The collected information is:
a) 1. House_ID and 2. Neighborhood: Categorical (Nominal) 3. Mail_Zip: Categorical (Ordinal) 4. Acres, 5. Yr_Built, 6. Full_Market_Value, 7. SFLA: Quantitative (Continuous)
b) House_ID: Categorical and nominal, serves as an identifier variable.
c) Neighborhood: Categorical and nominal, represents different neighborhood categories.
a) For each variable:
1. House_ID: Categorical and nominal. House_ID is a unique identifier for each house, and there is no inherent order to the values.
2. Neighborhood: Categorical and nominal. Neighborhood is a categorical variable that can be divided into different categories, such as "Greenfield Manor", "Dublin", and "Arcady". There is no inherent order to the values.
3. Mail_Zip: Categorical and ordinal. Mail_Zip is a categorical variable that can be divided into different categories, such as "12859", "12801", and "12309". The values are ordered in ascending order, with 12859 being the smallest value and 12309 being the largest value.
4. Acres: Quantitative and continuous. Acres is a quantitative variable that can take on any value between 0 and infinity. The units of measurement are acres.
5. Yr_Built: Quantitative and discrete. Yr_Built is a quantitative variable that can take on any value between 1955 and 1997. The units of measurement are years.
6. Full_Market_Value: Quantitative and continuous. Full_Market_Value is a quantitative variable that can take on any value between $67,100 and $190,000. The units of measurement are dollars.
7. SFLA: Quantitative and continuous. SFLA is a quantitative variable that can take on any value between 900 and 1620 square feet. The units of measurement are square feet.
b) Describe the variable House_ID. Choose the correct answer below.
A. The variable House_ID is categorical and ordinal. Incorrect
B. The variable House_ID is categorical and nominal. Correct
C. The variable House_ID is an identifier variable. Correct
D. The variable House_ID is quantitative, with units house number. Incorrect
c) Describe the variable Neighborhood. Choose the correct answer below.
A. The variable Neighborhood is categorical and ordinal. Incorrect
B. The variable Neighborhood is quantitative, with units neighborhood name. Incorrect
C. The variable Neighborhood is categorical and nominal. Correct
D. The variable Neighborhood is quantitative, with units number of neighborhoods. Incorrect
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How many students are enrolled in a course either in calculus, discrete mathematics, data structures, 7. or programming languages at a school if there are 507, 292, 312, and 344 students in these courses, respectively; 14 in both calculus and data structures; 213 in both calculus and programming languages; 211 in both discrete mathematics 558 and data structures; 43 in both discrete mathematics and programming languages; and no student may take calculus and discrete mathematics, or data structures and programming languages, concurrently
Answer:
974
Step-by-step explanation:
Let assume that:
The set of student that took part in Calculus be = C
Those that took part in discrete mathematics be = D
Let those that took part in data structures be = DS; &
Those that took part in Programming language be = P
Thus;
{C} = 507
{D} = 292
{DS} = 312
{P} = 344
For intersections:
{C ∩ DS} = 14
{C ∩ P} = 213
{D ∩ DS} = 211
{D ∩ P} =43
{C ∩ D} = 0
{DS ∩ P} = 0
{C ∩ D ∩ DS ∩ P} = 0
According to principle of inclusion-exclusion;
{C ∪ D ∪ DS ∪ P} = {C} + {D} + {DS} + {P} - {C ∩ D} - {C ∩ DS} - {C ∩ P} - {D ∩ DS} - {D ∩ P} - {DS ∩ P}
{C ∪ D ∪ DS ∪ P} = 507 + 292 + 312 + 344 - 14 - 213 - 211 - 43 - 0
{C ∪ D ∪ DS ∪ P} = 974
Hence, the no of students that took part in either course = 974
. In a volleyball game, Alexis scored 4 points more than twice the
number of points Jessica scored. Jessica scored 3 points. How many
points did Alexis score?
F. 1 point G. 7 points H. 10 points I. 12 points
Answer: 10
Step-by-step explanation:
Alexis Scored 4 more than twice the number of points Jessica scored.
Jessica scored 3
twice the number of 3 would be 3 x 2 which equals six
4 more than twice the number which is 6 would be 10, 4+6=10
For a random variable X where X ~ N(p, p(1-p)/k) and 0<=p<=1, find the value of k for which X will estimate to p within an accuracy of 0.2 with probability greater than 0.9
The value of k for which X will estimate to p within an accuracy of 0.2 with probability greater than 0.9 is {0.2^2 p(1-p)}/{1.645^2}
Given a random variable X where X ~ N(p, p(1-p)/k) and 0<=p<=1, we need to find the value of k for which X will estimate to p within an accuracy of 0.2 with probability greater than 0.9.
In general, if X ~ N(μ,σ²), then
P[|X-μ| < a] = 2Φ(a/σ) - 1
where Φ(z) is the standard normal cumulative distribution function.
Therefore, we can say that
P[|X-p| < 0.2] = 2Φ(0.2/√(p(1-p)/k)) - 1 ≥ 0.9
or 2Φ(0.2/√(p(1-p)/k)) ≥ 1.9
or Φ(0.2/√(p(1-p)/k)) ≥ 0.95
or 0.2/√(p(1-p)/k) ≥ Φ^(-1)(0.95)
where Φ^(-1)(z) is the inverse of the standard normal cumulative distribution function.
Therefore, Φ^(-1)(0.95) = 1.6450.2/√(p(1-p)/k) ≥ 1.645
or k ≤ 0.2²p(1-p)/1.645²
From the above inequality, we get the maximum value of k for which X will estimate to p within an accuracy of 0.2 with probability greater than 0.9 is given by the formula:
k ≤{0.2^2 p(1-p)}/{1.645^2}
Therefore, the value of k for which X will estimate to p within an accuracy of 0.2 with probability greater than 0.9 is {0.2^2 p(1-p)}/{1.645^2}
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An insurance policy sells for $600. Based on past data, an average of 1 in 50 policyholders will file a $5,000 claim, and average of 1 in 100 policyholders will file a $10,000 claim, and an average of 1 in 200 policyholders will file a $30,000 claim. What is the expected value per policy sold?
Answer:
$250
Step-by-step explanation:
Calculation to determine the expected value per policy sold
Expected value per policy sold =$600-(1/50)*$5,000-(1/100)*$10,000-(1/200)*$30,000
Expected value per policy sold =$600-$100-$100-$150
Expected value per policy sold =$250
Therefore the expected value per policy sold will be $250
The distance y (in miles) that a truck travels on x gallons of gasoline is represented by the equation y=18x The graph shows the distance that a car travels. Which vehicle gets the better gas mileage?
Answer:
Car M:
50.4/2 = 25.2
car M uses up 1 gallon every 25.2 miles
Car P:
Just from the graph, you can see that it uses up 1 gallon every 30 miles
The two graphs vary the /miles slightly but it is around their zones of 25.2 and 30. It varies slightly because the cars may be traveling at a fast speed or slower speed thus using up more or less fuel by the time they've reached the recorded distances on the graphs.
Answer:
Step-by-step explanation:
An after school music program has 15 out 50 students practicing. Write 15/50 (15 over 50) as a decimal and as a percent.
Decimal -
Percent -
Answer:
Percent- 30
decimal-0.3
Step-by-step explanation:
Hope this helps and have a wonderful day!!!
find the missing side x
Answer:
[tex]\sqrt{968}[/tex]
Step-by-step explanation:
Since this is a right triangle, we are able to use pythagorean theorem, a^2+b^2=c^2. In this case x would be the "c", so 22^2+22^2=x^2. Isolate the variable and solve for x. 484+484=x^2
968=x^2
[tex]\sqrt{968\\}[/tex]=x
Find the area of the square. Round to one decimal place.
Answer:
309.8 mm
Step-by-step explanation:
17.6 x 17.6= 309.76
309.76 rounded is 309.8
Answer:
309.8
Step-by-step explanation:
The formula for area of square is one of its sides times another (or its side squared).
So if one of the side is 17.6, it would be 17.6^2 which is 309.76.
You then round one decimal place and get 309.8
Have a good day
PLZZZ HELPPPPPP ILL GIVE BRAINLIESTTTTT
N = visitors
1030 = 1300 - 18(P - 30)
1030 - 1300 = -18(P - 30)
-270 = -18(P - 30)
-270/-18 = (P - 30)
15 = P - 30
45 = P
ANSWER: 45simplify this answer pls
Answer:
D
Step-by-step explanation:
when it's a power of the power we multiply the powers to get a single value for the power.
(6^(1/4))^4=6^(4*(1/4)) (4*(1/4)=1)
=6^1=6
so the answer is D
please help, tysm for your assistance if you do :)
Answer:
27/49
plz mark me as brainliest
A Store owners offers a discount of 20% off the regular price of all jackets. Jessica has a coupon that gives her an additional 5% off the discount price. The original price of jacket Jessica buys is $84. What is the price of the jacket after the discount and Jessica coupon?
Answer:
$63
Step-by-step explanation:
The store is 20% off, Jessica has a coupon that is 5% off add that together and it's 25% off. $84 - 25% = $63
Students deliver catalogues and leaflet to houses. One day they have to deliver 384 catalogues and 1890 leaflets. Each student can deliver either 16 catalogues or 90 leaflets in hour. Each student can only work for 1 hour. All students hired are paid £51.30 per day, even if they don't work a full day. If the minimum number of wages are hired, how much will the wage bill be
Answer:
£2308.5 per day
Step-by-step explanation:
Since in one day they have to deliver 384 catalogues and 1890 leaflets and each student can deliver either 16 catalogues or 90 leaflets in hour, the amount of students required to deliver 384 catalogues in one hour is 384/16 = 24 students.
Also, the number of students required to deliver 1890 leaflets in one hour is 1890/90 = 21 students.
So the total number of students required to make the delivery is thus 24 + 21 = 45 students. This is the minimum number of students required for the delivery.
Since all students hired are paid £51.30 per day, even if they don't work a full day, so the amount of wage paid for this minimum amount of students is thus minimum amount × wage = 45 × £51.30 per day = £2308.5 per day
Answer:
£307.80
Step-by-step explanation:
Wow seems the verified answer is wrong.
Who would've thought?
16*384=24
90*1890=21
21+24=45
45/8=5.62500
5.625 rounds to 6
51.30*6=£307.80
Thats your working out
You have to divide 45 by 8 because there are 8 hours in a day in which they can work.
Then round the number as you cant have a fraction of a person
Which you would then multiply by 51.30
Brainliest would be appreciated <33
Hope it helps!
To figure out the distance for a trip, you use a ruler to measure the distance from Orlando to Gainesville on the map. You measure 2.3 cm. Find the actual mileage
between the two cities, rounded to the nearest mile.
will give u brainlist
Answer:
The answer is 71
Step-by-step explanation:
Why because
1 cm /31 mi = 2.3 cm / m
1 x m = 31 x 2.3
n = 71.3
71.3 rounded to nearest mile is 71.
let $p$ and $q$ be the two distinct solutions to the equation$$\frac{4x-12}{x^2 2x-15}=x 2.$$if $p > q$, what is the value of $p - q$?
let $p$ and $q$ be the two distinct solutions to the equation$$\frac{4x-12}{x^2 2x-15}=x 2.$$if $p > q$. The value of $p - q$ is 4.
To find the value of $p - q$, we first need to solve the given equation and determine the values of $p$ and $q$.
The equation is:
$$\frac{4x-12}{x^2 - 2x - 15} = x^2.$$
Step 1: Factorize the denominator:
The denominator can be factored as $(x - 5)(x + 3)$.
Step 2: Simplify the equation:
$$\frac{4x-12}{(x - 5)(x + 3)} = x^2.$$
Step 3: Multiply both sides of the equation by $(x - 5)(x + 3)$ to eliminate the denominator:
$$(4x - 12) = x^2(x - 5)(x + 3).$$
Step 4: Expand and rearrange the equation:
$$4x - 12 = x^4 - 2x^3 - 15x^2 + 25x.$$
Step 5: Rearrange the equation and combine like terms:
$$x^4 - 2x^3 - 15x^2 + 21x - 12 = 0.$$
Step 6: Factorize the equation:
$$(x - 3)(x + 1)(x - 2)(x + 2) = 0.$$
From this, we get four possible solutions: $x = 3$, $x = -1$, $x = 2$, and $x = -2$.
However, we are interested in the two distinct solutions $p$ and $q$, where $p > q$. Therefore, the values of $p$ and $q$ are $p = 3$ and $q = -1$.
Finally, we can find the value of $p - q$:
$$p - q = 3 - (-1) = 3 + 1 = 4.$$
Hence, the value of $p - q$ is 4.
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if i do something to the numerator of a fraction, am i supposed to do the same to the denominator too? and if yes,why?
for example i want to multiply 2/2 over 6/2, is it necessary to multiply 2/2 or can I just multiply 2?
Step-by-step explanation:
When performing operations on fractions, it is important to maintain the relationship between the numerator and the denominator. In general, if you do something to the numerator, you should also do the same to the denominator.
In your example, if you want to multiply the fraction 2/2 by 6/2, it is necessary to multiply both the numerator and the denominator by the same value. Here's why:
When you multiply fractions, you multiply the numerators together and the denominators together. So, in this case, the multiplication would be:
(2/2) * (6/2) = (2 * 6) / (2 * 2) = 12/4
If you had only multiplied the numerator (2) by 6, the result would have been:
(2 * 6) / 2 = 12/2
As you can see, these two results are different. The correct result is 12/4, which simplifies to 3/1 or simply 3. If you only multiplied the numerator, you would have obtained 12/2, which simplifies to 6.
So, it's necessary to apply the same operation (in this case, multiplication by 2) to both the numerator and the denominator in order to maintain the value of the fraction.
The playground at a park is shaped like a trapezoid the dimensions what is the area of the playground in square feet
Answer:
[tex]Area = 1560ft^2[/tex]
Step-by-step explanation:
Given
See attachment for playground
Required
Determine the area
The playground is a trapezoid. So;
[tex]Area = \frac{1}{2}(Sum\ parallel\ sides) * Height[/tex]
From the attachment, the parallel sides are: 68ft and 36ft
The height is: 30ft
So, the area is:
[tex]Area = \frac{1}{2}(68ft + 36ft) * 30ft[/tex]
[tex]Area = \frac{1}{2}(104ft) * 30ft[/tex]
[tex]Area = 52ft * 30ft[/tex]
[tex]Area = 1560ft^2[/tex]
1 Which is an arithmetic sequence?
F)2, 5, 9, 14, ...
G)100, 50, 12.5, 1.6, ...
H)3, 10, 17, 24,...
j) -2,-1,-1/2,-1/4
Answer:
H) 3, 10, 17, 24, ...Step-by-step explanation:
An arithmetic sequence is when the difference of the terms is same
F)2, 5, 9, 14, ...
14 - 9 = 5, 9 - 5 = 4. 5-2 = 35 ≠ 4 ≠ 3, no
G)100, 50, 12.5, 1.6, ...
1.6 - 12.5 = -10.912.5 - 50 = -37.550 - 100 = -50-10.9 ≠ -37.5 ≠ -50, no
H)3, 10, 17, 24,...
24-17 = 717 - 10 = 710 - 3 = 77 is the common difference, yes
j) -2,-1,-1/2,-1/4
-1/4 - (-1/2) = 1/4-1/2 - (-1) = 1/2-1 - (-2) = 11/4 ≠ 1/2 ≠ 1, no
How many solutions does this equation have? 8 + 10z = 3 + 9z
-no solution
-one solution
-infinitely many solutions
find w such that 2u v − 3w = 0. u = (−6, 0, 0, 2), v = (−3, 5, 1, 0)
To find the value of w that satisfies the equation 2u v - 3w = 0, where u = (-6, 0, 0, 2) and v = (-3, 5, 1, 0), we can substitute the given values into the equation and solve for w.
Substituting the given values of u and v into the equation 2u v - 3w = 0, we have:
2(-6, 0, 0, 2)(-3, 5, 1, 0) - 3w = 0.
Expanding the scalar multiplication and performing the dot product, we get:
(-12, 0, 0, 4)(-3, 5, 1, 0) - 3w = 0,
(36 + 0 + 0 + 0) - 3w = 0,
36 - 3w = 0.
Simplifying the equation, we have:
36 = 3w,
w = 12.
Therefore, the value of w that satisfies the equation is 12. By substituting w = 12 into the equation 2u v - 3w = 0, we get:
2(-6, 0, 0, 2)(-3, 5, 1, 0) - 3(12) = 0,
(-12, 0, 0, 4)(-3, 5, 1, 0) - 36 = 0,
36 - 36 = 0,
0 = 0.
Hence, the value of w = 12 makes the equation true, satisfying the given condition.
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pls help i’ll give brainliest
Answer:
The answer is 56.33 in decimal form but in fraction form the answer is 5633/
100
Step-by-step explanation:
6.55 x 8.6
A recipe uses 6 tablespoons of butter for every 8 oz of cheese. the rate is __ tablespoons for every 1 oz. the raze is __ oz for every 1 tablespoon.
1/4 or .75
6 divided by 4 equal 1/4 or .75
Equation in slope intercept form that represents their shown
Answer:
I think the answer would be Y= -2X+5 .
Hope it helps u ^^♥️
From her eye, which stands 1.75 meters above the ground, Myesha measures the angle of elevation to the top of a prominent skyscraper to be 19 degrees
. If she is standing at a horizontal distance of 337 meters from the base of the skyscraper, what is the height of the skyscraper? Round your answer to the nearest hundredth of a meter if necessary.
The height of the skyscraper is approximately 115.25 meters (rounded to the nearest hundredth of a meter).
To find the height of the skyscraper, we can use trigonometry and the information provided about the angle of elevation and the horizontal distance.
Let's denote the height of the skyscraper as h. We are given that Myesha's eye height above the ground is 1.75 meters, and she measures the angle of elevation to be 19 degrees.
In a right triangle formed by Myesha's eye, the top of the skyscraper, and a point on the ground directly below the top of the skyscraper, the angle of elevation (θ) is the angle between the line of sight from Myesha's eye to the top of the skyscraper and the horizontal ground.
The opposite side of the triangle is the height of the skyscraper (h), and the adjacent side is the horizontal distance from Myesha to the base of the skyscraper (337 meters).
Using the trigonometric function tangent (tan), we can set up the following equation:
tan(θ) = h / 337
Since we know the value of the angle of elevation (θ = 19 degrees), we can substitute it into the equation:
tan(19 degrees) = h / 337
Now we can solve for h:
h = tan(19 degrees) * 337
Using a calculator or trigonometric tables, we find that tan(19 degrees) is approximately 0.34202. Substituting this value into the equation:
h = 0.34202 * 337
h ≈ 115.25
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There’s a picture of my question plz help :)
Answer:
1,534 inches squared
Step-by-step explanation:
To find surface area we just solve for the area of all the sides and add those together. A rectangular prism (a box like above) has 6 sides. There are...
2 sides each of the following dimensions:
2(13×26)=
2(338)=676
2(13×11)=
2(143)=286
2(26×11)=
2(286)=572
Add the area of all 6 sides...
676+286+572=1,534
Remember it is squared not cubed.
The design for the palladium window shown includes a semicircular shape at the top. The bottom is formed by squares of equal size. A shade for the window will extend 4 inches beyond the perimeter of the window, shown by the dashed line around the window. Each square in the window has an area of 169 in2. Round your answers to the nearest whole number.
Answer:
[tex](a)\ Area = 3765.32[/tex]
[tex](b)\ Area = 4773[/tex]
Step-by-step explanation:
Given
[tex]A_1 = 169in^2[/tex] --- area of each square
[tex]Shade = 4in[/tex]
See attachment for window
Solving (a): Area of the window
First, we calculate the dimension of each square
Let the length be L;
So:
[tex]L^2 = A_1[/tex]
[tex]L^2 = 169[/tex]
[tex]L = \sqrt{169[/tex]
[tex]L=13[/tex]
The length of two squares make up the radius of the semicircle.
So:
[tex]r = 2 * L[/tex]
[tex]r = 2*13[/tex]
[tex]r = 26[/tex]
The window is made up of a larger square and a semi-circle
Next, calculate the area of the larger square.
16 small squares made up the larger square.
So, the area is:
[tex]A_2 = 16 * 169[/tex]
[tex]A_2 = 2704[/tex]
The area of the semicircle is:
[tex]A_3 = \frac{\pi r^2}{2}[/tex]
[tex]A_3 = \frac{3.14 * 26^2}{2}[/tex]
[tex]A_3 = 1061.32[/tex]
So, the area of the window is:
[tex]Area = A_2 + A_3[/tex]
[tex]Area = 2704 + 1061.32[/tex]
[tex]Area = 3765.32[/tex]
Solving (b): Area of the shade
The shade extends 4 inches beyond the window.
This means that;
The bottom length is now; Initial length + 8
And the height is: Initial height + 4
In (a), the length of each square is calculated as: 13in
4 squares make up the length and the height.
So, the new dimension is:
[tex]Length = 4 * 13 + 8[/tex]
[tex]Length = 60[/tex]
[tex]Height = 4*13 + 4[/tex]
[tex]Height = 56[/tex]
The area is:
[tex]A_1 = 60 * 56 = 3360[/tex]
The radius of the semicircle becomes initial radius + 4
[tex]r = 26 + 4 = 30[/tex]
The area is:
[tex]A_2 = \frac{3.14 * 30^2}{2} = 1413[/tex]
The area of the shade is:
[tex]Area = A_1 + A_2[/tex]
[tex]Area = 3360 + 1413[/tex]
[tex]Area = 4773[/tex]
Decide whether the normal sampling distribution can be used. If it can be used, test the claim about the difference between two population proportions p_1 and p_2 at the given level of significance α using the given sample statistics. Assume the sample statistics are from independent random samples.
Claim: p_1 = p_2, α = 0.05
Sample statistics: x_1 = 32, n_1 = 119 and x_2 = 183, n_2 = 203
C. H_o: p_1 = p_2
H_a:p_1>p_2
D. H_o:p_1
H_a: p_1 = p_2
E. A normal sampling distribution cannot be used, so the claim cannot be tested.
Find the critical values. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
A. The critical values are - z_o = - 1.96 and z_o = 1.96 (Round to two decimal places as needed.)
B. A normal sampling distribution cannot be used, so the claim cannot be tested.
Find the standardized test statistic. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. Z= ______(Round to two decimal places as needed.)
B. A normal sampling distribution cannot be used, so the claim cannot be tested.
The normal sampling distribution can be used
The critical values at α = 0.05 are z₀ = -1.96 and z₀ = 1.96
The standardized test statistic is -11.652
Deciding whether the normal sampling distribution can be usedFrom the question, we have the following parameters that can be used in our computation:
Claim: p₁ = p₂, α = 0.05Sample statistics: x₁ = 32, n₁ = 119 and x₂ = 183, n₂ = 203In the above we can see that the sample sizes are greater than 30 as required by the central limit theorem
This means that the normal sampling distribution can be used and the parameters are
H₀: p₁ = p₂
H₁: p₁ > p₂
Finding the critical valueIn (a), we have
α = 0.05
The critical values at α = 0.05 are z₀ = -1.96 and z₀ = 1.96
Finding the standardized test statistic.Start by calculating the pooled sample proportion using
p = (x₁ + x₂)/(n₁ + n₂)
So, we have
p = (32 + 183)/(119 + 203)
p = 0.67
So, we have
z = (x₁/n₁ - x₂/n₂)/√[p(1 - p)/n₁ + p(1 - p)/n₂)
substitute the known values in the above equation, so, we have the following representation
z = (32/119 - 183/203)/√[0.67(1 - 0.67)/119 + 0.67(1 - 0.67)/203]
Evaluate
z = -11.652
Hence, the standardized test statistic is -11.652
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Find the area of the region that lies inside both the curves.
r = sin 2θ , r = sin θ
The area of the region that lies inside both the curves r = sin 2θ and r = sin θ is π/3 + (1/16)√3.
To find the area of the region that lies inside both the curves, we need to determine the limits of integration for the angle θ.
The curves r = sin 2θ and r = sin θ intersect at certain values of θ. To find these points of intersection, we can set the two equations equal to each other and solve for θ:
sin 2θ = sin θ
Using the trigonometric identity sin 2θ = 2sin θ cos θ, we can rewrite the equation as:
2sin θ cos θ = sin θ
Dividing both sides by sin θ (assuming sin θ ≠ 0), we have:
2cos θ = 1
cos θ = 1/2
θ = π/3, 5π/3
Now we have the limits of integration for θ, which are π/3 and 5π/3.
The formula for calculating the area in polar coordinates is given by:
A = (1/2) ∫[θ₁,θ₂] (r(θ))² dθ
In this case, the function r(θ) is given by r = sin 2θ. Therefore, the area is:
A = (1/2) ∫[π/3,5π/3] (sin 2θ)² dθ
To evaluate this integral, we can simplify the expression (sin 2θ)²:
(sin 2θ)² = sin² 2θ = (1/2)(1 - cos 4θ)
Now, the area formula becomes:
A = (1/2) ∫[π/3,5π/3] (1/2)(1 - cos 4θ) dθ
We can integrate term by term:
A = (1/4) ∫[π/3,5π/3] (1 - cos 4θ) dθ
Integrating, we get:
A = (1/4) [θ - (1/4)sin 4θ] |[π/3,5π/3]
Evaluating the integral limits:
A = (1/4) [(5π/3 - (1/4)sin (20π/3)) - (π/3 - (1/4)sin (4π/3))]
Simplifying the trigonometric terms:
A = (1/4) [(5π/3 + (1/4)sin (2π/3)) - (π/3 + (1/4)sin (4π/3))]
Finally, simplifying further:
A = (1/4) [(5π/3 + (1/4)√3) - (π/3 - (1/4)√3)]
A = (1/4) [(4π/3 + (1/4)√3)]
A = π/3 + (1/16)√3
Therefore, the area of the region that lies inside both the curves r = sin 2θ and r = sin θ is π/3 + (1/16)√3.
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The answers are:
5
10
35
55
please help
Answer:
35.
Step-by-step explanation:
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jus solved it.
help I will give brainiest if you can atleast do three
1.) A=pi(r)^2
2.) V=Bh
3.) 3.1
4.) 20
5.)36
6.) 10
7.)18
Answer:
Step-by-step explanation:
1.) formula of circle =pi times r^2
2.)volume of cylinder =pi times r^2 times h
3.)value of pi rounded = 3.14
4.) diameter of can A =2r=2(10) = 20
diameter of Can A is 20
5.)diameter of can B =2r =2(18) =36
diameter of Can B is 36
6.)radius = 10
7.)radius =18
I did all of them.