Describe the correlation between highway mileage and engine size

the solution to the equation |x-1|+|x-2|=3 is x = 3.

What is inequality?

Mathematical expressions with inequalities on both sides are known as inequalities. In an inequality, we compare two values as opposed to equations. In between, the equal sign is changed to a less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

|x-1|+|x-2|=3

In this sub-case, we can rewrite the equation as:

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

Simplifying, we get:

-2x + 5 = 3

Which gives us x = 1.

However, x < 2 in this sub-case, so x = 1 is not a valid solution.

Sub-case 2.2: x >= 2

In this sub-case, we can rewrite the equation as:

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

Simplifying, we get:

2x - 3 = 3

Which gives us x = 3.

Therefore, the solution to the equation |x-1|+|x-2|=3 is x = 3.

Since we found that x >= 1, the inequality that represents the solution is:

x >= 1.

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Answer:

\(f(t) = 7.23( {1.0114}^{t} )\)

t = 0 represents January 1, 2014

(a)

\(f(6) = 7.23( {1.0114}^{6} ) = 7.739\)

The population of the world is expected to be about 7.739 billion people on January 1, 2020.

(b)

\(7.23( {1.0114}^{t} ) = 10\)

\(t = about \: 28.61 \: years\)

The population of the world is expected to be 10 billion people in about 28.61 years after January 1, 2014 (sometime in August 2042).

Answer:

480 People.

Step-by-step explanation:

120,000(0.004) = 480

Answer:

i think 18

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Given

10(3x + 2) > 7(2x - 4) ← distribute parenthesis on both sides

30x + 20 > 14x - 28 ( subtract 14x from both sides )

16x + 20 > - 28 ( subtract 20 from both sides )

16x > - 48 ( divide both sides by 16 )

x > - 3 → C

Step-by-step explanation:

To convert decimal number 639 to quinary, follow these steps:

Then just write down the remainders in the reverse order to get the answer, The decimal number 639 converted to quinary is therefore equal to :

10024

Answer:

56.2

Explanation:

There is a way to remember the ways to solve for right triangles, SOH CAH TOA which stands for each of the ways to solve for angles or sides:

Sine: Opposite over Hypotenuse

Cosine: Adjacent over Hypotenuse

Tangent: Opposite over Adjacent

In this case, with the information we have, we would use tangent since we have both the opposite side, b, and the adjacent side, a.

It would be the inverse of tangent (tan⁻¹) since you are solving for the angle and not a side.

You would use a calculator to solve this, by dividing b by a.

tan⁻¹(b/a)

tan⁻¹(46.7/31.3) = 56.1686012868

Round to the nearest tenth = 56.2

*Make sure your calculator is in degrees mode or it will give you an incorrect result.

Answer:

40 minutes is your answer

Answer: It will take a 1/2 hour or 30min to paint one full wall.

The statement that f has a simple zero at z=0 and vanishes nowhere else in |z|≤1 implies that the function f is non-vanishing and has a derivative that does not vanish at z=0.

From this, we can use the Implicit Function Theorem which states that if f is holomorphic in a neighborhood of a point (a,b) and f(a,b)=0 and ∂f/∂y(a,b)≠0, then there exists an open neighborhood U of a and a unique holomorphic function g:U→R such that g(a)=b and (x,g(x)) is a solution of the equation f(x,y)=0 for all x in U.

In this case, since f(z) has a simple zero at z=0 and f'(0)≠0, by the Implicit Function Theorem, there exists an open neighborhood U of 0 and a unique holomorphic function h:U→C such that h(0)=0 and f(h(ϵ))=0 for all ϵ in U. Hence, fϵ(z) has a unique zero in |z|≤1.

Also, since f and g are holomorphic in a region containing the disc |z|≤1 and ϵ is continuous, it follows that fϵ is holomorphic in the same region. Thus, by the holomorphicity of fϵ and h, the mapping ϵ↦zϵ is continuous.

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Margin of error is statistical expressing the amount of a random sampling error in survay results not the error term from biased sampling method. So, correct answer is False.

Margin of error in statistics represents the amount of random sampling error in the survey results. The larger the margin of error, the less confident that the survey results reflect the results of the census of the entire population. It is denoted by E or MOE. It is calculated by dividing the square root of the sample size by the standard deviation of the population. 99% level is the most conservative, 90% level is the least conservative. The sampling error is a statistical error that occurs when the analyst does not select a sample that is representative of the entire data population.

False - Margin of error only account for sample variability (the fact that my sample differs from many others' samples and therefore provides different statistics.

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Based on the given data, the probability of rolling a 4 on the next roll of this die is 0.3 or 30%.

It is used to predict and estimate the likelihood of future events and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

The probability of rolling next is a 4:

The total number of times the die was rolled is:

⇒ 8 + 4 + 3 + 9 + 2 + 4 = 30

The number of times the die landed on 4 is 9.

Then, the probability of rolling next a 4 is:

⇒ 9/30 = 3/10

⇒ 9/30 = 0.3

Therefore, based on the given data, the probability of rolling a 4 on the next roll of this die is 0.3 or 30%.

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Answer:Total cost for bread:$48.75

Total cost for peanut butter:$384

Total cost for jelly:$192

Last step:$361.75

Step-by-step explanation:I just took an assignment and got all right.

Answer:

otal cost for bread:$48.75

Total cost for peanut butter:$384

Total cost for jelly:$192

Last step:$361.75

Step-by-step explanation:I just took an assignment and got all right.

Step-by-step explanation:

Answer:

This is trapezium.

Area of this figure =1/2h(d1-d2)

1/2×5(14-8)

=30/2

=15cm^2

Answer:

-6 < x < -5

Step-by-step explanation:

(x+7)^5 = 20

Raise both sides to the (1/5) power

x + 7 = 1.820564203

Subtract 7 from both sides

x = -5.179435797

-6 < x < -5

Answer: x = y + −3/2

Step-by-step explanation:

Let's solve for x.

−3+5y=2x+3y

Step 1: Flip the equation.

2x+3y=5y−3

Step 2: Add -3y to both sides.

2x+3y+−3y=5y−3+−3y

2x=2y−3

Step 3: Divide both sides by 2.

2x/2 = 2y - 3/2

ANSWER: x = y + -3/2

The dot product of vectors a and b  || a |= 6,|| b ||= 4 and the angle between the vectors θ = π/3 is (c) 12.

The dot product of two vectors, we can use the formula:

a · b = ||a|| ||b|| cos(theta)

where ||a|| and ||b|| represent the magnitudes of vectors a and b, respectively, and theta is the angle between the vectors.

In this case, we are given that ||a|| = 6, ||b|| = 4, and the angle between the vectors is theta = π/3.

Substituting these values into the formula, we have:

a · b = 6 × 4 × cos(π/3)

To evaluate cos(π/3), we can use the fact that it is equal to 1/2. So we have:

a · b = 6 × 4 × 1/2

= 12

Therefore, the dot product of vectors a and b is 12.

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Answer:

20

Step-by-step explanation:

To determine the number of 9s between 1 and 100, we can consider the numbers from 1 to 99 since we want to exclude 100.

In the range from 1 to 99, we can observe the following patterns:

There is one 9 in each of the units' places (9, 19, 29, ..., 89, 99), giving us 10 occurrences.

There is one 9 in each of the tens' places (90, 91, 92, ..., 99), giving us 10 occurrences.

Therefore, there are a total of 10 + 10 = 20 occurrences of the digit 9 between 1 and 100.

Answer:

x = \(\frac{-14}{3}\)

Step-by-step explanation:

-2(3x + 8) -2 = 10  Distribute the -2

-6x - 16 -2 = 10 Combine like terms

-6x - 18 = 10   Add 18 to both sides

-6x = 28  Divide both sides by -6

x = \(\frac{-28}{6}\) = \(\frac{-14}{3}\)

Using Manning's equation, we find that the slope of the bed of a rectangular channel with a width of 5m, water depth of 2m, and flow rate of 20 m³/s is approximately 0.239.

Manning's equation relates the flow rate, channel parameters, and roughness coefficient.

Manning's equation is given by:

Q = (1/n) * A * R^(2/3) * S^(1/2)

Where:

Q = Flow rate (m³/s)

n = Manning's roughness coefficient

A = Cross-sectional area of the channel (m²)

R = Hydraulic radius (m)

S = Channel slope (dimensionless)

For a rectangular channel, the cross-sectional area (A) and hydraulic radius (R) is calculated using the width (b) and depth (y) of the channel:

A = b * y

R = A / (2 * (b + y))

Width (b) = 5 m

Depth (y) = 2 m

Flow rate (Q) = 20 m³/s

Manning's roughness coefficient (n) = 50

First, we calculate the cross-sectional area:

A = b * y

A = 5 m * 2 m

A = 10 m²

Next, we calculate the hydraulic radius:

R = A / (2 * (b + y))

R = 10 m² / (2 * (5 m + 2 m))

R = 10 m² / (2 * 7 m)

R = 10 m² / 14 m

R ≈ 0.714 m

Now, we rearrange Manning's equation to solve for the channel slope (S):

Q = (1/n) * A * R^(2/3) * S^(1/2)

Solving for S:

S = (Q / ((1/n) * A * R^(2/3)))^2

S = (Q / (n * A * R^(2/3)))^2

Substituting the given values:

S = (20 m³/s / (50 * 10 m² * (0.714 m)^(2/3)))^2

Calculating the slope:

S ≈ (20 / (50 * 10 * 0.818))^2

S ≈ (20 / 40.9)^2

S ≈ (0.489)^2

S ≈ 0.239

Therefore, the slope of the bed of the rectangular channel is approximately 0.239 (dimensionless).

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Answer:

yeheheehejehejejejjejjejejejejje

False. The margin of error only accounts for sampling variability (the fact that my sample will be different that many other people's and therefore provide different statistics.

Statistics is a technique for interpreting, analyzing, and summarizing data in mathematics. In light of these characteristics, the various statistical types are divided into: Statistics that are descriptive and inferential. We analyze and understand data based on how it is presented, such as through graphs, bar graphs, or tables.

Inferential statistics, which draws conclusions from information using statistical tests like the student's t-test, is one of the two main statistical methods used in data analysis. Descriptive statistics presents data using indices like mean and median.

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To determine the appropriate code for the `equals()` method in the `Point` class, we need to consider the requirements of equality for objects of the `Point` class. The `equals()` method should compare the `x` and `y` values of two `Point` objects and return `true` if they are equal and `false` otherwise.

The `equals()` method is used to compare two objects for equality. In the `Point` class, we can define equality based on the `x` and `y` values of the points. The code for the `equals()` method should compare these values of two `Point` objects and return `true` if they are equal, and `false` otherwise.

For example, a possible implementation of the `equals()` method in the `Point` class could be:

```

public boolean equals(Object obj) {

 if (this == obj) {

   return true;

 }

 if (obj == null || getClass() != obj.getClass()) {

   return false;

 }

 Point otherPoint = (Point) obj;

 return this.x == otherPoint.x && this.y == otherPoint.y;

}

```

This implementation checks if the object being compared is the same as the current object, and then checks if it is an instance of the `Point` class. Finally, it compares the `x` and `y` values of the two points to determine their equality.

The specific code for the `equals()` method may vary depending on the requirements and use case of the `Point` class. It is important to consider the desired behavior and ensure that the method accurately reflects the notion of equality for `Point` objects.


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