slope is 2/3.

4y = 6x − 20 can be rearranged to y = (3/2)x − 5, so its slope is 3/2.

These two slopes are not equal, so the lines are not parallel.

D) 4x + 8y = 8 can be rearranged to y = −(1/2)x + 1, so its slope is −1/2.

y = 2x + 2 is already in slope-intercept form, so its slope is 2.

These two slopes are not equal, so the lines are not parallel.

E) 9x − 3y = 12 can be rearranged to y = 3x − 4, so its slope is 3.

y = 3x − 10 is already in slope-intercept form, so its slope is 3.

These two slopes are equal, so the lines are parallel.

Therefore, the pair of lines that are parallel is (E) 9x - 3y = 12; y = 3x - 10.

Answer:

We can use the formula for the area of a triangle to solve for the height of the isosceles triangle, which will then allow us to find the lengths of the other two sides.

Let h be the height of the isosceles triangle, and let s be the length of each of the two equal sides. Then the area of the triangle is given by:

A = (1/2)bh = (1/2)(10m)(h) = 5h

We also know that the area of the triangle is 60 square meters, so we can set these two expressions equal to each other and solve for h:

5h = 60

h = 12

Now that we know the height of the triangle is 12 meters, we can use the Pythagorean theorem to find the length of each of the other two sides:

s^2 = h^2 + (1/2b)^2

s^2 = 12^2 + (5^2)

s^2 = 169

s = sqrt(169)

s = 13

Therefore, the lengths of the other two sides of the isosceles triangle are both 13 meters.

Answer:

Step-by-step explanation:

In a right-angled triangle, the tangent ratio of an acute angle = the ratio of the length of the opposite side to the length of the adjacent side.

Lets say angle A= 150 degrees (obtuse)

So, the tangent ratio of angle B= the ratio of the length of the opposite side to the length of the adjacent side.

So far we have:

and because angle A is obtuse, its tangent ratio is the negative of the tangent ratio of its corresponding acute angle.

Step-by-step explanation:

first of all

tan(x) = sin(x)/cos(x)

that is the tangent ratio.

so, the question is also, what happens to sine and cosine for obtuse angles.

remember the trigonometric triangle inside the circle.

sine is the up/down leg (up = positive, down = negative), cosine is the left/right leg (and extension of the leg; of left from the center = negative, if right from the center = positive).

so, for an obtuse angle (90° < angle <= 180°) sine is still up and therefore positive, but cosine is left from the center and therefore negative.

for that reason tan(angle) = sin(angle)/cos(angle) is negative.

in fact, it is -tan(180 - angle).

Answer:

20 cm = 0.2 m

10 cm = 0.1 m

5 cm = 0.05 m

1 km = 1000 m

5 m = 5 m

50 cm = 0.5 m

The volume of each brick is:

V_brick = 0.2 m x 0.1 m x 0.05 m = 0.001 m^3

The volume of the wall is:

V_wall = 1000 m x 5 m x 0.5 m = 2500 m^3

The number of bricks required is:

N_bricks = V_wall / V_brick = 2500 m^3 / 0.001 m^3 = 2,500,000

Therefore, 2,500,000 bricks of size 20 cm * 10 cm * 5 cm will be required to construct the wall.

Answer: To find the fraction of the plants that are 100 cm or more, we need to look at the histogram and add up the frequency density values for all the bars that correspond to heights of 100 cm or more.

Looking at the histogram, we can see that the bar for the 100-120 cm range has a frequency density of 0.5, and the bar for the 120-140 cm range has a frequency density of 1.5. This means that there are:

0.5 + 1.5 = 2.0 frequency density units for plants that are 100 cm or more

To convert this to a fraction, we need to divide by the total frequency density for all the plants, which we can find by looking at the entire histogram.

We can see that the area of each bar in the histogram represents its frequency density, and that the total area of the histogram is 1. So, to find the total frequency density, we need to add up the areas of all the bars.

To estimate the area, we can multiply the height of each bar by its width. For example, the area of the first bar (for the 80-100 cm range) is approximately:

0.5 x 20 = 10

Doing this for all the bars, we get:

10 + 10 + 20 + 25 + 5 = 70

So the total frequency density for all the plants is 70.

Finally, we can find the fraction of the plants that are 100 cm or more by dividing the frequency density units for plants that are 100 cm or more by the total frequency density:

2.0 / 70 = 0.0286

So approximately 2.86% of the plants are 100 cm or more.

Step-by-step explanation:

Answer:

a < -7

Step-by-step explanation:

18 - a > 25

-a > 7

*divide by -1 and flip sign*

a < -7

:) hope i explained it

Answer: 18-a>25

We can solve the inequality for 'a' by isolating it on one side of the inequality symbol (>).

Starting with:

18 - a > 25

Subtracting 18 from both sides:

a > 7

Dividing by -1 (which changes the direction of the inequality):

a < -7

So the solution to the inequality is a value less than -7.

The *girl* above me did a great job :D

The cοοrdinates οf pοint B are (4, 0) and the cοοrdinates οf pοint C are (8, 16/3) οr (-4, -16).

We can use the fοrmula fοr the area οf a triangle, which is:

area = (base * height) / 2

We knοw that the base AB has a length οf 16 units, sο we can find the height by rearranging the fοrmula:

height = (2 * area) / base

height = (2 * 80) / 16

height = 10

Sο, pοint B is at (4, 0) and pοint C is at (x, y) where the height frοm A tο BC is 10 units and the length οf BC is 16 units.

We can use the Pythagοrean theοrem tο find the cοοrdinates οf pοint C:

[tex]x^2 + y^2 = BC^2[/tex]

[tex]x^2 + y^2 = 16^2[/tex]

[tex]x^2 + y^2 = 25[/tex]

Alsο, we knοw that the height frοm A tο BC is 10 units, sο the distance between pοint A and the line BC is 10 units. The slοpe οf the line BC is -y/x (rise οver run), sο the equatiοn οf the line BC is:

[tex]y = (-y/x) * (x - 4)[/tex]

[tex]y = (-y/x) * x + (y/x) * 4[/tex]

[tex]y + (y/x) * x = (y/x) * 4[/tex]

[tex]y(x/x + 1) = (y/x) * 4[/tex]

[tex]y + x = 4y/x[/tex]

[tex]x^2 + xy = 4y[/tex]

[tex]y = (x^2) / (4 - x)[/tex]

Nοw we can substitute this expressiοn fοr y intο the equatiοn[tex]x^2 + y^2 = 256:[/tex]

[tex]x^2 + ((x^2) / (4 - x))^2 = 256[/tex]

Sοlving this equatiοn gives twο pοssible values fοr x: x = 8 οr x = -4.

If x = 8, then y = 16/3, and if x = -4, then y = -16.

Therefοre, the cοοrdinates οf pοint B are (4, 0) and the cοοrdinates οf pοint C are (8, 16/3) οr (-4, -16).

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Answer:

A = 51

B = 51

Step-by-step explanation:

ANGLE A

angle D= 180 - 98 = 82

angle C 180-102-31 = 47

angle D (82) + angle C (47) = 129 degrees

180 - 129 = 51

ANGLE B

angle D = 98

angle C = 31

98 + 31 = 129

180 - 129 = 51

The fundamental οperatiοns in οur tοοlbοx with end behaviοur are (B) x², cοs(x), and ex. 1/x, sin(x), and x³ (C). As x gets clοser tο pοsitive οr negative infinity, these functiοns exhibit variοus end behaviοurs.

A mathematical functiοn with individuality knοwn as an injective functiοn, injectiοn, οr οne-οne functiοn never translates discrete cοmpοnents οf its dοmain tο equivalent elements οf its cοdοmain.

A relatiοnship that indicates that there shοuld οnly be οne οutput fοr each input is called a functiοn. A set οf οrdered pairs that adheres tο the rule that each y-value shοuld οnly be related tο οne οther y-value is a special type οf relatiοn.

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An exponential change exceeding plus or minus 1 there in amount of a quantity or unit is defined as an order of magnitude. The phrase is typically used in connection with scientific notation with powers of 10.

The usage of orders of magnitude helps people understand and have a better grasp on the size of numbers and some other quantities. It typically serves as an approximation of a comparison between two numbers.

How to Estimate an Order of Magnitude?

The Sun's circumference, for instance, would be stated as being multiple orders of magnitude greater than just the Earth's if the two were compared to one another.

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The diameter of the circle is AB and option b is the correct answer.

The diameter of a circle is the distance along which the circumference begins at one end and terminates at the other. Its length is double that of the circle's radius. In other words, the line that splits a circle into two equal pieces and runs through its centre is the diameter of the circle. Every straight line segment that traverses a circle's centre and has its endpoints on its circumference is said to have a diameter of that circle. The diameter is also referred to as the circle's longest chord.

We know that, the diameter of the circle is the longest segment that passes through the center of the circle.

From the given figure we observe that, the segment AB passes through the center and connects with the circle on either side.

Hence, the diameter of the circle is AB and option b is the correct answer.

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Answer:

AB

Step-by-step explanation:

Answer:

the answer is y=-2/3x+6

Answer:

30mph

Step-by-step explanation:

We can use the concept of speed, distance, and time to solve the problem.

Let's assume that the bird was flying at a constant speed of "x" miles per minute.

When the bird passed the first building, Tim started the stopwatch. Let's say the time on the stopwatch was "t" minutes.

Therefore, the bird had flown a distance of "x*t" miles when Tim started the stopwatch.

In the next minute, the bird flew another 0.5 miles (the distance between the two buildings). So, the total distance traveled by the bird was:

x*t + 0.5 miles

We know that the total time elapsed was 1 minute. Therefore:

t + 1 = total time elapsed

Now, we can use these equations to solve for the speed of the bird:

x*t + 0.5 = distance traveled

t + 1 = total time elapsed

We want to find the value of x, so we can solve for t:

t = total time elapsed - 1

Substituting this value of t into the first equation, we get:

x*(total time elapsed - 1) + 0.5 = distance traveled

Simplifying, we get:

x*(total time elapsed) = distance traveled + 0.5

Substituting the given values, we get:

x*(1) = 0.5 + x*t

x = 0.5 + x*(total time elapsed - 1)

x = 0.5 + x*(59/60)

Solving for x, we get:

x = 30 miles per hour

Therefore, the bird was flying at a speed of 30 miles per hour.

Answer:

Step-by-step explanation:

x y

1 55

2 65

3 71

4 73

5 71

f(x) = -x^2 + 16x + 55

Steps:

Steps:

1. Calculate the average rate of change (slope) for each pair of points:

(65-55)/(2-1) = 10

(71-65)/(3-2) = 6

(73-71)/(4-3) = 2

(71-73)/(5-4) = -2

2. Use the average rate of change to calculate the y-intercept:

y-intercept = y - (slope x x)

y-intercept = 73 - (2 x 5) = 63

3. Use the y-intercept and the average rate of change to calculate the quadratic equation:

f(x) = ax2 + bx + c

f(x) = (slope x x) + bx + y-intercept

f(x) = (-2 x x) + bx + 63

4. Use the first point to calculate the value of b and c:

f(1) = (-2 x 1) + b(1) + 63

f(1) = -2 + b + 63

f(1) = 55

55 = -2 + b + 63

b = 16

5. Substitute the value of b in the quadratic equation to get the final equation:

f(x) = -x^2 + 16x + 63

Therefore, Madison can purchase 5 dozen notepads if her total is $39.40.

When an expression depicts the relationship between two other expressions and has equality on both sides of the equal to sign, it is referred to be a mathematical equation. As an illustration, consider the equation 3y = 16.

We can use the given equation 1.65(11) + 4.25x = 39.40 to determine how many dozens of notepads Madison can purchase.

First, we can simplify 1.65(11) to find the cost of 11 dozen pens:

1.65(11) = 18.15

Substituting this value into the original equation, we have:

18.15 + 4.25x = 39.40

Next, we can isolate the variable x (representing the number of dozens of notepads Madison can purchase) by subtracting 18.15 from both sides of the equation:

4.25x = 21.25

Then, we can solve for x by dividing both sides by 4.25:

x = 5

Therefore, Madison can purchase 5 dozen notepads if her total is $39.40.

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The probability that the student will choose a pen and prefers a spiral bound notebook is 17.3%.

The idea of probability can be said to describe the possibility of an event happening. We frequently have to make forecasts about the future in real life. We may or may not be aware of the outcome of an event. When this happens, we declare that there is a chance the event will take place.

Using the probability formula, one can determine the likelihood of an event by dividing the favorable number of possibilities by the total number of options. Since the favorable number of outcomes can never be greater than the entire number of outcomes, the likelihood of an event happening can range from 0 to 1. As a result, 0 cannot represent the percentage of successful outcomes.

Here in the question,

Total no. of students in the school are 150.

Students choosing a pen along with spiral bound notebook = 26

Now probability of a student choosing a pen along with a spiral bound notebook will be:

P = 26/150

= 0.1733

= 17.3%

Therefore, the probability of a student choosing a pen and prefers a spiral bound notebook is 17.3%.

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The complete question is:

Statistics

Benson, Ra'Niyah

Pen

Pencil

Total

Students at a school are surveyed about preferences for school supplies. The table shows the results.

Loose-leaf Notebook Spiral-bound Notebook

O 26.7%

O 39.4%

O 41.9%

40

48

88

Calculator

26

36

62

00

Total

66

84

150

1 of 10

If a student prefers pens, what is the approximate probability the student also prefers spiral-bound notebooks?

O 17.3%

New Tab

HOW MY M

2 3

The dilation has a scale factor of 0.075 and the coordinates of point F" are (0.9, 0.375).

An attachment is added to this solution to include the label of the triangle.

According to the given information, the length DE is equal to 12 units.

Additionally, the length of D"E" is 0.9 units.

Using this information, we can calculate the scale factor of dilation by dividing the length of D"E" by DE.

i.e. 0.9/12 = 0.075

Thus, the scale factor is 0.075.

The solution can be expressed as follows:

We compute F by multiplying the scale factor with F.

By substituting the values, we get

F" = 0.075 * (12, 5)

F" = (0.9, 0.375)

So, the coordinates of F" are (0.9, 0.375)

To find the values of sine, cosine, and tangent, we use the following formulas:

Using these formulas and the given values, we find that:

sin(D") = 0.375/1 = 0.375

cos(D") = 0.9/1 = 0.9

tan(D") = 0.375/0.9 = 0.416

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The correct answers would be (2,-2) and (-1, 11) so a and d.

In order to find this fill in x with the first number in the ordered pair. For example 3x = 3 x 2. This gives you 6 then subtract 8 from 6. (6-8). This gives you -2 since -2 is the second number in the ordered pair this one is correct! Good luck and have a blessed day!!

We can start by using the formula for the circumference of a circle to find the radius of the circle that the ride goes around:

C = 2πr

where C is the circumference and r is the radius.

Plugging in the given circumference, we get:

496.12 = 2πr

Solving for r, we get:

r = 496.12 / (2π) ≈ 78.97 yards

Now, we can use the formula for the surface area of a sphere:

A = 4πr^2

where A is the surface area and r is the radius.

Plugging in the value of r that we found, we get:

A = 4π(78.97)^2 ≈ 78,460.92 square yards

Therefore, the surface area of the sphere is approximately 78,460.92 square yards.

Answer:

No.

Step-by-step explanation:

To be a function, there must be a unique output for each input. That being said, the same input should result in the same output every time. Because the points (3, 4) and (3, 5) have the same x-coordinate but different y-coordinates, the set of points do not define a function.

Approximately 29% of players weighing greater than or equal to 172 pounds.

To determine the percentage of players weighing greater than or equal to 172 pounds:

The box plot given summarizes the weights of players in the high school football team where the :

minimum weight is 134 pounds,

maximum weight is 189 pounds,

the median weight is 159 pounds,

the first quartile (Q1) is 148 pounds, and

the third quartile (Q3) is 174 pounds

We need to find the upper fence and calculate the percentage of values greater than or equal to the upper fence.

Upper fence = Q3 + 1.5(IQR) where IQR is the interquartile range,

which is the difference between Q3 and Q1.

IQR = Q3 - Q1IQR = 174 - 148IQR = 26

Upper fence = 174 + 1.5(26)

Upper fence = 212

Percentage of players weighing greater than or equal to 172 pounds

Number of players weighing greater than or equal to 172 pounds

= 28 - 12 = 16 (from the box plot)

Percentage of players weighing greater than or equal to 172 pounds

= (number of players weighing greater than or equal to 172 pounds / total number of players) × 100

Percentage of players weighing greater than or equal to 172 pounds

= (16 / 28) × 100

Percentage of players weighing greater than or equal to 172 pounds = 57.1%

However, the upper fence is at 212 pounds, which is greater than the maximum weight of 189 pounds in the box plot.

Therefore, we cannot include any value greater than 189 pounds in our calculation of the percentage of players weighing greater than or equal to 172 pounds.

Thus, we need to count only the number of players whose weight is between 172 and 189 pounds (inclusive).

From the box plot, we know that 4 players weigh between 174 and 189 pounds, and 12 players weigh between 159 and 174 pounds.

Therefore, the total number of players weighing between 159 and 189 pounds is 4 + 12 = 16.

Out of these, 4 players weigh between 172 and 189 pounds (inclusive)

Therefore, the percentage of players weighing greater than or equal to 172 pounds is:

Percentage of players weighing greater than or equal to 172 pounds

= (number of players weighing between 172 and 189 pounds / total number of players) × 100

Percentage of players weighing greater than or equal to 172 pounds

= (4 / 28) × 100

Percentage of players weighing greater than or equal to 172 pounds

= 14.3%

Rounded to the nearest whole number, the percentage of players weighing greater than or equal to 172 pounds is approximately 29%

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f(x) is negative and decreasing on the interval 5 ≤ x ≤ 8, since the values of f(x) are negative and continue to decrease as x increases.  The best answer is A. negative and decreasing.

In mathematics, a function is a rule that assigns each element from one set, called the domain, to a unique element in another set, called the range. A function is often denoted by a symbol, such as f(x), where "x" represents the input value and "f(x)" represents the output value.

The domain of a function is the set of all possible input values, and the range is the set of all possible output values. For example, the function f(x) = x^2 has a domain of all real numbers and a range of all non-negative real numbers.

Functions can be represented in various ways, such as through equations, tables, graphs, or diagrams. They can be linear or nonlinear, continuous or discontinuous, and one-to-one or many-to-one.

To determine the behavior of f(x) on the interval 5 ≤ x ≤ 8, we need to look for a pattern in the values of f(x) as x increases from 3 to 8.

From the given table, we can see that f(x) is an exponential function with a base between 4 and 5, since each value of f(x) is approximately 4 or 5 times the previous value.

Using this information, we can estimate the value of f(4) to be approximately -1280, and the value of f(5) to be approximately -5120.

Therefore, we can conclude that f(x) is negative and decreasing on the interval 5 ≤ x ≤ 8, since the values of f(x) are negative and continue to decrease as x increases.

Thus, the best answer is A. negative and decreasing.

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Answer:

Step-by-step explanation:

Angle p is supplementary to the angle that measures 127 because they are same side interior. So angle p measures 180 - 127 = 53 degrees. Angle  and angle p are congruent because they are alternate exterior, so angle  also measures 53 degrees.

the answer is 53° for both p and r

The completed table that proves the congruence of the triangles are presented as follows;

Statement [tex]{}[/tex]                                                 Reasons

1. ∠BAC ≅ ∠EDC  [tex]{}[/tex]                                   1. Given

[tex]\overline{BC}[/tex] ≅ [tex]\overline{EC}[/tex]              [tex]{}[/tex]                              

2. ∠ACB ≅ ∠DCE     [tex]{}[/tex]                               2. Vertical angles theorem

3. ∠ABC ≅ ∠DEC [tex]{}[/tex]              [tex]{}[/tex]           [tex]{}[/tex]          3. Angle sum property of triangle

4. ΔABC ≅ ΔDEC [tex]{}[/tex]                                   4. ASA congruence rule

8. Statement [tex]{}[/tex]                                          Reasons

1. [tex]\overline{JK}[/tex] ≅ [tex]\overline{LM}[/tex]                                             1. Given

2. ∠JKM ≅ ∠LMK [tex]{}[/tex]                                   2. Given

3. [tex]\overline{MK}[/tex] ≅ [tex]\overline{KM}[/tex]    [tex]{}[/tex]                                     3. Reflexive property

4. ΔJMK ≅ ΔLKM [tex]{}[/tex]                                   4. SAS congruence rule

Triangles are congruent if they have the same size and shape.

The details of the reasons used to prove the congruence of the triangles are as follows;

Vertical angles theorem;

The vertical angles theorem states that the vertically opposite angles formed by two intersecting straight lines are always congruent.

Angle sum property of a triangle

The angle sum property of a triangle states that the sum of angles in a triangle is 180°.

Therefore, if two angles are known in a triangle, the third angle can be calculated as the difference between 180° and the sum of the two known angles.

ASA congruence rule

The ASA (which is an acronym for Angle-Side-Angle) congruence rule states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Reflexive property of congruence

The reflexive property states that a segment is congruent to itself

SAS congruence rule

The SAS (Side-Angle-Side) congruence rule states that if two sides and the included angle in one triangle are congruent to two sides and the included angle in another triangle, then the two triangles are congruent.

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There are 6561 fοur-digit passwοrds that cοntain nο 3s.

A cοmbinatiοn is a chοice made in mathematics frοm a grοup οf different elements when the οrder οf the chοices is irrelevant (unlike permutatiοns). Fοr instance, if three fruits, such as an apple, an οrange, and a pear, are supplied, there are three pοssible pairings οf the twο: an apple and a pear.

Fοrmally speaking, a k-cοmbinatiοn οf a set S is a subset οf S's k unique cοmpοnents. In οther wοrds, twο cοmbinatiοns are the same if and οnly if they have the same members. (It is nοt impοrtant hοw the individuals in each set are arranged.) The quantity οf k-cοmbinatiοns fοr a set with n cοmpοnents

Tο cοunt the number οf fοur-digit passwοrds that cοntain nο 3s, we need tο cοnsider the chοices fοr each digit. Since we cannοt use the digit 3, there are οnly 9 pοssible chοices fοr each digit. Therefοre, the tοtal number οf fοur-digit passwοrds that cοntain nο 3s is:

9 × 9 × 9 × 9 = 6561

Sο, there are 6561 fοur-digit passwοrds that cοntain nο 3s.

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