find the taylor series for f(x) centered at the given value of a. (assume that f has a power series expansion. do not show that rn(x) 0.) f(x) = x3, a = -1

The Probablity that the exam will be finished in under 74 minutes is 0.9332, or roughly 93.32%. By standardising the provided data to the standard normal distribution, which has a mean of 0 and a standard deviation of 1, we can use the standard normal distribution to address this issue. 

The formula: can be used to accomplish this. z = (x - μ) / σ where x equals the number that is provided (74 minutes), equals the mean (62 minutes), and equals the standard deviation. (8 minutes). z = (74 - 62) / 8 z = 1.5

The chance that a standard normal random variable is less than 1.5 can then be determined using a calculator or a chart of the standard normal distribution. The likelihood is roughly 0.9332.

Therefore, the likelihood that the exam will be finished in under 74 minutes is 0.9332, or roughly 93.32%.

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The surface area of the triangular prism 5ft 11ft 15 ft is 515 sq ft.

To find the surface area of a triangular prism, we need to calculate the area of each face and then add them together.

The triangular base has dimensions of 5ft and 15ft, so its area is:

Area of triangular base = (1/2) x 5ft x 15ft = 37.5 square feet

There are two identical triangular faces, so the total area of the triangular faces is:

Total area of triangular faces = 2 x 37.5 = 75 square feet

The rectangular faces have dimensions of 5ft x 11ft and 11ft x 15ft, so their areas are:

Area of first rectangular face = 5ft x 11ft = 55 square feet

Area of second rectangular face = 11ft x 15ft = 165 square feet

There are two identical rectangular faces, so the total area of the rectangular faces is:

Total area of rectangular faces = 2 x (55 + 165) = 440 square feet

Hence, the triangular prism's total surface area is:

Total surface area = Total area of triangular faces + Total area of rectangular faces

Total surface area = 75 + 440 = 515 square feet

The triangular prism offered has a surface area of 515 square feet.

The complete question is:-

Find the surface area of the triangular prism below 5ft 11ft 15 ft

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Step-by-step explanation:

Let's start by representing the change in depth of the snowdrift as negative, since it decreased by 8 inches over the first four days.

Change from Monday to Thursday = -8 inches

Now we need to find the change in depth from Thursday to Friday. We're told that the depth changed by half as much as it did from Monday to Thursday. So we can start by finding half of -8 inches:

Half of -8 inches = (-8)/2 = -4 inches

Therefore, the change in depth from Thursday to Friday is -4 inches.

To summarize:

Change from Monday to Thursday = -8 inches

Change from Thursday to Friday = -4 inches

These findings support the histograms in that data set 1 is skewed to the right while data set 3 is skewed to the left.

(a) A histogram for each of the data sets is as follows:Data set (1) is skewed to the right.Data set (2) has a normal distribution.Data set (3) is skewed to the right.(b) For each of the data sets, we will compute the sample mean and sample median.Sample Mean for Data Set 1: [tex]$\frac{19+24+12+19+18+24+8+5+9+20+13+11+1+12+11+10+22+21+7+16+15+15+26+16+1+13+21+21+20+19}{30}$ = 15.4[/tex]

Sample Median for Data Set 1:Arrange data set in order: {1, 1, 5, 7, 8, 9, 10, 11, 11, 12, 12, 13, 13, 15, 15, 16, 16, 18, 19, 19, 19, 20, 20, 21, 21, 21, 21, 22, 24, 24}Median = 18Sample Mean for Data Set 2: $\frac{17+24+21+22+26+22+19+21+23+11+19+14+23+25+26+15+17+26+21+18+19+21+24+18+16+20+21+20+23+33}{30}$ = 21

Sample Median for Data Set 2:Arrange data set in order: {11, 14, 15, 15, 16, 17, 17, 18, 18, 19, 19, 19, 20, 21, 21, 21, 21, 22, 22, 23, 23, 24, 24, 25, 26, 26, 26, 33}Median = 21

Sample Mean for Data Set 3: $\frac{56+52+13+34+33+18+44+41+48+75+24+19+35+27+46+62+71+24+66+94+40+18+15+39+53+23+41+78+15+35}{30}$ = 43.7333

Sample Median for Data Set 3:Arrange data set in order: {13, 15, 15, 18, 18, 19, 23, 24, 24, 27, 33, 34, 35, 35, 39, 40, 41, 41, 44, 46, 48, 52, 53, 56, 62, 66, 71, 75, 78, 94}Median = 41The mean and median of data set 1 and data set 3 are not the same. In data set 1, the mean is less than the median. In data set 3, the mean is greater than the median.

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Answer:

x = 3, y = -2

Step-by-step explanation:

Rotating a point (x, y) 90° clockwise around the origin will result in the point:

(y, -x)

Applying this to point A:

A = (2, 3)

A' = (3, -2)

x = 3, y = -2

Answer:

The cheapest flight from Washington, D.C. to Portland was found 87 days before departure, on average. Book at least 2 weeks before departure in order to get a

Step-by-step explanation:

The two lengths that separate the top 10% and the bottom 10% are  3.25 cm and 3.04 cm.

This is used to measure how different an individual data point is from the mean of the data set and is a helpful tool when comparing data points to each other.

To find the two lengths, we start by finding the z-scores that correspond to the top 10% and the bottom 10%. The z-score for the top 10% is 1.28 and the z-score for the bottom 10% is -1.28. We then use these z-scores to find the two lengths.

To find the two lengths, we use the following formula:

length = mean + (z-score * standard deviation)

For the top 10%:

length = 3.15 + (1.28 * 0.08)

length = 3.25 cm

For the bottom 10%:

length = 3.15 + (-1.28 * 0.08)

length = 3.04 cm

Therefore, the two lengths that separate the top 10% and the bottom 10% are 3.25 cm and 3.04 cm.

These lengths could serve as limits used to identify which nails should be rejected.

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Answer:

1. x ≈ 15,73

P = 104,96

.

2. x ≈ 50,51

P = 136,26

.

3.

[tex] \cos( \alpha ) = \frac{ \sqrt{3} }{3} [/tex]

P ≈ 24,88

Step-by-step explanation:

1.

Use trigonometry:

[tex] \cos(70°) = \frac{x}{46} [/tex]

Cross-multiply to find x:

[tex]x = 46 \times \cos(70°) ≈15.73[/tex]

In order to find the perimeter, we have to know all three side lengths of the triangle

Let's find the third one by using the Pythagorean theorem:

[tex] {bc}^{2} = {ab}^{2} - {ac}^{2} [/tex]

[tex] {bc}^{2} = {46}^{2} - ({15 .73})^{2} = 1868.5671[/tex]

[tex]bc > 0[/tex]

[tex]bc = \sqrt{1868.5671} ≈43.23[/tex]

Now, we can find the perimeter (the sum of all side lengths):

P = AB + BC + AC

P = 46 + 43,23 + 15,73 = 104,96

.

2.

[tex] \tan(29°) = \frac{28}{x} [/tex]

[tex]x = \frac{28}{ \tan(29°) } ≈50.51[/tex]

[tex] {ab}^{2} = {ac}^{2} + {cb}^{2} [/tex]

[tex] {ab}^{2} =( {50.51})^{2} + {28}^{2} = 3335.2601[/tex]

[tex]ab > 0[/tex]

[tex]ab = \sqrt{3335.2601} ≈57.75[/tex]

P = 57,75 + 28 + 50,51 = 136,26

.

3.

[tex] \cos( \alpha ) = \frac{ac}{ab} [/tex]

[tex] \cos( \alpha ) = \frac{6}{6 \sqrt{3} } = \frac{ \sqrt{3} }{3} [/tex]

[tex]p = 6 + 6 \sqrt{2} + 6 \sqrt{3} ≈24.88[/tex]

Thus, using the slope intercept form of for the equation of line: equation 11 = 6 + k  can be written as: 11 = 2*3 + k.

Every equation that describes the slope and at least one point on a line is said to be the equation of that line.

We can bypass point-slope form and directly enter the numbers into the slope-intercept equation if the observed point of such an equation is the y-intercept. If not, we must enter the numbers into point-slope, solve for y, and then transform the data into slope-intercept form.

Given data:

Passing point (2,11)

Equation of line:

11 = 6 + k  

11 = 2*3 + k ...eq 1

The standard equation of line in slope intercept form is:

y = mx + c

In which, m is the slope and c is the y-intercept.

The given passing points must satisfy the line. So, putting the values in standard form.

11 = 2m + c  ...eq 2

Comparing the eq 1 and 2

slope m = 3 and c = k.

Thus, using the slope intercept form of for the equation of line: equation 11 = 6 + k  can be written as: 11 = 2*3 + k.

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Answer: compensation strategy

Step-by-step explanation:

the probability that a top-selling red and voss tire wears out before 80,000 miles is about 2.56%.

The student question asks about the probability that a top-selling red and voss tire, rated for 80,000 miles, wears out before reaching 80,000 miles. The tire's lifespan follows a normal distribution with a mean of 94,000 miles and a standard deviation of 7200 miles.
To find the probability, we need to calculate the z-score first. The z-score is a measure of how many standard deviations away from the mean a particular value is. We can use the following formula to calculate the z-score:
z = (X - μ) / σ
where X is the value (in this case, 80,000 miles), μ is the mean (94,000 miles), and σ is the standard deviation (7200 miles).

Calculate the z-score:
z = (80,000 - 94,000) / 7200
z = -14,000 / 7200
z ≈ -1.944
The z-score is approximately -1.944, which means the tire wearing out at 80,000 miles is about 1.944 standard deviations below the mean.
Find the probability:
Now, we can use the z-score to find the probability. We can look up the z-score in a standard normal distribution table or use a calculator with a built-in function for this purpose.
Using a standard normal distribution table or calculator, we find that the probability corresponding to a z-score of -1.944 is approximately 0.0256 or 2.56%.

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A sample of bacteria is grown in a petri dish. It contains 1,000 bacteria, and the population doubles every half hour. The inequality 1,000(2)^(2t)>50,000, where t is the number of hours, models when the population of the bacteria sample will be greater than 50,000.

Based on the inequality, the population in the sample will be greater than 50,000 after 2 hours. To solve the inequality, we need to isolate the variable t.

First, divide both sides of the inequality by 1,000:2^(2t)>50/1,0002^(2t)>1/20Next, take the logarithm of both sides of the inequality (base 2):2t>log2(1/20)t>log2(1/20)/2t>−4/2t>−2Therefore, the population of the bacteria sample will be greater than 50,000 after 2 hours.

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Therefore , the solution of the given problem of expressions comes out to be hire 15 chairs in order for the rental costs to be equal.

Instead of producing approximations at random, it is better to use moving numeral variables, which may be rising, declining, or blocking. They could only help one another by sharing materials, information, or solutions to issues. The justifications, parts, and mathematical comments for equation techniques like additional disapproval, production.

Here,

Assume that Erin needs to hire x chairs in order for the rental costs to be equal.

The following equation provides the price for purchasing from A-1 Rental:

=> C(A-1) = 1.74x + 61.31

The following equation provides the price for purchasing from Tonka Tents:

=> C(Tonka) = 1.99x plus 57.56

We must solve the following equation to determine how many chairs Erin must hire in order for the rental costs to be equal:

=> C(A-1) = C(Tonka)

=> 1.74x + 61.31 = 1.99x + 57.56

1.74x and 57.56 are subtracted from both sides to yield:

=> 0.25x = 3.75

By multiplying both parts by 0.25, we obtain:

=> x = 15

Erin must therefore hire 15 chairs in order for the rental costs to be equal.

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The questions can be answered directly with statistical reasoning are:  how many observations do I need?, how do we control for other factors? option C and F.

Statistical reasoning entails considering and comprehending uncertainty as well as creating mental models to represent important features of occurrences that occur in the actual world. Students should be able to create questions about data and decide what data they need to answer these questions as they reason with this uncertainty. They then compile, arrange, analyse, and present this material in order to summarise and draw conclusions that will aid in resolving their queries.

The capacity to apply models that quantify significant features of data that might contain uncertainty, noise, and mistake allows students to reason about and debate what data means when they are competent in statistical and probabilistic reasoning.

The context of the data or events can affect both statistical and probabilistic reasoning. Furthermore, the calibre of students' statistical reasoning may be impacted by their past information, views, and any misperceptions they may have regarding chance or uncertain circumstances.

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The magnitude of w is approximately 25.298 and its direction is approximately 64.654 degrees counterclockwise from the positive x-axis.

In the context of vectors, the term "magnitude" refers to the size or length of a vector. It is a scalar value that represents the distance between the initial point and the terminal point of the vector in a geometric space.

The size W = ❬–9, –19❭ is obtained from the formula:

||w|| = square((-9)² (-19)²) = square(81+361) = square(442) ≈ 25.298

Therefore ||w|| is approximately 25.298.

The direction of W measured counterclockwise from the positive x-axis is given by the following formula:

θ = arctan (-19/-9) ≈ 64.654°

Therefore, the direction of w is approximately 64.654°.

Therefore the answer is: ||w|| = 25.298; 6 = 64.654°.

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Answer:

3 more kids

Step-by-step explanation:

Answer:

3 kids can join in on the fun.

Step-by-step explanation:

Total number of kids who can jump on the trampoline = 6

Kids jumping currently = 3

Therefore, The number of kids who can join the fun will be the difference of the total number of kids who can jump on the trampoline and kids jumping currently.

= 6 - 3

= 3

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The hotel owner needs approximately 2,248 square feet of fabric to make a pool covering for the winter for their regular hexagonal pool with a side-to-side length of 30 feet.

To calculate the area of the pool, we first need to find the apothem (the distance from the center of the hexagon to the midpoint of any side). For a regular hexagon, the apothem is equal to the side length times the square root of 3 divided by 2. So, the apothem of this hexagonal pool is:

apothem = 30 × √3/2 = 25.980762

The area of a regular hexagon is given by the formula:

area = 3 × √3/2 × apothem^2

Substituting the value of the apothem, we get:

area = 3 × √3/2 × 25.980762^2 = 2247.72

Rounding this to the nearest square foot, the hotel owner will need approximately 2,248 square feet of fabric to construct the cover for the pool.

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Answer:

The college will have about 480 students who prefer cookies.

Step-by-step explanation:

We Know

The table shows the preference of 225 students.

Ice Cream, Candy, Cake, Pie, Cookies

81              , 9         , 72    , 36,   27

Which statement is the best prediction about the number of cookies the college will need?

We Take

4000 / 225 ≈ 17.78

Then we take

27 x 17.78 = 480.06 cookies

So, The college will have about 480 students who prefer cookies.

The exact value of cscθ / csc(π - θ) is 1.

What is simplest radical form ?

The simplest radical form is the expression of a radical where the radicand (the number under the radical sign) has been simplified as much as possible.

First, we need to determine the hypotenuse of the right triangle formed by the terminal side of angle θ and the x-axis.

Using the Pythagorean theorem, we have:

[tex]h^{2}[/tex] = 16+ 1*1

[tex]h^{2}[/tex] = 16 + 1

[tex]h^{2}[/tex] =17

h = [tex]\sqrt{17}[/tex]

Now, we can find the value of sine and cosine of angle θ:

sinθ = opposite/hypotenuse = 1/ [tex]\sqrt{17}[/tex]

cosθ = adjacent/hypotenuse = -4/[tex]\sqrt{17}[/tex]

Therefore, cscθ = 1/sinθ = [tex]\sqrt{17}[/tex]

Now, we can substitute these values into the expression cscθ / csc(π - θ):

cscθ / csc(π - θ) = [tex]\sqrt{17}[/tex]) / csc(π - θ)

We know that csc(π - θ) = 1/sin(π - θ), and since sin(π - θ) = sinθ, we have:

csc(π - θ) = 1/sinθ = [tex]\sqrt{17}[/tex]

Substituting this back into the expression, we have:

cscθ / csc(π - θ) = [tex]\sqrt{17}[/tex]/ [tex]\sqrt{17}[/tex]  = 1

Therefore, the exact value of cscθ / csc(π - θ) is 1.

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Scatterplot: We can see that there is a linear relationship between length of courtship and length of marriage. The higher the courtship the longer the marriage.

A scatter chart is a graphical or mathematical plot for data that uses Cartesian coordinates to display the results of two variables, usually. An additional difference may occur if the content is encoded. The data is displayed as a collection of points, and at each point the value of one variable increases to determine the position on the horizontal axis, and the value among other variables determines the position of the vertical axis.

Scatter plots can be used when one continuous variable is under the experimenter's control and the other is independent of it, or when both continuous variables are independent. If there are increasing and/or decreasing processes, they are called uncontrolled or independent variables and are usually plotted along the horizontal axis. The index or dependent variable is usually plotted along the vertical axis. If there is no difference, you can plot the two variables on two axes, and the scatter plot shows the relationship (not the reason) between the two variables.

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Angle L is 67.5 degrees. Angles F and L are opposite each other, yet the same angle degree.

Alternate interior angles are a pair of angles that are on opposite sides of a transversal and are located between two lines.

More specifically, alternate interior angles are formed when a transversal intersects two parallel lines. These angles are congruent, which means that they have the same measure or degree of rotation.

In the figure,we can see that ∠F and ∠L are alternate interior angles.

So the angles are ∠F=∠L=67.5

Hence Angle L is 67.5 degrees. Angles F and L are opposite each other, yet the same angle degree.

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This results in the systematic measurement error as the deviation is consistently in one direction. Hence, this is an

example of systematic measurement error.

In the given scenario, the researcher reviews study data about head circumference in newborns and notes that study

personnel are measuring from the end of the measuring tape and not from the zero point, which is 1 cm from the end.

This is an example of systematic measurement error.

Systematic measurement error refers to a consistent deviation from the true value in a particular direction in a series of

measurements.

This error is also referred to as bias. In the given scenario, the personnel are measuring from the end of the measuring

tape and not from the zero point, which is 1 cm from the end.

This results in the systematic measurement error as the deviation is consistently in one direction. Hence, this is an

example of systematic measurement error.

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Assuming that the "9ft" and "11ft" refer to the dimensions of a right circular cone, we can find the surface area of the cone using the formula:

A = πr² + πrl

where r is the radius of the base of the cone, l is the slant height of the cone, and π is approximately equal to 3.14.

To find the radius and slant height, we can use the Pythagorean theorem.

Let's assume that 9ft is the height of the cone, and 11ft is the slant height.

Then, we have:

r² + 9² = 11²

r² + 81 = 121

r² = 40

r ≈ 6.32 ft

Now that we have the radius and slant height, we can find the surface area of the cone:

A = πr² + πrl

A = π(6.32)² + π(6.32)(11)

A ≈ 199.3 square feet

Therefore, the surface area of the cone is approximately 199.3 square feet.

Therefore, the solution to the inequality is: -8 < x ≤ 1 or x = 2. In interval notation, we can write the solution as: (-8, 1] ∪ {2}.

Inequality is a mathematical statement that compares two quantities or expressions and indicates that one is greater than, less than, or not equal to the other. An inequality is typically expressed using symbols such as < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), or ≠ (not equal to).

Here,

Since the function f is increasing, we know that if x₁ < x₂, then ƒ(x₁) < ƒ(x₂). To solve the inequality, we need to isolate x on one side of the inequality. We'll start by applying the function ƒ to both sides of the inequality:

ƒ(4x − 3) ≥ ƒ(2 − x²)

Since ƒ is increasing, we can apply it to each side of the inequality without changing the direction of the inequality:

4x − 3 ≥ 2 − x²

Next, we'll simplify the right side of the inequality by expanding the square:

4x − 3 ≥ 2 + x²

Now we'll move all the terms to one side of the inequality:

x² - 4x + 5 ≤ 0

We can factor the quadratic expression to get:

(x - 2)(x - 2 + 1) ≤ 0

Simplifying further:

(x - 2)(x - 1) ≤ 0

Now we need to determine the sign of the expression (x - 2)(x - 1) over the domain D = (-8, 4). We can do this by using a sign chart:

x x - 2 x - 1 (x - 2)(x - 1)

-8 -10 -9 +90

-1 -3 -2 +2

1 -1 0 0

4 2 3 -6

We see that (x - 2)(x - 1) is negative (less than zero) over the interval (-8,1) and positive (greater than zero) over the interval (1,4).

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Answer: 125

Step-by-step explanation: First you need to find the surface area of triangles which the equation to find it is 1/2(base x height).

1/2(10x5) = 25

Then because there are 4 sides alike you multiply it by 4 which would be 100

In order to find the surface of a square which is relatively easy you would do 5x5 which is 25.

The last step is to add both numbers together which would leave us to your answer 125  I really hope this helped!!

The value of the probability P(sum of 6) is five thirty sixths

When rolling a 6-sided die, there are 6 possible outcomes: {1, 2, 3, 4, 5, 6}.

The sum of two rolls can be any number between 2 (when both rolls are 1) and 12 (when both rolls are 6).

To find the probability of getting a sum of 6, we need to count how many ways we can get a sum of 6, and then divide that by the total number of possible outcomes.

We can get a sum of 6 in the following ways:

P(1,5) + P(2,4) + P(3,3) + P(4,2) + P(5,1)

Therefore, the probability of getting a sum of 6 is:

P(sum of 6) = P(1,5) + P(2,4) + P(3,3) + P(4,2) + P(5,1)

This gives

P(sum of 6) = 1/6 + 1/6 + 1/6 + 1/6 + 1/6

P(sum of 6) = 5/36

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According to the similarity rule, the required values are:

M = 25.2 units

∠N = 9.0°

∠P = 10.0°

Euclidean geometry states that two objects are comparable if they have the same shape or the same shape as each other's mirror image.

One can be created from the other more precisely by evenly scaling, possibly with the inclusion of further translation, rotation, and reflection.

Triangles are similar if they have two of the same angle type, or AA (Angle-Angle).

Triangles are identical if they have two sets of proportional sides and equal included angles, or SAS (Side-Angle-Side).

So, here we have two similar figures.

First, observe the pattern of the sides of the figure.

Then, we know that:

M = 25.2 units

And in the angles:

∠N = 90/10 = 9.0°

∠P = 100/10 = 10.0°

Therefore, according to the similarity rule, the required values are:

M = 25.2 units

∠N = 9.0°

∠P = 10.0°

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If there are 40 bottles in the machine when is it to be serviced, 40 number will go in the second column.

Numbers are used to performing arithmetic calculations. Examples of numbers are natural numbers, whole numbers, rational and irrational numbers, etc. 0 is also a number that represents a null value.

A number has many other variations such as even and odd numbers, prime and composite numbers.

To determine the number that will go in the second column, we need to understand the context of the problem.

Assuming the second column refers to the number of bottles in the machine when it should be serviced, the answer

would be 40.

The machine should be serviced when there are 40 bottles in it.

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Question

A vending machine in an office building sells bottled beverages. The machine keeps track of all changes in the number of bottles from sales and from machine refills and maintenance. This record shows the changes for every 5-minute period over one hour.  The machine must be emptied to be serviced. If there are 40 bottles in the machine when it is to be serviced, what number will go in the second column in the table?

time number of bottles

8:00–8:04 -1

8:05–8:09 +12

8:10–8:14 -4

8:15–8:19 -1

8:20–8:24 -5

8:25–8:29 -12

8:30–8:34 -2

8:35–8:39 0

8:40–8:44 0

8:45–8:49 -6

8:50–8:54 +24

8:55–8:59 0

service

Answer:

180

Step-by-step explanation:

6 different letters.

we need to pick groups of 4.

no repetitions, but the sequence matters (code words), as e.g. RAGE is different to GEAR, although they contain the same letters.

so, we need basic permutations (instead of combinations) :

P(6, 4) = 6! / (6 - 4)! = 6! / 2! = 6×5×4×3 = 360

that is simply because regularly we would have 6 choices for the first letter, then 5 for the second, 4 for the third, and 2 for the fourth letter.

the second to the last letter is the second letter from the left in a 4-letter word.

so, we have 3 vowels for that second position.

normally, such a restriction would mean

6×3×4×3 = 216 possibilities.

but we have to distinguish the 2 cases that we pick a vowel for the first position - or not.

if not, we have 3 consonants for the first, 3 vowels for the second position as options.

if yes, we have 3 vowels for the first and 2 vowels for the second position.

that means we get

3×3×4×3 + 3×2×4×3 = 108 + 72 = 180

possibilities.

this makes also sense, when we simply say that this restriction eliminates half of our possible permutations (all with a consonant in the second position) : 360/2 = 180.