Anybody pls help me. Plus, working. Thank you ​

The formation of a triangle with 15 dots can vary depending on the arrangement of the dots. To form a triangle, we need at least 3 points connected by straight lines.

One possible arrangement is to have 3 dots arranged in a straight line. By connecting these dots, we can form a triangle. Another possibility is to have 4 dots in a square shape, where the diagonals of the square connect to form a triangle.

Additionally, we can arrange the dots in a pattern where the first row has 1 dot, the second row has 2 dots, the third row has 3 dots, and so on, forming a triangular pattern. In this case, we would need a total of 15 dots to complete the triangular pattern.

Overall, there are multiple ways to form a triangle with 15 dots, but we need to ensure that there are at least 3 dots connected by straight lines.

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To estimate the number of new users that would be added during time period 7, we can use the Bass diffusion model, which is commonly used to model the adoption of new products or technologies.

The Bass diffusion model is given by the formula:

\(\[N(t) = \frac{{p \cdot q}}{{q + (p/q) \cdot e^{-((p+q) \cdot t)}}}\]\)

where:

- N(t) represents the cumulative number of adopters at time \(t\).

- p is the innovation parameter, representing the coefficient of innovation.

- q is the imitation parameter, representing the coefficient of imitation.

- e is the base of the natural logarithm.

Given a population size of 67 million, an innovation parameter of 0.005, and an imitation parameter of 0.84 for Color TV, we can substitute these values into the Bass diffusion model and calculate the number of new users added during time period 7.

\(\[N(7) - N(6) = \frac{{p \cdot q}}{{q + (p/q) \cdot e^{-((p+q) \cdot 7)}}} - \frac{{p \cdot q}}{{q + (p/q) \cdot e^{-((p+q) \cdot 6)}}}\]\)

Substituting the given values into the equation:

\(\[N(7) - N(6) = \frac{{0.005 \cdot 0.84}}{{0.84 + (0.005/0.84) \cdot e^{-((0.005+0.84) \cdot 7)}}} - \frac{{0.005 \cdot 0.84}}{{0.84 + (0.005/0.84) \cdot e^{-((0.005+0.84) \cdot 6)}}}\]\)

Evaluating the expression will give us the estimated number of new users added during time period 7.

In LaTeX, the solution can be represented as:

\(\[N(7) - N(6) = \frac{{0.005 \cdot 0.84}}{{0.84 + (0.005/0.84) \cdot e^{-((0.005+0.84) \cdot 7)}}} - \frac{{0.005 \cdot 0.84}}{{0.84 + (0.005/0.84) \cdot e^{-((0.005+0.84) \cdot 6)}}}\]\)

After evaluating this expression, you will obtain the estimated number of new users added during time period 7.

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The function of the town's population is an exponential growth

From the question, we have the following parameters that can be used in our computation:

Initial population = 3800

Growth  rate = 2% every year

From the above, we understand that

There is a growth in the population by 2% every year

Using the above as a guide, we have the following:

This means that the function is an exponential growth

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To evaluate the integral ∫∫R 5y^2 dA, where R is the region bounded by the curves xy, we can use the given transformation. Since R is bounded by the curves xy, it means that the region is bounded by the lines x=0, y=0, and xy=1.

To perform the transformation, we substitute x=uv and y=u/v into the integral. The Jacobian of this transformation is 1/v^2. The new limits of integration can be found by considering the original bounds of R.

For x=0, we have uv=0, which implies that u=0 or v=0. For y=0, we have u/v=0, which means that u=0.

For xy=1, we have uv=1, which implies that u/v=1.

Therefore, the transformed region, let's call it S, is bounded by u=0, v=0, and u/v=1.

Now, we can rewrite the integral as ∫∫S 5(u/v)^2 (1/v^2) dudv. Simplifying this expression, we get ∫∫S 5u^2/v^4 du dv.

Evaluating this double integral in region S will give us the desired result.

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The mean of a discrete uniform random variable can be found by taking the average of the minimum and maximum values in its range. The correct answer is 18.0 (option c).

The mean represents the average value of the random variable. In a discrete uniform distribution, all values in the range have equal probabilities, and the mean is the midpoint of the range. In this case, the range is from 12 to 24, so the midpoint is (12 + 24) / 2 = 18.

In this case, the random variable X ranges from 12 to 24. Therefore, the mean of X is the average of these two values, which is 18. Therefore, the mean of the discrete uniform random variable X is 18..So, the correct answer is 18.0 (option c).

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The constant variation (k) is  \(-\frac{2}{3}\)  .

From given details :

x = 12 & y = -8

we can find k when given any point by dividing the y-coordinate by the x-coordinate.

For example, if y varies directly as x, and y = 6 when x = 2, the constant of variation is k = = 3

So,  k =  y / x  = 12 / -8 =  \(-\frac{2}{3}\)

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Answer:

Step-by-step explanation:

the answer is  (f-g)(x) = 4^x -5x -14

Answer:

(2x-1)(2x+3)

Step-by-step explanation:

4x^2 + 4x - 3

4x^2 + 6x - 2x - 3

2x(2x + 3) - 1(2x + 3)

(2x - 1) (2x + 3)

Answer:

C and D

Step-by-step explanation:

f(x) = x² + 2x + 3

Dy/dx = 2x + 2

At minimum

Dy/dx = 0

2x + 2 = 0

2x = -2

Divide both sides by 2

x = -2/2

x = -1

At maximum

y = x² + 2x + 3

y = (-1)² + 2(-1) + 3

y = 1 - 2 + 3

y = -1 + 3

y = 2

Which of the statement is true.

Option A is wrong because the minimum value of the first equation is -1 not 2

Option B is wrong because the minimum value of f(x) = x² + 2x + 3 is -1 which is less than 2 not greater than 2

Option C is correct because the minimum value of x² + 2x + 3 is -1 which is less than 2

Option D is correct because the maximum of f(x) = x² + 2x + 3 is 2

The structure theorem in computer science states that any computer program can be constructed using only three basic control structures:

Sequential: This structure involves executing statements in a sequential order, one after the other.

Conditional: This structure allows a program to make decisions based on the truth value of certain conditions. It involves using if-else statements and switch-case statements.

Iteration or loop: This structure allows a program to repeat a certain sequence of statements multiple times, based on certain conditions. It involves using for loops, while loops, and do-while loops.

These three control structures are sufficient to create any algorithm or program, regardless of how complex it may be. The structure theorem is an important concept in programming and computer science, as it highlights the fundamental building blocks of all programs.

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The top right graph could show the arrow's height above the ground over time.

The initial and the final height are both at eye level, which is the reference height, that is, a height of zero.

This means that the beginning and at the end of the graph, it is touching the x-axis, hence either the top right or bottom left graphs are correct.

The trajectory of the arrow is in the format of a concave down parabola, hitting it's maximum height and then coming back down to eye leve.

Hence the top right graph could show the arrow's height above the ground over time.

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Answer:

The number of times a variable appears in a date set is called a constant.

Given:

The rectangular stage at Radio City Music Hall in New York City measures 144 feet wide and 60 feet deep.

We will find the area by multiplying the width by the deep

So, the area =

So, the answer will be Area = 8640 square yards

The correct answer is D. f(x) = 11x - 4 and g(x) = (x + 4)/11

To determine which pair of functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.

Let's test each option:

Option A:

f(x) = x/2 + 15

g(x) = 12x - 15

f(g(x)) = (12x - 15)/2 + 15 = 6x - 7.5 + 15 = 6x + 7.5 ≠ x

g(f(x)) = 12(x/2 + 15) - 15 = 6x + 180 - 15 = 6x + 165 ≠ x

Option B:

f(x) = ∛3x

g(x) = (x/3)^3 = x^3/27

f(g(x)) = ∛3(x^3/27) = ∛(x^3/9) = x/∛9 ≠ x

g(f(x)) = (∛3x/3)^3 = (x/3)^3 = x^3/27 = x/27 ≠ x

Option C:

f(x) = 3/x - 10

g(x) = (x + 10)/3

f(g(x)) = 3/((x + 10)/3) - 10 = 9/(x + 10) - 10 = 9/(x + 10) - 10(x + 10)/(x + 10) = (9 - 10(x + 10))/(x + 10) ≠ x

g(f(x)) = (3/x - 10 + 10)/3 = 3/x ≠ x

Option D:

f(x) = 11x - 4

g(x) = (x + 4)/11

f(g(x)) = 11((x + 4)/11) - 4 = x + 4 - 4 = x ≠ x

g(f(x)) = ((11x - 4) + 4)/11 = 11x/11 = x

Based on the calculations, only Option D, where f(x) = 11x - 4 and g(x) = (x + 4)/11, satisfies the condition for being inverses of each other. Therefore, the correct answer is:

D. f(x) = 11x - 4 and g(x) = (x + 4)/11

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Answer:

9

Step-by-step explanation:

it is the odd one out, also because it is spread away from the other data points

Answer: two hundred and fifty thousand people were left without homes in the earthquake.

They were there for every major disaster.

Step-by-step explanation:

To determine which weight is more extreme relative to their respective groups, we compare the z-scores of a male weighing 1500 g and a female weighing 205 g. The weight with the higher absolute z-score is considered more extreme.

To compare the weights, we calculate the z-scores for both the male and the female weights. The z-score measures how many standard deviations a data point is away from the mean. The formula for calculating the z-score is (x - μ) / σ, where x is the data point, μ is the mean, and σ is the standard deviation.

For the male weighing 1500 g:

z_male = (1500 - 3234.8) / 758.7 = -1.92

For the female weighing 205 g:

z_female = (205 - 3075.6) / 576.0 = -4.09

Comparing the absolute values of the z-scores, we find that |z_female| = 4.09 > |z_male| = 1.92.

Since the absolute value of the z-score for the female weight is larger, the female weight of 205 g is more extreme relative to the group from which it came. This indicates that the female weight is significantly lower compared to the mean weight of newborn females, while the male weight of 1500 g is relatively closer to the mean weight of newborn males.

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There are 6 pairwise comparisons that need to be made in order to gain a complete understanding of which treatment effects differ significantly from others.

In order to determine which treatment effects differ significantly from others, we need to make pairwise comparisons between all possible pairs of treatment groups. Let's consider an example with four treatment groups labeled A, B, C, and D.

To determine which treatment effects differ significantly from others, we need to compare the mean scores of each treatment group with the mean scores of every other treatment group. This means we need to make the following pairwise comparisons:

A vs B

A vs C

A vs D

B vs C

B vs D

C vs D

Therefore, there are 6 pairwise comparisons that need to be made in order to gain a complete understanding of which treatment effects differ significantly from others.

It's worth noting that when making multiple pairwise comparisons, there is an increased risk of making a Type I error (i.e., rejecting the null hypothesis when it is actually true) due to the multiple testing problem. To control for this, researchers may choose to adjust the significance level or use methods such as the Bonferroni correction to adjust the p-values of the individual tests.

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According to the central limit theorem for sums, if you keep taking sums from bigger and bigger samples, the sums will eventually form their own normal distribution (the sampling distribution), which will become more similar to a normal distribution as the sample size grows.

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Decrease taxes by $75 to increase GDP by $300.

To calculate the change in taxes required to increase GDP by $300, we need to use the multiplier formula:

Multiplier = 1 / (1 - MPC)

where MPC is the marginal propensity to consume.

In this case, MPC = 0.75, so the multiplier is:

Multiplier = 1 / (1 - 0.75) = 4

To increase GDP by $300, we need to increase aggregate demand by $300 / Multiplier:

Increase in aggregate demand = $300 / 4 = $75

Since decreasing taxes will increase aggregate demand, we need to decrease taxes by $75 to increase GDP by $300, assuming an MPC of 0.75.

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The least positive integer n such that \sigma(a^n) - 1 is divisible by 2021 for all positive integers a is \boxed{966}.

To find the least positive integer n such that \sigma(a^n) - 1 is divisible by 2021 for all positive integers a, we need to analyze the divisors of 2021. The prime factorization of 2021 is 43 \times 47.

Let's consider a prime p dividing 2021. For any positive integer a, \sigma(a^n) - 1 will be divisible by p if and only if a^n - 1 is divisible by p. This condition is satisfied if n is a multiple of the multiplicative order of a modulo p.

Since 43 and 47 are distinct primes, we can consider the multiplicative orders of a modulo 43 and modulo 47 separately. The smallest positive integers that satisfy the condition for each prime are 42 and 46, respectively.

To find the least common multiple (LCM) of 42 and 46, we factorize them into prime powers: 42 = 2 \times 3 \times 7 and 46 = 2 \times 23. The LCM is 2 \times 3 \times 7 \times 23 = 966.

Therefore, the least positive integer n such that \sigma(a^n) - 1 is divisible by 2021 for all positive integers a is \boxed{966}.

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Given the decimal value 8.05.

First we need to express as a fraction as shown;

8.05 = 805/100

Write in ots simplest form

805/100 = 5 * 161/5*20

805/100 = 161/20

Hence the decimal 8.05 as an improper fraction is 161/20

Express as mixed fraction;

161/20 = [(20*8) + 1]20

161/20 = (20*8)/20 + 1/20

161/20 = 8 + 1/20

161/20 = 8 1/20

Hence the deco

The correct statement that describes the relationship between the number of hours spent working/playing video games is given by:

Greater hours worked, fewer hours spent playing video games.

From the dots given, when the value of x(hours worked) increases, the value of x(hours playing video games) decreases, hence the variables are inverse proportional the correct option is given by:

Greater hours worked, fewer hours spent playing video games.

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Answer:

See below

Step-by-step explanation:

8.2 + 2/3w  = 10.7 + 1/6 w

   1/2 w    = 2.5

      w = 5 weeks

Answer:

3) 4.47 miles

Step-by-step explanation:

AC is the the hypotenuse

so, 6*6 = 36, and 4*4 = 16

36-16=20

square root of 20 is 4.472135...

so, 4.47

If we pick two people at random, the probability that they both own a dog would be 0.0324 or 3.24%.

If 18% of people own dogs, then the probability that a randomly chosen person owns a dog is 0.18.

To find the probability that two randomly chosen people both own dogs, we need to use the multiplication rule for independent events, which states that the probability of two independent events A and B both occurring is equal to the product of their individual probabilities:

P(A and B) = P(A) × P(B)

In this case, let A be the event that the first person owns a dog, and B be the event that the second person owns a dog. Since the events are independent, the probability of both events occurring is:

P(A and B) = P(A) × P(B)

P(A and B) = 0.18 × 0.18

P(A and B) = 0.0324

Therefore, the probability that two random chosen people both own a dog is 0.0324, or 3.24% as a percentage, assuming that the ownership of dogs is independent between people.

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Domain of the radical function of the form f(x) = √(ax + b) + c is given by the solution of the inequality ax + b ≥ 0 and the range is the all possible values obtained by substituting the domain values in the function.

We know that the general form of a radical function is,

f(x) = √(ax + b) + c

The domain is the possible values of x for which the function f(x) is defined.

And in the other hand the range of the function is all possible values of the functions.

Here for radical function the function is defined in real field if and only if the polynomial under radical component is positive or equal to 0. Because if this is less than 0 then the radical component of the function gives a complex quantity.

ax + b ≥ 0

x ≥ - b/a

So the domain of the function is all possible real numbers which are greater than -b/a.

And range is the values which we can obtain by putting the domain values.

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The formula for area of a triangle is 1/2 x base x height.

Let the height = x

Then the base (length) = 2x ( twice the height)

You know have 16 = 1/2 * 2x * x

Multiply both sides by 2 to remove the 1/2:

32 = 2x * x

Simplify the right side:

32 = 2x^2

Divide both sides by 2:

16 = x^2

Take the square root of both sides:

X = 4

The height is 4 units and the length is 8 Units