Find the most suitable system of coordinates to describe cylindrical shell of height 10 determined by the region between two cylinders with the same center, parallel rulings, and radii of 2 and 6 respectively.
Answers
Answer:
The answer is explained below
Step-by-step explanation:
We have a system that would be a cylindrical shell with a certain length. I will attach an allusive image, they ask us to determine which would be the most suitable system of coordinates:
Most suitable surface is cylindrical annular for this annular 30 disk most suitable coordinate system would be Cylindrical Coordinate System as one at coordinate "z" remains constant and that would be advantageous
Related Questions
The price-earnings ratios of a sample of stocks have a mean value of 13.5 and a standard deviation of 2. If the ratios have a bell-shaped distribution, what can be said about the proportion of ratios that fall between 11.5 and 15.5
Answers
Answer:
[tex]P(11.5<X<15.5)=P(\frac{11.5-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{13.5-\mu}{\sigma})=P(\frac{11.5-13.5}{2}<Z<\frac{15.5-13.5}{2})=P(-1<z<1)[/tex]
And we can find the probability with this difference
[tex]P(-1<z<1)=P(z<1)-P(z<-1)[/tex]
And we can use the normal standard distribution or excel and we got:
[tex]P(-1<z<1)=P(z<1)-P(z<-1)=0.841-0.159=0.682[/tex]
So then we expect a proportion of 0.682 between 11.5 and 13.5
Step-by-step explanation:
Let X the random variable that represent the price earning ratios of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(13.5,2)[/tex]
Where [tex]\mu=13.5[/tex] and [tex]\sigma=2[/tex]
We want to find the following probability
[tex]P(11.5<X<15.5)[/tex]
And we can use the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using this formula we got:
[tex]P(11.5<X<15.5)=P(\frac{11.5-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{13.5-\mu}{\sigma})=P(\frac{11.5-13.5}{2}<Z<\frac{15.5-13.5}{2})=P(-1<z<1)[/tex]
And we can find the probability with this difference
[tex]P(-1<z<1)=P(z<1)-P(z<-1)[/tex]
And we can use the normal standard distribution or excel and we got:
[tex]P(-1<z<1)=P(z<1)-P(z<-1)=0.841-0.159=0.682[/tex]
So then we expect a proportion of 0.682 between 11.5 and 13.5
Abinomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experime
n=10, p=0.4.X=4
P(4)=
(Do not round unul the final answer. Then round to four decimal places as needed.)
Answers
Answer:
The probability of exactly '4' success
P( X=4) = 0.2508
Step-by-step explanation:
Step(i):-
Given sample size 'n' = 10
Given probability of success 'p' = 0.4
q = 1 -p = 1 - 0.4 = 0.6
Step(ii):-
Let 'X' be the successes in binomial distribution
[tex]P( x = r) = n_{C_{r} } p^{r} q^{n-r}[/tex]
The probability of exactly '4' success
[tex]P( x = 4) = 10_{C_{4} } (0.4)^{4} (0.6)^{10-4}[/tex]
we will use factorial notation
[tex]10C_{4} = \frac{10!}{(10-4)!4!} = \frac{10 X 9 X 8 X 7 X6!}{6! 4!} = \frac{10 X 9 X8 X7}{4X 3X 2X1} = 210[/tex]
[tex]P( x = 4) = 210 X 0.0256 X0.0466[/tex]
P( X=4) = 0.2508
conclusion:-
The probability of exactly '4' success
P( X=4) = 0.2508
A video game requires at least 4 points to advance. Each solved puzzle is worth two points. Each solved riddle is worth 1 point. If x is the number of solved puzzles and y is the number of solved riddles, which graph represents the overall equation represented by this scenario (all points may not apply to the scenario)? On a coordinate plane, a solid straight line has a negative slope and goes through (0, 2) and (4, 0). Everything below the line is shaded. On a coordinate plane, a solid straight line has a negative slope and goes through (0, 2) and (4, 0). Everything above the line is shaded. On a coordinate plane, a solid straight line has a negative slope and goes through (0, 4) and (2, 0). Everything to the left of the line is shaded. On a coordinate plane, a solid straight line has a negative slope and goes through (0, 4) and (2, 0). Everything to the right of the line is shaded.
Answers
Answer:
Its D The Last Graph
Step-by-step explanation:
it just is my guy
what is the sum of 4m(m-6) and 8(m-4)?
Answers
Step-by-step explanation:
4m2 - 24m + 8m - 32
4m2 - 16m - 32
Given a normal distribution with (mean) μ= 50 and (standard deviation) σ = 4, what is the probability that:__________.
a) x>43
b) x<42
c) x>57.5
d) 42
e) x<40 or x>55
f) 5% of the values are less than what X value?
g) 60% of the values are between what two X values (symmetrically distributed around the mean)?
h) 85% of the values will be above what X value?
Answers
Answer:
a) P(x > 43) = 0.9599
b) P(x < 42) = 0.0228
c) P(x > 57.5) = 0.03
d) P(x = 42) = 0.
e) P(x<40 or x>55) = 0.1118
f) 43.42
g) Between 46.64 and 53.36.
h) Above 45.852.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 50, \sigma = 4[/tex]
a) x>43
This is 1 subtracted by the pvalue of Z when X = 43. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{43 - 50}{4}[/tex]
[tex]Z = -1.75[/tex]
[tex]Z = -1.75[/tex] has a pvalue of 0.0401
1 - 0.0401 = 0.9599
P(x > 43) = 0.9599
b) x<42
This is the pvalue of Z when X = 42.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{42 - 50}{4}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a pvalue of 0.0228
P(x < 42) = 0.0228
c) x>57.5
This is 1 subtracted by the pvalue of Z when X = 57.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{57.5 - 50}{4}[/tex]
[tex]Z = 1.88[/tex]
[tex]Z = 1.88[/tex] has a pvalue of 0.97
1 - 0.97 = 0.03
P(x > 57.5) = 0.03
d) P(x = 42)
In the normal distribution, the probability of an exact value is 0. So
P(x = 42) = 0.
e) x<40 or x>55
x < 40 is the pvalue of Z when X = 40. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{40 - 50}{4}[/tex]
[tex]Z = -2.5[/tex]
[tex]Z = -2.5[/tex] has a pvalue of 0.0062
x > 55 is 1 subtracted by the pvalue of Z when X = 55. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{55 - 50}{4}[/tex]
[tex]Z = 1.25[/tex]
[tex]Z = 1.25[/tex] has a pvalue of 0.8944
1 - 0.8944 = 0.1056
0.0062 + 0.1056 = 0.1118
P(x<40 or x>55) = 0.1118
f) 5% of the values are less than what X value?
X is the 5th percentile, which is X when Z has a pvalue of 0.05, so X when Z = -1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.645 = \frac{X - 50}{4}[/tex]
[tex]X - 50 = -1.645*4[/tex]
[tex]X = 43.42[/tex]
43.42 is the answer.
g) 60% of the values are between what two X values (symmetrically distributed around the mean)?
Between the 50 - (60/2) = 20th percentile and the 50 + (60/2) = 80th percentile.
20th percentile:
X when Z has a pvalue of 0.2. So X when Z = -0.84.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.84 = \frac{X - 50}{4}[/tex]
[tex]X - 50 = -0.84*4[/tex]
[tex]X = 46.64[/tex]
80th percentile:
X when Z has a pvalue of 0.8. So X when Z = 0.84.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.84 = \frac{X - 50}{4}[/tex]
[tex]X - 50 = 0.84*4[/tex]
[tex]X = 53.36[/tex]
Between 46.64 and 53.36.
h) 85% of the values will be above what X value?
Above the 100 - 85 = 15th percentile, which is X when Z has a pvalue of 0.15. So X when Z = -1.037.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.037 = \frac{X - 50}{4}[/tex]
[tex]X - 50 = -1.037*4[/tex]
[tex]X = 45.852[/tex]
Above 45.852.
A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 1.4 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building?
Answers
Answer:
the length of his shadow on the building is decreasing at the rate of 0.525 m/s
Step-by-step explanation:
From the diagram attached below;
the man is standing at point D with his head at point E
During that time, his shadow on the wall is y = BC
ΔABC and Δ ADE are similar in nature; thus their corresponding sides have equal ratios; i.e
[tex]\dfrac{AD}{AB} = \dfrac{DE}{BC}[/tex]
[tex]\dfrac{8}{12} = \dfrac{2}{y}[/tex]
8y = 24
y = 24/8
y = 3 meters
Let take an integral look at the distance of the man from the building as x, therefore the distance from the spotlight to the man is 12 - x
∴
[tex]\dfrac{12-x}{12}=\dfrac{2}{y}[/tex]
[tex]1- \dfrac{1}{12}x = 2* \dfrac{1}{y}[/tex]
To find the derivatives of both sides ;we have:
[tex]- \dfrac{1}{12}dx = 2* \dfrac{1}{y^2}dy[/tex]
[tex]- \dfrac{1}{12} \dfrac{dx}{dt} = 2* \dfrac{1}{y^2} \dfrac{dy}{dt}[/tex]
During that time ;
[tex]\dfrac{dx}{dt }= 1.4 \ m/s[/tex] and y = 3
So; replacing the value into above ; we have:
[tex]-\dfrac{1}{12}(1.4) = - \dfrac{2}{9} \dfrac{dy}{dt}[/tex]
[tex]\dfrac{dy}{dt} = \dfrac{\dfrac{ 1.4} {12 } }{ \dfrac{2}{9}}[/tex]
[tex]\dfrac{dy}{dt} = {\dfrac{ 1.4} {12 } }*{ \dfrac{9}{2}}[/tex]
[tex]\dfrac{dy}{dt} =0.525 \ m/s[/tex]
Thus; the length of his shadow on the building is decreasing at the rate of 0.525 m/s
Suppose that we want to generate the outcome of the flip of a fair coin, but that all we have at our disposal is a biased coin which lands on heads with some unknown probability p that need not be equal to1/2. Consider the following procedure for accomplishing our task:
1. Flip the coin.
2. Flip the coin again.
3. If both flips land on heads or both land on tails, return to step 1. 4. Let the result of the last flip be the result of the experiment.
(a) Show that the result is equally likely to be either heads or tails.
(b) Could we use a simpler procedure that continues to flip the coin until the last two flips are different and then lets the result be the outcome of the final flip?
Answers
Answer:
Step-by-step explanation:
Given that;
the following procedure for accomplishing our task are:
1. Flip the coin.
2. Flip the coin again.
From here will know that the coin is first flipped twice
3. If both flips land on heads or both land on tails, it implies that we return to step 1 to start again. this makes the flip to be insignificant since both flips land on heads or both land on tails
But if the outcomes of the two flip are different i.e they did not land on both heads or both did not land on tails , then we will consider such an outcome.
Let the probability of head = p
so P(head) = p
the probability of tail be = (1 - p)
This kind of probability follows a conditional distribution and the probability of getting heads is :
[tex]P( \{Tails, Heads\})|\{Tails, Heads,( Heads ,Tails)\})[/tex]
[tex]= \dfrac{P( \{Tails, Heads\}) \cap \{Tails, Heads,( Heads ,Tails)\})}{ {P( \{Tails, Heads,( Heads ,Tails)\}}}[/tex]
[tex]= \dfrac{P( \{Tails, Heads\}) }{ {P( \{Tails, Heads,( Heads ,Tails)\}}}[/tex]
[tex]= \dfrac{P( \{Tails, Heads\}) } { {P( Tails, Heads) +P( Heads ,Tails)}}[/tex]
[tex]=\dfrac{(1-p)*p}{(1-p)*p+p*(1-p)}[/tex]
[tex]=\dfrac{(1-p)*p}{2(1-p)*p}[/tex]
[tex]=\dfrac{1}{2}[/tex]
Thus; the probability of getting heads is [tex]\dfrac{1}{2}[/tex] which typically implies that the coin is fair
(b) Could we use a simpler procedure that continues to flip the coin until the last two flips are different and then lets the result be the outcome of the final flip?
For a fair coin (0<p<1) , it's certain that both heads and tails at the end of the flip.
The procedure that is talked about in (b) illustrates that the procedure gives head if and only if the first flip comes out tail with probability 1 - p.
Likewise , the procedure gives tail if and and only if the first flip comes out head with probability of p.
In essence, NO, procedure (b) does not give a fair coin flip outcome.
Write the expression in simplest form 3(5x) + 8(2x)
Answers
Answer:
31x[tex]solution \\ 3(5x) + 8(2x) \\ = 3 \times 5x + 8 \times 2x \\ = 15x + 16x \\ = 31x[/tex]
hope this helps...
Good luck on your assignment...
The expression [tex]3(5x) + 8(2x)[/tex] in simplest form is 31x.
To simplify the expression [tex]3(5x) + 8(2x)[/tex], we can apply the distributive property:
[tex]3(5x) + 8(2x)[/tex]
[tex]= 15x + 16x[/tex]
Combining like terms, we have:
[tex]15x + 16x = 31x[/tex]
Therefore, the expression [tex]3(5x) + 8(2x)[/tex] simplifies to [tex]31x.[/tex]
To learn more on Expressions click:
https://brainly.com/question/14083225
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(please help!) find x.
Answers
Answer:
x = 6√2
Step-by-step explanation:
It is a 45°45°90° triangle so you can use the ratio.
x : x√2
x = 6√2
Subtract -6 4/9-3 2/9-8 2/9
Answers
Answer:
[tex]-\frac{161}{9}=\\or\\-16\frac{8}{9}[/tex]
Step-by-step explanation:
[tex]-6\frac{4}{9}-3\frac{2}{9}-8\frac{2}{9}=\\\\-\frac{58}{9}-\frac{29}{9}-\frac{74}{9}=\\\\-\frac{161}{9}=\\\\-16\frac{8}{9}[/tex]
Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x4 ln(x) (a) Find the interval on which f is increasing. (Enter your answer using interval notation.) Find the interval on which f is decreasing. (Enter your answer using interval notation.) (b) Find the local minimum and maximum values of f. local minimum value local maximum value (c) Find the inflection point. (x, y) = Find the interval on which f is concave up. (Enter your answer using interval notation.) Find the interval on which f is concave down. (Enter your answer using interval notation.)
Answers
Answer: (a) Interval where f is increasing: (0.78,+∞);
Interval where f is decreasing: (0,0.78);
(b) Local minimum: (0.78, - 0.09)
(c) Inflection point: (0.56,-0.06)
Interval concave up: (0.56,+∞)
Interval concave down: (0,0.56)
Step-by-step explanation:
(a) To determine the interval where function f is increasing or decreasing, first derive the function:
f'(x) = [tex]\frac{d}{dx}[/tex][[tex]x^{4}ln(x)[/tex]]
Using the product rule of derivative, which is: [u(x).v(x)]' = u'(x)v(x) + u(x).v'(x),
you have:
f'(x) = [tex]4x^{3}ln(x) + x_{4}.\frac{1}{x}[/tex]
f'(x) = [tex]4x^{3}ln(x) + x^{3}[/tex]
f'(x) = [tex]x^{3}[4ln(x) + 1][/tex]
Now, find the critical points: f'(x) = 0
[tex]x^{3}[4ln(x) + 1][/tex] = 0
[tex]x^{3} = 0[/tex]
x = 0
and
[tex]4ln(x) + 1 = 0[/tex]
[tex]ln(x) = \frac{-1}{4}[/tex]
x = [tex]e^{\frac{-1}{4} }[/tex]
x = 0.78
To determine the interval where f(x) is positive (increasing) or negative (decreasing), evaluate the function at each interval:
interval x-value f'(x) result
0<x<0.78 0.5 f'(0.5) = -0.22 decreasing
x>0.78 1 f'(1) = 1 increasing
With the table, it can be concluded that in the interval (0,0.78) the function is decreasing while in the interval (0.78, +∞), f is increasing.
Note: As it is a natural logarithm function, there are no negative x-values.
(b) A extremum point (maximum or minimum) is found where f is defined and f' changes signs. In this case:
Between 0 and 0.78, the function decreases and at point and it is defined at point 0.78;After 0.78, it increase (has a change of sign) and f is also defined;Then, x=0.78 is a point of minimum and its y-value is:
f(x) = [tex]x^{4}ln(x)[/tex]
f(0.78) = [tex]0.78^{4}ln(0.78)[/tex]
f(0.78) = - 0.092
The point of minimum is (0.78, - 0.092)
(c) To determine the inflection point (IP), calculate the second derivative of the function and solve for x:
f"(x) = [tex]\frac{d^{2}}{dx^{2}}[/tex] [[tex]x^{3}[4ln(x) + 1][/tex]]
f"(x) = [tex]3x^{2}[4ln(x) + 1] + 4x^{2}[/tex]
f"(x) = [tex]x^{2}[12ln(x) + 7][/tex]
[tex]x^{2}[12ln(x) + 7][/tex] = 0
[tex]x^{2} = 0\\x = 0[/tex]
and
[tex]12ln(x) + 7 = 0\\ln(x) = \frac{-7}{12} \\x = e^{\frac{-7}{12} }\\x = 0.56[/tex]
Substituing x in the function:
f(x) = [tex]x^{4}ln(x)[/tex]
f(0.56) = [tex]0.56^{4} ln(0.56)[/tex]
f(0.56) = - 0.06
The inflection point will be: (0.56, - 0.06)
In a function, the concave is down when f"(x) < 0 and up when f"(x) > 0, adn knowing that the critical points for that derivative are 0 and 0.56:
f"(x) = [tex]x^{2}[12ln(x) + 7][/tex]
f"(0.1) = [tex]0.1^{2}[12ln(0.1)+7][/tex]
f"(0.1) = - 0.21, i.e. Concave is DOWN.
f"(0.7) = [tex]0.7^{2}[12ln(0.7)+7][/tex]
f"(0.7) = + 1.33, i.e. Concave is UP.
what 826,497 in standard form answer
Answers
Answer:8.2 x 10^5
Step-by-step explanation:
It is known that the number of hours a student sleeps per night has a normal distribution. The sleeping time in hours of a random sample of 8 students is given below. See Attached Excel for Data. Compute a 98% confidence interval for the true mean time a student sleeps per night and fill in the blanks appropriately. We have 98 % confidence that the true mean time a student sleeps per night is between and hours. (round to 3 decimal places)
Answers
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is:
It is known that the number of hours a student sleeps per night has a normal distribution. The sleeping time in hours of a random sample of 8 students is given below. 7.4, 6.2, 8.5, 6.3, 5.4, 5.5, 6.3, 8.3 Compute a 98% confidence interval for the true mean time a student sleeps per night and fill in the blanks appropriately. We have 98% confidence that the true mean time a student sleeps per night is between _____ and ____ hours. (Keep 3 decimal places)
Solution:
Mean = (7.4 + 6.2 + 8.5 + 6.3 + 5.4 + 5.5 + 6.3 + 8.3)/8 = 6.7375
Standard deviation = √(summation(x - mean)²/n
Summation(x - mean)² = (7.4 - 6.7375)^2 + (6.2 - 6.7375)^2 + (8.5 - 6.7375)^2 + (6.3 - 6.7375)^2 + (5.4 - 6.7375)^2 + (5.5 - 6.7375)^2 + (6.3 - 6.7375)^2 + (8.3 - 6.7375)^2 = 9.97875
Standard deviation = √(9.97875/8
s = 1.12
Confidence interval is written in the form,
(Sample mean - margin of error, sample mean + margin of error)
The sample mean, x is the point estimate for the population mean.
Margin of error = z × s/√n
Where
sample standard deviation
number of samples
From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score
In order to use the t distribution, we would determine the degree of freedom, df for the sample.
df = n - 1 = 8 - 1 = 7
Since confidence level = 98% = 0.98, α = 1 - CL = 1 - 0.98 = 0.02
α/2 = 0.02/2 = 0.01
the area to the right of z0.01 is 0.01 and the area to the left of z0.01 is 1 - 0.01 = 0.99
Looking at the t distribution table,
z = 2.998
Margin of error = 2.998 × 1.12/√8
= 1.19
the lower limit of this confidence interval is
6.738 - 1.19 = 5.548
the upper limit of this confidence interval is
6.738 + 1.19 = 7.928
We have 98 % confidence that the true mean time a student sleeps per night is between 5.548 hours and 7.928 hours.
Suppose the proportion X of surface area in a randomly selected quadrat that is covered by a certain plant has a standard beta distribution with α = 4 and β = 3.(a) Compute E(X) and V(X). (Round your answers to four decimal places.)E(X) = Correct: Your answer is correct.V(X) = Correct: Your answer is correct.(b) Compute P(X ≤ 0.5). (Round your answer to four decimal places.)
Answers
Answer:
(a) The value of E (X) is 4/7.
The value of V (X) is 3/98.
(b) The value of P (X ≤ 0.5) is 0.3438.
Step-by-step explanation:
The random variable X is defined as the proportion of surface area in a randomly selected quadrant that is covered by a certain plant.
The random variable X follows a standard beta distribution with parameters α = 4 and β = 3.
The probability density function of X is as follows:
[tex]f(x) = \frac{x^{\alpha-1}(1-x)^{\beta-1}}{B(\alpha,\beta)} ; \hspace{.3in}0 \le x \le 1;\ \alpha, \beta > 0[/tex]
Here, B (α, β) is:
[tex]B(\alpha,\beta)=\frac{(\alpha-1)!\cdot\ (\beta-1)!}{((\alpha+\beta)-1)!}[/tex]
[tex]=\frac{(4-1)!\cdot\ (3-1)!}{((4+3)-1)!}\\\\=\frac{6\times 2}{720}\\\\=\frac{1}{60}[/tex]
So, the pdf of X is:
[tex]f(x) = \frac{x^{4-1}(1-x)^{3-1}}{1/60}=60\cdot\ [x^{3}(1-x)^{2}];\ 0\leq x\leq 1[/tex]
(a)
Compute the value of E (X) as follows:
[tex]E (X)=\frac{\alpha }{\alpha +\beta }[/tex]
[tex]=\frac{4}{4+3}\\\\=\frac{4}{7}[/tex]
The value of E (X) is 4/7.
Compute the value of V (X) as follows:
[tex]V (X)=\frac{\alpha\ \cdot\ \beta}{(\alpha+\beta)^{2}\ \cdot\ (\alpha+\beta+1)}[/tex]
[tex]=\frac{4\cdot\ 3}{(4+3)^{2}\cdot\ (4+3+1)}\\\\=\frac{12}{49\times 8}\\\\=\frac{3}{98}[/tex]
The value of V (X) is 3/98.
(b)
Compute the value of P (X ≤ 0.5) as follows:
[tex]P(X\leq 0.50) = \int\limits^{0.50}_{0}{60\cdot\ [x^{3}(1-x)^{2}]} \, dx[/tex]
[tex]=60\int\limits^{0.50}_{0}{[x^{3}(1+x^{2}-2x)]} \, dx \\\\=60\int\limits^{0.50}_{0}{[x^{3}+x^{5}-2x^{4}]} \, dx \\\\=60\times [\dfrac{x^4}{4}+\dfrac{x^6}{6}-\dfrac{2x^5}{5}]\limits^{0.50}_{0}\\\\=60\times [\dfrac{x^4\left(10x^2-24x+15\right)}{60}]\limits^{0.50}_{0}\\\\=[x^4\left(10x^2-24x+15\right)]\limits^{0.50}_{0}\\\\=0.34375\\\\\approx 0.3438[/tex]
Thus, the value of P (X ≤ 0.5) is 0.3438.
The percent defective for parts produced by a manufacturing process is targeted at 4%. The process is monitored daily by taking samples of sizes n = 160 units. Suppose that today’s sample contains 14 defectives. Determine a 88% confidence interval for the proportion defective for the process today. Place your LOWER limit, rounded to 3 decimal places, in the first blank. For example, 0.123 would be a legitimate answer. Place your UPPER limit, rounded to 3 decimal places, in the second blank. For example, 0.345 would be a legitimate entry.
Answers
Answer:
The 88% confidence interval for the proportion of defectives today is (0.053, 0.123)
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 160, \pi = \frac{14}{160} = 0.088[/tex]
88% confidence level
So [tex]\alpha = 0.12[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.12}{2} = 0.94[/tex], so [tex]Z = 1.555[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.088 - 1.555\sqrt{\frac{0.088*0.912}{160}} = 0.053[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.088 + 1.555\sqrt{\frac{0.088*0.912}{160}} = 0.123[/tex]
The 88% confidence interval for the proportion of defectives today is (0.053, 0.123)
if rectangle ABCD was reflected over the y-axis, reflected over x axis, and rotated 180°, where would point A' lie?
Answers
Answer:
Option C (-4,-1) (In Quadrant III)
Step-by-step explanation:
Coordinate = (-4,1)
=> Reflecting over y-axis will make the coordinate (4,1)
=> Reflecting across x-axis will make the coordinate (4,-1)
=> Rotating 180 will make it (-4,-1)
A nationwide survey of seniors by the University of Michigan reveals that almost 18.0% disapprove of daily pot smoking. If 8 seniors are selected at random, what is the probability that at least 2 disapprove of daily pot smoking.
Answers
Answer:
[tex] P(X\geq 2)=1- P(X<2)= 1-[P(X=0) +P(X=1)][/tex]
And using the probability mass function we can find the individual probabilities:
[tex]P(X=0)=(8C0)(0.18)^0 (1-0.18)^{8-0}=0.2044[/tex]
[tex]P(X=1)=(8C1)(0.18)^1 (1-0.18)^{0-1}=0.3590[/tex]
And replacing we got:
[tex] P(X\geq 2)=1 -[0.2044 +0.3590]= 0.4366[/tex]
Then the probability that at least 2 disapprove of daily pot smoking is 0.4366
Step-by-step explanation:
Let X the random variable of interest "number of seniors who disapprove of daily smoking ", on this case we now that:
[tex]X \sim Binom(n=8, p=0.18)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
And we want to find this probability:
[tex] P(X\geq 2)=1- P(X<2)= 1-[P(X=0) +P(X=1)][/tex]
And using the probability mass function we can find the individual probabilities:
[tex]P(X=0)=(8C0)(0.18)^0 (1-0.18)^{8-0}=0.2044[/tex]
[tex]P(X=1)=(8C1)(0.18)^1 (1-0.18)^{0-1}=0.3590[/tex]
And replacing we got:
[tex] P(X\geq 2)=1 -[0.2044 +0.3590]= 0.4366[/tex]
Then the probability that at least 2 disapprove of daily pot smoking is 0.4366
5. Joan sold half of her comic books and then bought 8 more. She now has 14.how many did she
begin with?
Answers
Answer:
Dear ishika
Answer to your query is provided below
She begin with 12 comic books.
Step-by-step explanation:
After reading question , you will get that she sell half of comic books ; that is (12/2) = 6
And
Bought = 8 books
And
now have 14 books
Verify =
14 = 6+8
A sample of 1500 people from a certain industrial community showed that 800 people suffered from a lung disease. A sample of 1000 people from a rural community showed that 300 suffered from the same lung disease. Assume these two proportions give good estimates of population proportions, respectively. Find the probability that the difference of the proportions (industrial - rural) is greater than 0.2 if two samples of size 150 and 100 are drawn from the two populations, respectively.
Answers
Answer:
The probability that the difference of the proportions (industrial - rural) is greater than 0.2 is 0.7054
Step-by-step explanation:
Solution
Given that:
n₁ = 1500
x₁ = 800
p₁ =800/1500 =0.533
q₁ = 1- 0.533 = 0.467
Thus,
n₂ =1000
x₂ = 300
p₂ = 300/1000 = 0.3
q₂ = 1-0.3 =0.7
So,
p₁ - p₂ = 0.533 - 0.3
=0.233
Now,
SE (p₁ - p₂ ) =√0.533 * 0467/150 + 0.3 * 0.7/1000
=0.0613
So,
p ( p₁ - p₂ > 0.2
= p ( Ƶ > 0.2 - 0.233/0.0613
p = ( Ƶ > - 0.54)
= 0.7054
Please help me find Jebel dhanna in UAE map.
Answers
Answer:
The full name of the place is the "Danat Jebel Dhanna". The Jebel Dhanna is currently located in the Abu Dhabi. It is said that it is one of the most best beach in the UAE, they also say that it is the biggest resort, of course, with a bunch of hotels.
hope this helps ;)
best regards,
`FL°°F~` (floof)
What is the slope and y-intercept of the equation on the graph?
A. M=3/2,y-int=-3
B.m=3/2,y-int=3
C.m=2/3,y-int=-3
D.m=2/3,y-int=4
Answers
Answer:
m = 3/2, y intercept = 3
Step-by-step explanation:
The y intercept is where it crosses the y axis. It crosses at 3
The slope is found by using two points on the line
(-2,0) and (0,3)
m= (y2-y1)/(x2-x1)
= (3-0)/(0- -2)
= 3 / +2
=3/2
The y intercept is where it crosses the y axis.
It crosses at 3
slope is found by using 2 points on the line
(-2,0) and (0,3)
m= (y2-y1)/(x2-x1)
= (3-0)/(0- -2)
= 3 / +2
=3/2
A financial advisor is analyzing a family's estate plan. The amount of money that the family has invested in different real estate properties is normally distributed with a mean of $225,000 and a standard deviation of $50,000. Use a calculator to find how much money separates the lowest 80% of the amount invested from the highest 20% in a sampling distribution of 10 of the family's real estate holdings.
Answers
Answer:
The amount of money separating the lowest 80% of the amount invested from the highest 20% in a sampling distribution of 10 of the family's real estate holdings is $238,281.57.
Step-by-step explanation:
Let the random variable X represent the amount of money that the family has invested in different real estate properties.
The random variable X follows a Normal distribution with parameters μ = $225,000 and σ = $50,000.
It is provided that the family has invested in n = 10 different real estate properties.
Then the mean and standard deviation of amount of money that the family has invested in these 10 different real estate properties is:
[tex]\mu_{\bar x}=\mu=\$225,000\\\\\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{50000}{\sqrt{10}}=15811.39[/tex]
Now the lowest 80% of the amount invested can be represented as follows:
[tex]P(\bar X<\bar x)=0.80\\\\\Rightarrow P(Z<z)=0.80[/tex]
The value of z is 0.84.
*Use a z-table.
Compute the value of the mean amount invested as follows:
[tex]\bar x=\mu_{\bar x}+z\cdot \sigma_{\bar x}[/tex]
[tex]=225000+(0.84\times 15811.39)\\\\=225000+13281.5676\\\\=238281.5676\\\\\approx 238281.57[/tex]
Thus, the amount of money separating the lowest 80% of the amount invested from the highest 20% in a sampling distribution of 10 of the family's real estate holdings is $238,281.57.
Luther evaluated 2 to the power of 3 as 9 and wade evaluated 3 to the power of 2 as 9 are both students correct explain why or why not
Answers
Answer:
Luther is wrong
Wade is right
Step-by-step explanation:
Luther's case 2^3 = 2x2x2 = 8
Wade's case 3^3 = 3 x 3 = 9
Answer:
Luther is incorrect, while Wade is correct. (2)(2)(2)=8, not 9. (3)(3)= 9.
Step-by-step explanation:
I put that as my answer and it was counted as right.
In a recent study on world happiness, participants were asked to evaluate their current lives on a scale from 0 to 10, where 0 represents the worst possible life and 10 represents the best possible life. The mean response was 5.6 with a standard deviation of 2.6. (a) What response represents the 85th percentile? (b) What response represents the 62nd percentile? (c) What response represents the first quartile?
Answers
Answer:
a) 8.2962
b) 6.3956
c) 3.845
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 5.6, \sigma = 2.6[/tex]
(a) What response represents the 85th percentile?
This is X when Z has a pvalue of 0.85. So X when Z = 1.037.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.037 = \frac{X - 5.6}{2.6}[/tex]
[tex]X - 5.6 = 2.6*1.037[/tex]
[tex]X = 8.2962[/tex]
(b) What response represents the 62nd percentile?
This is X when Z has a pvalue of 0.62. So X when Z = 0.306.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.306 = \frac{X - 5.6}{2.6}[/tex]
[tex]X - 5.6 = 2.6*0.306[/tex]
[tex]X = 6.3956[/tex]
(c) What response represents the first quartile?
The first quartile is the 100/4 = 25th percentile. So this is X when Z has a pvalue of 0.25, so X when Z = -0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.675 = \frac{X - 5.6}{2.6}[/tex]
[tex]X - 5.6 = 2.6*(-0.675)[/tex]
[tex]X = 3.845[/tex]
You are given an n×n board, where n is an even integer and 2≤n≤30. For how many such boards is it possible to cover the board with T-shaped tiles like the one shown? Each cell of the shape is congruent to one cell on the board.
Answers
Answer:
7
Step-by-step explanation:
The number of cells in a tile is 4. If colored alternately, there are 3 of one color and 1 of the alternate color. To balance the coloring, an even number of tiles is needed. Hence the board dimensions must be multiples of 4.
In the given range, there are 7 such boards:
4×4, 8×8, 12×12, 16×16, 20×20, 24×24, and 28×28
Point P is the center of dilation. Triangle A B C is dilated to create triangle A prime B prime C prime. The length of P A is 2 and the length of P B is 3. The Length of A A prime is 4 and the length of B B prime is 5. Is triangle A'B'C' a dilation of triangle ABC? Explain. Yes, it is an enlargement with a scale factor of 3. Yes, it is an enlargement with a scale factor of Eight-thirds. No, it is not a dilation because the points of the image are not moved away from the center of dilation proportionally. No, it is not a dilation because the sides of the image are proportionally reduced from the pre-image.
Answers
Answer:
C. No, it is not a dilation because the points of the image are not moved away from the center of dilation proportionally.
Step-by-step explanation:
Dilation is the process in which the size i.e dimensions of a given figure is either increased or decreased by a scale factor, without changing the shape of the figure.
Given that: PA = 2, PB = 3, A[tex]A^{I}[/tex] = 4, B[tex]B^{I}[/tex] = 5.
So that: P[tex]A^{I}[/tex] = 6, P[tex]B^{I}[/tex] = 8.
Therefore, triangle A'B'C' is not an exact dilation of triangle ABC. So that the correct option is; No, it is not a dilation because the points of the image are not moved away from the center of dilation proportionally.
Answer:
the answer is c
Step-by-step explanation:
The length of a rectangle is 9 more than the width. The area is 162 square centimeters. Find the length and width of the rectangle.
Answers
Answer:
Length: 18
Width: 9
Step-by-step explanation:
Denote the width as x, hence the length is x+9. As a result, you can create the equation x(x+9) = 162. Solving, you find x = 9.
Tasha wants to take money out of the ATM for a taxi fare. She wants to do a quick estimate to see if taking $120 out of her bank account will overdraw it. She knows she had $325 in the account this morning when she checked her balance. Today she bought lunch for $19, a dress for $76, a pair of shoes for $53, and a necklace for $23. She also saw a movie with a friend for $12. Rounding each of her expenses to the nearest tens place, estimate how much money Tasha has left in her account before she goes to the ATM. Do not include the $ in your answer.
Answers
Answer:145
Step-by-step explanation: $19=20 76=80 53=50 23=20 12=10 total = 180 325-180 =145
The volume of a trianglular prism is 54 cubic units. What is the value of x?
3
5
7
9
Answers
Answer:
X is 3 units.
Step-by-step explanation:
Volume of prism is cross sectional area multiplied by length. So 1/2 ×2× x ×2 into 3x, which is equal to 6x^2. So, 6x^2=54. Therefore, x=3.
Decide whether the data in the table represent a linear function or an
exponential function. Explain how you know.
Answers
Answer:
D. The data represent an exponential function because there is a common ratio of 1/3.
Step-by-step explanation:
To find a common ratio, find out what the first "y" must be multiplied by to get to the next "y."
162 = 54x
162 ÷ 54 = 3
However, the common ratio is not 3 because the y values are decreasing. The common ratio is 1/3 because 162 × 1/3 = 54.
I hope this helps :))
Answer:
D
Step-by-step explanation: