Final answer:
To find the unit rate, divide 768.57 meters by 41.1 hours resulting in a unit rate of 18.70 meters per hour.
Explanation:
The question asks for the unit rate of 768.57 meters over 41.1 hours. To calculate this, divide the distance by the time:
First, write the given ratio as a fraction. 768.57 m over 41.1 h.Second, divide 768.57 by 41.1 to find the unit rate in meters per hour. 768.57 m ÷ 41.1 h = 18.70 m/h (rounded to two decimal places as per the significant figures in the original distance).The division, 768.57 m ÷ 41.1 h, yields a unit rate of 18.70 m/h (rounded to two decimal places to match the precision of the original distance). Hence, the unit rate for this scenario is 18.70 meters per hour.
Therefore, the unit rate is 18.70 meters per hour.
On a bike trip, Erika rides 5 miles in the first 30 minutes and 13 miles in the next hour. What is her average rate of speed?
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 function d(x) = 1375 − 110x represents the distance (in miles) a high-speed
train is from its destination after x hours. (Section 3.3)
a. How far is the train from its destination after 8 hours?
b. How long does the train travel before reaching its destination?
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.
A fisherman drops his net to a depth of -8 feet below the surface of the water. How far does he need to raise the net to bring it back to the surface of the water?
A group of 48 friends meets for lunch. They greet each other by exchanging fist bumps. How many fist bumps are exchanged if each friend must bump with each of the 47 others?
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.
what is 15% of 60 using a model to prove your answer
Daniel is completing a home project. He needs 13 pieces of wood, each 112 feet long, to complete the project. How much wood does Daniel need to complete his home project? 823 ft
Answer:
its a
Step-by-step explanation:
Answer:
19 1/2 ft
Step-by-step explanation:
hope this helped
Line F passes through the points (7, 13) and (9, -3). What is the slope of a line parallel to line F?
A) -8
B) -1/8
C) 1/8
D) 8
Laura sends an average of 27 text messages per month to each of f friends. Her cell phone provider charges her a flat rate of $3.50 per month and $0.04 per text message. The function t(f) gives the total number of text messages Laura sends each month to f friends, and g(t) gives the amount Laura is charged by her cell phone provider for t text messages.
find t(f) and g(t)
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.
Use what you know about compound statements to determine if "A piece of paper is an object that can be drawn on " would be considered a good definition. Explain.
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:
A compound statement is a statement that consists of two simple statements combined into one statementThe 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;
The given statement is a simple statement and not a compound statementLearn more about compound statements here:
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Noah visited 40 people in 4 hours. How long will it take him to visit 120 people?
Ummmmmmmmmmmm. What is 90% of 550?
Solve the inequality. 2−6/5x≥−4
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:
2 - (6/5)x + (6/5)x >= -4 + (6/5)xNext, we add 4 to both sides to get:
2 + 4 >= (6/5)xNow we divide both sides by (6/5) to solve for x:
5 >= xFinally, 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.
Which data set is represented by the box plot below?
A. 10, 10, 10, 14, 23, 25, 26, 28, 30, 31, 34, 34, 44, 50, 50
B. 10, 10, 11, 12, 14, 18, 18, 18, 19, 20, 22, 26, 36, 42, 50
C. 10, 14, 18, 18, 19, 22, 31, 32, 33, 34, 40, 42, 43, 46, 50
D. 10, 14, 17, 24, 27, 32, 34, 34, 37, 38, 39, 39, 40, 43, 50
can someone help me please
to convert feet to miles you would use a ratio of feet over miles
so the answer would be B
Candidates for employment at a city fire department are required to take a written aptitude test. scores on this test are normally distributed with a mean of 280 and a standard deviation of 60. a random sample of nine test scores was taken.
The question asks for statistical analysis of aptitude test scores for firefighters, requiring an understanding of probability, statistics, normal distribution, and sample observations.
Explanation: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.
1.5(−2.4+(−5.3)) please hurry
a country's people consume 7.7 billion pounds of candy per year Express this quantity in terms of pounds per person per month. note that the population of the country is 303 million
how do you work out 21120÷5280 in long division?
Suppose that f(t) is continuous and twice-differentiable for t≥0. Further suppose f″(t)≥9 for all t≥0 and f(0)=f′(0)=0. Using the Racetrack Principle, what linear function g(t) can we prove is less than or equal to f′(t) (for t≥0)?
The linear function g(t) = 9t satisfies the condition g(t) ≤ f′(t) for t ≥ 0, as guaranteed by the Racetrack Principle.
What linear function g(t) satisfies g(t) ≤ f′(t) for t ≥ 0?Racetrack principle is a mathematical concept that involves bounding a function based on its second derivative and initial conditions.
Given data:
f(t) is continuous and twice-differentiable for t ≥ 0.f″(t) ≥ 9 for all t ≥ 0.f(0) = f′(0) = 0.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.
Explanation: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 cook has 2 2/3 cups of flour. A recipe calls for 2 3/4 cups of flour. Does the cook have enough flour? If not, how much more flour is needed
How do you find absolute extrema for a function?
f(x)= (8+x)/(8-x); Interval of [4,6]
round 26,891 to the nearest ten-thousands place
$720, 4.25%, 3 months
The interest earned on $720 at a rate of 4.25% over a period of 3 months is $30.60.
Explanation: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.
An accepted relationship between stopping distance, d in feet, and the speed of a car, in mph, is d(v)=1.1v+0.06v^2 on dry, level concrete.
a) how many feet will it take a car traveling 45 mph to stop on dry, level concrete?
b) if an accident occurs 200 feet ahead, what is the maximum speed at which one can travel to avoid being involved in the accident?
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.
Explanation: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.
an electric generator can power 3550 watts of electricity. write and solve an equation to find how many 75 watt light bulbs a generator could power.
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.
Solve using the standard algorithm 232 * 4 =
20 yards for $30.00
35 yards for $45.00
50 yards for $70.00
65 yards for $85.00
You work for a dress makers. Your boss sends you to the fabric store to buy blue fabric. She tells you to buy the best deal. What is the savings per unit between the best deal and worst deal?
A) $55.00
B) $27.00
C) 2 cents
D) 21 cents
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 shorter leg of a 30°- 60°- 90° right triangle is 12.5 inches. How long are the longer leg and the hypotenuse?
Describe the transformation of the graph from f(x) to g(x)
1) f(x)=2x+1
g(x)=2x+4
2) f(x)=x+3
g(x)=-x+1
3) f(x)=x^2
g(x)=(x-1)^2 +3
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.
Explanation:We have three functions, f(x) and g(x), and we will describe the transformation from f(x) to g(x) for each:
Vertical Shift: For the functions f(x)=2x+1 and g(x)=2x+4, g(x) represents a vertical shift up by 3 units from f(x).Reflection and Vertical Shift: For f(x)=x+3 and g(x)=-x+1, g(x) is f(x) reflected across the x-axis (due to the negative sign before x) and then a vertical shift down by 2 units.Horizontal Shift and Vertical Shift: Lastly, from f(x)=x^2 to g(x)=(x-1)^2+3, the graph of g(x) is the graph of f(x) shifted to the right by 1 unit and then up by 3 units.The transformations can be sketched by plotting specific (x, y) data pairs and shifting the graphs accordingly.
a bicycle costs $198.99. If the sales tax is 8%, what will be the final cost of the bicycle including tax (in dollars)?