What does an octagon shape look like?

The answer is two base cases, using induction.

What is induction ?

Weak induction is when an inductive mathematical proof holds true for all integers in a set of countable proofs. Natural numbers typically use this. The base step and inductive step are used to prove a set, making it the simplest type of mathematical induction.

Two examples make up an induction proof. Without requiring any prior knowledge of other examples, the first, or base case, establishes the claim for n = 0. The induction process, which is used in the second case, demonstrates that if the assertion is true for any particular scenario where n = k, it must also be true for the subsequent case where n = k + 1.

If a statement true  for n= k, accordily to induction it have to hold good for n = k+1,

Hence, base cases does a proof by the weak form of the principle of mathematical induction requires 2 bases.

Learn more about an induction , by the following link

https://brainly.com/question/27849036

#SPJ4

Answer:

Step-by-step explanation:

(x+1)(x-3)(x-4) = (x+1)(x²-7x+12) = x³-6x²+5x+12

:::::

(x+3)(x-0)(x-0)(x-5) = (x+3)(x²)(x-5) = (x²-2x-15)x² = x⁴-2x³-15x²

:::::

(x+2)³ = x³ + 3·x²·2 + 3·x·2² + 2³ = x³ + 6x² + 12x + 8

:::::

(x+3)²(x+1) = (x²+6x+9)(x+1) =  x³ + 7x² + 15x + 9

Answer:

Step-by-step explanation:

Answer:

uhhh 16

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

Answer:

The intersection point of the two curves is \((x,y) = \left(\frac{3}{2}\,kton.m, 185\,USD \right)\).

Step-by-step explanation:

From statement we get the following equations:

Supply curve

\(90\cdot x - y = -50\) (1)

Demand curve

\(10\cdot x + y = 200\) (2)

Where:

\(x\) - Quantity, measured in thousands of metric tons.

\(y\) - Price, measured in US dollars per metric tons.

If we add both equations, then we find that quantity is:

\((90\cdot x -y )+(10\cdot x +y) = -50+200\)

\(100\cdot x = 150\)

\(x = \frac{3}{2}\,kton.m\)

Then, we finally find the price by substituting on (2):

\(y = 200-10\cdot \left(\frac{3}{2} \right)\)

\(y = 200-15\)

\(y = 185\,USD\)

The intersection point of the two curves is \((x,y) = \left(\frac{3}{2}\,kton.m, 185\,USD \right)\).

The Mean for June 2006 and 2005 is  $345,909 and $335,977 respectively. The median for June 2006 and 2005 is $254,000 and $139,000 respectively, there's no mode in this question.

In statistics, the mean, mode, and median are three measures of central tendency that describe a set of numerical data.

The mean is the average of a set of numbers, calculated by adding up all the values and dividing by the number of values. For example, if a set of data contains the values {1, 2, 3, 4, 5}, the mean is (1 + 2 + 3 + 4 + 5) / 5 = 3.

The mode is the value that appears most frequently in a set of data. For example, if a set of data contains the values {1, 2, 2, 3, 4, 4, 4, 5}, the mode is 4, because it appears three times, which is more than any other value.

The median is the middle value in a set of data when it is ordered in ascending or descending order. For example, if a set of data contains the values {1, 2, 3, 4, 5}, the median is 3, because it is the middle value. If there is an even number of values, then the median is the average of the two middle values.

It is important to note that different sets of data may have different measures of central tendency, and sometimes none of these measures may be appropriate.

Measures of central tendency are used to summarize and describe a set of data. The most common measures of central tendency are the mean, median, and mode.

1. Mean:

• Mean for June 2006: (508+435+538+913+367+033+254+240+137+022+160+548+260+458+358+035+222+879+136+371+127+586+201+316)/22 = $345,909

• Mean for June 2005: (422+843+469+588+245+803+199+409+132+054+139+728+254+725+345+065+210+740+134+334+125+455+184+853)/22 = $335,977

2. Median:

• Median for June 2006: Median of ordered data is the value in the middle of the data set, It is the 11th value in order set. we can see that it is $254,000

• Median for June 2005: Median of ordered data is the value in the middle of the data set, It is the 11th value in order set. we can see that it is $139,000

3. Mode:

• Mode for June 2006: There is no mode, because no value is repeated.

• Mode for June 2005: There is no mode, because no value is repeated.

Conclusions:

• The mean housing price in June 2006 is higher than the mean housing price in June

To know more about mode visit:

https://brainly.com/question/12789483

#SPJ1

Answer:

2nd Option

Step-by-step explanation:

Answer:

Step-by-step explanation:

Ratio of snakes to crocodile

36 : 9

In simplest form

4 : 1

The probability that more than a minute foes by without a hit is  0.0498.

Let X denote the waiting time in minutes until the next hit.

From the question, we have

The probability density function of exponential distribution is,

f(x)=λe^(-λ*)        λ>0

Probability =

P(X>1) =∫_1^∞  3e^(-3x) dx

=3(e^(-3z)/(-3))_1^∞

=e^(-3)

=0.0498

Probability = 0.0498

Probability:

Possibility is referred to as probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is.

To learn more about probability visit: https://brainly.com/question/11234923

#SPJ4

The sampling distributions are used for statistical tets.

Hence,The sampling distributions are used for statistical tets.

learn more about sampling tets click here:

https://brainly.com/question/24466382

#SPJ4

Answer:

The points are (0, 4) and (5, 1).

Using the formula for slope, we have:

\(m = \frac{1 - 4}{5 - 0} = - \frac{3}{5} \)

\(y = - \frac{3}{5} x + 4\)

Answer:

C. m4/n2    :))))

Answer:

Step-by-step explanation:

3. To convert 6 inches and 46 inches into feet and inches, we can start by dividing the total number of inches by 12 to get the number of feet, and then take the remainder as the number of inches.

Adding 6 inches and 46 inches, we get:

6 inches + 46 inches = 52 inches

Dividing 52 by 12, we get:

52 ÷ 12 = 4 with a remainder of 4

This means we have 4 feet and 4 inches. Therefore, the conversion is:

6 inches + 46 inches = 4 ft 4 in

9. To convert 45 inches to yards and inches, we can use the fact that there are 36 inches in one yard. We can divide the total number of inches by 36 to get the number of yards, and then take the remainder as the number of inches.

Dividing 45 by 36, we get:

45 ÷ 36 = 1 with a remainder of 9

This means we have 1 yard and 9 inches. Therefore, the conversion is:

45 inches = 1 yard 9 inches

Since 2k2 + 5k + 4 is an integer, it follows that n2 + 3n + 5 is odd.

Direct proof of the statement (in order):

Let T be even. By the definition of even, there exists an integer k such that T = 2k.

Let n be odd. By the definition of odd, there exists an integer k such that n = 2k + 1.

It follows thatn

2 + 3n + 5 = (2k + 1)2 + 3(2k + 1) + 5

= 4k2 + 10k + 9

= 2(2k2 + 5k + 4) + 1.

Since 2k2 + 5k + 4 is an integer, it follows that n2 + 3n + 5 is odd.

To know more about integer visit:

https://brainly.com/question/490943

#SPJ11

Answer:

Step-by-step explanation:

You have to use the distance formula to find that distance.  The formula is:

\(d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}\)

Let's call the first point x1, y1 (4, -1) and the second point x2, y2 (0, -2). Plugging into our formula then gives us this:

\(d=\sqrt{ (0-4)^2+(-2-(-1))^2}\)

which simplifies to

\(d=\sqrt{(-4)^2+(-1)^2}\) which is

\(d=\sqrt{17}\) ≈ 4.123 units

Answer:

400

Step-by-step explanation:

\(\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=7\\ h=19 \end{cases}\implies V=\pi (7)^2(19)\implies V\approx 2924.8~ft^3\)

Answer:

The sum of 7/13 and 11/26 is 25/26.

Step-by-step explanation:

7/13 + 11/26

The common denominator is 26

7/13 *2/2 +11/26

14/26 + 11/26

25/26

The characteristic that is not associated with the normal probability distribution is "99.72% of the time the random variable assumes a value within plus or minus 1 standard deviation of its mean."

In a normal distribution, which is also known as a bell curve, the mean is equal to the median, which is also equal to the mode. This means that the center of the distribution is located at the peak of the curve, and it is symmetrically balanced on either side.

Additionally, the total area under the curve is always equal to 1. This indicates that the probability of any value occurring within the distribution is 100%, since the entire area under the curve represents the complete range of possible values.

However, the statement about 99.72% of the time the random variable assuming a value within plus or minus 1 standard deviation of its mean is not true. In a normal distribution, approximately 68% of the values fall within one standard deviation of the mean, which is different from the provided statement.

In summary, while the mean-median-mode equality and the total area under the curve equal to 1 are characteristics of the normal probability distribution, the statement about 99.72% of the values falling within plus or minus 1 standard deviation of the mean is not accurate.

Know more about probability here,
https://brainly.com/question/31828911

#SPJ11

Sandra have 40 coins in total out of 120 coins.

Let the coins with Sandra be x

Then Joel has 1/2 as many coins as Sandra coins so x/2 coins and

mark has 3 times as many as Joel so 3x/2 coins in total.

There amount is 120 coins in total

therefore ,

3x/2 + x/2 + x = 120

4x/2 + x = 120

2x + x = 120

3x = 120

x = 40

So Sandra has total of 40 coins out of 120 coins.

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C.

Learn more about Linear equation:

https://brainly.com/question/1848296

#SPJ4

By applying the relative frequency concept, we make this table to represent the relative frequency of the problem:

                                Lunch order

                  Sandwich      Pasta      Total

Volleyball        27%            21%        49%

Swimming       37%            14%         51%

Total                64%            36%       100%

Relative frequency is a percentage number that states the amount of data in a certain group.

Relative frequency is given by the number of desired outcomes, also called frequency, divided by the number of total outcomes.

We already have the following information:

                                        Lunch order

                        Sandwich       Pasta         Total

Volleyball              19                15               34

Swimming             26               10               36

Total                      45               25              70

Now we want to find the relative frequency and put it into the following table:

                                                            Lunch order

                            Sandwich                      Pasta                        Total

Volleyball     19/70*100% = 27%     15/70*100% = 21%    34/70*100% = 49%

Swimming    26/70*100% = 37%    10/70*100% = 14%    36/70*100% = 51%

Total             45/70*100% = 64%    25/70*100% = 36%  70/70*100% = 100%

To learn more about relative frequency, click here: https://brainly.com/question/26177128

#SPJ4

The means of a stock that has a beta measure of 2.5 is 2.5%.

A beta measure of 2.5 indicates that the stock is 2.5 times as volatile as the market.

This means that if the market goes up by 1%, the stock is expected to go up by 2.5%.

The beta measure is a measure of the volatility of a stock relative to the market.

If the market goes down by 1%, the stock is expected to go down by 2.5%.

Therefore,

The stock is considered to be more risky than the average stock in the market.

A beta measure of 2.5 indicates that the stock is 2.5 times as volatile as the market.

This means that if the market goes up by 1%, the stock is expected to go up by 2.5%.

Conversely, if the market goes down by 1%, the stock is expected to go down by 2.5%.

For similar question on beta measures:

https://brainly.com/question/30023263

#SPJ11

Step-by-step explanation:

4x² -6x⁶+2x³+12-5x³+4x⁴

combine like terms

4x² -6x⁶- 3x³ + 12 + 4x⁴

since nothing else can combine due to no exponents being the same number you now have to put in order from biggest exponent to the smallest

-6x⁶ + 4x⁴- 3x³ + 4x² + 12

$5.25 (option A)

Explanation:

Cost of a pound of flour = $1.12

Cost of 4.5 pounds = 4.5 × $1.12

Cost of 4.5 pounds= $5.04

Cost of a pound of baking soda = $0.82

Cost of 0.25 pound of baking soda = 0.25 × $0.82

Cost of 0.25 = $0.205

The total cost of 4.5 pounds of flour and 0.25 pounds of baking soda = Cost of 4.5 pounds + Cost of 0.25 pound of baking soda

= $5.04 + $0.205

The total cost of 4.5 pounds of flour and 0.25 pounds of baking soda = $5.245

Approximately to the nearest cent

The total cost of 4.5 pounds of flour and 0.25 pounds of baking soda = $5.25 (option A)

Answer:

x+5y+5=0

Step-by-step explanation:

y=5x+6

Therefore the gradient of the line = 5

Now reciprocate the gradient and negate it

i.e -1/5

let (x,y) and (-15,2) be points on the line

y-2/x-(-15)=-⅕

5y-10=-x-15

5y-10+15+x=0

x+5y+5=0

Therefore the equation of the line =

x+5y+5=0

Answer:

14,00

Step-by-step explanation:

14 bru

Based on the table (see attachment), the time which corresponds to the mode of this data set is: B. 9:00 P.M.

A mode simply refers to a statistical term that is used to denote the value that appears most often or occurs repeatedly in a given data set.

This ultimately implies that, a mode represents the value (number) with the highest frequency and this is 9:00 P.M with a frequency of 25.

Read more on mode here: https://brainly.com/question/542771

#SPJ1

Answer: B 9:00

Step-by-step explanation:

So, the percentage of data values represented on a box plot that falls between the lower quartile and the upper quartile is 50%.

In a box plot, the lower quartile (Q1) represents the 25th percentile, and the upper quartile (Q3) represents the 75th percentile. The interquartile range (IQR) is the range between the lower quartile and the upper quartile. To determine the percentage of data values that fall between the lower quartile and the upper quartile, we need to consider the IQR.

The IQR represents the middle 50% of the data. Therefore, the percentage of data values between the lower quartile and the upper quartile is 50%. In other words, half of the data values are within the IQR range, while the remaining 50% are outside this range, including the lower 25% below the lower quartile and the upper 25% above the upper quartile.

To know more about percentage,

https://brainly.com/question/14618268

#SPJ11