3
TIME REMAINING
42:13
Which graph represents a density curve, and why?
graph A only, because the curve is above the
horizontal axis, and the area under the curve is 1
Ograph B only, because the curve is above the
horizontal axis, and the area under the curve is 1
Oboth graph A and graph B, because both curves are
above the horizontal axis, and the areas under both
curves equal 1
neither graph A nor graph B, because, even though
both curves are above the horizontal axis, the area
cannot be determined for graph B
Answers
Graph A only, because the curve is above the horizontal axis, and the area under the curve is 1. Then the correct option is A.
Given that:
The graph is shown below.
When the two curves intersect then they bound the region is known as the area bounded by the curve.
The area under the curve is calculated as,
[tex]\begin{aligned} A&= \int_{-1}^3 \dfrac{1}{4}dx \\A &= \dfrac{1}{4} \left [x \right ] _{-1}^3\end{aligned}[/tex]
Substitute the limits, then we have
A = (1/4) x (3 + 1)
A = 1
Graph A only, because the curve is above the horizontal axis, and the area under the curve is 1. Then the correct option is A.
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Related Questions
you are asked if you believe if the population variance of the student gpas is .15. how do you respond?
Answers
Answer: yes I do believe
VYWY
ZYXY
Z
W
Are triangles ZYV and XYW congruent?
O Yes, by SAS
OYes by SSA
O No, they are facing opposite directions
O No, not enough information
Answers
Yes, the triangles are congruent.
Given that a figure, where VY ≅ WY and ZY ≅ XY, we need to see whether the triangles ZYV and XYW are congruent,
So, in triangles ZYV and XYW,
VY ≅ WY [given]
ZY ≅ XY [given]
∠ZYV ≅ ∠XYW [vertical angles]
Therefore, the triangles ZYV and XYW are congruent, by SAS rule.
Hence the triangles are congruent.
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which of the following is false regarding evaluating forecasting errors? multiple choice mean squared error can be heavily influenced by one single large forecast error. mean squared error aggregates forecast errors without canceling out positive and negative forecast errors. mean squared error and mean absolute error always agree on which forecast is better. mean squared error goes beyond averaging out the forecast errors.
Answers
The false statement regarding evaluating forecasting errors is mean squared error and mean absolute error always agree on which forecast is better. The correct option is mean squared error and mean absolute error always agree on which forecast is better.
- Mean squared error (MSE) is heavily influenced by one single large forecast error because it squares each forecast error, and this is true.
- Mean squared error aggregates forecast errors without canceling out positive and negative forecast errors, which is also true as it squares each error.
- Mean squared error goes beyond averaging out the forecast errors since it squares each error before calculating the mean, so this statement is true as well.
However, MSE and mean absolute error (MAE) don't always agree on which forecast is better because they measure errors differently. MSE penalizes larger errors more than MAE, so they can lead to different conclusions about forecast accuracy. The correct option is mean squared error and mean absolute error always agree on which forecast is better.
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divorce and prison rates: this scatterplot shows u.s. divorce rates (per 1,000) and prison rates for drug offenses (percentage admitted to state prison for drug offenses) for 7 years during 1960-1986. the correlation is 0.67. what can we conclude from this data?
Answers
Answer: The data could be used as a starting point for further research and analysis to investigate any potential causal relationships or underlying factors.
Step-by-step explanation:
The scatterplot shows a positive correlation between U.S. divorce rates and prison rates for drug offenses. The fact that the correlation coefficient is 0.67 indicates a moderate positive linear relationship between the two variables.
However, correlation does not necessarily imply causation. While the data suggests that there may be some association between divorce rates and drug-related prison rates, it does not tell us which variable is causing the other, or if there is any causal relationship at all.
There could be other factors that affect both divorce rates and drug-related prison rates, or there could be a third variable that influences both. Therefore, we cannot draw any causal conclusions from this data alone.
However, the data could be used as a starting point for further research and analysis to investigate any potential causal relationships or underlying factors.
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if i^3x-1 = 1, where i = the square root of -1, then which of the followng is a solution for x?
Answers
If i^3x-1 = 1, where i = the square root of -1 the solutions are x = -3 and x = -4.
To solve the equation i^3x-1 = 1, we need to simplify the left-hand side. Since i = the square root of -1, we can rewrite i^3 as (i^2) * i = (-1) * i = -i.
Substituting this value, we get -i^(x-1) = 1. To find the solution for x, we can use the fact that i^4 = 1. Multiplying both sides of the equation by i^4, we get -i^(x+3) = i^4.
Simplifying further, we get -i^(x+3) = 1. Since i^4 = 1, we can rewrite this as -i^(x+3) = -1^0. Now, we have two options: either x+3 is even, in which case i^(x+3) = 1, or x+3 is odd, in which case i^(x+3) = -1.
Let's try both options: - If x+3 is even, then we can write x+3 = 2n for some integers n. This gives us i^(x+3) = i^(2n) = (i^2)^n = (-1)^n. Substituting into the equation, we get -(-1)^n = -1^0. This is true for n = 0 (when x = -3), but not for any other value of n.
Therefore, x = -3 is the only even solution. - If x+3 is odd, then we can write x+3 = 2n+1 for some integer n. This gives us i^(x+3) = i^(2n+1) = i^(2n) * i = (-1)^n * i.
Substituting into the equation, we get -(-1)^n * i = -1^0. This is true for n = 0 (when x = -4), but not for any other value of n. Therefore, x = -4 is the only odd solution.
In summary, the solutions for x are x = -3 and x = -4.
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find the area of polygon QRST formed by the coordinates given below.
Q(5,-3)
R(5,7)
S(-2,7)
T(-2,-3)
A. 88 square units
B. 34 square units
C. 70 square units
D. 12 square units
Answers
Check the picture below.
y is inversely proportional to a^3
when a =2, y=10
a is directly proportional to x
when x=4, =20
find the formula for y in terms of x
give your answer in it simplest form
Answers
The formula for y in terms of x, in its simplest form, is y = 80/x.
To begin, let's start by writing out the inverse proportionality relationship between y and a^3:
y ∝ 1/a^3
We can then use the given information that when a = 2, y = 10 to solve for the constant of proportionality.
10 ∝ 1/2^3
10 ∝ 1/8
10(8) = 1
So the formula for y in terms of a is:
y = 8/a^3
Next, we can use the given information that a is directly proportional to x when x = 4 and y = 20.
a ∝ x
a = kx
Substituting this into our formula for y:
y = 8/(kx)^3
y = 8/k^3 * x^-3
Finally, we can solve for the constant of proportionality, k:
When x = 4, y = 20
20 = 8/k^3 * 4^-3
20 = 2/k^3
k^3 = 2/20
k^3 = 0.1
k = (0.1)^(1/3)
Simplifying our expression for y in terms of x:
y = 8/(0.1) * x^-1
y = 80x^-1
Therefore, the formula for y in terms of x, in its simplest form, is y = 80/x.
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Max has a summer job handing out water toys at Wild Water Waves Park. The table below shows the toys he has handed out so far today.
Water toy Number of toys
pool noodle 18
single inner tube 13
double inner tube 9
beach ball 12
Based on the data, estimate how many pool noodles will be among the next 20 water toys Max hands out.
If necessary, round your answer to the nearest whole number.
Answers
Step-by-step explanation:
Out of a total of ( 18+13+9+12 = 52) toys 18 were noodles
or 18/52 which is 9/26 ths were noodles
What is 9/26 ths of 20 ?
9/26 * 20 = 6.92 = ~ 7 noodles
Can someone please help me ASAP?? It’s due today!!
I will give brainliest If It’s correct!!
Answers
Based on the box and whisker plots, the true statement is C. The Fitness Center has a larger range in employee hourly wages than Fitness Plus.
What is the range?The range describes the difference between the lowest and highest values.
The range is computed as the difference between the maximum and the minimum.
Range of employee hourly wages at Fitness Center = 7 (15 to 22)
Range of employee hourly wages at Fitness Plus = 6 (14 to 20)
Thus, Option C is correct.
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The garden shown is divided into two sections by a fence. If the quadrilateral section is a square, what is the garden’s area?
Answers
The area of the garden will be 800 square centimetres.
An area is a mathematical concept that refers to the extent or size of a two-dimensional surface or region. It is a measurement that quantifies the amount of space contained within the boundaries of a shape or object.
The unit of measurement for an area depends on the system being used. In the metric system, the most common unit is the square meter (m²), while in the imperial system, units such as square feet (ft²) or square inches (in²) are used.
From the given figure the area of the quadrilateral will be calculated as,
Area = 2 x ( L + W)
Area = 2 x ( 20 + 20 )
Area = 800 square centimetres
Therefore, the area will be 800 square centimetres.
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If one thired of a circle is worth 27 cents then how much are two circles worth
Answers
Two circles would be worth of 162 cents.
If one-third of a circle is worth 27 cents, then one circle would be worth 3 times that amount, since there are 3 equal parts in a circle.
So, One circle is worth:
= 27 cents/part × 3 parts/circle
= 81 cents
Now, two circles would be worth twice that amount:
= 81 cents/circle × 2 circles
= 162 cents
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Darren and Darcie took off from the same spot at the same time and headed in the same direction. If Darren travels at 12 mph and Darcie travels at 8 mph, how long will it take for Darren to be 26 miles ahead of Darcie?
right answer I will make brainliest
Answers
Answer:
6.5 hour
Step-by-step explanation:
We calculate this using speed distance formula
that is Speed = Distance / Time
When both the person is travelling in the same direction their relative speed would be v1 ( Speed of Darren ) - v2 ( Speed of Darcie)
Thus relative speed is 12 - 8 = 4 mph
By using the above equation
Time = Distance / speed
= 26 / 4 = 6.5 h
In 6.5 h Darren will be 26 miles ahead of Darcie
Please help me its due tommorrow!:)
Answers
The Area of tile is 190 cm².
We have a trapezoid whose dimensions are:
base 1 = 12 cm
base 2 = 26 cm
Height= 10 cm
Now, the formula for Area of Trapezoid is
= 1/2 x (sum of parallel base) x height
= 1/2 x (base 1 + base 2) x height
So, Substituting the value of base and height in the above formula we get
Area of Trapezoid
= 1/2 x (12 + 26) x 10
= 1/2 x 38 x 10
= 19 x 10
= 190 cm²
Thus, the Area of tile is 190 cm².
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Compare the function given in the graph, f(x), with g(x)
= x + 3. Which statements comparing the functions are
true? Check all that apply.
Of(x) has two x-intercepts while g(x) has none.
Of(x) and g(x) have the same y-intercept.
The domain of each function is all real numbers.
The range of each function is all real numbers
greater than or equal to -3.
Of(x) has the smallest minimum.
Answers
The statements comparing the functions that are true include the following:
A. f(x) has two X-intercepts while g(x) has none.
C. The domain of each function is all real numbers.
E. f(x) has the smallest minimum.
What is the x-intercept?In Mathematics and Geometry, the x-intercept is also referred to as horizontal intercept and the x-intercept of the graph of any function simply refers to the point at which the graph of a function crosses or touches the x-coordinate (x-axis) and the y-value or value of "y" is equal to zero (0).
By critically observing the graph, f(x) has two x-intercepts while g(x) has no x-intercept.
By critically observing the graph shown in the image attached below, we can reasonably and logically deduce the following domain and range for f(x):
Domain = [-∞, ∞] or all real numbers.
Range = [-3, ∞] or {y | y ≥ -3}
In conclusion, the minimum of f(x) is equal to -3 while the minimum of g(x) is 3.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
suppose that we roll a pair of fair dice until the sum of the numbers on the dice is seven. what is the expected number of times we roll the dice?
Answers
The expected number of times we roll the dice until the sum of the numbers is seven is 6.
To calculate the expected number of rolls, we need to consider the probabilities of rolling different sums. There are six possible outcomes that result in a sum of seven: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1). Each of these outcomes has a 1/36 probability since each die has six equally likely outcomes.
Since the expected value is the sum of the products of each outcome and its corresponding probability, we have:
Expected value = (1/36) * 1 + (1/36) * 2 + (1/36) * 3 + (1/36) * 4 + (1/36) * 5 + (1/36) * 6 = 6/36 = 1/6.
Therefore, the expected number of times we roll the dice until the sum of the numbers is seven is 6.
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Triangle A B C. Point D extends from side A B. Angle A is 35 degrees, angle B is 90 degrees, and angle C is x degrees. Exterior angle D A C is y degrees.
Consider triangle ABC with exterior angle ∠DAC. Find the missing angle measures.
x =
y =
Answers
The missing angle measures are x = 55 degrees and y = 125 degrees.
The missing angle measures are:
x = 55 degrees
y = 125 degrees
In a triangle, the sum of the three interior angles is always 180 degrees. Therefore, we can find the measure of angle C by subtracting the measures of angles A and B from 180:
angle C = 180 - angle A - angle B = 180 - 35 - 90 = 55 degrees
The measure of the exterior angle ∠DAC is equal to the sum of the measures of angles C and A, so we can find the measure of y by adding the measures of angles C and A:
angle y = angle C + angle A = 55 + 35 = 125 degrees.
Therefore, the missing angle measures are x = 55 degrees and y = 125 degrees.
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Answer:
x=55 degrees
y=145 degrees
Step-by-step explanation:
I got it right.
on tuesday jenny bought 8 bagels and 3 cups of coffee spends $14.45. on wednesday spends $16.15 for 4 bagels and 5 cups of coffee. What does the coffee cost?
Answers
The cost of one cup of coffee is $2.98.
To find the cost of coffee, we need to first determine the cost of bagels on both days.
On Tuesday, Jenny bought 8 bagels and 3 cups of coffee for a total of $14.45. Let's assume the cost of bagels was x and the cost of coffee was y. Then we can write the equation:
8x + 3y = 14.45
On Wednesday, she bought 4 bagels and 5 cups of coffee for a total of $16.15. Again, assuming the cost of bagels is x and the cost of coffee is y, we can write the equation:
4x + 5y = 16.15
Now we can use these two equations to solve for the cost of coffee (y).
First, let's solve for x in both equations:
8x + 3y = 14.45
8x = 14.45 - 3y
x = (14.45 - 3y)/8
4x + 5y = 16.15
4(14.45 - 3y)/8 + 5y = 16.15
5.725 - 1.5y + 5y = 16.15
3.5y = 10.425
y = 2.98
Therefore, the cost of one cup of coffee is $2.98.
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Keiko made a shirt using 5/8 yards of green fabric and 1/4 yards of blue fabric. How many yards of green fabric did Keiko use? Write your answer as a fraction in simplest form
Answers
Keiko used 5/8 yards of green fabric to make the shirt.
To arrive at this answer, we first need to recognize that the question is asking for the amount of green fabric used, and that there are two types of fabric being used - green and blue. The amounts of each fabric are given as fractions of a yard.
To find the amount of green fabric used, we simply need to look at the fraction given for the green fabric, which is 5/8 yards. This means that Keiko used five-eighths of a yard of green fabric. It is already in its simplest form, so the answer is 5/8 yards.
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Suppose y varies jointly as x and z. Find y when x = –10 and z = 20, if y = 179 when x = –5 and z = –11. Round your answer to the nearest hundredth, if necessary
Answers
The value of y = -651. To find the value of y when x = -10 and z = 20, given that y varies jointly as x and z and y = 179 when x = -5 and z = -11, follow these steps:
Step 1: Understand that "y varies jointly as x and z" means y = kxz, where k is the constant of variation.
Step 2: Use the given values (y = 179, x = -5, z = -11) to find k. Substitute these values into the equation:
179 = k(-5)(-11)
Step 3: Solve for k:
179 = 55k
k = 179 / 55
k = 3.2545 (rounded to the nearest hundredth)
Step 4: Use the found value of k (3.2545) and the new values of x (-10) and z (20) to find the new value of y:
y = (3.2545) (-10)(20)
Step 5: Calculate y:
y = -651
So, when x = -10 and z = 20, y = -651.
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write the following function in terms of its cofunction. cot(3π10). Write your angle in radians, and make sure to use parentheses. For example, your answer might take the form cos(pi/9)
Answers
In cofunction cot(3π/10) can be expressed as tan(9π/10).
How to express cot(3π/10) in terms of its cofunction?To express cot(3π/10) in terms of its cofunction, we'll utilize the relationship between cotangent and its cofunction, tangent.
The cofunction of an angle is the value of the corresponding trigonometric function with the complementary angle.
Since the complementary angle of 3π/10 radians is π/2 - 3π/10, we can express cot(3π/10) in terms of its cofunction as:
cot(3π/10) = tan(π/2 - 3π/10).
Now, let's simplify this expression:
cot(3π/10) = tan(π/2 - 3π/10)
= tan(π/2 + 3π/10 - π)
= tan(2π/2 + 3π/10 - π)
= tan(2π/2 - π/10)
= tan(π - π/10)
= tan(9π/10).
Therefore, cot(3π/10) in terms of its cofunction is equal to tan(9π/10).
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Express each of the following decimals as fraction in its simplest term 7.25
Answers
Answer:
The answer is 29/4
Step-by-step explanation:
7.25 in simplest form
=725/100=29/4
Answer:
29/4
Step-by-step explanation:
7.25/1 = 14.5/2 = 21.75/3 = 29/4 it is 29/4 because fractions can't include decimals
.a. Approximate the given quantity using Taylor polynomials with
n=3.
b. Compute the absolute error in the approximation assuming the exact value is given by a calculator.
sinh (0.24)
a. Approximate the given quantity using Taylor polynomials with
n=3.
b. Compute the absolute error in the approximation assuming the exact value is given by a calculator.
sinh (0.17)
Answers
a. To approximate the given quantity using Taylor polynomials with n=3, we need to use the formula for the Taylor polynomial of degree n:
Pn(x) = f(a) + f'(a)(x-a) + (1/2!)f''(a)(x-a)^2 + (1/3!)f'''(a)(x-a)^3 + ... + (1/n!)f^(n)(a)(x-a)^n
where f(x) = sinh(x), a = 0. The derivatives of sinh(x) are:
f'(x) = cosh(x), f''(x) = sinh(x), f'''(x) = cosh(x), and so on.
Therefore, the Taylor polynomial of degree 3 for sinh(x) centered at a = 0 is:
P3(x) = x + (1/2!)(x)^3
To approximate sinh(0.24), we substitute x = 0.24 into the formula above:
P3(0.24) = 0.24 + (1/2!)(0.24)^3 = 0.240008
b. To compute the absolute error in the approximation assuming the exact value is given by a calculator, we need to subtract the actual value of sinh(0.24) from the approximation we obtained in part a:
Error = |P3(0.24) - sinh(0.24)| = |0.240008 - 0.241663| = 0.001655
Therefore, the absolute error in the approximation is 0.001655.
To approximate sinh(0.17), we use the same formula and substitute x = 0.17:
P3(0.17) = 0.17 + (1/2!)(0.17)^3 = 0.170005
To compute the absolute error in this case, we subtract the actual value of sinh(0.17) from the approximation we obtained:
Error = |P3(0.17) - sinh(0.17)| = |0.170005 - 0.17031| = 0.000305
Therefore, the absolute error in the approximation for sinh(0.17) is 0.000305.
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There are 10 stations at your new job. Your manager trains you on 4 stations at random. What is the probability that you are not trained on the most desirable station?
Answers
Answer:
0.6 or 60%.
Step-by-step explanation:
First find the number of favorable outcomes (being trained on any station except the most desirable) and the total number of possible outcomes (being trained on any 4 stations).
Assuming all stations are equally likely to be selected for training, if there are 10 stations in total, the probability of not being trained on the most desirable station is as follows:
1) Favorable outcomes: Selecting 4 stations out of the 9 remaining stations (excluding the most desirable one): C(9, 4).
2) Total outcomes: Selecting any 4 stations out of the 10 available stations: C(10, 4).
P(not trained on most desirable) = Favorable outcomes / Total outcomes
= C(9, 4) / C(10, 4)
C(9, 4) = 9! / (4! * (9-4)!) = 9! / (4! * 5!) = (9 * 8 * 7 * 6) / (4 * 3 * 2 * 1) = 126
C(10, 4) = 10! / (4! * (10-4)!) = 10! / (4! * 6!) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1) = 210
P(not trained on most desirable) = 126 / 210 = 6 / 10 = 0.6
Therefore, the probability of not being trained on the most desirable station is 0.6 or 60%.
The index of a radical expression will always be a positive integer. True or False
Answers
True. The index of a radical expression must always be a positive integer.
Is the index of a radical expression always a positive integer?The index of a radical expression, which is represented by the "√" symbol, refers to the root being taken. The index indicates the degree of the root and must be a positive integer greater than zero.
For example, if we have √x, the index is 2, indicating that we are taking the square root of x. Similarly, if we have ∛x, the index is 3, indicating that we are taking the cube root of x.
The index being a positive integer is a requirement for the proper interpretation of the radical expression. Non-integer or negative indices are not defined within the realm of real numbers.
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the scores of individual students on the american college testing (act) program composite college entrance examination have a normal distribution with mean 18.6 and standard deviation 6.0. forty-nine randomly selected seniors take the act test. what is the probability that their mean score is greater than 20? round your answer to 4 decimal places.
Answers
The probability that the mean score of the 49 seniors is greater than 20 is 0.0516. To solve this problem, we need to use the central limit theorem, which states that the distribution of sample means from a population with any distribution will approach a normal distribution as the sample size increases.
First, we need to find the standard error of the mean (SEM), which is the standard deviation of the sampling distribution of the mean. We can use the formula SEM = σ / √n, where σ is the population standard deviation, and n is the sample size.
In this case, σ = 6.0 and n = 49, so SEM = 6.0 / √49 = 0.857.
Next, we need to standardize the sample mean using the z-score formula: z = (x - μ) / SEM, where x is the sample mean, μ is the population mean, and SEM is the standard error of the mean.
In this case, x = 20, μ = 18.6, and SEM = 0.857, so z = (20 - 18.6) / 0.857 = 1.63.
Finally, we need to find the probability that a standard normal distribution is greater than 1.63, which is 0.0516 when rounded to 4 decimal places.
Therefore, the probability that the mean score of the 49 seniors is greater than 20 is 0.0516.
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An art exhibit displays prize-winning artwork on a wall. There are 4
rows of artwork with 7 pieces of artwork in each row. How many
pieces of artwork are displayed?
Show your work on a separate sheet of paper.
Answers
Your answer: In the art exhibit, 28 prize-winning pieces of artwork are displayed.
To find the total number of pieces of artwork displayed in the exhibit, you need to multiply the number of rows by the number of artwork pieces in each row.
Step 1: Identify the number of rows and pieces of artwork in each row.
- There are 4 rows of artwork.
- There are 7 pieces of artwork in each row.
Step 2: Multiply the number of rows by the number of artwork pieces in each row.
- 4 rows * 7 pieces of artwork per row = 28 pieces of artwork
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The measure of angle C is 12°. Angles C and D are complementary angles. Find m2D.
Answers
Answer: ∠D=78
Step-by-step explanation:
Complementary angles have a sum of 90°
∠C + ∠D = 90°
The following system of equations is _____.
y = -1/3x + 2/3
2x + 6y = 4
equivalent
independent
inconsistent
Answers
The system of equations are equivalent
Given data ,
Let the system of equations be represented as A and B
Now , the value of A and B are
y=( -1/3 )x+2/3 be equation (1)
2x+6y=4 be equation (2)
Multiply by 3 on both sides of equation (1) , we get
3y=-x+2
Adding x on both sides , we get
3y+x=2
Multiply by 2 on both sides , we get
6y+2x=4 equation (3)
So , the equation (2) = equation (3)
Hence , they are equivalent
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What is the code to disarm the security system? Horatios Haunted House
Answers
The correct answer is 2.3 with a repeating decimal is equivalent to the simplified fraction 7/3.
To rewrite 2.3 with a repeating decimal as a simplified fraction, we can use a mathematical technique called algebraic manipulation. We start by letting x be equal to 2.3 with a repeating decimal, and then we subtract x from 10x to eliminate the repeating part of the decimal. 10x - x = 23.3333... - 2.3333... = 21
Simplifying, we get: 9x = 21
Dividing both sides by 9, we get: x = 21/9
This fraction can be simplified further by dividing the numerator and denominator by their greatest common factor, which is 3. x = 21/9 = (21 ÷ 3)/(9 ÷ 3) = 7/3
Therefore, 2.3 with a repeating decimal is equivalent to the simplified fraction 7/3.
Repeating decimals can be challenging to work with, but the technique of algebraic manipulation allows us to convert them to equivalent fractions, which can be easier to understand and work with in many contexts.
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12. An airplane flies from its headquarters at night to a city 510 miles away and
returns back the next morning. The total flying time for the round-trip flight
is 3.9 h. The plane travels the first half of the trip at 255 mph with no wind.
a. How strong is the wind on the return flight? Round your answer to the
nearest tenth.
b. Is the wind on the return flight a headwind or a tailwind?
Answers
An airplane flies from its headquarters at night to a city 510 miles away and returns the next morning. The wind speed is approximately -167 mph and is headwind.
To solve this problem, let's assume that the wind speed is represented by 'w' (in mph).
a. We know that the total flying time for the round-trip is 3.9 hours. The first half of the trip, which is 255 miles, is traveled at a speed of 255 mph with no wind. Therefore, the time taken for the first half of the trip is:
Time = Distance / Speed = 255 miles / 255 mph = 1 hour
Since the total flying time is 3.9 hours, the return trip must have taken 3.9 - 1 = 2.9 hours.
Now, we can use the formula: Time = Distance / Speed to calculate the speed of the return trip. The distance for the return trip is also 255 miles.
2.9 hours = 255 miles / (255 mph + w)
To solve for 'w', we rearrange the equation:
2.9(255 mph + w) = 255 miles
739.5 mph + 2.9w = 255 miles
2.9w = 255 miles - 739.5 mph
2.9w = -484.5 mph
w ≈ -167 mph
The wind speed is approximately -167 mph. Since wind speeds are typically reported as positive values, we take the magnitude of the wind speed, which is approximately 167 mph.
Thus, since the wind speed is negative, the wind on the return flight is a headwind.
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The solution is 13 miles per hour strong is the wind on the return flight.
Here, we have,
If the first half of the trip was travelled at the speed of 255 mph and the distance from the headquarters to the city is 510 miles, the time of travel for the first half is:
255 miles ------- 1 hour
510 miles ------- ? hours
= 510/255 × 1/1
= 2 hours
So, since the first half of the journey was at the speed of 255 miles per hour, therefore it took the plane 2 hours to get to the city from the headquarters (covering a distance of 510 miles).
But, if the time for the entire round trip is 3.9 hours, the return time is therefore:
3.9 hours ---------2 hours
= 1.9 hours( so this is the return time)
Since returning will still entail covering the same distance of 510 miles, then the speed of return is:
Speed = distance/time
= 510/1.9 = 268.42 mph.
To determine how strong the wind was on the return, we subtract the speed of the first half of the trip from the speed of the return flight:
= 268.42 - 255
= 13 miles per hour (13 mph)
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