Due to the symmetry of the paraboloid about the z-axis, you can treat this is a surface of revolution. Consider the curve [tex]y=x^2[/tex], with [tex]1\le x\le2[/tex], and revolve it about the y-axis. The area of the resulting surface is then
[tex]\displaystyle2\pi\int_1^2x\sqrt{1+(y')^2}\,\mathrm dx=2\pi\int_1^2x\sqrt{1+4x^2}\,\mathrm dx=\frac{(17^{3/2}-5^{3/2})\pi}6[/tex]
But perhaps you'd like the surface integral treatment. Parameterize the surface by
[tex]\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath+u^2\,\vec k[/tex]
with [tex]1\le u\le2[/tex] and [tex]0\le v\le2\pi[/tex], where the third component follows from
[tex]z=x^2+y^2=(u\cos v)^2+(u\sin v)^2=u^2[/tex]
Take the normal vector to the surface to be
[tex]\dfrac{\partial\vec s}{\partial u}\times\dfrac{\partial\vec s}{\partial u}=-2u^2\cos v\,\vec\imath-2u^2\sin v\,\vec\jmath+u\,\vec k[/tex]
The precise order of the partial derivatives doesn't matter, because we're ultimately interested in the magnitude of the cross product:
[tex]\left\|\dfrac{\partial\vec s}{\partial u}\times\dfrac{\partial\vec s}{\partial v}\right\|=u\sqrt{1+4u^2}[/tex]
Then the area of the surface is
[tex]\displaystyle\int_0^{2\pi}\int_1^2\left\|\dfrac{\partial\vec s}{\partial u}\times\dfrac{\partial\vec s}{\partial v}\right\|\,\mathrm du\,\mathrm dv=\int_0^{2\pi}\int_1^2u\sqrt{1+4u^2}\,\mathrm du\,\mathrm dv[/tex]
which reduces to the integral used in the surface-of-revolution setup.
Based on aâ poll, among adults who regret gettingâ tattoos, 18â% say that they were too young when they got their tattoos. Assume that eight adults who regret getting tattoos are randomlyâ selected, and find the indicated probability. Complete partsâ (a) throughâ (d) below.
a. Find the probability that none of the selected adults say that they were too young to get tattoos.
b. Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos.
c. Find the probability that the number of selected adults saying they were too young is 0 or 1.
d. It we randomly select 9 adults. Is 1 a significantly low number who day that they were too young to get tattoos?
Answer:
a) 20.44% probability that none of the selected adults say that they were too young to get tattoos.
b) 35.90% probability that exactly one of the selected adults says that he or she was too young to get tattoos.
c) 56.34% probability that the number of selected adults saying they were too young is 0 or 1.
d) No
Step-by-step explanation:
For each adult, there are only two possible outcomes. Either they say they were too young when they got their tattoos, or they don't say that. Each adult is independent of each other. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
18% say that they were too young when they got their tattoos.
This means that [tex]p = 0.18[/tex]
Eight adults who regret getting tattoos are randomly selected
This means that [tex]n = 8[/tex]
a. Find the probability that none of the selected adults say that they were too young to get tattoos.
This is P(X = 0).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{8,0}.(0.18)^{0}.(0.82)^{8} = 0.2044[/tex]
20.44% probability that none of the selected adults say that they were too young to get tattoos.
b. Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos.
This is P(X = 1).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{8,1}.(0.18)^{1}.(0.82)^{7} = 0.3590[/tex]
35.90% probability that exactly one of the selected adults says that he or she was too young to get tattoos.
c. Find the probability that the number of selected adults saying they were too young is 0 or 1.
Either a. or b.
20.44 + 35.90 = 56.34
56.34% probability that the number of selected adults saying they were too young is 0 or 1.
d. It we randomly select 9 adults. Is 1 a significantly low number who day that they were too young to get tattoos?
Now [tex]n = 9[/tex]
It is significantly low if it is more than 2.5 standard deviations below the mean.
The mean is [tex]E(X) = np = 9*0.18 = 1.62[/tex]
The standard deviation is [tex]\sqrt{V(X)} = \sqrt{n*p*(1-p)} = \sqrt{9*0.18*0.82} = 1.15[/tex]
1 > (1.62 - 2.5*1.15)
So the answer is no.
A sample of carbon-12 has a mass of 6.00 g. How many atoms of carbon-12 are in the sample?
3.01 x 10^23
6.02 x 10^23
1.20 x 10^24
3.60 x 10^24
Answer:
The answer is 3.01 x 10’23
Step-by-step explanation:
I got the answer to wrong and guessed the first one and it was correct
Select and place the symbol that will make the statement true |-a| |a|
Answer:
|-a|=|a|
Step-by-step explanation:
The lines beside the a's mean that you are trying to find the absolute value of what's inside. The absolute value of something is the distance it is from 0. You can't have a negative distance so anything inside of absolute value line are positive.
Therefor this is how we can solve this.
|-a| __ |a|
a __ a
a=a
The perimeter of the rectangle is 28 units.
A rectangle with perimeter 28 units is shown. The length of the sides is w, and the length of the top and bottom sides are 2 w minus 1.
What is the value of w?
5 units
7 units
14 units
15 units
Answer:
5 units
Step-by-step explanation:
P=2(w)+2(2w-1)
28=2w+4w-2
30=6w
w=5
Answer:
5
Step-by-step explanation:
Solve:
|x-7|<-1.
zero solutions
one solution
infinite solutions
all real numbers
Step-by-step explanation:
In mathematics, the absolute value |x|, is the non-negative result of x without regard to its sign.
An absolute function, can never have a negative result.
By this alone, you can solve the question because the inequality is false, and therefore there are zero solutions.
Please see the attachment of f(x) = |x - 7|.
When you look at the graph, you can easily confirm that there is no value which can result in a negative y- coordinate like -2. In fact, that is the whole purpose of any absolute value or function. The result of an absolute function can never be negative.
You are going to sell your Samsung so you can get the new iPhone. You purchased your Samsung 2 years ago for $200. It's
value decreases at a rate of 2% each month. To the nearest dollar, how much is your Samsung worth now?
Answer:
[tex]\boxed{\ 123 \ dollars\ }[/tex]
Step-by-step explanation:
its value decreases at a rate of 2% each month
in 2 years there are 12*2=24 months
so the Samsung worth [tex]200(0.98)^{24}\\[/tex]
it gives 123 rounded to the nearest dollar
Answer:
$123
Step-by-step explanation:
initial price= $200
value decrease rate= 2% = 0.98 times a month
time = 2 years
current value= $200*0.98²⁴= $123
What is another way to write 2×5 without using the multiplication sign?
Answer:
see below
Step-by-step explanation:
You could write it as 2+2+2+2+2 or 5+5 bc multiplication is like repeated addition.
Answer:
You can use the repeated additional as given below.
Step-by-step explanation:
2+2+2+2+2 or 5+5
Determine whether the geometric series 192 + 48 + 12 + ... converges or diverges, and identify the sum if it exists.
A.) Converges: 768
B.) Diverges
C.) Converges; 64
D.) Converges; 256
Answer:
D.) Converges; 256
Step-by-step explanation:
x0= 192
x1 = 48 = 192/4
x2 = 12 = 192/(4 x 4)
Therefore, this series can be written as:
[tex]x_n = \frac{192}{4^n}[/tex]
Applying limits at infinity:
[tex]\lim_{n \to \infty} x_n= \lim_{n \to \infty} (\frac{192}{4^n}) = \frac{192}{\infty}=0[/tex]
Since the terms of the series tend to zero, we can affirm that the series converges.
The sum of an infinite converging series is:
[tex]S=\frac{x_0}{1-r} \\S=\frac{192}{1-\frac{1}{4} }\\S=256[/tex]
Thus, the answer is D.) Converges; 256
Design and complete a frequency table for Belinda.
Belinda ask 20 people, how many hours of TV did you watch last week?
Here is the results
3,17,4,4,6,11,14,14,1,20,9,8,9,6,12,7,8,13,13,9.
Belinda wants to show these result in a frequency table.
She will use 4 equal groups.
The first group will start with 1 hour and the last group will end with 20 hours.
Answer:
Step-by-step explanation:
Since she will use 4 groups or class intervals, the the class width would be 20/4 = 5 hours
The class groups would be
1 to 5
5 to 10
10 to 15
15 to 20
The class mark for each class is the average of the minimum and maximum value of each class. Therefore, the class marks are
(1 + 5)/2 = 3
(5 + 10)/2 = 7.5
(10 + 15)/2 = 12.5
(15 + 20)/2 = 17.5
The frequency table would be
Class group Frequency
1 - 5 4
5 - 10 8
10 - 15 6
15 - 20 2
The total frequency is 4 + 8 + 6 + 2 = 20
Explain how to find the product of 3/7 X 7/9 . Use complete sentences in your answer.
Answer:
1/3 simplifed.
Step-by-step explanation:
To find the product of 3/7*7/9. We can multiply top and bottom. Top: 3*7=21 Bottom: 7*9=63. Our final answer is just the Top/Bottom= 21/63. We can also simplify this into 1/3 which is our final answer.
Find and of the function = − −( − ).
Answer:
Thats not possible
Step-by-step explanation:
There is no:
numbersvariablesonly negative signsPlease help . I’ll mark you as brainliest if correct !
Answer:
4 ( a+2)
Step-by-step explanation:
The average rate of change is
(f(a) - f(2))/(a-2)
f(a) = 4a^2 -8
f(2) = 4*2^2 -8 = 4*4 -8 = 16-8 = 8
(4a^2 - 8 - 8))/(a-2)
(4a^2 -16) / (a-2)
Factor the numerator
4( a^2 -4) / (a-2)
4( a-2)(a+2) / (a-2)
Cancel
4 ( a+2)
What is the answerrrrrrrrrrrr :(((((((((((
Answer: The answer is choice 3
Step-by-step explanation:
i think the answer is c
Step-by-step explanation:
i don't think u would want a whole explanation
30 points. WILL MARK BRAINLIEST
Which would be a correct first step to solve the following system of equations using the elimination method?
x + 3y = 16
2x + y = -18
A: Add the two equations together
B: Subtract the first equation from the second equation
C: Multiply the first equation by -2
D: Multiply the second equation by 2
Answer:
C: Multiply the first equation by -2
Step-by-step explanation:
-2 * (x + 3y = 16) = -2x-6y=-32
The resulting equation would be -2x-6y=-32
In the next if you add the two equations, you will successfuly eliminate x and can now solve for y.
-2x-6y=-32
2x + y = -18
Answer:
c
Step-by-step explanation:
x+3y=16________________eqn 1
2x+y=-18_______________eqn 2
multiply first equation by - 2
-2(x+3y=16)
-2x-6y= -32______________eqn 3
using elimination method
-2x-6y= -32
+
2x+y= -18
0-5y= -50
-5y= -50
divide both sides by -5
-5y/5= -50/5
y=10
substitute y in eqn 2 to find the value of x
2x+y= -18
2x+(10)= -18
2x+10= -18
2x= -18-10
2x= -28
divide both sides by 2
2x/2= -28/2
x= -14
Graph: y = 3/4 x + 5
Answer: The graph is
The graph is plotted and attached.
What is a Function?A function is a law that relates a dependent and an independent variable.
The function is y = 3/4 x + 5
The slope of the line is (3/4)
and the y intercept is 5.
The graph is plotted and attached with the answer.
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Problem PageQuestion The mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of per day. Find the half-life of this substance (that is, the time it takes for one-half the original amount in a given sample of this substance to decay).
Answer:
8.55 days for a decay rate parameter of 8.1% per day
Step-by-step explanation:
Assuming a decay rate parameter of 8.1% per day
the general equation for radioactive decay is;
N = N₀e^(-λt)
x - decay constant (λ) - rate of decay
t- time
N - amount remaining after t days , since we are calculating the half life, amount of time it takes for the substance to to be half its original value, its N₀/2
N₀ - amount initially present
substituting the values
N₀/2 = N₀e^(-0.081t)
0.5 = e^(-0.081t)
ln (0.5) = -0.081t
-0.693 = -0.081t
t = 0.693 / 0.081 = 8.55
half life of substance is 8.55 days
What is the answer to x>-8
Answer:
Sorry, I cant understand rewrite it again.
Complete the statements with equal to, greater than, or less than. 5 6 × 6 9 is ? 5 6 . 6 × 5 6 is ? 5 6 . 5 6 × 9 9 is ? 5 6 . 5 6 × 8 7 is ? 5 6 . 7 7 × 5 6 is ? 5 6 . 5 6 × 5 6 is ? 5 6 .
Answer:
someone already answered
Step-by-step explanation:
srry
B point is (-5,-4) moves through the translation (x+1 , y-3) what will be the coordinates of B
Answer:
(-4,-7)
Step-by-step explanation:
Adding 1 to the x and subtracting 3 from the y we get
-5+1= -4
And
-4-3= -7
An urn contains 8 black and 6 pink balls. Five balls are randomly drawn from from the urn in succession, with replacement. That is, after each draw, the selected ball is returned to the urn. What is the probabillity that all the 5 balls drawn from the urn are pink? Round your answer to 3 decimal places. (IF necessary, consult a list of formulas)
Answer:
2.143
Step-by-step explanation:
An urn contains 8 black and;
6 pink balls.
5 balls are randomly drawn from the urn in succession, with replacement.
What is the probability that all the 5 balls drawn from the urn are pink?
The probability of drawing a pink ball in the first draw is 6/14The probability of drawing a pink ball in the second draw is 6/14The probability of drawing a pink ball in the third draw is 6/14The probability of drawing a pink ball in the fourth draw is 6/14The probability of drawing a pink ball in the fifth draw is 6/14The probability that all the 5 balls drawn is pink is 5 × 6/14 = 30/14 = 2.143 (rounded off to 3 decimal places)
The probability of drawing 5 pink balls is 0.271
Since the balls are replaced after each draw, the probability of drawing a pink ball each time is always
6/14
=3/7
Since we are drawing 5 balls, the probability of drawing 5 pink balls with replacement is
[tex](3/7)^{5}[/tex]
≈0.2706
Rounding to 3 decimal places, the probability is 0.271
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Consider a manufacturing process with a quality inspection station. In the past, 10% of parts are defective. As soon as one defective part is found, the process is stopped. If 6 parts have been inspected without finding a defective part, what is the probability that at least 9 total parts will be inspected before the process is stopped
Answer:
0.9
Step-by-step explanation:
10% is equal to 0.1
The probability of having defective parts in a pile of parts is 0.1
Before the process is stopped, 1 part has to be defective.
In a pile of 9 parts, the probability that a part is defective 0.1 of 9, which is = 0.9 hence, approximately one (1) part will be defective in a pile of 9 parts and the process will be stopped.
Since there was no defective part among the first 6 parts, P(d) was 0
That is, probability of a defective part was zero.
Please answer this correctly
Answer:
5
Step-by-step explanation:
There are two ways you can solve this. First is to just count all the numbers in the list given that are within the range 15-19. This is an inclusive range meaning the numbers 15 and 19 are a part of it. The second method is to count how many numbers are in the list given and count all the numbers that have already been put on the table. There are 19 total numbers, and 14 have already been counted. If you subtract you are left with 5 numbers that are within the range. So the answer is 5.
Explanation:
One method is to count all of the values that are between 15 and 19. Those values are highlighted in the diagram below. There are 5 values marked.
An alternative method is to note there are 19 values total. The items in the given table add to 5+2+1+2+4 = 14, so there must be 19-14 = 5 items missing to completely fill out the table.
Simplify 1 · 0 - . can someone please help out
Answer:
That would be just 0 because anything multiplied by 0 is 0.
An English teacher needs to pick 10 books to put on her reading list for the next school year, and she needs to plan the order in which they should be read. She has narrowed down her choices to 4 novels, 6 plays, 8 poetry books, and 4 nonfiction books. Step 1 of 2 : If she wants to include no more than 3 poetry books, how many different reading schedules are possible? Express your answer in scientific notation rounding to the hundredths place.
Answer:
the number of possible reading schedules is 1.064301638 × 10¹²
Step-by-step explanation:
Given that :
The English teacher needs to pick 10 books to put on her reading list for the next school year.
If the English teacher picks at most 3 poetry books i.e no more than 3 poetry books from 8 books. and other books are picked from (6+4+4 ) = 14 books
Thus; the number of ways to pick the books are :
[tex]\left[\begin{array}{c}8\\0\\ \end{array}\right] \ \left[\begin{array}{c}14\\10\\ \end{array}\right]+ \left[\begin{array}{c}8\\1\\ \end{array}\right] \left[\begin{array}{c}14\\9\\ \end{array}\right] + \left[\begin{array}{c}8\\2\\ \end{array}\right] \left[\begin{array}{c}14\\8\\ \end{array}\right] + \left[\begin{array}{c}8\\3\\ \end{array}\right] \left[\begin{array}{c}14\\7 \\ \end{array}\right][/tex]
[tex]= [ \dfrac{8!}{0!(8-0)!}* \dfrac{14!}{10!(14-10!)} ] + [ \dfrac{8!}{1!(8-1)!}* \dfrac{14!}{9!(14-9)!}]+ [ \dfrac{8!}{2!(8-2)!}* \dfrac{14!}{8!(14-8)!}] + [ \dfrac{8!}{3!(8-3)!}* \dfrac{14!}{7!(14-7)!}][/tex]
[tex]= [ 1*1001]+[8*2002]+[28*3003]+[56*3432][/tex]
[tex]\mathbf{= 293293}[/tex]
However, to determine how many reading schedules that are possible we use the relation:
Number of ways to pick a book × [tex]^{10}P_{10}[/tex]
[tex]= 293293* \dfrac{10!}{(10-10)!}[/tex]
= 293293 × 10!
= 1.064301638 × 10¹²
Thus , the number of possible reading schedules is 1.064301638 × 10¹²
A textile manufacturer has historically found an average of 0.1 flaws per square meter of cloth. Let X be the number of flaws in a bolt of 2000 square meters of cloth. How is X distributed
Answer:
Poisson distribution
Step-by-step explanation:
Given that :
There is an average of 0.1 flaws per square meter of cloth
So X = the number of flaws in a bolt of 2000 square meters of cloth.
The objective is to deduce how is X distributed.
Well, we can say X undergoes Poisson distribution.
Because, the flaw can be randomly positioned on the cloth and also dictate how many times the event is likely to occur within a specified period of time.
Most time Poisson distribution is majorly used for independent events.
An independent is an event which contains two types of events occuring at a time say event [tex]E_1[/tex] and event [tex]E_2[/tex] and the event [tex]E_1[/tex] does not in any way affects the occurrence of the event [tex]E_2[/tex] .
If z=32 and z/2+37=x what is x
Answer:
53
Step-by-step explanation:
Plugging in 32 for z, you get:
(32)/2+37=x
16+37=x
x=53
Hope this helps!
The solution of the linear equation z/2 + 37 = x at x at z = 32 will be 53.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given below.
z/2 + 37 = x
Then the solution of the linear equation z/2 + 37 = x at z = 32. Then the equation will be
x = 32/2 + 37
x = 16 + 37
x = 53
Thus, the solution of the linear equation z/2 + 37 = x at z = 32 will be 53.
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URGERNT!!!PLS AT LEAST TAKE A LOOK!!! SHARE YO SMARTNESSS!! AND BLESS YOUR GRADES!
Which sign explains the relationship between m∠1 and m∠2 in the diagram?
A) not equal to
B) >
C) <
D) =
Answer:
Dear Laura Ramirez
Answer to your query is provided below
Option D is correct.
Reason - Because of Hinge and Converse of Hinge theorem
Let x represent the number. Use the given conditions to write an equation. Solve the equation and find the number.
The product of 8 and a number is 96. Find the number.
Write an equation for the given conditions.
Answer:
12
Step-by-step explanation:
8x=96
x=96/8
x=12
Answer:
12
Step-by-step explanation:
8x=96
96/8
x=12
so the the product of 8and 12=96
What is the measure of XYZ?
please help me out
Answer:
The answer is C.
Step-by-step explanation:
You have to divide it by 2 :
∠XYZ = 148° ÷ 2
= 74°
solve 5(x+4)<75 sdsdsd
Answer:
x < 11
Step-by-step explanation:
[tex]5(x+4)<75 \\ open \: the \: bracket \: using \: 5 \\ 5x + 20 < 75 \\ subtract \: - 20 \: from \: both \: sides \: [/tex]
[tex]5x + 20 - 20 < 75 - 20 \\ 5x < 55 \\ divide \: both \: sides \: of \: the \: equation \: \\ by \: 5[/tex]
[tex] \frac{5x}{5} < \frac{55}{5} \\ x < 11[/tex]
The required solution of inequality is,
⇒ x < 11
We have to simplify the expression,
⇒ 5 (x + 4) < 75
We can simplify it by definition of inequality as,
⇒ 5 (x + 4) < 75
⇒ 5x + 20 < 75
Subtract 20 both side,
⇒ 5x + 20 - 20 < 75 - 20
⇒ 5x < 55
⇒ 5x - 55 < 0
⇒ 5 (x - 11) < 0
⇒ x - 11 < 0
⇒ x < 11
Therefore, The required solution of inequality is,
⇒ x < 11
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