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Heron's formula states that the area of a triangle can be found using the following formula:[tex]A = √s(s-a)(s-b)(s-c)[/tex] where s is the semiperimeter of the triangle [tex](s = (a + b + c)/2)[/tex].

In the case of an equilateral triangle, all three sides (a, b, and c) are the same length. So, if we set x = y = z in the formula, we get [tex]A = √s(s-x)(s-x)(s-x).[/tex] Simplifying this expression yields [tex]A = (√s/4) * x^2[/tex].

We can also write the perimeter of the triangle as P = 3x. Substituting this into the area formula, we get [tex]A = [(P/3)*√3/4] * (P/3)^2[/tex]. This expression can be simplified to [tex]A = (1/12) * P^2 * √3.[/tex]

This shows that for a fixed perimeter, the area of an equilateral triangle is maximized. This is due to the fact that the area is proportional to the square of the sides, and in an  equilateral triangle all sides are equal, thus maximizing the area. Heron's formula states that the area of a triangle can be found using the following formula: A = √s(s-a)(s-b)(s-c) where s is the semiperimeter of the triangle (s = (a + b + c)/2).

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From the set a, b, c, d, e, f, g, we can derive 15 3-element subsets having the letter "a".

We can select 2 more elements from the set's remaining 6 components to create a 3-element subgroup that includes the letter "a": a, b, c, d, e, f, g.

The binomial coefficient indicates the number of possible methods to select 2 elements from a set of 6:

C(6,2) = 6! / (2! * (6-2)!) = 15

The positive numbers that appear as coefficients in the binomial theorem are known as binomial coefficients in mathematics. A binomial coefficient is frequently written as ( ) and is indexed by the pair of numbers n k 0.displaystyle "tbinom" nk. It is the multiplicative formula that can be used to calculate the coefficient of the xk component in the polynomial expansion of the binomial power (1 + x)n.

Thus, from the set a, b, c, d, e, f, g, we can derive 15 3-element subsets having the letter "a".

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1/4  is the probability of drawing a blue marble .

What does math probability mean?

The area of mathematics known as probability explores potential outcomes of events, along with the likelihoods and distributions of those occurrences. It is predicated on the likelihood that something will occur. The logic underpinning probability serves as the foundation for theoretical probability.

                         For instance, the theoretical chance of receiving a head while tossing a coin is 12. There are four primary categories of probability: axiomatic, axiomatic, classical, and empirical. Probability is the area of mathematics that deals with the possibility of a random event.

total red balls = 5

total green balls = 3

total blue balls = 2

The probability of drawing a blue marble is now = 1/4.

The probability of drawing a red marble = 2/5.

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The probability that outmost 15 calls will be received is 0.2

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

The probability of receiving more than 15 calls is 0.8 i.ep( > 15) = 0.8

The total probability is 1

Therefore ,

the probability of receiving at most 15 calls is 0.2

i.e p( ≤15 ) = 1-0.8

= 0.2

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True. Systems that can absorb any type of data, structured or not, from any type of source are often referred to as schema-less.

In a schema-less system, there is no predefined structure or schema that the data must conform to, allowing for greater flexibility in handling a variety of data formats and sources.

This can be particularly useful in big data environments, where data may come from a wide range of sources and be in a variety of formats. Schema-less systems typically rely on techniques such as dynamic schema discovery and schema-on-read to interpret and process the data.

A schema-less system is a type of database management system that allows for flexible and dynamic data structures, without requiring a pre-defined schema or structure.  

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The area of the given figure will be 145.13 m².

The area of a rectangle is calculated as length multiplied by width, while the area of a semi-circle is half the area of a circle with the same radius. We can calculate the combined area of the rectangle and semi-circle as follows:

Area of rectangle = length x width = 15 m x 8 m = 120 m^2

Area of semi-circle = 1/2 x pi x radius^2 = 1/2 x pi x 4^2 = 8 pi m^2

To find the total combined area, we add the area of the rectangle to the area of the semi-circle:

Total combined area = Area of rectangle + Area of the semi-circle

= 120 m² + 8π m²

= 120 m² + 25.13 m² (using π= 3.14159)

= 145.13 m

Therefore, the combined area of the rectangle and semi-circle is 145.13 square meters (rounded to two decimal places).

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The solar radius R² from its luminosity and effective temperature is R ≈ 695586.468 km.

We can find solar radius by direct substitution of values into Eqn 1.3

See the pic below,

Given L = 4πR²σT⁴

where,

L is the Luminosity

R solar radius

T the effective temperature

σ is the Stefan Boltman's constant

From 1 solar radius can be written as,

R² = L/4πσT⁴

L = 3.846 x 10²⁶

R² = 3.846x10²⁶/4x3.14x5.6703x10⁻⁸ x 5780⁴

R ≈ 695586.468 km

Therefore, the solar radius is R ≈ 695586.468 km

g = GM/r²

g = 6.67x10⁻¹¹ x 1.99 x 10³⁰/(6.95x10⁸)²

g = 274.13m/s² about 30 times that of earth.

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(a) Descriptive statistics from the survey are 44%, 11.8%.

(b)  All investment managers is estimated to have an average expected 12-month return on equities of 11.8%.

(c)  Based on the sample, we can estimate that it will take an average of 2.9 years for technology and telecom stocks

Descriptive statistics from the survey are: (i) 44% of managers classified themselves as bullish or very bullish on the stock market, and (ii) the average expected return over the next 12 months for equities was 11.8%.

Based on the sample, we can infer that the population of all investment managers is estimated to have an average expected 12-month return on equities of 11.8%.

Based on the sample, we can estimate that it will take an average of 2.9 years for technology and telecom stocks to resume sustainable growth according to the population of all investment managers.

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Answer:

if my calculation is correct the answer is 16 3/8-9 5/8 - fraction calculator. The result is 27/4 = 6 3/4 = 6.75 = twenty-seven quarters (or six and three quarters)

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

DE is   MID segment.....so it cuts AC in half....then x = 6

(a) The answer is 3. To solve 4610 mod 7, we start by dividing 4610 by 7, which gives us 658 with a remainder of 4. Next, we divide 658 by 7, which gives us 93 with a remainder of 5. We keep dividing by 7 until we reach a number below 7. This gives us a remainder of 3, so the answer is 3.

(b) The answer is 6. To solve 345 mod 9, we start by dividing 345 by 9, which gives us 38 with a remainder of 3. Next, we divide 38 by 9, which gives us 4 with a remainder of 2.

We keep dividing by 9 until we reach a number below 9. This gives us a remainder of 6, so the answer is 6.

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The equations can be used to solve for y, the length of the room follows:

B. y² – 5y = 750, C. 750 – y(y – 5) = 0 and E. (y + 25)(y – 30) = 0

The area of a rectangle is defined as the product of the length and width.

The area of a rectangle = L × W

Where W is the width of the rectangle and L is the length of the rectangle

As per the question, we have

length L = y

width W = y - 5

Since the area of a rectangular room is 750 square feet.

So  L × W = 750

y(y - 5) = 750

y² – 5y = 750 ....(i)

This can be also written as:

750 – y(y – 5) = 0 ....(ii)

Factorizing the equation (i), we get

(y + 25)(y – 30) = 0

Thus, the correct answer would be options (B), (C), and (E).

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Answer:

it's C

the square root of 10 is 3.162277

The value of the probability p(s2) is 1.36, p(s3) is 1/18, p(s4) is 1/12, p(s5) is 1/9, p(s6) is 5/36, p(s7) is 1/6, and p(s8) 5/36

The sample space for this problem can be represented as all the possible outcomes when two dice are thrown.

Each die has six sides with numbers 1 through 6, so there are 6 x 6 = 36 possible outcomes. We can represent each outcome as a pair of numbers (i, j) where i is the number on the first die and j is the number on the second die.

Now, we want to find the probability of getting a certain total when the two dice are thrown. We can define an event Sj as the event where the total of the values on the dice is j.

To calculate the probability of each event, we need to count the number of outcomes that belong to each event, and divide by the total number of outcomes (which is 36).

Let's start with S2. The only outcome that belongs to this event is (1, 1), so the probability of getting a total of 2 is 1/36.

For S3, we can get a total of 3 in two ways: (1, 2) and (2, 1). So the probability of getting a total of 3 is 2/36 or 1/18.

For S4, we can get a total of 4 in three ways: (1, 3), (2, 2), and (3, 1). So the probability of getting a total of 4 is 3/36 or 1/12.

For S5, we can get a total of 5 in four ways: (1, 4), (2, 3), (3, 2), and (4, 1). So the probability of getting a total of 5 is 4/36 or 1/9.

For S6, we can get a total of 6 in five ways: (1, 5), (2, 4), (3, 3), (4, 2), and (5, 1). So the probability of getting a total of 6 is 5/36.

For S7, we can get a total of 7 in six ways: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1). So the probability of getting a total of 7 is 6/36 or 1/6.

Finally, for S8, we can get a total of 8 in five ways: (2, 6), (3, 5), (4, 4), (5, 3), and (6, 2). So the probability of getting a total of 8 is 5/36.

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The equation that gives the number of bacteria in the population after 2 hours is -

P{ 2 }  = 260 + (1/4 x 260)

The exponential function is given by -

y = eˣ

Given is that in a lab experiment, a population of 200 bacteria is able to quadruple every hour.

The population of the bacteria after the first hour is -

P{ 1 }  = 200 + (1/4 x 200) = 200 + 60 = 260 bacterias.

The population of the bacteria after the second hour is -

P{ 2 }  = 260 + (1/4 x 260) = 260 + 65 = 325 bacterias

After the second hour, the population of the bacteria would be -

P{ 2 }  = 260 + (1/4 x 260)

Therefore, the equation that gives the number of bacteria in the population after 2 hours is -

P{ 2 }  = 260 + (1/4 x 260)

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Answer:

Here's the completed input-output table for the function f(x) = 3x²+2:

X f(X)

-2 14

-1 5

0 2

1 5

2 14

Step-by-step explanation:

a) Probability will be [tex]nb(x; 2, 0.4) = (x + 1 choose 2) * (0.4)^2 * (0.6)^(x)[/tex]

b)Probability is b(2; 4, 0.4) = [tex](4 choose 2) * (0.4)^2 * (0.6)^2[/tex] = 0.2304 (rounded to four decimal places)

c)b(2; 2, 0.4) =[tex](2 choose 2) * (0.4)^2 * (0.6)^0[/tex] = 0.16

d)E(X) = r*(1-p)/p = 2*0.6/0.4 = 3 boxes

(a) The probability that x boxes do not have the desired prize can be modeled by a negative binomial distribution with parameters r=2 (since we want to obtain 2 prizes), p=0.4 (since the probability of obtaining the prize in any given box is 0.4), and x being the number of boxes purchased before obtaining the second prize. Therefore, the probability is given by:

[tex]nb(x; 2, 0.4) = (x + 1 choose 2) * (0.4)^2 * (0.6)^(x)[/tex]

(b) The probability of purchasing four boxes and obtaining two prizes can be modeled by a binomial distribution with parameters n=4 (since four boxes are purchased), k=2 (since we want to obtain two prizes), and p=0.4 (since the probability of obtaining the prize in any given box is 0.4). Therefore, the probability is given by:

b(2; 4, 0.4) = [tex](4 choose 2) * (0.4)^2 * (0.6)^2[/tex] = 0.2304 (rounded to four decimal places)

(c) The probability of purchasing at most four boxes and obtaining two prizes can be found by summing the probabilities of purchasing 2, 3, or 4 boxes and obtaining two prizes. Using the binomial distribution with parameters n=2 and p=0.4 for the case of purchasing 2 boxes and obtaining two prizes, we have:

b(2; 2, 0.4) =[tex](2 choose 2) * (0.4)^2 * (0.6)^0[/tex] = 0.16

Using the negative binomial distribution with parameters r=2 and p=0.4 for the case of purchasing 3 boxes and obtaining two prizes, we have:

nb(1; 2, 0.4) = (1 + 2 choose 2) * (0.4)^2 * (0.6)^1 = 0.288

Using the negative binomial distribution with parameters r=2 and p=0.4 for the case of purchasing 4 boxes and obtaining two prizes, we have:

nb(2; 2, 0.4) = (2 + 2 choose 2) * (0.4)^2 * (0.6)^2 = 0.3456

Therefore, the probability of obtaining two prizes in at most four boxes is:

0.16 + 0.288 + 0.3456 = 0.7936 (rounded to four decimal places)

(d) The expected number of boxes without the desired prize can be found by multiplying the number of boxes needed to obtain the prize (on average) by the probability of not obtaining the prize, which is given by:

E(X) = (1 - p)/p = 0.6/0.4 = 1.5 boxes

The expected number of boxes needed to obtain two prizes can be found using the negative binomial distribution with parameters r=2 and p=0.4, which gives:

E(X) = r*(1-p)/p = 2*0.6/0.4 = 3 boxes

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As an exponential equation, the log equation log (x²- 5x + 14) = 2x + 4 is 9514 1404 393

Given,

x² - 5x + 14 = 10^(2x +4)

The relationship is ...

log(a) = b   ⇔   a = 10^b

Using this with a = x² - 5x + 14 and b = 2x + 4, we have ...

x² - 5x + 14 = 10^(2x +4)

The complete question is:

Write the log equation as an exponential equation. You do not need to solve for x. log (x^2– 5x + 14) = 2x + 4

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Answer:

49 athletes attended the pizza party

Step-by-step explanation:

Number of soccer team players = 15

Number of tennis  players =  4 more than one-third that number
This translates to

Number of tennis  players = 15/3 + 4 = 5 + 4 = 9

Number of basketball players = 2 less than three times the number of students that are on the tennis team
which translates to
3 x 9 - 2 = 25

So total number of players on all teams = 15 + 9 + 25 =49

Yes, we can find the equation of the best fitting line given the information provided.

Since all the points lie perfectly on a straight line going uphill, we know that there is a perfect linear relationship between x and y. Therefore, we can use the method of least squares to find the equation of the best fitting line.

The method of least squares involves finding the line that minimizes the sum of the squared distances between the observed data points and the predicted values on the line.

Given that the mean of x and the mean of y are both 2, we know that the line must pass through the point (2,2).

Since the standard deviations of x and y are exactly the same, we know that the slope of the line must be 1 (i.e., a unit increase in x corresponds to a unit increase in y).

Using the "5 number" approach, we can also find the equation of the line by calculating the correlation coefficient (r) between x and y. Since all the points lie perfectly on a straight line going uphill, the correlation coefficient will be either 1 or -1. In this case, since the line goes uphill, we know that the correlation coefficient must be 1.

Therefore, the equation of the best fitting line is y = x, or in slope-intercept form, y = 1x + 0.

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Answer:  1/27, or 0.037

Step-by-step explanation:

The fractional probability that Mary answered all three correctly is 1/27, or 0.037. This is because for each of the three questions, Mary had a 1 in 3 chance of getting the correct answer (1/3). Since she had three questions, the probability of her getting all three correct is the product of the three probabilities (1/3 x 1/3 x 1/3 = 1/27).

Answer:

Mary's probability of guessing all three questions correctly is 1/27 or approximately 0.037. This is because each multiple choice question has 3 possible answer choices, and her chances of randomly picking the correct choice are 1/3. Since she has three questions, the probability of randomly getting all three answers correct is 1/3 x 1/3 x 1/3, which equals 1/27.

Answer: the number is 12.

Step-by-step explanation:

Let's call the two-digit number "x". We know that the sum of its digits is 7, so we can represent the number as 10a + b, where a and b are the digits of the number and a is the tens digit and b is the units digit.

The statement that "reversing its digits increases the number by 9" means that the number obtained by reversing the digits is x + 9. We can represent this reversed number as 10b + a.

So, we have two equations:

10a + b = x

10b + a = x + 9

Now, we can substitute the value of x from the first equation into the second equation:

10b + a = 10a + b + 9

Expanding both sides, we get:

10b + a = 10a + b + 9

9b = 9a + 9

b = a + 1

We know that 0 < a < 9, since the number is a two-digit number. So, we can conclude that 0 < b < 10.

We can now substitute the value of b into the first equation:

10a + (a + 1) = x

11a + 1 = x

11a = x - 1

a = (x - 1) / 11

Since a is the tens digit of the number, it must be an integer. We can test different values of x to find the value that satisfies this condition.

If x = 20, then a = (20 - 1) / 11 = 1. This gives us b = a + 1 = 2. The original number is 10a + b = 10 + 2 = 12, which satisfies all the conditions.

So, the number is 12.

The color of a mixture that is 3/5 red is given as follows:

Purple.

To obtain the color, we must look at the proportions in the context of the problem.

The proportion of red of each mixture is obtained dividing the number of red drops by the total number of drops, hence:

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answer: 7 is where they intercept I think, I also hope this helps

Answer:

/9 gr2146787. 2665444755554

Answer:

121 3

Step-by-step explanation:

The population size varies in several ways. The sample size was insufficient, which is the best explanation for why the simulation of the sampling distribution is not roughly normal.

A person's or a researcher's choice of sample size will limit the study's statistical power if it is too small or inadequate for the alpha level and the analyses they have decided to do.

Because of the aforementioned, it is much harder to determine from one's sample whether a statistical effect is existent in the population.

A sample size that is either too small or too large can affect the ability to extrapolate the results, with the latter increasing the detection of differences and accentuating statistical differences that are not clinically significant.

The complete question is:-

A recent survey indicated that the mean time spent on a music streaming service is 210 minutes per week for the population of a certain country. A simulation was conducted to create a sampling distribution of the sample mean for a population with a mean of 210. The following histogram shows the results of the simulation.Which of the following would be the best reason why the simulation of the sampling distribution is not approximately normal?

A. The samples were not selected at random.

B . The sample size was not sufficiently large.

C. The population distribution was approximately normal.

D. The samples were selected without replacement.

E. The sample means were less than the population mean.

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