DETAILS SCALCCC4 13.2.007. .. 1-/10 Points) Erauate the line integral, where C is the given curve. Sony dx + (x - y)dy C consists of line segments from (0,0) to (3,0) and from (3,0) to (4,2).
Answers
the line integral of the given curve C is 23/2.
To evaluate the line integral of the given curve C, we will compute the line integral along each segment of the curve separately and then add the results.
First, we consider the line segment from (0, 0) to (3, 0). Parametrize this segment as follows:
x(t) = t, y(t) = 0, for 0 ≤ t ≤ 3.
The differential path element is given by dx = dt and dy = 0. Substituting these values into the line integral expression, we have:
∫[C1] (xdx + (x - y)dy) = ∫[0,3] (t dt + (t - 0) (0) dy)
= ∫[0,3] t dt
= [t^2/2] evaluated from 0 to 3
= (3^2/2) - (0^2/2)
= 9/2.
Next, we consider the line segment from (3, 0) to (4, 2). Parametrize this segment as follows:
x(t) = 3 + t, y(t) = 2t, for 0 ≤ t ≤ 1.
The differential path element is given by dx = dt and dy = 2dt. Substituting these values into the line integral expression, we have:
∫[C2] (xdx + (x - y)dy) = ∫[0,1] ((3 + t) dt + ((3 + t) - 2t) (2dt))
= ∫[0,1] (3dt + t dt + (3 + t - 2t) (2dt))
= ∫[0,1] (3dt + t dt + (3 + t - 2t) (2dt))
= ∫[0,1] (3dt + t dt + (3 + t - 2t) (2dt))
= ∫[0,1] (7dt)
= [7t] evaluated from 0 to 1
= 7.
Finally, we add the results from the two line segments:
∫[C] (xdx + (x - y)dy) = ∫[C1] (xdx + (x - y)dy) + ∫[C2] (xdx + (x - y)dy)
= 9/2 + 7
= 23/2.
Therefore, the line integral of the given curve C is 23/2.
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Related Questions
Interest can be compounded for different time periods, such as monthly or yearly. If you were investing money, would you prefer interest compounded monthly or yearly? If you were borrowing money would you prefer interest compounded monthly or yearly?
A. Monthly for both
B. Yearly for both
C. Yearly for investing ABC monthly for borrowing
D. Monthly for investing and yearly for borrowing
Answers
Answer:
D. monthly for investing and yearly for borrowing
Step-by-step explanation:
Most people only think of interest in terms of how high or low a rate is. But understanding how interest is calculated, or compounds, is important, too. Knowing how compound interest works can help you avoid expensive mistakes and make the most of your money, whether you're depositing it, investing it, borrowing it, or spending it.
While compound interest is arguably the most important component to wealth-building, it can also be one of the best ways to wreck your finances: Having to pay compound interest can cause debt to spiral out of control.
You have been asked to check EOQ figures. You have been given the following data: demand is 19012 units per quarter, 5 - \( \$ 120 \) per ordes, Brice = 35 per unte and holding using their current ord
Answers
Based on the given data,the calculated Economic Order Quantity( EOQ) is approximately 360.50 units.
Based on the given data, we can calculate the Economic Order Quantity (EOQ) using the formula:
EOQ = sqrt((2 * demand * setup cost) / holding cost)
First, we need to determine the setup cost, which is given as $120 per order. The holding cost is $35 per unit.
Demand = 19012 units per quarter
Setup cost = $120 per order
Holding cost = $35 per unit
Substituting these values into the EOQ formula:
EOQ = sqrt((2 * 19012 * 120) / 35)
= sqrt(4562880 / 35)
≈ sqrt(130082.29)
≈ 360.50
Therefore, the calculated EOQ is approximately 360.50 units.
To check the EOQ figures, you would compare this result to their current order quantity. If their current order quantity is close to 360.50 units, then the EOQ figures are in line with their current practice. However, if the current order quantity significantly differs from 360.50 units, further analysis may be required to understand the factors influencing their ordering decisions.
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Determine whether or not the vector field is conservative. If it is conservative, find a function f such that
F =∇.f
F(x, y, z) = eyzi + xzeyzj + xyeyzk
Answers
The vector field F(x, y, z) = eyzi + xzeyzj + xyeyzk is conservative, and a potential function f is f(x, y, z) = xeyzi + xy²ezj + xyzek + C
How to determine vector field?
To determine if a vector field is conservative, we need to check if its curl is zero. If the curl is zero, it implies that the vector field can be expressed as the gradient of a scalar function.
Taking the curl of F, we have:
curl(F) = (∂F₃/∂y - ∂F₂/∂z)i + (∂F₁/∂z - ∂F₃/∂x)j + (∂F₂/∂x - ∂F₁/∂y)k
Evaluating the partial derivatives, we get:
curl(F) = (z - z) i + (x - x) j + (y - y) k
= 0
Since the curl of F is zero, the vector field F is conservative. We can find a potential function f by integrating each component of F with respect to its respective variable:
f(x, y, z) = ∫eyzi dx = xeyzi + g₁(y, z)
∫xzeyzj dy = xy²ezj + g₂(x, z)
∫xyeyzk dz = xyzek + g₃(x, y)
Here, g₁, g₂, and g₃ are arbitrary functions of the remaining variables. Combining these results, we obtain the potential function:
f(x, y, z) = xeyzi + xy²ezj + xyzek + C
Where C is the constant of integration. Therefore, a potential function f exists for the given vector field F, and it is given by f(x, y, z) = xeyzi + xy²ezj + xyzek + C.
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Multiply the vector in the graph by a scale factor of Negative one-half.
The resulting vector will be
✔ shorter than
the original vector.
The resulting vector will be in Quadrant
✔ II
shorter than and II are the answers
Answers
Answer: The answer is shorter than and ll
Step-by-step explanation:
When multiplying the vector in the graph by a scale factor of -1/2. The resulting vector will be shorter than and II. Option D is correct.
Multiply the vector in the graph by a scale factor of Negative one-half.The resulting condition for the vector is to be determined.
What is the scale factor?
The scale factor is defined as the ratio of modified change in length to the original length.
What is a vector?A vector is defined as phenomenon that has two independent belongings magnitude and direction. The term also denotes the mathematical or geometrical replica of such a quantity. Norms of vectors in nature are velocity, momentum, force, electromagnetic fields, and weight.
Here, The scale factor is -1/2, where a negative sign shows that the vector will get inverted and 1/2 implies that it will be shortened by 1/2.
Thus, when multiplying the vector in the graph by a scale factor of 1/2. The resulting vector will be shorter than and II. Option D is correct.
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What is the equation of the line that contains the slopem = 2and passes through the point(1, 3)?
Express your answer in slope-intercept form
Enter your answer in the box.
hi
Answers
Answer:
y = 2x + 1
Step-by-step explanation:
If we consider the gradient m = 2 and point (1, 3) through which the line passes, we can use the equation y - y1 = m (x - x1) to express the equation of the line in the form y = mx + c.
y - 3 = 2 * (x - 1)
y - 3 = 2x - 2
y - 2x = -2 + 3
y - 2x = 1
y = 2x + 1
John wanted to estimate the average literacy rate for all countries. He randomly selected 35 countries and researched the literacy rate for the 35 countries. The statistical unit for John's study is:
A. the 35 countries
B. a literacy rate. C. a country O
D. an individual
Answers
The statistical unit for John's study is A. the 35 countries. John is trying to estimate the average literacy rate across all countries, and he randomly selected 35 countries to research their literacy rates. The statistical unit in this case is the individual country, as each country's literacy rate is being used to calculate the average.
The statistical unit for John's study is A. the 35 countries. This is because John's study is based on a sample of 35 countries that he randomly selected. The sample is used to estimate the average literacy rate for all countries. The sample size of 35 countries is large enough to provide a representative sample of the population of countries. If John had selected only a few countries or individuals, his estimate of the average literacy rate would not have been reliable. However, by selecting a sample of 35 countries, John can make a more accurate estimation of the average literacy rate for all countries. In conclusion, the statistical unit for John's study is the sample of 35 countries that he researched to estimate the average literacy rate for all countries.
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If I1 ⊇ I2 ⊇ .... In ⊇... is a nested sequence of intervals and if In = [an; bn], show that a1 ≤ a2 ≤ ....... ≤ an ≤ ........ and b1 ≤ b2 ≤..... bn ≤ ......
Answers
The intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:
1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.
To show that a1 ≤ a2 ≤ ... ≤ an ≤ ..., we need to use the fact that the sequence of intervals is nested, meaning that each interval is contained within the next one.
First, we know that I1 contains I2, so every point in I2 is also in I1. That means that a1 ≤ a2 and b1 ≥ b2.
Now consider I2 and I3. Again, every point in I3 is also in I2, so a2 ≤ a3 and b2 ≥ b3.
We can continue this process for all the intervals in the sequence, until we reach In. So we have:
a1 ≤ a2 ≤ ... ≤ an-1 ≤ an
and
b1 ≥ b2 ≥ ... ≥ bn-1 ≥ bn
This shows that the endpoints of the intervals are ordered in the same way.
Given that I₁ ⊇ I₂ ⊇ ... In ⊇ ... is a nested sequence of intervals and In = [an; bn], we can show that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... as follows:
Since the intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:
1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.
Continuing this pattern for all intervals in the sequence, we can conclude that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... .
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The number in scientific notation is written as a decimal. 5.03x10^5
Answers
Answer:
50,300,000,000
Step-by-step explanation:
1) 225
What is the square root of 225 simplified?
Answers
Answer: 15
Step-by-step explanation: This is one of those square roots you'll memorize really quickly. You don't even have to simplify it, since it's an integer.
Calculating brilliance in epidemiology Context. What follows is a data table showing the development of brilliance among a small class of PHE 450 students. NOTE: Student #8 came in as an existing case of brilliance and did not develop brilliance as a result of exposure to PHE 450. Student WK 1 WK 2 WK 3 WK 4 WK 5 WK6 WK 7 WK 8 WK 9 WK 10 CASE CASE CASE CASE DROP 1 2 3 4 5 6 7 8 9 10 11 12 CASE CASE CASE DROP CASE DROP ASSIGNMENT Referring to the data above, please answer the following questions What is the point prevalence of brilliance at the end of Week 1? What is the point prevalence of brilliance at the end of Week 2? • What is the point prevalence of brilliance at the end of Week 3? • Using person-weeks as your denominator, what is the incidence of brilliance over the course of the 10-week course?
Answers
The point prevalence of brilliance at the end of Week 1 is 0.08 or 8%.
The point prevalence of brilliance at the end of Week 2 is 0.17 or 17%.
The point prevalence of brilliance at the end of Week 3 is 0.33 or 33%.
Using person-weeks as denominator, the incidence of brilliance over the course of the 10-week course is 0.017 or 1.7%
In epidemiology context, brilliance can be calculated through calculating point prevalence, cumulative incidence, and incidence rate. The provided data table can be used to determine the point prevalence, incidence, and incidence rate of brilliance among PHE 450 students. So, the calculations of point prevalence, cumulative incidence, and incidence rate based on the provided data are as follows:
The point prevalence of brilliance at the end of Week 1 can be calculated by the following formula; Point prevalence = Total number of existing cases at a given time ÷ Total population at that time
Student #8 was the only existing case of brilliance at the beginning of Week 1, so the point prevalence of brilliance at the end of Week 1 is; Point prevalence = 1 ÷ 12 = 0.08 or 8%.
The point prevalence of brilliance at the end of Week 2 can be calculated by the following formula; Point prevalence = Total number of existing cases at a given time ÷ Total population at that time
Student #3 and Student #8 were existing cases of brilliance at the beginning of Week 2, so the point prevalence of brilliance at the end of Week 2 is; Point prevalence = 2 ÷ 12 = 0.17 or 17%.
The point prevalence of brilliance at the end of Week 3 can be calculated by the following formula; Point prevalence = Total number of existing cases at a given time ÷ Total population at that time
Student #3, #4, #6, and #8 were existing cases of brilliance at the beginning of Week 3, so the point prevalence of brilliance at the end of Week 3 is; Point prevalence = 4 ÷ 12 = 0.33 or 33%.
The incidence of brilliance can be calculated by the following formula; Incidence = Total number of new cases ÷ Total person-weeks of observation
Student #5 and Student #7 developed brilliance during the 10-week course, so the incidence of brilliance over the course of the 10-week course is; Incidence = 2 ÷ 120 = 0.017 or 1.7%.
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An airplane is moving with the constant speed of 850 km/h at an angle θ=30
∘
. At an altitude of 5000 m a box release from the airplane. Assume a constant air resistance can create a
x
=−0.5 m/s
2
and a
y
=−0.5 m/s
2
. Find the velocity of the box when it hits the ground? (Find the magnitude and its direction)
Answers
When the box hits the ground, its velocity magnitude is approximately 235.75 m/s, and its direction is approximately 29.5° below the horizontal axis. The horizontal displacement is approximately 8600.5 meters.
To find the velocity of the box when it hits the ground, we can break down the initial velocity of the box into its horizontal and vertical components.
Speed of the airplane (constant): 850 km/h
Angle of motion of the airplane: θ = 30°
Altitude at release: 5000 m
Air resistance components: aₓ = -0.5 m/s², aᵧ = -0.5 m/s²
First, let's convert the speed of the airplane from km/h to m/s:
850 km/h = (850 * 1000) m/3600 s = 236.11 m/s
Now, we can calculate the initial velocity components:
Horizontal component: vₓ = v * cosθ
Vertical component: vᵧ = v * sinθ
vₓ = 236.11 m/s * cos(30°) = 236.11 m/s * (√3/2) = 204.38 m/s
vᵧ = 236.11 m/s * sin(30°) = 236.11 m/s * (1/2) = 118.06 m/s
Next, we'll calculate the time it takes for the box to hit the ground using the vertical component of motion:
Using the equation: h = vᵧ₀ * t + (1/2) * aᵧ * t²
h = -5000 m (negative because the box is falling)
vᵧ₀ = 118.06 m/s (initial vertical velocity)
aᵧ = -0.5 m/s² (vertical acceleration due to air resistance)
-5000 = 118.06 * t + (1/2) * (-0.5) * t²
Simplifying the equation:
-0.25t² + 118.06t + 5000 = 0
Solving this quadratic equation, we find t ≈ 42.09 seconds.
Now, we can calculate the horizontal displacement of the box during this time:
x = vₓ₀ * t + (1/2) * aₓ * t²
Since aₓ = -0.5 m/s² and x = -0.5 m/s², we can calculate the x-component of the velocity as -0.5 m/s² * t.
x = 204.38 m/s * 42.09 s + (1/2) * (-0.5 m/s²) * (42.09 s)²
x ≈ 8600.5 m
Therefore, the horizontal displacement is approximately 8600.5 meters.
Finally, we can find the magnitude and direction of the velocity when the box hits the ground using the horizontal and vertical components:
Magnitude of velocity:
v = √(vₓ² + vᵧ²) = √(204.38 m/s)² + (118.06 m/s)² ≈ 235.75 m/s
Direction of velocity:
θ' = arctan(vᵧ/vₓ) = arctan(118.06 m/s / 204.38 m/s) ≈ 29.5° (measured from the horizontal axis)
Therefore, when the box hits the ground, its velocity magnitude is approximately 235.75 m/s, and its direction is approximately 29.5° below the horizontal axis.
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I just need help with this algebra question 1 and 2 part!!
Answers
Answer:
rate of change: -3000 feet per minute
the rate of change is showing how many feet the plane descents each minute
Find the solution of the following initial value problem.g'(x)= 3x(x^2 -1/3) ; g(1) = 2
Answers
According to the question we have the solution of the given differential equation initial value problem is: g(x) = (3/4)x^4 - x + 9/4 .
To solve the given initial value problem, we need to integrate both sides of the differential equation. We have:
g'(x) = 3x(x^2 - 1/3)
Integrating both sides with respect to x, we get:
g(x) = ∫[3x(x^2 - 1/3)] dx
g(x) = ∫[3x^3 - 1] dx
g(x) = (3/4)x^4 - x + C
where C is the constant of integration.
To find the value of C, we use the initial condition g(1) = 2. Substituting x = 1 and g(x) = 2 in the above equation, we get:
2 = (3/4)1^4 - 1 + C
2 = 3/4 - 1 + C
C = 9/4
Therefore, the solution of the given initial value problem is:
g(x) = (3/4)x^4 - x + 9/4
In more than 100 words, we can say that the given initial value problem is a first-order differential equation, which can be solved by integrating both sides of the equation. The resulting function is a family of solutions that contain a constant of integration. To find the specific solution that satisfies the initial condition, we use the given value of g(1) = 2 to determine the constant of integration. The resulting solution is unique and satisfies the given differential equation as well as the initial condition.
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Find the length of. Use that length to find the length of. What is the length of ? round to the nearest tenth. 2. 3 cm 4. 0 cm 10. 7 cm 18. 6 cm.
Answers
Given: in ΔABC ∠ B = 30° , AB= 10 cm
in ΔADC ∠ D = 25° , AC = Perpendicular = 5 cm
to find: length of CD, AC
final answer: CD = 10.7 cm, AC = 5 cm
trigonometry is a subfield of mathematics that deals with the connections between angles and length-to-width ratios. the most commonly used trigonometry ratios are sin, cos and tan. we can use these with respect to triangles and apply trigonometry identities to find your answer.
using trigonometry identity in ΔABC ∠ B = 30° , AB= 10 cm,
sin = perpendicular/ hypotenuse
sin 30 = AC/ 10 (sin 30 = 1/2)
AC = 1/2 *10 = 5 cm
using trigonometry identity in ΔADC ∠ D = 25° , AC = Perpendicular = 5 cm,
tan = perpendicular/ base
tan 25 = 5/CD (tan 25 ° = 0.466 (approx))
CD = 5/0.466
CD = 10 .7cm ( approx )
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The complete question is:
Find the length of AC. Use that length to find the length of CD. What is the length of CD? Round to the nearest tenth.
A) 2.3 cm
B) 4.0 cm
C) 10.7 cm
D) 18.6 cm
I don’t understand what it’s asking me to do
Answers
Step-by-step explanation:
Rise means how many units you move up or down from point to point. On the graph that would be a change in the y values. Run means how far left or right you move from point to point. right it as a fraction then simplify the fraction. OR write it as a simplified equation. that's what I think
1-07 What is the length of the marked portion of each line segment? Copy the
segmentomto your paper before finding the missing length. Assume that the entire
ime segment is suborvided into equal sections. Homework Help
Answers
Answer:
A. 25 B. 45 C. 30
Step-by-step explanation:
A.
75 ÷ 3 = 25
25 × 1 = 25
B.
75 ÷ 5 = 15
15 × 3 = 45
C.
50 ÷ 5 = 10
10 × 3 = 30
need help asap. low geometry grade
Answers
Answer:
x=9.3
Step-by-step explanation:
use SohCahToa
in this case u use cos
cos(41°)=7/x
x=7/cos(41)
x=9.275090953
x=9.3
A train travels 250 km with a average speed of 75 km/hr and 350 km with 70km/hr and 200 km with average speed of 30km/hr. What will the average speed of whole journey of the train?
Answers
Answer:
53 1/3 km/h
Step-by-step explanation:
average speed = (total distance)/(total time)
average speed = distance/time
time * average speed = distance
time = distance/(average speed)
250 km at 75 km/h
distance = 250 km
time = (250 km)/(75 km/h) = 3.33333... hours
350 km at 70 km/h
distance = 350 km
time = (350 km)/(70 km/h) = 5 hours
200 km at 30 km/h
distance = 200 km
time = (200 km)/(30 km/h) = 6.6666... hour
total distance = 250 km + 350 km + 200 km = 800 km
total time = 3.33333... hours + 5 hours + 6.66666... hours = 15 hours
average speed = (total distance)/(total time)
average speed = (800 km)/(15 hours)
average speed = 53 1/3 km/h
The average speed of whole journey of the train is 45 km/hr
Average speed is the ratio of total distance travelled to total time taken. It is given by:
Average speed = total distance / total time
Given that a train travels 250 km with a average speed of 75 km/hr, hence:
75 = 250/time
time = 3.33 hours
It the travel 200 km with average speed of 30km/hr, hence:
30 = 200/time
time = 6.67 hours
The total distance = 200 km + 250 km = 450 km
The total time = 3.33 hr + 6.67 hr = 10 hours
Average speed = total distance/total time = 450 km/10 hours = 45 km/hr
The average speed of whole journey of the train is 45 km/hr
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A cable company charges 150 to install equipment. Then there is a $50 charge each month. Write an equation to express this relationship
Answers
Which is closest to the height of the building?
(Round to nearest tenth
Answers
Answer:
\(let \: it \: be \: x \\ \cos(70 \degree) = \frac{12}{x} \\ x = \frac{12}{ \cos(70 \degree) } \\ x = 35.1 \: ft\)
\(height = \sqrt{ {35.1}^{2} - {12}^{2} } \\ = \sqrt{1088.01} \\ = 33.0 \: ft\)
Solve C = AB + D for B
Answers
Answer:
C-D/A=B
C minus D all of that over A = B
Evaluate for x=2
|2x-18| + |3x-7|
Answers
Answer:
15
Step-by-step explanation:
2(2) - 18 = -14 |-14| = 14
3(2) -7 = -1 |-1| = 1
14+1=15
state what additional information is required in order to know that the triangles are congruent by SAS
Answers
Answer:
IJK angle. = VKJ angleFirst answer is correct
Step-by-step explanation:
JI = VK (side)
IJK = VKJ (angle)
JK = JK (side)
so, JKI TRIANGLE IS CONGRUENT TO JVK TRIANGLE
hope this helps
brainliest appreciated
good luck! have a nice day!
How do you get a probability from a graph
Answers
Answer:multiplication between probability density values (Y-axis) and tips amount (X-axis)
Step-by-step explanation:
What is the surface area of the cube, in square inches?
Answers
Answer:
The surface area of the cube is 648.96 sq in.
Step-by-step explanation:
This problem is made a lot easier by the fact that it's a cube.
So we first calculate the area of one of the faces. The length of the side of the side is 10.4 inches, and 10.4 * 10.4 = 100.16.
There are six faces, so we multiply the area of 1 face by 6. 100.16 * 6 = 648.96.
Therefore, the surface area of the cube is 648.96 sq inches.
Hope This Helps!
Find parametric equations for the line that is tangent to the given curve at the given parameter value. True or false?.
Answers
Find parametric equations for the line that is tangent to the given curve at the given parameter value. This statement is False.
In order to find parametric equations for a line tangent to a curve at a given parameter value, we need to know the equation of the curve. The terms "parametric equations" and "tangent to the given curve" indicate that we are dealing with a parametric curve. Therefore, we cannot determine if the statement is true or false without additional information.
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Each gallon of gasoline costs $2.35. The
equation y = 2.35x can be used to represent this
situation. What is the constant of
What does the constant of
proportionality?
proportionality represent in the context of the
problem?
Answers
The proportionality constant for the above equation y = 2.35x is 2.35.
What is the equation?An equation can be defined in several ways. Algebraically speaking, an equation is a statement that shows the equivalence of two mathematical expressions.
A linear equation could have more than one variable. If a variable's maximum power constantly equals one, an equation is considered to be linear.
Let us x ∝ y.
Following that, x = ky, where k is a constant or proportional.
When two variables that were in proportion are split, it will result in a constant proportional because k = x/y.
The constant of proportionality for the above equation y = 2.35x will be y/x = 2.35.
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If 5(4- x)
3x + 1-5(4 - x) = y + 12
3x + 1 5(4 + x)
5(4 - x) <3x + 1
5(4- x) + 3x + 1 = y + 12
Answers
Answer:
the third one 5(4-x)<3x+1
Answer:
number 3 hope this helps one year later
Step-by-step explanation:
Cual es la respuesta 5%9(12-32)
Answers
Answer:
i need more detail
Step-by-step explanation:
A particular fruit's weights are normally distributed, with a mean of 204 grams and a standard deviation of 16 grams. If you pick 23 fruits at random, then 7% of the time, their mean weight will be greater than how many grams
Answers
If we pick 23 fruits at random, then 7% of the time, their mean weight will be greater than 210.8 grams.
To solve this problem, we need to use the Central Limit Theorem, which states that the sampling distribution of the means of a random sample from any population will be approximately normally distributed if the sample size is large enough.
In this case, since we are picking 23 fruits at random, we can assume that the sampling distribution of the mean weight of the fruits will be approximately normal with a mean of 204 grams and a standard deviation of 16/sqrt(23) grams.
To find the weight of the fruits such that their mean weight will be greater than a certain amount 7% of the time, we need to find the z-score associated with that probability using a standard normal distribution table. The z-score can be calculated as:
z = invNorm(0.93) = 1.475
where invNorm is the inverse normal function. This means that the weight of the fruits such that their mean weight will be greater than this amount 7% of the time is:
x = 204 + 1.475*(16/sqrt(23)) = 210.8 grams (rounded to one decimal place)
To learn more about standard normal distribution click here
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