The number 72 is between what two perfect squares? Enter a numerical answer only

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.

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.

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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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:

its a

Step-by-step explanation:

Answer:

19 1/2 ft

Step-by-step explanation:

hope this helped

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.

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

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.

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.

Transformations of the functions include a vertical shift, reflection and vertical shift, and a horizontal and vertical shift for three different pairs respectively. Specific (x, y) data pairs demonstrate these transformations on the graphs.

We have three functions, f(x) and g(x), and we will describe the transformation from f(x) to g(x) for each:

The transformations can be sketched by plotting specific (x, y) data pairs and shifting the graphs accordingly.

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.

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.

to convert feet to miles you would use a ratio of feet over miles

 so the answer would be B