Check the answer that best describes the relationship between f(x) and x. (for example if f(x) is θ(x)θ(x) check that as your answer and not o(x)o(x) or ω(x)ω(x) even though these are true also in this case.)

We are given the function:

d (x) = 1375 – 110 x

A. To solve for the distance between the train and its destination after 8 hours, we simply have to plug in, x = 8 into the equation. That is:

d (x) = 1375 – 110 * 8

d (x) = 495 miles

Therefore the train is now only 495 miles away from the destination.

B. To solve for the total time needed to reach its destination, we must set d = 0 and find for the value of x:

0 = 1375 – 110 x

110 x = 1375

x = 12.5 hours

Therefore it takes 12.5 hours for the train to reach its destination.

Answer:

12 miles per hour

Step-by-step explanation:

Speed is the ratio of distance travelled to the time used.

The total distance covered = (5 + 13) miles

                                             = 18 miles

The whole journey took 1 hour + 30 minutes = 1.5 hours

                    Average rate of speed = [tex]\frac{total distance covered}{total time taken}[/tex]

                                                           = [tex]\frac{18 miles}{1.5 hours}[/tex]

                                                           = 12 miles per hour

Therefore, her average rate of speed is 12 miles per hour.

The linear function g(t) = 9t satisfies the condition g(t) ≤ f′(t) for t ≥ 0, as guaranteed by the Racetrack Principle.

Racetrack principle is a mathematical concept that involves bounding a function based on its second derivative and initial conditions.

Given data:

We want to find a linear function g(t) that satisfies g(t) ≤ f′(t) for t ≥ 0.

Since f″(t) ≥ 9 for all t ≥ 0, we will use Racetrack Principle to establish an upper bound for f(t) based on its second derivative:

= f(t) ≤ (1/2) * 9 * t^2

= 4.5t^2

Now, we need to find a linear function g(t) such that g(t) ≤ f′(t) for t ≥ 0. To do this, we differentiate the upper bound we found for f(t):

= f′(t) ≤ 9t

So, we can see that g(t) = 9t satisfies g(t) ≤ f′(t) for t ≥ 0.

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The Racetrack Principle can be used to find a linear function that is less than or equal to f'(t). We can prove this by comparing the initial conditions and the second derivative of the functions.

The Racetrack Principle states that if two objects are traveling at the same initial and final velocities, but one of them has a greater magnitude of acceleration, then the object with the greater acceleration will overtake the other or be ahead of it at some point in time.

In this case, since f''(t) = 9 and f(0) = f'(0) = 0, we can use the Racetrack Principle to find a linear function g(t) that is less than or equal to f'(t).

Let g(t) = 3t (since 3 is the square root of 9). We can prove that g(t) is less than or equal to f'(t) by showing that g(0) = f'(0) and g''(t) ≥ f''(t) for all t ≥ 0.

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total pounds

to add, find a common deonmenator (bottom numbers)

the denomenantors are 6,3,2

the common denominator is 6 because 6*1=6, 3*2=6, 2*3=6

multiply each by 1 or a/a where a=a to make the common denomenators so we can add

remember that [tex]\frac{a}{b}+\frac{c}{b}=\frac{a+c}{b}[/tex]

5/6 times 1/1=5/6

2/3 times 2/2=4/6

1/2 times 3/3=3/6

so

[tex]\frac{5}{6}+\frac{2}{3}+\frac{1}{2}=[/tex]

[tex]\frac{5}[6}+\frac{4}[6}+\frac{3}{6}=[/tex]

[tex]\frac{5+4+3}{6}=[/tex]

[tex]\frac{12}{6}=[/tex]

[tex]2[/tex]

2 pounds total of special mix

I found my answer using maths

The distance it will take a car traveling at 45 mph to stop on dry, level concrete is 171 feet. If an accident occurs 200 feet ahead, one can travel at a maximum speed of approximately 58.4 mph to avoid the accident. The answers were calculated using the given equation for stopping distance and the speed of the car.

To address this question, we first need to make use of the equation d(v)=1.1v+0.06v²

First, let's answer part a): to find how many feet it will take a car traveling at 45 mph to stop, we simply substitute v with 45 in the equation, resulting in d = 1.1(45) + 0.06(45)² = 49.5 + 121.5 = 171 feet.

For part b), we need to solve the equation for v when d is equal to 200 feet. This is a quadratic equation (1.1v + 0.06v^2 = 200) and can be solved using the quadratic formula, or a method such as factoring or completing the square. Using the quadratic formula, we find that v ≈ 58.4 mph.

Therefore, if an accident happens 200 feet ahead, the maximum speed at which one can travel to avoid being involved in the accident is approximately 58.4 mph.

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a) At 45 mph, stopping distance is 171 feet. b) To avoid a 200-ft accident, max speed is 48.33 mph.

a) To find the stopping distance when the car is traveling at 45 mph, substitute v = 45 into the equation:

d(45) = 1.1(45) + 0.06(45)^2

= 49.5 + 121.5

= 171 feet

b) To find the maximum speed to avoid a 200 feet accident, set d(v) = 200 and solve for v:

1.1v + 0.06v^2 = 200

0.06v^2 + 1.1v - 200 = 0

Using the quadratic formula:

v = [-b ± √(b^2 - 4ac)] / (2a)

v = [-1.1 ± √(1.1^2 - 4(0.06)(-200))] / (2 * 0.06)

v ≈ [-1.1 ± √(1.21 + 48)] / 0.12

v ≈ [-1.1 ± √49.21] / 0.12

Now, solve for v:

v ≈ [-1.1 ± 7] / 0.12

This gives two solutions:

v ≈ (-1.1 + 7) / 0.12 ≈ 48.33 mph (Approx.)

v ≈ (-1.1 - 7) / 0.12 ≈ -63.33 mph (Not applicable)

Therefore, the maximum speed to avoid the accident is approximately 48.33 mph.

Answer:

The correct answer is 1128 fist bumps exchanged.

Step-by-step explanation:

Each friend exchanges 47 fist bumps, one for each friend on the group.  

If the group is made up of 48 friends, and each exchange is done by 2 friends, you have to divide by 2 each interaction:

(48 friends * 47 first bumps) / 2 friends = (2256 friends per first bumps exchanged) / 2 friends = 1128 fist bumps exchanged.

Answer:

D) 21 cents

Step-by-step explanation:

Best deal: $45.00/35 = 1.29 each

Worst deal: $30.00/20 = 1.50 each

1.50 - 1.29 = 21 cents

A compound statement can be represented in symbolic logic as p ∧ q

The statement "A piece of paper is an object that can be drawn on" is not a compound statement

Reason:

The given statement is "A piece of paper is an object that can be drawn on"

The given statement is made up of just one subject which is 'a piece of paper'. The statement also has just one predicate, which is 'is an object that can be drawn on'

Therefore;

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Answer:

Step-by-step explanation:

1. A negative correlation between the temperature and the amount of snow still on the ground

This is casual since temperature and amount of snow are inversely proportional to each other.

2. A negative correlation between the number of digital photos uploaded to a website and the amount of storage space that is left

This is casual since the number of digital photos uploaded and the amount of storage space are  inversely proportional to each other.

3. A positive correlation between the length of the side of a pool and its depth

.

This is not casual since the length of the side of a pool and its depth  are not related.

4. A positive correlation between the height of a woman and the height of her brother

.

This is not casual since the height of a woman and the height of her brother  are not related.

5. A negative correlation between the volume of water in a pot and the amount of time that the water takes to boil

This is not casual since the volume of water in a pot and the amount of time that the water takes to boil are directly proportional.

A relationships would most likely be causal,

a negative correlation between the temperature and the amount of snow still on the ground.

a negative correlation between the number of digital photos uploaded to a website and the amount of storage space that is left

1. A negative correlation between the temperature and the amount of snow still on the ground

This is casual since temperature and amount of snow are inversely proportional to each other.

2. A negative correlation between the number of digital photos uploaded to a website and the amount of storage space that is left

This is casual since the number of digital photos uploaded and the

amount of storage space is inversely proportional to each other.

3. A positive correlation between the length of the side of a pool and its depth

This is not casual since the length of the side of a pool and its depth are not related.

4. A positive correlation between the height of a woman and the height of her brother

This is not casual since the height of a woman and the height of her brother are not related.

5. A negative correlation between the volume of water in a pot and the amount of time that the water takes to boil

This is not casual since the volume of water in a pot and the amount of time that the water takes to boil are directly proportional.

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The interest earned on $720 at a rate of 4.25% over a period of 3 months is $30.60.

The question is asking about $720, at an interest rate of 4.25%, over a period of 3 months.

To calculate the interest earned, we multiply the principal amount ($720) by the interest rate (4.25%) and divide by 100:

Interest = ($720 * 4.25) / 100 = $30.60

Therefore, the interest earned on $720 at a rate of 4.25% over a period of 3 months is $30.60.

The generator can power up to 47 light bulbs of 75 watts each. This is calculated by dividing the total power output of the generator by the power rating of a single light bulb.

To solve this question, let's set up the equation:

Total power of generator = Number of bulbs * Power rating of each bulb

Given the generator can produce 3550 watts and each light bulb consumes 75 watts, we need to find the number of bulbs (N) the generator can power. So the equation will be:

3550 = N * 75

To find N, we can rearrange the equation and solve for N:

N = 3550 / 75

Calculating this gives:

N = 47.33

Since the number of light bulbs must be a whole number, the generator can power up to 47 light bulbs.

Summary

The generator can power up to 47 light bulbs of 75 watts each.

t(f) = 27*f

g(t) = $0.04*27*f

without the value for f (the number of friends) that is the farthest this can be solved.

Probability lies at the heart of this mathematics question, involving the selection of two students at random from a college. The calculations involve determining the joint probability for the two students being of the same sex, either both male or both female, from the given student population distribution.

The subject of this problem is probability. Here, in this liberal arts college, we've been given that 40% of 10,000 students, i.e., 4000 students are males; hence, 60% i.e., 6000 students are females.

When selecting two students at random, there are two possibilities: (1) both students are male or (2) both students are female.

The probability of both students being male can be calculated by multiplying: the probability of the first student being male (which is 4000/10000 = 0.4) by the probability of the second student also being male (which, after the first extraction, would be 3999/9999 since the total number of students and the number of male students both decrease by 1). Hence, the joint probability for two male students is: 0.4 * (3999/9999).

Similarly, we can calculate the joint probability for two female students using the same approach: 0.6 * (5999/9999).

The total probability that the two selected students are of the same gender would be the sum of these two probabilities.

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To solve the inequality 2 - (6/5)x >= -4, isolate x to find that x must be less than or equal to 5.

To solve the inequality 2 - (6/5)x >= -4, we first need to isolate the variable x. Let's start by adding (6/5)x to both sides of the inequality:

Next, we add 4 to both sides to get:

Now we divide both sides by (6/5) to solve for x:

Finally, we can write the solution to the inequality:

x <= 5

So, x must be less than or equal to 5 to satisfy the inequality 2 - (6/5)x >= -4.

The question asks for statistical analysis of aptitude test scores for firefighters, requiring an understanding of probability, statistics, normal distribution, and sample observations.

The question concerns the statistical analysis of employment test scores, specifically discussing aptitude tests for a firefighter position. These tests are normally distributed with a given mean and standard deviation. Understanding this concept is an application of probability and statistics, which involves analyzing data to make inferences about a population based on sample observations. Knowledge of the normal distribution and its properties is key to answering questions about what proportion of test scores fall within certain intervals, or to calculate probabilistic outcomes such as percentile ranks or cutoff scores.