ind the mass of a thin plate occupying the smaller region cut from the ellipse x
2
+
4
y
2
=
12
by the parabola x
=
y
2
if its density per unit area is δ
(
x
,
y
)
=
5
x
Answers
the mass of the thin plate occupying the smaller region cut from the ellipse is 5/21 units.
We can use double integration to find the mass of the thin plate. The mass of the thin plate can be given as:
m = ∬R δ(x, y) dA
Where R is the region cut by the ellipse x^2 + 4y^2 = 12 and the parabola x = y^2, and δ(x, y) is the density per unit area given by δ(x, y) = 5x.
To solve this integral, we need to convert the equation of the ellipse and the parabola to polar coordinates. We can use the transformation x = r cos(θ) and y = (1/2) r sin(θ) to get:
r^2 cos^2(θ) + 2r^2 sin^2(θ) = 12
r cos(θ) = (1/2) r^2 sin^2(θ)
Simplifying the second equation, we get:
r = 2 sin^2(θ)
Substituting r and δ(x, y) into the double integral, we get:
m = ∫[0,2π] ∫[0,2sin^2(θ)] 5r cos(θ) r dr dθ
Solving the inner integral first, we get:
∫[0,2sin^2(θ)] 5r^2 cos(θ) dr = [5/3 sin^6(θ)] cos(θ)
Substituting this back into the double integral and solving the outer integral, we get:
m = ∫[0,2π] [5/3 sin^6(θ)] cos(θ) dθ
Using a trigonometric identity, we can simplify this integral as:
m = [5/3] ∫[0,2π] sin^6(θ) d(sin(θ)) = [5/3] ∫[0,1] u^6 du
Solving the integral, we get:
m = [5/3] [1/7] = 5/21
Therefore, the mass of the thin plate occupying the smaller region cut from the ellipse x^2 + 4y^2 = 12 by the parabola x = y^2 is 5/21 units.
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Related Questions
how many 7-letter sequences (formed from the 26 letters in the alphabet, with repetition allowed) contain exactly one a and exactly two bs?
Answers
There are 34836480 number of 7-letter sequences (formed from the 26 letters in the alphabet, with repetition allowed) contain exactly one a and exactly two bs.
What is permutation?
A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."
In order to fix 7 − letter sequences (formed from the 26 letters in the alphabet, with repetition allowed) contains exactly one a and exactly two b, we know that For a sequence having n letters, it is called n letter sequence. Such sequences exist with 26^n cases with repetition of letters are allowed.
So, the number of desired cases are,
= \(\frac{7_P_3(24)^4}{2} = 34836480\)
Hence, there are 34836480 number of 7-letter sequences (formed from the 26 letters in the alphabet, with repetition allowed) contain exactly one a and exactly two bs.
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I have the answers I just need someone to work it out I’ll mark as brainlesttt
Answers
Answer:
Look Below
Step-by-step explanation:
The formula for a circle is πr².
Therefore, we can divide the area of the circle by 3.14, and then square root it. 490.63/3.14=156.25... If you square root that, you get 12.5. Same thing with the other circle. 219.45/3.14=69.888... If you square root that, you get 8.36. Now that we have the radius, we can multiply that by two to find the diameter. And we're done.
Feel free to tell me if I did anything wrong! :)
PLS HELP>>>Greenland has a population of x people. Barbados has a population of 4500 more than 5 times the population of Greenland.
What do you know? What do you not know?
Write a variable expression for the populations.
Answers
Answer:
900
Step-by-step explanation:
4500/5
At LaGuardia Airport for a certain nightly flight, the probability that it will rain is 0.11 and the probability that the flight will be delayed is 0.14. The probability that it will not rain and the flight will leave on time is 0.76. What is the probability that the flight would be delayed when it is raining? Round your answer to the nearest thousandth.
Answers
Since probabilities cannot be negative, we can conclude that the given probabilities are inconsistent or there might be an error in the information provided. Please verify the values and provide correct probabilities so that we can accurately calculate P(B|A), the probability of the flight being delayed when it is raining.
Let's denote the events as follows:
A: It will rain
B: The flight will be delayed
We are given the following probabilities:
P(A) = 0.11 (probability of rain)
P(B) = 0.14 (probability of flight delay)
P(A'∩B') = 0.76 (probability of no rain and on-time departure)
We can use the probability formula to calculate the probability of the flight being delayed when it is raining, P(B|A), which is the probability of B given A.
We know that:
P(B|A) = P(A∩B) / P(A)
To find P(A∩B), we can use the formula:
P(A∩B) = P(A) - P(A'∩B')
Substituting the given values:
P(A∩B) = P(A) - P(A'∩B')
P(A∩B) = 0.11 - 0.76
P(A∩B) = -0.65
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Find x-component of
a
=(7.5 m/s
2
, negative x-direction ) Express your answer with the appropriate units. Part B Find y-component of
a
=(7.5 m/s
2
, negative x-direction). Express your answer with the appropriate units. Find x-component of
v
=(340 m/s,30
∘
below the positive x-axis ) Express your answer with the appropriate units. Part D Find y-component of
v
=(340 m/s,30
∘
below the positive x-axis ) Express your answer with the appropriate units. Find x-component of
r
=(11 m,31
∘
above the positive x-axis ). Express your answer with the appropriate units. Part F Find y-component of
r
=(11 m,31
∘
above the positive x-axis ). Express your answer with the appropriate units.
Answers
a) The x-component of vector a is -7.5 m/s². b) The y-component of vector a is 0 m/s². c) The x-component of vector v is 294.8 m/s. d) The y-component of vector v is -170 m/s. e) The x-component of vector r is 9.422 m. f) The y-component of vector r is 5.596 m.
a) The x-component of a vector is the magnitude of its displacement in the x-direction. In this case, the x-component of vector a is given as -7.5 m/s², indicating that the vector points in the negative x-direction.
b) The y-component of a vector is the magnitude of its displacement in the y-direction. Since vector a is stated to be in the negative x-direction, it does not have any displacement in the y-direction. Therefore, the y-component of vector a is 0 m/s².
c) For vector v, the x-component is given as 340 m/s. Since the vector is directed 30 degrees below the positive x-axis, the x-component can be found by multiplying the magnitude by the cosine of the angle. Thus, the x-component of vector v is approximately 294.8 m/s.
d) Similar to the x-component, the y-component of vector v is found by multiplying the magnitude by the sine of the angle. Given that vector v is 30 degrees below the positive x-axis, the y-component is calculated as -170 m/s.
e) Vector r has a magnitude of 11 m and is directed 31 degrees above the positive x-axis. To find the x-component, we multiply the magnitude by the cosine of the angle. Thus, the x-component of vector r is approximately 9.422 m.
f) Similarly, the y-component of vector r is determined by multiplying the magnitude by the sine of the angle. With an angle of 31 degrees above the positive x-axis, the y-component of vector r is approximately 5.596 m.
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Approximate +√40 to the nearest hundredth.
O 10.14
O 9.47
O9.14
6.32
Answers
Answer:
6.32
Step-by-step explanation:
The sqrt(40) is between the sqrt(36) and sqrt(49). The sqrt(36) = 6 and the sqrt(49) = 7. Therefore, we know it is somewhere between 6 and 7. The only answer is 6.32.
hope this helps! <3
Answer:
9.47
Step-by-step explanation:
because 9.46559265359 rounded to the nearest hundredth is 9.47
A journalist in a town with a population of 15,200 takes a random sample of 200 people and finds that 60 of them read the local newspaper. Based on this sample, which of the following is the best estimate for the number of people in the town that read the local newspaper?
a. 5
b. 45
c. 450
d. 4500
Answers
Based on this sample, the best estimate for the number of people in the town that read the local newspaper is d. 4500.
Using this formula
Number of people=(Population-Random sample)/Random sample× Number of people that read local newspaper
Let plug in the formula
Number of people=(15,200-200/200)×60
Number of people=(15,000/200)×60
Number of people=75×60
Number of people=4500
Inconclusion the best estimate for the number of people in the town that read the local newspaper is d. 4500.
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A car traveling at an average speed of 100km covers a certain distance 3 hours 20 minutes. At what speed must the car travel to cover the Same distance in 2 hours 40 minutes
Answers
The car must travel at a speed of 125 km/h to travel the same distance in 2 h and 40 minutes.
How do you find speed in math?Speed is calculated as follows: speed = distance / time. Knowing the units for distance and time is necessary to calculate the units for speed. The units will be in metres per second (m/s) in this example since the distance is measured in metres (m) and the time is measured in seconds (s).Speed, expressed in terms of metres per second, is the rate at which an object's location changes. An item moves one metre in one second, for instance, if it starts at the origin and moves three metres in three seconds.The formula for an object's general speed is [Speed = Distance /Time]. M/s is the SI unit of speed.Given data :
d = ?
v1 = 100km/h
t1 = 3 hours and 20 minutes = 200 minutes
v2 = ?
t2 = 2 hours and 40 minutes
The distance covered by the car in 200 minutes at a speed of 100km/h is equal to the product of speed and travel time. This distance is 333.33 km. To cover the same distance at a travel time of 2 hours and 40 minutes, the speed must be calculated by dividing 333.33 km by 2.67 h. The speed is 1000/8 km/h or 125 km/h.
Computing for the speed of the car
speed = distance traveled / elapsed time
speed = (1000 km / 3 h) * (3/8 h/km)
speed = 1000 km / 8 h
speed = 125 km/h
The car must travel at a speed of 125 km/h to travel the same distance in 2 h and 40 minutes.
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Question is below!!!!!!! Please help
Answers
Answer:y=10
Step-by-step explanation:u see the right side numbers increase by 7
The larget taco contained approximately 1 kg of onion for every 6. 6 kg grilled teak. The total weight of thee two ingredient wa 617. 3 kg. How many kilogram of each ingredient were ued?
Answers
The largest taco contained approximately 1 kg of onion for every 6. 6 kg grilled teak. then Amount of grilled steak used: 6.6 (79.17) = 538.356 kg
What is a unit amount in math?
When a price is expressed as a quantity of 1, such as $25 per ticket or $0.89 per can, it is called a unit price. If you have a non-unit price, such as $5.50 for 5 pounds of potatoes, and want to find the unit price, divide the terms of the ratio
1 k + 6.6 k = 617.3
Where “k” is a constant value, a multiplier.
Solving for k:
7.8 k = 617.3
k = 617.3 /7.8
k= 79.17
So:
Amount of onion used:
1 (79.17) = 79.17 kg
Amount of grilled steak used:
6.6 (79.17) = 538.356 kg
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the height and age of each child in a random sample of children was recorded. the value of the correlation coefficient between height and age for the children in the sample was 0.80.8. based on the least-squares regression line created from the data to predict the height of a child based on age, which of the following is a correct statement?
Answers
The correct statement is C.) The proportion of the variation in height that is explained by a regression on age is 0.64.
How can the correct statement be determined?The coefficient of determination (R2), which ranges from 0 to 1, expresses how accurately a statistical model forecasts a result.
The correlation Coefficient R = 0.8, which demonstrates the strong correlation between children's age and height. With the correlation coefficient value, we can calculate the coefficient of determination (R2), which indicates the proportion of variation that the regression model can account for.
Coefficient of determination \((R^{2} ) = 0.8^{2}\)
= 0.64.
0.64 of the variation in children's height that can be attributed to age and 0.36 to other factors.
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missing Options :
A.) On average, the height of a child is 80% of the age of the child.
B.) The least-squares regression line of height versus age will have a slope of 0.8.
C.) The proportion of the variation in height that is explained by a regression on age is 0.64.
D.) The least-squares regression line will correctly predict height based on age 80% of the time.
E.) The least-squares regression line will correctly predict height based on age 64% of the time.
Suppose that you were offered a lottery with a 0.50 probability of winning $500 and a 0.50 probability of winning nothing or a guaranteed payoff of $300. If you choose the lottery, you would be considered O a risk taker O a risk-neutral individual O a risk avoider O a risk-creator
Answers
If you choose the lottery, you would be considered a risk taker.
By opting for the lottery with a 0.50 probability of winning $500 and a 0.50 probability of winning nothing, you are demonstrating a willingness to take a chance and accept the uncertainty associated with the potential outcomes. A risk taker is someone who is willing to engage in risky or uncertain situations for the possibility of gaining a favorable outcome. In this case, you are accepting the risk of potentially winning nothing in exchange for the chance to win a larger amount.
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what is the mass of a 7.91cm3 piece of lead having a density of 11.34g/cm
Answers
Answer:
89.6994g
Step-by-step explanation:
M = DV
= 11.34g/cm^3 * 7.91cm^3
= 89.6994g
Hope this helps!
the record distance in the sport of throwing cowpats is 81.1 m. this record toss was set by steve urner of the united states in 1981. assuming the initial launch angle was 45° and neglecting air resistance, answer the following.
Answers
(a) The initial speed of the projectile - 28.2m/s
(b)The total time interval the projectile was in flight - 4.07s.
a) When a projectile is launched with speed \(v_{i}\) at an angle above the horizontal, the initial velocity components are \(v_{xi}\) = \(v_{i}\) cos\(θ\) and \(v_{yi}\)= \(v_{i}\) sin\(θ\) . Neglecting air resistance, the vertical velocity when the projectile returns to the level from which it was launched (in this case, the ground) will be \(v_{y} = - v_{yi}\) .
From this information, the total time of flight is found \(v_{yf} = v_{yi} + a_{y}\) to be
\(t_{total} = \frac{v_{yf} - v_{yi} }{a_{y}}\) = \(\frac{-v_{yi} - v_{yi} }{-g}}\) = \(\frac{2v_{yi} }{g}\)
\(t_{total} = \frac{2v_{i}sinθ }{g}\)
Since the velocity of a projectile with no air resistance is constant, the horizontal distance it will travel in this time is given by
R = \(v_{xi} t_{total} = (v_{i} cosθ_{i}) \frac{2v_{i}sinθ }{g}\) = \(\frac{v^{2}_{i}}{g}( 2sinθ_{i} cosθ_{i} )\) = \(\frac{v^{2} _{i} (sin2θ_{i} ) }{g}\)
Thus, if the projectile is to have a range of R=81.1m when launched at an angle of \(θ_{i}\)=45.0°, the required initial speed is
\(v_{i} = \sqrt{\frac{81.1 * 9.80}{sin90} }\) = 28.2 m/s
Therefore, the initial speed of the projectile - 28.2m/s
b) With \(v_{i}\)=28.2m/s and \(θ_{i}\) = 45.0°, the total time of flight (as found
above) will be
\(t_{total} = \frac{2v_{i}sinθ }{g}\) = \(\frac{2(28.2 m/s) sin45}{9.80m/s^{2}}\) = 4.07s
∴The total time interval the projectile was in flight - was 4.07s.
c) Note that at \(θ_{i}\) =45.0° that sin(2\(θ_{i}\)) will decrease as \(θ_{i}\) is increased above this optimum launch angle. Thus, if the range is to be kept constant while the launch angle is increased above 45.0°, we see from \(v_{i}\) = \(\sqrt{\frac{Rg}{sin2θ_{i}} }\)that the required initial velocity will increase.
Observe that for \(θ_{i}\) <90°, the function sin\(θ_{i}\) increases as \(θ_{i}\) it increased. Thus, increasing the launch angle above 45.0° while keeping the range constant means that both \(v_{i}\) sins will increase. Considering the expression \(t_{total}\) given above, we see that the total time of flight will increase.
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The correct question is :
The record distance in the sport of throwing cowpats is 81.1m. This record toss was set by Steve Urner of the United States in 1981. Assuming the initial launch angle was 45° and neglecting air resistance, determine (a) the initial speed of the projectile and (b) the total time interval the projectile was in flight. (c) How would the answers change if the range were the same but the launch angle was greater than 45°? Explain.
3/5 x 1/4 find each product
Answers
Answer:
3/20 or 0.15 as a decimal.
Please answer correctly !!!! Will mark brainliest !!!!!!!!!!
Answers
Answer:
\(2x^2-x+3\)
Step-by-step explanation:
So just divide the areas by the length:
\(2x^2-x+3\)
And that is your width.
Answer:
iddk
Step-by-step explanation:
Please could someone explain me why the answer is not 10x5?
Answers
Answer:
20x^5
Step-by-step explanation:
You have to first find the prime factors of each term in order to find the greatest common factor.
4⋅(2+5)
Line 1
4
⋅
2
+
4
⋅
5
4⋅2+4⋅5
Line 2
The expression was rewritten using the
.
4
⋅
(
2
+
5
)
4⋅(2+5) equals
4
⋅
4⋅
which equals
.
4
⋅
2
+
4
⋅
5
4⋅2+4⋅5 equals
+
+
which equals
.
Answers
Answer: 4⋅(2+5) = 4 * (2+5) = 4 * 7 = 28
Step-by-step explanation:
Line 1 shows the original expression and Line 2 shows the expression is simplified by using the distributive property.
4⋅2 + 4⋅5 = 8+20 = 28
So the final result is 28.
Which pairs of figures are congruent? Which pairs are similar?
Answers
Answer: Look at the explanation
Step-by-step explanation: To understand what figures are congruent and what figures are similar, you need to understand what the terms mean.
Congruent figures have the same shape and size.
Similar figures have the same shape but different size.
The 1st figure is not congruent but it is similar.
2nd figure is congruent and similar which are rectangles. Wheather the figure is rotated or reflected, it is still congruent and similar.
3rd figure is both, congruent and similar which are both triangles.
4th figure is neither. There is a circle and an elipse, which are both round but different shapes.
By knowing the terms congruent and similar, you should have no problem in identifying geometric shapes and sizes.
Hope this helps. Happy learning!
Find the measure of angle b
A=108 degrees
C=72 degrees
D=81 degrees
Answers
Answer:
the anwser is c plz give brainlist
I need help with this also I had was to repost it again because someone deleted it
Answers
Answer: 8:05
Step-by-step explanation:
Answer: 8:05
Step-by-step explanation:
15 POINTS! WILL MARK BRAINLIEST
If f(x) and g(x) are inverse functions, use the information shown to find g(x)
f(2x - 10) = x + 1
f(-10) = 1
f(-12) = 0
f(2x - 12) = x
Answer Choices:
g(x) = -12
g(x) = 2x - 10
g(x) = -10
g(x) = 2x - 12
Answers
The function g(x) is defined as follows:
g(x) = 2x - 12.
How to obtain the inverse function?The inverse function is obtained exchanging the variables x and y, and then isolating y, thus:
The fact that the variables are exchanged means that the functions are symmetric over the line y = x.
As the lines are symmetric over the line y = x, these following statements regarding the composition of a function with it's inverse is given as follows:
f(g(x)) = x.g(f(x)) = x.We have that f(2x - 12) = x, hence the function g(x) is defined as follows:
g(x) = 2x - 12.
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If a family has five girls and plans to have another child, answer the following if the probability of the event of a boy being born is \( \frac{1}{2} \), and births are independent events. a. What is
Answers
In a family with five girls and the probability of a boy being born is 1/2, the probability of the next child being a boy is still 1/2.
The previous births do not affect the probability of the next birth since each birth is an independent event.
The probability of an event occurring is determined by the ratio of the number of favorable outcomes to the total number of possible outcomes. In this case, the event of interest is the birth of a boy.
Since each birth is an independent event, the probability of having a boy on any given birth is always 1/2, regardless of the previous children born.
In the given scenario, the family already has five girls. This information is not relevant to the probability of the next child being a boy. The gender of the previous children does not affect the probability of the next child being a boy or a girl.
Therefore, the probability of the next child being a boy remains 1/2, as it is for any independent birth event.
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a representative of a car manufacturer in the united states made the following claim in a news report. ten years ago, only 53 percent of americans owned american-made cars, but that figure is significantly higher today. a research group conducted a study to investigate whether the claim was true. the group found that 56 percent of a randomly selected sample of car owners in the united states owned american-made cars. a test of the appropriate hypotheses resulted in a p-value of 0.283. assuming the conditions for inference were met, is there sufficient evidence to conclude, at the significance level of a
Answers
There isn't enough evidence to indicate that the percentage of Americans who own American-made cars is more than 53 percent.
A representative of a car manufacturer in the United States claimed that 53 percent of Americans owned American-made cars ten years ago.
However, today, the percentage is higher.
A research group conducted a study to find out whether the statement was true.
They found out that 56 percent of a random sample of car owners in the United States owned American-made cars. The appropriate hypothesis test produced a p-value of 0.283.
Assuming the conditions for inference were satisfied, is there sufficient evidence to conclude, at the level of significance of α = 0.05
At α = 0.05, we want to see if there is enough evidence to reject the null hypothesis.
Therefore, since α = 0.05, the null hypothesis (H0) should be tested against the alternative hypothesis (Ha).
H0: μ ≤ 0.53 (The percentage of Americans who own American-made cars is no higher than 53%).
Ha: μ > 0.53 (The percentage of Americans who own American-made cars is higher than 53%).
It is clear that the researcher's claim was not supported by the evidence since the p-value of 0.283 was far above the significance level of α = 0.05.
Therefore, there is no statistically significant evidence to reject the null hypothesis (H0).
The research group discovered that 56 percent of a randomly selected sample of car owners in the United States owned American-made cars.
The null hypothesis states that the percentage of Americans who own American-made cars is no higher than 53 percent.
Since the p-value was greater than 0.05, we failed to reject the null hypothesis.
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round 9.777 to the nearest hundredth
Answers
Answer:
9.78
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
Find the slope of the line going through the points (2,4) and (12)
Answers
Step-by-step explanation:
If there are 2 points (a,b) and (c,d),
then the slope = (d - b)/(c - a) = (b - d)/(a - c)
Therefore slope = (10 - 4)/(4 - 2) = 6/2 = 3
The point-slope form of a line is
y = mx + b, where m is the slope and b is the y-intercept Substituting either point (2,4) or (4,10) into the equation is fine.
(4) = (3)(2) + b
4 = 6 + b
b = 4 - 6 = -2
y = 3x - 2
Or
(10)=(3)(4) + b
10 = 12 + b
b = 10 - 12 = -2
y = 3x - 2
Solve the system by substitution. Check your answer.
a+b-4c =4
- 2b + c = -11
C= - 1
Answers
Answer: c=-1,b=5,a=-5
Step-by-step explanation: If c=-1, substitute it into the second equation first. The second equation becomes -2b-1=-11, simplify it becomes -2b=-10, divide by 2 it becomes -b=-5, so b=5. Then you substitute b and c into the first equation. The first equation becomes a+5+-(-4)=4, simplify it becomes a+5+4=4, Simplify again it becomes a=-5.
The 8th term of an ap is -4,-2,0
Answers
The 8th term of an arithmetic progression (AP) is T8 = - 10.
What is Arithmetic Progression ?
The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount.A.P. and G.P. application: A series of terms known as an arithmetic progression (AP) have identical differences. In a geometric progression (GP), the common ratio is multiplied by the previous term to produce each succeeding term.an ap = -4,-2,0,............
a = 4
d = 2-4 = -2
°•° Tn = a + (n-1) d
T8 = 4 + (8-1)*-2
T8 = 4 - 14
T8 = - 10
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Luis has a square pasture with a surface area of 1800 m² and is not fenced. In the center of the pasture there is a tree from which he ties his horse with a rope that reaches exactly to the corners of the pasture and allows the horse to surround the terrain.What area can the horse tread outside of the pasture?
Answers
ANSWER
\(A=1027.43m^2\)EXPLANATION
First, let us make a sketch of the situation:
From the diagram:
=> The square with side length L represents the square pasture with an area of 1800 m²
=> The straight line, D, represents the distance between the corners of the square (the diagonal of the square)
=> The circle represents the area that the horse can tread in total.
=> The inner circle represents the tree at the center.
To solve this, we first have to find the radius of the circle, in order to find the area of the circle (the area the horse can tread in total).
The area of the square is 1800 m², this means that the length of the side of the square can be found using the formula for the area of a square:
\(\begin{gathered} A=L^2 \\ L=\text{length of the side of the square} \\ \Rightarrow1800=L^2 \\ L=\sqrt[]{1800} \\ L=30\sqrt[]{2}m \end{gathered}\)Now, we can find the length of the diagonal of the square, D, using the Pythagoras theorem:
\(\begin{gathered} D^2=L^2+L^2 \\ \Rightarrow D^2=2L^2 \\ D^2=2(30\sqrt[]{2})^2 \\ D^2=2\cdot1800=3600 \\ D=\sqrt[]{3600} \\ D=60m \end{gathered}\)D represents the diameter of the circle, but to find its area, we need to find its radius, R, using :
\(\begin{gathered} D=2\cdot R \\ R=\frac{D}{2} \end{gathered}\)Therefore:
\(R=\frac{60}{2}=30m\)The area of the circle is:
\(\begin{gathered} A=\pi R^2 \\ A=\pi\cdot30^2 \\ A=2827.43m^2 \end{gathered}\)Finally, to find the area that the horse can tread outside the pasture, we have to subtract the area of the square pasture from the circle that the horse can tread in total, that is:
\(A_{\text{treadoutside}}=A_{\text{treadtotal}}_{}-A_{\text{pasture}}\)Therefore, the answer is:
\(\begin{gathered} A=2827.43-1800 \\ A=1027.43m^2 \end{gathered}\)
(a) a box contains 3 red balls, 2 white balls, and 5 black balls. two balls are drawn at random from the box (with replacement of the first before the second is drawn). what is the probability of getting a red ball on the first draw and a white ball on the second? (enter your probability as a fraction.)
Answers
Answer:2
Step-by-step explanation:i did it