What is the distance between -70 and -30

When Alec is paid $200 each month to mow the grass and weed the garden, this is a linear function.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

Here, Alec is paid $200 each month to mow the grass and weed the garden. In addition, he earns $6.50 per hour for the number of hours he works as a dishwasher at the local diner. This will be:

= 200 + 6.5h

This is a linear function.

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In mathematical modeling, some values are considered fixed and cannot vary without consequence. These values are often referred to as constants or parameters, and they represent physical or environmental properties that are assumed to be constant throughout the problem.

For example, in a mathematical model of the motion of a pendulum, the length of the pendulum, the mass of the weight, and the force of gravity are typically considered constants that cannot vary without consequence. If any of these values were to change, the motion of the pendulum would be affected, and the solution to the problem would be different.

Similarly, in a mathematical model of heat transfer, the thermal conductivity of the material, the heat source or sink, and the boundary conditions are typically considered constants that cannot vary without consequence. If any of these values were to change, the temperature distribution and heat transfer rate within the system would be affected, and the solution to the problem would be different.

The choice of which values to consider as constants or parameters depends on the specific problem being modeled and the assumptions made.

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For a real number x, by using mathematical induction it is shown that a\((1 + x)^{2n}\) > 1 + 2nx for every positive integer n.

To prove the inequality a\((1 + x)^{2n}\) > 1 + 2nx  for every positive integer n, we will use mathematical induction.

The inequality holds true for n = 1, and we will assume it is true for some positive integer k.

We will then show that it holds for k + 1, which will complete the proof.

For n = 1, the inequality becomes a\((1 + x)^2\) > 1 + 2x.

This can be expanded as a(1 + 2x + \(x^2\)) > 1 + 2x, which simplifies to a + 2ax + a\(x^2\) > 1 + 2x.

Now, let's assume the inequality holds true for some positive integer k, i.e., a\((1 + x)^{2k}\) > 1 + 2kx.

We need to prove that it holds for k + 1, i.e., a\((1 + x)^{2(k+1)}\) > 1 + 2(k+1)x.

Using the assumption, we have a\((1 + x)^{2k}\) > 1 + 2kx.

Multiplying both sides by \((1 + x)^2\), we get a\((1 + x)^{2k+2}\) > (1 + 2kx)\((1 + x)^2\).

Expanding the right side, we have a\((1 + x)^{2k+2}\) > 1 + 2kx + 2x + 2k\(x^2\) + 2\(x^2\).

Simplifying further, we get a\((1 + x)^{2k+2}\) > 1 + 2(k+1)x + 2k\(x^2\) + 2\(x^2\).

Since k and x are positive, 2k\(x^2\) and 2\(x^2\) are positive as well.

Therefore, we can write a\((1 + x)^{2k+2}\) > 1 + 2(k+1)x + 2k\(x^2\) + 2\(x^2\) > 1 + 2(k+1)x.

This proves that if the inequality holds for some positive integer k, it also holds for k + 1.

Since it holds for n = 1, it holds for all positive integers n by mathematical induction.

Therefore, we have shown that a\((1 + x)^{2n}\) > 1 + 2nx  for every positive integer n.

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Answer:

right

is the correct answer

Answer: A right Angle

Step-by-step explanation: it has the half square meaning it is a 90 degree angle

a) The probability that the port handles less than 5 million tons of cargo per week is 0.266.

b) The probability that the port handles 3 million or more tons of cargo per week is 0.823.

c) The probability that the port handles between 3 million and 4 million tons of cargo per week is 0.394.

d) The number of tons of cargo per week that will require the port to extend its operating hours is 4.699 million tons.

To calculate the probabilities, we need to use the information provided:

Mean cargo volume per week = 3.7 million tons

Standard deviation of cargo volume per week = 0.8 million tons

a) To find the probability that the port handles less than 5 million tons of cargo per week, we can use the z-score formula and the standard normal distribution:

z = (5 - 3.7) / 0.8 ≈ 1.625

Using a standard normal distribution table or a calculator, we find that the probability corresponding to a z-score of 1.625 is approximately 0.947.

The probability of handling less than 5 million tons is 1 - 0.947 ≈ 0.053.

b) To find the probability that the port handles 3 million or more tons of cargo per week, we can use the complement rule:

P(cargo ≥ 3 million tons) = 1 - P(cargo < 3 million tons)

Using the z-score formula, we find:

z = (3 - 3.7) / 0.8 ≈ -0.875

Using a standard normal distribution table or a calculator, we find that the probability corresponding to a z-score of -0.875 is approximately 0.191.

P(cargo < 3 million tons) ≈ 0.191

P(cargo ≥ 3 million tons) = 1 - 0.191 ≈ 0.809

c) To find the probability that the port handles between 3 million and 4 million tons of cargo per week, we can subtract the probability of handling less than 3 million tons from the probability of handling less than 4 million tons:

P(3 million ≤ cargo < 4 million) = P(cargo < 4 million) - P(cargo < 3 million)

Using the z-score formula, we find:

z1 = (4 - 3.7) / 0.8 ≈ 0.375

z2 = (3 - 3.7) / 0.8 ≈ -0.875

Using a standard normal distribution table or a calculator, we find the probabilities corresponding to z1 and z2:

P(cargo < 4 million tons) ≈ 0.647

P(cargo < 3 million tons) ≈ 0.191

P(3 million ≤ cargo < 4 million) ≈ 0.647 - 0.191 ≈ 0.456

d) To determine the number of tons of cargo per week that will require the port to extend its operating hours, we need to find the z-score corresponding to the 85th percentile of the standard normal distribution. This represents the point below which 85% of the data falls.

Using a standard normal distribution table or a calculator, we find the z-score that corresponds to an area of 0.85 is approximately 1.036.

Using the z-score formula, we can solve for the number of tons (x):

1.036 = (x - 3.7) / 0.8

Simplifying the equation:

0.8 * 1.036 = x - 3.7

0.8288 + 3.7 = x

x ≈ 4.699 million tons

a) The probability that the port handles less than 5 million tons of cargo per week is approximately 0.266.

b) The probability that the port handles 3 million or more tons of cargo per week is approximately 0.823.

c) The probability that the port handles between 3 million and 4 million tons of cargo per week is approximately 0.394.

d) The number of tons of cargo per week that will require the port to extend its operating hours is approximately 4.699 million tons.

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Answer:

-19/2

Step-by-step explanation:

Substitute x for -2, then solve for y

9(-2)-4y=20

-18-4y=20

-4y=38

y=-38/4=-19/2

the answer should be y= -9.5

A multiplier of 1.2 means the value is multiplied or increased by a factor of 1.2.

A multiplier is a term used to represent a factor by which a value is multiplied or increased. It is a numeric value that indicates the extent of the increase or expansion of a given quantity. Multiplication by a multiplier results in scaling or changing the magnitude of the original value.

A multiplier of 1.2 indicates that a value will be increased by 20% or multiplied by a factor of 1.2. This means that when the multiplier is applied to the original value, the resulting value will be 1.2 times the original.

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We can conclude that if g o f is onto, it does not necessarily mean that f is onto.

To answer this question, we need to understand what it means for a function to be onto. A function f : X -> Y is onto if every element in the codomain Y is mapped to by at least one element in the domain X. In other words, for every y in Y, there exists an x in X such that f(x) = y. Now, let's consider the functions f : X -> Y and g : Y -> Z. If g o f is onto, this means that every element in the codomain of g o f is mapped to by at least one element in the domain of g o f. Recall that g o f means applying f first and then g. So, for every z in Z, there exists an x in X such that g(f(x)) = z. This tells us that f(x) is mapped to some element y in Y such that g(y) = z. But does this guarantee that f is onto? The answer is no. Here's a counterexample: Let X = {1}, Y = {2, 3}, and Z = {4}. Define f(1) = 2 and g(2) = g(3) = 4. Then g o f(1) = g(f(1)) = g(2) = 4, which means that g o f is onto. However, f is not onto because it only maps 1 to 2 and not to 3.
Therefore, we can conclude that if g o f is onto, it does not necessarily mean that f is onto.

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Answer:

Step-by-step explanation:

find the semiperiter (1/2 perimeter or L+W)

80 : 2 = 40

now we know that 4z + 2 + 3z + 3 = 40

we solve for z with an equation

4z + 2 + 3z + 3 = 40

7z = 40 - 2 - 3

7z = 35

z = 35 : 7

z = 5

now we find CD

3z + 3 =      (z=5)

3 * 5 + 3 =

15 + 3 =

18

-------------------------------

check (remember pemdas)

4z + 2 + 3z + 3 = 40

4*5+2+3*5+3 = 40

20+2+15+3=40

40 = 40

the answer is good

Answer:

a. B is the correct equation

b. u = 5.8 sin(64°) = 5.2

Hello !

\(y=3+x\\y = 3x + 8\)

\(\boxed{y=}3+x\\\boxed{y=} 3x + 8\)

We know that y = y, so :

\(3 + x = 3x + 8\)

3.1 Solve x

\(\\\\\\\\3+x = 3x + 8\\\\3 + x - x = 3x + 8 -x\\\\3 = 2x + 8\\\\3 - 8 = 2x + 8 - 8\\\\-5=2x\\\\x = -\frac{5}{2}\\\\\boxed{x = -2,5}\)

3.2 Solve y

\(y = 3 + x\\\\y = 3 + (-2,5)\\\\y = 3 - 2,5\\\\\boxed{y = 0,5}\)

x = -2,5

y = 0,5

Answer:

X(2xt+7y)

Step-by-step explanation:

5xy-x^2t+2xy+3x^2t

Combining like terms

-x^2t+3x^2t+5xy+2xy

2x^2t +7xy

X(2xt+7y)

Answer:

7xy+2x^2t

Step-by-step explanation:

Simplify expression by collecting like terms.

So in:

5xy - x^2t + 2xy + 3x^2t, the like terms are 5xy and 2xy and -x^2t and 3x^2t

Complete the performance required for each pair:

5xy + 2xy = 7xy

- x^2t + 3x^2t = 2x^2t

Now, put them back together. Use a + sign between them because both are positive.

7xy+2x^2t

Hope this Helps

Good Luck.

Answer:

2,4 B and D

Step-by-step explanation:

Answer:

B and D

Step-by-step explanation:

The intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:

1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.

To show that a1 ≤ a2 ≤ ... ≤ an ≤ ..., we need to use the fact that the sequence of intervals is nested, meaning that each interval is contained within the next one.

First, we know that I1 contains I2, so every point in I2 is also in I1. That means that a1 ≤ a2 and b1 ≥ b2.

Now consider I2 and I3. Again, every point in I3 is also in I2, so a2 ≤ a3 and b2 ≥ b3.

We can continue this process for all the intervals in the sequence, until we reach In. So we have:

a1 ≤ a2 ≤ ... ≤ an-1 ≤ an

and

b1 ≥ b2 ≥ ... ≥ bn-1 ≥ bn

This shows that the endpoints of the intervals are ordered in the same way.

Given that I₁ ⊇ I₂ ⊇ ... In ⊇ ... is a nested sequence of intervals and In = [an; bn], we can show that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... as follows:

Since the intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:

1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.

Continuing this pattern for all intervals in the sequence, we can conclude that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... .

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Answer:

9

Step-by-step explanation:

180 x 0.05

Answer:0.375

Step-by-step explanation:

3/4=0.75

0.75/2=0.375

(3/4)/2=0.375

The probability that a randomly selected person from the survey prefers bacon would be 60% in this example. However, without knowing the specific numbers, we cannot calculate the probability accurately.

To determine the probability that a randomly selected person from the survey prefers bacon, we need additional information such as the total number of respondents in the survey and the number of people who prefer bacon. Without this information, it is not possible to calculate the exact probability.

The probability can be calculated by dividing the number of people who prefer bacon by the total number of respondents in the survey. If the survey provides these specific numbers, we can use the formula:

Probability = Number of people who prefer bacon / Total number of respondents

For example, if the survey includes 100 respondents and 60 of them prefer bacon, the probability would be:

Probability = 60 / 100 = 0.6 or 60%

Therefore, the probability that a randomly selected person from the survey prefers bacon would be 60% in this example. However, without knowing the specific numbers, we cannot calculate the probability accurately.

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(a) Assuming that the size of the fish population satisfies the logistic equation, find an expression for the size of the population after t years.

Logistic equation: dp/dt=rP(1−P/K)Where, P = population r = the rate of growth K = the carrying capacity

The initial population = 80 fish. The carrying capacity = 2000 fish. The number of fish triples in the first year, which is 3 × 80 = 240 fish. Initial population, P0 = 80 fish. So, P0 = 80 fish.

P(t) = ?I

f the population is tripled, then the value of P(1) = 240.Substituting P0 = 80, P(1) = 240, and K = 2000 in the logistic equation. dp/dt=rP(1−P/K)dp/dt=rP−rP2/K. Now, we need to solve the differential equation. dp/dt=rP−rP2/K

Separate the variables. P−P2/K=dP/rdt Integrate both sides with respect to time. dt∫rddP=P−P2/K∫ddP

Here, the integral of dP/P(1−P/K) is ln⁡|P−K|−ln⁡|P|. The integral of dP/P is ln⁡|P|, and the integral of ddP is t.+C=−1Kr+ln⁡|P−K|−ln⁡|P| Simplifying the expression, +C=ln⁡|K/P|+1Kr=ln⁡|K/P|+C1Substituting P = 80 and C1 = r, the constant of integration, the value of C = ln⁡|2000/80|+C1.r=ln⁡|25|+C1Therefore, the general solution is P=K/(1+Ae^−rt)Where A = 1999/80 and r = ln⁡|25|+C1.(b) How long will it take for the population to increase to 1000? (Round your answer to two decimal places.)To find out how long it will take for the population to increase to 1000 fish, substitute P = 1000 in the logistic equation. P=K/(1+Ae^−rt)1000=2000/(1+1999/80e^−rt)Simplifying the expression,1+1999/80e^−rt=2e^−rt=−80/1999ln⁡|−80/1999|=rt Therefore, t = (−1/r)ln⁡|−80/1999|.t = (−1/ln⁡|25|+C1)ln⁡|−80/1999| = 0.15 (rounding off to two decimal places).

Therefore, it will take 0.15 years for the population to increase to 1000 fish.

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Validation of the model and answering the question "what are my options" occur in the design phase of the IDC (Intelligence, Design, and Choice) framework.

The IDC framework is a decision-making process that consists of three phases: Intelligence, Design, and Choice. Each phase corresponds to a specific set of activities and objectives.

In the intelligence phase, the focus is on gathering information, identifying the problem or decision to be made, and understanding the factors and variables involved. This phase involves data collection, analysis, and exploration to gain insights and knowledge about the problem domain.

In the design phase, the emphasis is on developing and evaluating potential options or solutions to address the problem or decision at hand. This phase involves creating models, prototypes, or simulations to represent the problem and exploring different alternatives.

Validation of the model is an important aspect of this phase to ensure that the proposed solutions align with the problem requirements and objectives.

The question "what are my options" is a fundamental question that arises during the design phase. It implies the exploration and generation of various possible choices or solutions that can be evaluated and compared.

Therefore, the design phase of the IDC framework encompasses the activities of validating the model and answering the question "what are my options." It involves refining and testing potential solutions to make informed decisions in the subsequent choice phase.

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Answer: the answer is 10

Step-by-step explanation:  you look at the number in middle and you see the middle # is 10.

Answer:

C

Step-by-step explanation:

Answer:

i think its C

Step-by-step explanation:

lol

Using the normal distribution and the central limit theorem, it is found that there is a 0.5934 = 59.34% probability that there is an error of at most $1000.

In a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

Researching the problem on the internet, it is found that the population has mean and standard deviation given, respectively, by \(\mu = 57300, \sigma = 9600\).

For samples of 64, the standard error is given by:

\(s = \frac{9600}{\sqrt{64}} = 1200\)

The probability of an error of at most $1000 is the probability of a sample mean between $56,300 and $58,300, which is the p-value of Z when X = 58300 subtracted by the p-value of Z when X = 56300, hence:

X = 58300:

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem:

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{58300 - 57300}{1200}\)

Z = 0.83

Z = 0.83 has a p-value of 0.7967.

X = 56300:

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{56300 - 57300}{1200}\)

Z = -0.83

Z = -0.83 has a p-value of 0.2033.

0.7967 - 0.2033 = 0.5934.

0.5934 = 59.34% probability that there is an error of at most $1000.

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Arthur gets paid 11.5 per hour if Arthur gets paid 74.75 for working 6.5 hours.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

Arthur gets paid 74.75 for working 6.5 hours.

The amount earned by Arthur = 74.75

A number of hours = 6.5 hours

The earning per hour = 74.75/6.5 per hour

The earning per hour = 11.5 per hour

Thus, Arthur gets paid 11.5 per hour if Arthur gets paid 74.75 for working 6.5 hours.

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Answer: the denominator is 9. Improper fraction. This is a fraction where the numerator is greater than the denominator. Mixed number.

Step-by-step explanation:

There are 720 different ways to award gold, silver, and bronze medals to the ten finalists in the winter Olympics skating competition in 2022.

There are ten possible candidates for the gold medal if there are ten finalists. There are nine candidates for the silver medal after one athlete receives the gold medal. There are eight candidates for the bronze medal after one athlete receives the silver medal.

As a result, there are three ways to award gold, silver, and bronze medals:

10 x 9 x 8 = 720

So there are 720 different ways to award gold, silver, and bronze medals to the ten finalists in the winter Olympics skating competition in 2022.

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Answer:

radius = 5

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here r² = 25 ( take the square root of both sides )

r = \(\sqrt{25}\) = 5

The balance in the fund at the end of 23 years, with monthly deposits of $1,150 and a 3.25% annual interest rate, is approximately $449,069.51. The amount of interest earned over the period is approximately $420,630.49.

a. The balance in the fund at the end of the 23-year period, considering a monthly deposit of $1,150 and an annual interest rate of 3.25% compounded annually, is approximately $449,069.51.

To calculate the balance, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where A is the accumulated balance, P is the monthly deposit, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

In this case, we have monthly deposits, so we need to convert the annual interest rate to a monthly rate:

Monthly interest rate = (1 + 0.0325)^(1/12) - 1 = 0.002683

Using this monthly interest rate, we can calculate the accumulated balance over the 23-year period:

A = 1150 * [(1 + 0.002683)^(12*23) - 1] / 0.002683 = $449,069.51

Therefore, the balance in the fund at the end of the 23-year period is approximately $449,069.51.

b. The amount of interest earned over the 23-year period can be calculated by subtracting the total deposits from the accumulated balance:

Interest earned = (Monthly deposit * Number of months * Number of years) - Accumulated balance

Interest earned = (1150 * 12 * 23) - 449069.51 = $420,630.49

Therefore, the amount of interest earned over the 23-year period is approximately $420,630.49.

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