In polar coordinates, the inequality changes to
[tex]x^2+y^2\le4x\implies r^2\le4r\cos\theta\implies r\le4\cos\theta[/tex]
which is a circle of radius 2 and centered at (2, 0). The set D is then
[tex]D=\left\{(r,\theta)\mid0\le r\le4\cos\theta\land0\le\theta\le\pi\right\}[/tex]
The integral is then
[tex]\displaystyle\iint_D\frac{y^2}{x^2+y^2}\,\mathrm dx\,\mathrm dy=\int_0^\pi\int_0^{4\cos\theta}\frac{r^2\sin^2\theta}{r^2}r\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\displaystyle\int_0^\pi\int_0^{4\cos\theta}r\sin^2\theta\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\displaystyle\frac12\int_0^\pi((4\cos\theta)^2-0^2)\sin^2\theta\,\mathrm d\theta[/tex]
[tex]=\displaystyle8\int_0^\pi\cos^2\theta\sin^2\theta\,\mathrm d\theta[/tex]
There are several ways to compute the remaining integral; one would be to invoke the double-angle formula,
[tex]\sin(2\theta)=2\sin\theta\cos\theta[/tex]
so that the integral is
[tex]=\displaystyle8\int_0^\pi\frac{\sin^2(2\theta)}4\,\mathrm d\theta[/tex]
[tex]=\displaystyle2\int_0^\pi\sin^2(2\theta)\,\mathrm d\theta[/tex]
Then invoke another double-angle formula,
[tex]\sin^2\theta=\dfrac{1-\cos(2\theta)}2[/tex]
to change the integral to
[tex]=\displaystyle\int_0^\pi1-\cos(4\theta)\,\mathrm d\theta[/tex]
[tex]=(\pi-\cos(4\pi))-(0-\cos0)=\boxed{\pi}[/tex]
A population of protozoa develops with a constant relative growth rate of 0.7781 per member per day. On day zero the population consists of six members. Find the population size after four days. (Round your answer to the nearest whole number.) P(4)
Answer:
[tex] P(t) = A (1+r)^t [/tex]
Where P represent the population after t days. a the initial amount on this case 6 and r the growth factor rate of 0.7781. so then our model would be given by:
[tex] P(t)= 6(1.7781)^t [/tex]
And replacing t=4 we got:
[tex] P(4) = 6(1.7781)^4 =59.975 \approx 60[/tex]
So then after 4 days we would expect about 60 protzoa
Step-by-step explanation:
For this case we can use the following function to model the population of protzoa:
[tex] P(t) = A (1+r)^t [/tex]
Where P represent the population after t days. a the initial amount on this case 6 and r the growth factor rate of 0.7781. so then our model would be given by:
[tex] P(t)= 6(1.7781)^t [/tex]
And replacing t=4 we got:
[tex] P(4) = 6(1.7781)^4 =59.975 \approx 60[/tex]
So then after 4 days we would expect about 60 protzoa
The following crosstabulation summarizes the data for two categorical variables, x and y. The variable x can take on values low, medium, or high and the variable y can take on values yes or no.
Y
X Yes No Total
Low 20 10 30
Medium 15 35 50
High 20 5 25
Total 55 50 105
1. Compute the row percentage
2. Construct a sketch percentage of frequency bar chat with x on horozontal axis.
Answer:
Step-by-step explanation:
From the given data:
The row percentage can be determined by: taking each box in each row and by dividing it with its total on that line, after that we will multiply it by 100 to get the result of it's equivalent percentage.
Table reconstruct the table from the question ; we have:
y
x Yes No Total
Low 20 10 30
Medium 15 35 50
High 20 5 25
Total 55 50 105
For Low; the total on the row is 30 ;
so for Yes: we have 20/30 × 100 = 66.7
for No ; we have 10/30 × 100 = 33.3
For Medium ; the total on the row is 50 ;
so for Yes: we have 15/50 × 100 = 30
for No ; we have 35/50 × 100 = 70
For High ; the total on the row is 25;
so for Yes: we have 20/25 × 100 = 80
for No ; we have 5/25 × 100 = 20
y
x Yes No Total
Low 66.7 33.3 100
Medium 30 70 100
High 80 20 100
b. The construction of a sketch percentage of the frequency bar chat with x on horizontal axis is shown in the attached file below.
A construction company has to complete a project no later than 4 months from now or there will be significant cost overruns. The manager of the construction company believes that there are four possible values for the random variable X, the number of months from now it will take to complete this project: 2, 2.5, 3, and 3.5. It is currently believed that the probabilities of these four possibilities are .4, .3, .2, and .1, respectively. What is the expected completion time (in months) of this project from now?
Answer:
The expected completion time of this project from now is 2.5 months.
Step-by-step explanation:
To find the expected completion time for the project, we multiply each projection by it's probability.
We have that:
0.4 = 40% probability it takes 2 months to complete the project.
0.3 = 30% probability that it takes 2.5 months to complete the project.
0.2 = 20% probability it takes 3 months to complete the project.
0.1 = 10% probability it takes 3.5 months to complete the project.
What is the expected completion time (in months) of this project from now?
E = 0.4*2 + 0.3*2.5 + 0.2*3 + 0.1*3.5 = 2.5
The expected completion time of this project from now is 2.5 months.
Mario’s Restaurant is planning to tile the floor of their outdoor dining area, represented by the composite figure below. The tile costs $1.50 per square foot. How much should the restaurant plan to spend on tile to complete the job?
Answer:
Cost of tiling the floor of the restaurant = $346.5
Step-by-step explanation:
Since Mario's restaurant is in the shape of a composite figure.
Area of the composite figure = Area of the rectangle + Area of trapezoid
Area of the rectangle = 3 × 9
= 27 square feet
Area of the trapezoid = [tex]\frac{1}{2}(b_{1}+b_{2}).h[/tex]
Here [tex]b_{1}[/tex] and [tex]b_{2}[/tex] are the parallel sides of the trapezoid and 'h' is the distance between these sides.
Area of the trapezoid = [tex]\frac{1}{2}[12+(31-9)]\times 12[/tex]
= 17 × 12
= 204 square feet
Total area of the floor = 27 + 204
= 231 square feet
Cost of the tiles = $1.5 per square feet
Total Cost of tiling the floor of Mario's restaurant will be,
= per square feet cost × Area of the floor
= 1.50 × 231
= $346.5
Answer:
THE ANSWER IS .B 346.50
Step-by-step explanation:
I NEED HELP PLEASE SOMEONE HELP ME
Answer:
2nd option is the correct answer
Step-by-step explanation:
3 times a number decreased by 6 is - 2
Can someone please help me with this I’m stuck and I need to finish but I don’t understand
Answer:
28
Step-by-step explanation:
Because the lines are parallel:
[tex]\dfrac{m}{21}=\dfrac{8}{6} \\\\m=\dfrac{8}{6}\cdot 21=28[/tex]
Hope this helps!
WILL MARK BRAINLIEST PLEASE HELP
Answer:
1) h = -1/2t^2 +10t
2) h = -1/2(t -10)^2 +72
3) domain: [0, 20]; range: [0, 50]
Step-by-step explanation:
1.) I find it easiest to start with the vertex form when the vertex is given. The equation of the presumed parabolic path for Firework 1 is ...
h = a(t -10)^2 +50
To find the value of "a", we must use another point on the graph. (0, 0) works nicely:
0 = a(0 -10)^2 +50
-100a = 50 . . . . . . subtract 100a
a = -1/2 . . . . . . . . . divide by -100
Then the standard-form equation is ...
h = (-1/2)(t^2 -20t +100) +50
h = -1/2t^2 +10t
__
2.) The path of Firework 2 is translated upward by 22 units from that of Firework 1.
h = -1/2(t -10)^2 +72
__
3.) The horizontal extent of the graph for Firework 1 is ...
domain: 0 ≤ t ≤ 20
The vertical extent of the graph for Firework 1 is ...
range: 0 ≤ h ≤ 50
What is the value of X ? A-17 B-26 C-39 D-41
Answer:
D.
Step-by-step explanation:
It's a right triangle so
[tex]x^2=40^2+9^2[/tex]
x = 41
A sample of 899 Americans provides enough evidence to conclude that marketing campaign was effective. Provide a statement that should be put out by the marketing department. A. There is not sufficient evidence to conclude that the mean consumption of popcorn has risen. B. There is sufficient evidence to conclude that the mean consumption of popcorn has risen. C. There is sufficient evidence to conclude that the mean consumption of popcorn has stayed the same. D. There is not sufficient evidence to conclude that the mean consumption of popcorn has stayed the same.
Answer:
The correct answer to the following question will be Option A.
Step-by-step explanation:
Marketing Analyst seems to be responsible for information and evaluation that directs its marketing team and directs its marketing approach by defining the target clients as well as the competitiveness of the product.A survey of 899 American citizens requires appropriate evidence to demonstrate that perhaps the marketing strategy is working even though there was not considerable evidence to suggest that even the total demand for popcorn had increased.Other given choices are not related to the given circumstances. So that option A seems to be the appropriate choice.
Will give Brainliest Talia took the bus from her home to the bank and then walked back to her home along the same route. The round trip took 0.9 hours total. The bus traveled at an average speed of 40 km/h and she walked at an average speed of 5 km/h. The rate of Trip 2 is blank km/h. The time of Trip 1 is blank hours.
Answer:
The rate of trip 2 is 5 km/h
The time of trip 1 is 0.9-x
Step-by-step explanation:
The rate of trip 2 is 5 km/h because it tells you she walked at an avg speed of 5 km/h.
The time of trip 1 is 0.9-x. It's because the time in trip 2 is x, and it says the total is 0.9. So just subtract 0.9-x.
Also I took the test on edge and attached a pic.
The sum of two fractions can always be written as a
Answer: decimal
Step-by-step explanation:
because i did this quiz
Mr.Rice students ran a 40 yard dash in the following times 6.8,7.3,7.1 ,7.0,7.2,7.3,7.0 how many race times are recorded
The number of race times recorded as portrayed by the number of data points is seven(7).
What is the number of race times recorded for the dash?From the task content;
It follows that the distance ran be Mr. Rice students was 40 yards.Additionally, it follows from the task content that the times recorded were; 6.8,7.3,7.1 ,7.0,7.2,7.3 and 7.0.
On this note, the number of race times recorded as portrayed by the number of data points is seven(7).
Read more on data points;
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Here are three number cards.
The numbers are hidden.
?
?
?
The mode of the three numbers is 7.
The highest number is not 7.
The range is 4.
What are the three numbers? Write them in the boxes, from smallest to larges
O
INN
Answer:
7, 7, 11 are the three numbers.
Step-by-step explanation:
Given:
Mode of the three numbers = 7
Range of numbers i.e. difference between the smallest and the largest number is = 4
Value of highest number card [tex]\neq[/tex] 7
As per the definition of Mode:
Mode is the number that occurs the most number of times in the given set of numbers. In other words, mode is the number whose frequency is the highest in the given set of numbers.
Here, we have three numbers and mode is 7 that means 7 occurs at least two times in the three numbers.
Also, we are given that 7 is not highest number, plus 4 is the range that means 7 occurs exactly two times out of three numbers.
So, two numbers are 7 and 7.
7 is not highest and 4 is the range, so third number = 7+4 = 11
So, the numbers on the cards are 7, 7 and 11.
tank contains 20002000 liters (L) of a solution consisting of 112112 kg of salt dissolved in water. Pure water is pumped into the tank at the rate of 1212 L/s, and the mixturelong dash—kept uniform by stirringlong dash—is pumped out at the same rate. How long will it be until only 88 kg of salt remains in the tank?
The time taken in draining salt so that only 88 kg of salt remains in tank will be 35.71 sec.
It is given that a tank contains 2000 liters of a solution consisting 112 kg of salt is dissolved in water. Pure water is then pumped at rate of 12 L/sec.
We have to find out that how long it will take to drain out salt such that only 88kg of salt remains in tank.
What will be the amount of water flow ; if a water flows for 4 hours at constant speed of 120 liter /hour ?
The amount of water flow will be 120 liter / hour × 4 hour or 120 × 4 liter or 480 liters.
As per the question ;
In 2000 liters solution there is 112 kg salt.
The pumping speed of water into tank = 12 L/s
The salt pumping per second will be ;
= ( 12L/s × 112kg salt ) / 2000 L
= 0.672 Kg salt/sec
This means that 0.672 kg per second salt comes out .
It should be found that the amount of salt that must be drained so that only 88 kg of salt remain.
So , the amount of salt drained out will be ; (x kg)
⇒ 112kg salt - x kg salt = 88 kg salt
⇒ x kg salt = 112 - 88
⇒ x kg salt = 24 kg
The time taken until only 88 kg of salt remains in the tank will be ;
= 24 / 0.672
= 35.71 sec
Thus , the time taken in draining salt so that only 88 kg of salt remains in tank will be 35.71 sec.
To learn more about time and rate click here ;
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The web publisher www.exploreiceland.is (Links to an external site.)Links to an external site. provides information on traveling to Iceland. Access to the website is free but revenues are generated by selling ads that are posted on the website. In the following month, the website has committed to displaying ads to 650,000 viewers, i.e., 650,000 impressions. Based on data from previous months the traffic to the website is estimated to be normally distributed with a mean of 850,000 viewers and a standard deviation of 150,000.
How many impressions should the web publisher have taken on, to be able to guarantee a 95% service level?
Answer:
1096750 impressions
Step-by-step explanation:
Given that :
Mean = 850,000
Standard deviation = 150,000
If we assume that X should be the numbers of impressions created;
Then ;
[tex]X \approx N (\mu , \sigma^2)[/tex]
Now ; representing x as the value for the number of impression needed ; Then ;
[tex]P(X>x) = 0.95[/tex]
[tex]P(\dfrac{X- \mu}{\sigma} > \dfrac{x -850000}{150000}) = 0.95[/tex]
[tex]P(Z> \dfrac{ x -850000}{150000}) = 0.95[/tex]
From normal tables:
[tex]P(Z >1.645) = 0.95[/tex]
[tex]\dfrac{x - 850000}{150000} =1.645[/tex]
(x- 850000) = 1.645(150000)
x - 850000 = 246750
x = 246750 + 850000
x = 1096750 impressions
Savings accounts are a reliable way to store money for the future
Answer:
true
Step-by-step explanation:
just took test
Given AB intersects DE at point C. prove: DCB = ECA. What is the missing reason in step 5
Answer: the answer is linear pair
Step-by-step explanation:
Answer:
Linear pair postulate
Step-by-step explanation:
In a completely randomized design involving three treatments, the following information is provided: Treatment 1 Treatment 2 Treatment 3 Sample Size 5 10 5 Sample Mean 4 8 9 The overall mean for all the treatments is a. 7.00 b. 6.67 c. 7.25 d. 4.89
Answer:
c. 7.25
Step-by-step explanation:
Given the following information from an experiment:
[tex]\left\begin{array}{ccc}&$Sample Size&$Sample Mean \\$Treatment 1&5&4\\$Treatment 2&10&8\\$Treatment 3&5&9\end{array}\right[/tex]
Total Sample Size =5+10+5=20
Therefore, the overall mean
[tex]=\dfrac{(5 \times 4)+ (10 \times 8) + (5 \times 9)}{20} \\=\dfrac{145}{20}\\\\=7.25[/tex]
3. Which of the following values is not possible in probability?
A. P(x) = 1
B. x P(x) = 3 C. P(x) = 0.5
D. P(x) = -0.5
Answer:
D . P(x)=-0.5
Step-by-step explanation:
i think please mark my answer as a brainliest answer and follow me.
1. What is the approximate area of a circle with a diameter of 20 inches?
2. What is the volume of a cube with a side length of 3 cm?
3. What is the median of the data set { 35,20, 30,25,20 }?
Answer:
1. 100[tex]\pi[/tex]
2. 27 [tex]cm^{3}[/tex]
3. 30
Step-by-step explanation:
Area = [tex]\pi[/tex][tex]r^{2}[/tex]
= [tex]\pi[/tex] x [tex]10x^{2}[/tex]
= 100[tex]\pi[/tex]
Volume = l x w x h
= 3 x 3 x 3
= 27
The graph of g(x) = ax^2 opens downward and is narrower than the graph of f(x) = x^2. Which of the following could be the value of a?
The value of a should be less than -1.
Equation of parabola,The equation of a parabola is given by the following function,
[tex]y=f(x)=\pm a(x-h)^2+k[/tex]
where,
(h, k) denotes the coordinates of its vertex,
a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.
Given to us,[tex]f(x) = x^2[/tex]
[tex]g(x)=ax^2[/tex]
SolutionFor the parabola,g(x) to be narrower than the parabola f(x) the value of a should be less than 1. also for the parabola to open downward the value of a is needed to be negative.
Hence, the value of a should be less than -1.
Learn more about Equation of parabola:
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There are 390 students at Walker Elementary this year. This is a 30% increase from the previous year. How many students were at Walker Elementary last year?
Answer:
There were 300 students
Step-by-step explanation:
Original * 30 = increase
Add the increase to get the new number
original + increase = 308
original + original*30% = 390
Factor out original number
original ( 1+30%) = 390
Change to decimal form
original ( 1+.30) = 390
original ( 1.30) = 390
Divide by 1.3
original = 390/1.3
=300
Angle 6= (11x+8) and angle 7=(12x-4) what is the measure of angle 4
Answer:
Answer is m∠4=40
Step-by-step explanation:
take note that m∠6 & m∠7 are vertical angles. Vertical angles are equal to each other, therefore m∠6 is equal to m∠7.
m∠6 = m∠7 (vertical angles)
11x + 8 = 12x – 4
12x - 11x = 8 + 4
x = 12
so
m∠6 = 11x + 8
m∠6 = 11(12) + 8
m∠6 = 132 + 8
m∠6 = 140
m∠4 = 180 - m<6
m∠4 = 180 - 140
m∠4 = 40
Answer:
A
Step-by-step explanation: Took test
I NEED HELP PLEASE HELP ME
Answer:
3
Step-by-step explanation:
Solving the inequality
2x-1>=5
2x>=6
x>=3
The graph should have a shaded circle on 3 and a line pointing to values increasing.
g Question 6 1 pts A 3x3 matrix with real entries can have (select ALL that apply) Group of answer choices three eigenvalues, all of them real. three eigenvalues, all of them complex. two real eigenvalues and one complex eigenvalue. one real eigenvalue and two complex eigenvalues. only two eigenvalues, both of them real. only two eigenvalues, both of them complex. only one eigenvalue -- a real one. only one eigenvalue -- a complex one.
Answer:
(A)three eigenvalues, all of them real.
(D)one real eigenvalue and two complex eigenvalues.
(G)only one eigenvalue -- a real one.
Step-by-step explanation:
Given an [tex]n \times n[/tex] matrix, the characteristic polynomial of the matrix is the degree n polynomial in one variable λ:
[tex]p(\lambda) = det(\lambda I- A)[/tex]
If such [tex]n \times n[/tex] matrix A has real entries, its complex eigenvalues will always occur in complex conjugate pairs.
Therefore, for a [tex]3 \times 3[/tex] matrix with real entries, the following are possible:
(A)three eigenvalues, all of them real.
(D)one real eigenvalue and two complex eigenvalues.
(G)only one eigenvalue -- a real one.
A [tex]3 \times 3[/tex] matrix with real entries cannot have the following:
(B)three eigenvalues, all of them complex.
(C)two real eigenvalues and one complex eigenvalue.
(E)only two eigenvalues, both of them real.
(F)only two eigenvalues, both of them complex.
(H)only one eigenvalue -- a complex one.
For a long-distance person-to-person telephone call, a telephone company charges $ 0.72 for the first minute, $ 0.42 for each additional minute, and a $ 1.85 service charge. If the cost of a call is $ 8.03 comma how long did the person talk?
Answer:
13 mins
Step-by-step explanation:
8.03- 1.85= 6.18
-.72=5.46
/.42=13
Please help! I don’t get what I’m supposed to put in those boxes
The volume of any cylinder is
V = pi*r^2*h
where r is the radius and h is the height. We are keeping r = 2 the same the entire time, as the first part of the instructions indicate. In contrast, h is allowed to vary or change based on the values shown in the table.
If h = 1, then,
V = pi*r^2*h
V = pi*2^2*1
V = pi*4
V = 4pi
So you'll write "4pi", without quotes of course, in the V column next to h = 1. This first row shows a height of 1 leads to a volume of 4pi.
-------------
Then if h = 2, we have,
V = pi*r^2*h
V = pi*2^2*2
V = pi*8
V = 8pi ... this is written in the second box
and finally if h = 3, we would say,
V = pi*r^2*h
V = pi*2^2*3
V = pi*12
V = 12pi .... and this is placed in the third box
---------------
The values of V we got were: 4pi, 8pi, 12pi
This is for h = 1,2 and 3 respectively in that order.
The sequence 4,8,12 is linear because we are adding 4 each time. More specifically, it fits the equation y = 4x where x = 1,2,3. Think of y = 4x as y = 4x+0 and that fits the slope intercept form y = mx+b.
A hose fills a hot tub at a rate of 3.84 gallons per minute. How many hours will it take to fill a 305-gallon hot tub?
Answer:
1.56 hours
Step-by-step explanation:
300 gal × 1 min 3.2 gal × 1 hr 60 min = 1.56 hr.
Answer:
i thought the question said a 'HORSE' fills a hot tub...
Step-by-step explanation:
lol dont mind me i just want points :D
(02.04 MC) Choose the equation that represents the line passing through the point (2, - 5) with a slope of −3. y = −3x − 13 y = −3x + 11 y = −3x + 13 y = −3x + 1
Answer:
it is b
Step-by-step explanation:
the answer is b because
I don’t need you to explain just answer.
Answer: The answer is (x-5)^2
