a.) 0.5367 feet
b.) 0.5223 feet'
Given the rate at which an eucalyptus tree will grow modelled by the equation 0.5+6/(t+4)³ feet per year, where t is the time (in years).
The amount of growth can be gotten by integrating the given rate equation as shown:
[tex]\int\limits {0.5} \, + \frac{6}{(t+4)^{3} } dt[/tex]
[tex]=\int\limits {0.5} \,dt + \int\limits\frac{6}{(t+4)^{3} } dx[/tex]
[tex]=0.5t+\int\limits6u^{-3} du \, \,where \,u=t +4 \, and \, du=dt[/tex]
[tex]=0.5t+6*\frac{u^{-3} }{-2} + C[/tex]
[tex]=0.5t-3u^{-2}+C[/tex]
[tex]=0.5t-3(t+4)^{-2} +C[/tex]
a) The number of feet that the tree will grow in the second year can be gotten by taking the limit of the integral from t =1 to t = 2
[tex]\int\limits^2_1 {0.5} \,dt + \int\limits\frac{6}{(t+4)^{3} } dx \, =[0.5t-3(t+4)^{-2} ][/tex]
[tex]=[0.5(2)-3(2+4)^{-2} ]-[0.5-3(5)^{-2} ][/tex]
[tex]=\frac{11}{12}-\frac{1}{2}-\frac{3}{25}[/tex]
[tex]=0.9167-0.5+0.12[/tex]
[tex]=0.5367[/tex]
b) The number of feet that the tree will grow in the third year can be gotten by taking the limit of the integral from t =2 to t = 3
[tex]\int\limits^3_2 {0.5} \,dt + \int\limits\frac{6}{(t+4)^{3} } dx \,[/tex]
[tex]=[0.5t-3(t+4)^{-2} ][/tex]
[tex]=[1.5-\frac{3}{49} ]-[1-\frac{1}{12} ][/tex]
=1.439-0.9167
=0.5223 feet
To learn more about integration follow link : https://brainly.com/question/16789471
#SPJ4
If the simple interest on $2,000 for 7 years is $1,120, then what is the interest rate?
The rate is %.
Answer:
Rate= I*100/P*T
R= 1120 * 100/2000*7
R= 112000/14000
R= 8%
all prime number greater than 2 are odd?
Answer:
Prime numbers are odd that are greater than 2. Prime numbers are numbers that are not divisible by anything. EXAMPLE: 33 is not prime because if you take 3 times 11 then you get 33.
Step-by-step explanation:
write two monomials with a GCF of 7x^3y, one of which has a degree of 5
The monomials with a GCF of 7x³y with degree 5 are 7x⁴y and 14x³y².
What is the highest common factor?The Highest Common Factor (HCF) of two numbers is the highest possible number that is divisible by both numbers.
In other words, the highest common factor is the common factor between the two numbers but it should be the highest among all common factors.
As per the given GCF as 7x³y,
The GCF of 14 and 7 is 7.
The GCF of x⁴y and x³y² will be x³y.
Thus,
GCF of 7x⁴y and 14x³y² = 7x³y
So monomials are 7x⁴y and 14x³y².
Hence "The monomials are 7x⁴y and 14x³y²".
To learn more about the highest common factor,
https://brainly.com/question/128394
#SPJ1
use the reflection method to find a green's function that solves the problem on a semicircular region-AG(x, xo)= მ (x-xo) G(x, xo)=0 მ/მy G(x, xo) = 0in Ω = {x=(x, y): x^2+y^2 <1, y>0}, on T1 = {x=(x, y): x^2+y^2=1, y>0}, on T2 = {x=(x, 0): -1< x <1},
The Green's function that solves the problem on a semicircular region is given by G(x, xo) = მ (x-xo)(cos(θ)sin(θ)).
What is Green's function?
Green's function is an important mathematical tool used to solve differential equations. It is defined as a solution to a homogeneous linear differential equation with a source, or delta, function as its input. Green's functions are also known as impulse response functions and can be used to describe the response of a system to an arbitrary input. Green's functions provide a way to solve differential equations without having to solve the entire equation all at once. They are particularly useful for solving equations with boundary conditions that are difficult to solve without the use of Green's functions. Green's functions can also be used to solve integral equations and provide a powerful tool for solving many physical problems.
The reflection method for finding a Green's function for a problem on a semicircular region can be used as follows. First, we solve the problem on the half-plane by finding a Green's function G(x, xo) that satisfies the boundary conditions given. Then, we reflect the solution across the boundary of the semicircle, namely T1 and T2, to obtain the Green's function on the entire semicircle.
The Green's function on the half-plane is given by G(x, xo) = მ (x-xo). Using this solution, we can reflect it across the boundary of the semicircle. For T1, the reflected solution is given by G(x, xo) = მ (x-xo)cos(θ), where θ is the angle between the normal vector to T1 and the vector from xo to x. For T2, the reflected solution is given by G(x, xo) = მ (x-xo)sin(θ), where θ is the angle between the normal vector to T2 and the vector from xo to x.
Therefore, the Green's function that solves the problem on a semicircular region is given by G(x, xo) = მ (x-xo)(cos(θ)sin(θ)).
To learn more about Green's function
https://brainly.com/question/17890374
#SPJ4
Can anyone pls help me find the answer to this problem. I will give brainliest
Answer:
[tex]\log_{10}\sqrt{a} -\dfrac{3}{4}=\dfrac{1}{2}\log_{10}a-\dfrac{3}{4}[/tex]
Step-by-step explanation:
Given:
[tex]x=\dfrac{\sqrt{10a\sqrt{0.1}}}{10}[/tex]
Therefore:
[tex]\implies \log_{10}x=\log_{10}\left(\dfrac{\sqrt{10a\sqrt{0.1}}}{10} \right)[/tex]
[tex]\textsf{Apply the log quotient law}: \quad \log_a \left(\dfrac{x}{y}\right)=\log_ax - \log_ay[/tex]
[tex]\implies \log_{10}\sqrt{10a\sqrt{0.1}}-\log_{10}10[/tex]
[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]
[tex]\implies \log_{10}\sqrt{10a\sqrt{0.1}}-1[/tex]
[tex]\textsf{Apply radical rule: $\sqrt{ab}=\sqrt{a}\sqrt{b}$, \quad assuming $a \geq 0,\;b\geq 0$}[/tex]
[tex]\implies \log_{10}\left(\sqrt{10}\sqrt{a}\sqrt{\sqrt{0.1}}}\right)-1[/tex]
[tex]\textsf{Apply the log product law}: \quad \log_axy=\log_ax + \log_ay[/tex]
[tex]\implies \log_{10}\sqrt{10} + \log_{10}\sqrt{a} + \log_{10}\sqrt{\sqrt{0.1}}}\right)-1[/tex]
Rewrite the radicals:
[tex]\implies \log_{10} \left(10\right)^{\frac{1}{2}} + \log_{10}\sqrt{a} + \log_{10}\left(0.1\right)^{\frac{1}{4}\right)-1[/tex]
[tex]\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax[/tex]
[tex]\implies \dfrac{1}{2}\log_{10} 10 + \log_{10}\sqrt{a} + \dfrac{1}{4}\log_{10}0.1-1[/tex]
[tex]\textsf{Apply log laws}: \quad \log_aa=1 \quad \textsf{and} \quad \log_a\dfrac{1}{a}=-1[/tex]
[tex]\implies \dfrac{1}{2}(1) + \log_{10}\sqrt{a} + \dfrac{1}{4}(-1)-1[/tex]
[tex]\implies \dfrac{1}{2}+ \log_{10}\sqrt{a} -\dfrac{1}{4}-1[/tex]
[tex]\implies \log_{10}\sqrt{a} -\dfrac{3}{4}[/tex]
If you want to simplify further:
[tex]\implies \log_{10}\left(a\right)^{\frac{1}{2}} -\dfrac{3}{4}[/tex]
[tex]\implies \dfrac{1}{2}\log_{10}a-\dfrac{3}{4}[/tex]
Answer:
56
Step-by-step explanation: 10a+10 0.1 -=
A rectangle has length that is 4 inches greater than twice its width. The perimeter of the rectangle is 26 inches. What is the area?
Let X be a random variable representing the number of rolls of a fair die until we see the first 6. Next, choose with replacement a sample of size X from an urn with 5 red and 4 green balls. Let Y be the number of green balls in the sample. Find Var(Y).
As per the binomial distribution, the value of var(Y) is 0.00008
What is meant by binomial distribution?
In math, the Binomial distribution counts the number of successes in n trials, where sampling is done with replacement or the probability of success is constant from trial to trial
Here we have given that, X be a random variable representing the number of rolls of a fair die until we see the first 6. Next, choose with replacement a sample of size X from an urn with 5 red and 4 green balls. Let Y be the number of green balls in the sample.
And we need to find the value of var(Y).
Here we know that the value of n = 6 and the value of x is 4 and the probability is 0.05.
Then as per the binomial distribution formula, it can be calculated as,
By using a calculator, you can enter trials=6, p=0.05, and X=4 into a binomial probability distribution function (PDF). If doing this by hand, apply the binomial probability formula:
=> [6!/4!(6-4)!] x 0.05⁴ x (1- 0.05)⁶⁻⁴
=> 0.00008
To know more about Binomial distribution here.
https://brainly.com/question/14565246
#SPJ4
help me find the slope
Answer: Rise over Run
Step-by-step explanation: Take the change in the x coordinates, and divide by the change in y coordinates.
For example, to find slope when given 2 coordinates:
(2,5) (5, 10)
The change in the x coordinates is 3, because from 2-->5 it moves 3 places to the right. (run)
The change in the y coordinates is 5, because from 5-->10 it moves 5 places upwards. (rise)
Use rise/run.
Rise= 5 (change in y coordinate)
Run = 3 (change in x coordinate)
5/3 is the slope.
On questions like #6, the slope is -3. That is because the equation for slope is y=mx+b.
m is the coefficient of the x, so -3 is the slope.
Likewise, the slope of #2 is 7. The slope of #10 is 3/4.
Use wage data (Data is posted on blackboard) to estimate the following model and answer the questions: Wage= Bo+ Bi educ+ B2 exper+B3 gender +B4 race+Bs gender*exper+E Gender=1 for male and gender=0 for female Race=1 for white and race=0 for non-white 1- Interpret all the coefficients. 2- Is there a significant wage difference between white and non-white? at a=0.05 3- Test for global usefulness of the model at a=0.05. 4- Test if the experience is a significant determinant of wage at a=0.10.
A unit increase in gender will result in decrement of -52.73 in wage provided holding all other parameter constant.
What is parameter?
A parameter is a piece of information that an equation passes on. In terms of statistics, it means something different. In contrast to statistics, which only provide information about a small portion of the population, this value provides information about the entire population.
A parameter is constant because it was determined by surveying everyone (or everything). The average age of the students in your class, for instance, might be of interest to you. Maybe after asking everyone, you discovered that the average age was 25. Given that you polled the entire class, that qualifies as a parameter. Let's say you were curious about the median age of your grade or year.
Learn more about parameter here
brainly.com/question/13794992
#SPJ4
Your goal here is to find the least squares line y(x) = mx + b for the following data: (-2, 1), (2, 1), (-1,-1), (0, -2), (2,-2), and (-2, 1) Feel free to use a calculator! The normal equation for determining the approximating parameters ħ and în are: Then the least squares line is: y(x) = = number + number
The least squares line , y = mx + b form from given data is y = ( -32/100 )x + ( -39/100).
We have an equation of line is
y(x) = mx + b --(1)
given data, (-2, 1), (2, 1),(-1,-1), (0,-2), (2,-2) and (-2, 1)
plugging each point on above equation we get, 1 = -2m + b ; 1 = 2m + b ; -1 = -m + b ; -2 = 0m + b ;
-2 = 2m +b ; 1 = -2m + b
The above equations can be written in matrix form as,
[ -2 1 ; 2 1 ; -1 1 ; 0 1 ; 2 1 ; -2 1] [ m ; b]
= [ 1 ; 1 ; -1 ; -2 ; -2 ; 1]
AX = B
X = (Aᵀ A)⁻¹ AᵀB where Aᵀ is transpose of matrix A and (Aᵀ A)⁻¹ is inverse of (Aᵀ A).
AᵀA = [ -2 2 -1 0 2 -2 ; 1 1 1 1 1] [ -2 1 ; 2 1 ; -1 1 ; 0 1 ; 2 1 ; -2 1] = [ 17 -1 ; -1 6 ]
so, X = [ 17 -1 ; -1 6 ] ^-1 [ -2 2 -1 0 2 -2 ; 1 1 1 1 1][ 1 ; 1 ; -1 ; -2 ; -2 ; 1]
let [ 17 -1 ; -1 6 ] = P
[ 17 -1 ; -1 6 ]⁻¹ = adj.P/det P
det P = 17×6 - 1 = 101
P⁻¹ = 1/101 [ 6 1 ; 1 17 ]
Now, X = 1/101 [ 6 1 ; 1 17 ] [ -2 2 -1 0 2 -2 ; 1 1 1 1 1][ 1 ; 1 ; -1 ; -2 ; -2 ; 1]
=> X = 1/101[ 6 1 ; 1 17 ] [ -5 ; -2 ]
=> X = 1/101 [ -32 ; -39] = [ -32/100 ; -39/100 ]
=> [ m ; b ] = [ -32/100 ; -39/100 ]
=> m = -32/100 , b = -39/100
then, y = mx + b
=> y = ( -32/100 )x + ( -39/100)
Hence, the required equation is
y = ( -32/100 )x + ( -39/100).
To learn more about least squares line , refer :
https://brainly.com/question/24848242
#SPJ4
Question 1 A corporation has the following account balances: Common Stock, $1 par value, $80000; Paid-in Capital in Excess of Par Value, $2700000. Based on this information, the a. legal capital is $2780000 b. average price per share issued is $3.48 c. number of shares outstanding is 2780000. d. number of shares issued is 80000
The correct option is D , as the number of shares issued is 80000.
What is stock ?
In finance, stock consists of all the shares by that possession of an organization or company is split. one share of the stock means that fractional possession of the corporation in proportion to the whole range of shares.
Main body:
as per the information given in the question , Common Stock, $1 par value, $80000 which means the number of shares issued is 80000.
hence ,correct option is D as the number of shares issued is 80000.
To know more about arithmetic , visit:
https://brainly.com/question/24662212
#SPJ1
It takes Christina 2 minutes to read one page of her 250 page book. Which of the following represents the appropriate domain and range for a function relating the total time she has spent reading the book, x, and the number of pages she has read, y?
Answer:
Domain: 0<=x<=500
Range: 0<=y<=250
Step-by-step explanation:
I'm not sure if this is what you asked for. She spend 2 minutes reading 1 page, there are 250 pages, therefore: 250*2=500
the range is simply the total pages
Hope this help!
16.13- cerebral tumors and cell phone use. in a case-controlled study on cerebral tumors and cell phone use, tumors occurred more frequently on the same side of the head where cellular telephones had been used in 26 of 41 cases. test the hypothesis that there is an equal distribution of contralaterial and ipsilateral tumors in the population. use a two-sided alternative.
Null Hypothesis: H0: There is an equal distribution of contralateral and ipsilateral tumors in the population.Ha: There is not an equal distribution of contralateral and ipsilateral tumors in the population.
1) Calculate the observed value:
The observed value is 26 out of 41 cases.
2) Calculate the expected value:
The expected value is 20.5 out of 41 cases.
3) Calculate the test statistic:
The test statistic is (26-20.5)/sqrt(20.5) = 2.44
4) State the critical value:
The critical value for a two-sided test with a significance level of 0.05 is 1.96.
5) The test statistic (2.44) is greater than the critical value (1.96), so we reject the null hypothesis and conclude that there is not an equal distribution of contralateral and ipsilateral tumors in the population.
Learn more about null hypothesis here
https://brainly.com/question/28920252
#SPJ4
Let X denote the random variable that gives the sum of the faces that fall uppermost when two fair dice are rolled. Find P(X = 4). (Round your answer to two decimal places.)
The likelihood or the probability is 121, or 8.33%.
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
The likelihood that a population parameter will be less than a given value when the null hypothesis is true is expressed as the p-value, also known as a probability value or a measure of significance, for a particular statistical model.
We must make a table for easier comprehension in order to determine the P(x=4);
Refer to the attachment for table:
There are three different ways that P(x=4) can occur based on the table. Out of 36 possible results (6 x 6 = 36), they are (1,3), (2,2), and (3,1). As a result, the chance of the event is 363; it is then reduced to 121, or 8.33%.
To learn more about the probability from the given link
https://brainly.com/question/24756209
#SPJ1
The water tank at the institution is
full. A water truck begin to full the tank with
water at a rate of 8 litres per minute. After 15 minutes the tank was 5/2 full. Calculate
the number of litres of water that the tank can hold
The number of litres of water the tank can hold is 48 litres
What is Volume?Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.
Volume can be measured in cubic units, litres and gallons.
If the rate of pump is 8minutes per minute, therefore in 15 minutes, 15×8 = 120 litres is in the tank.
120 litres is 5/2 full
the volume of the tank will be 120×2/5
= 240/5
= 48litres
Therefore the volume of the tank is 48litres
learn more about volume from
https://brainly.com/question/1972490
#SPJ1
Given inputs A, B, C, D, E, design a CMOS circuit to implement the logic function: Y(not) = A(B+C) + D + E
Given inputs A, B, C, D, E, design a CMOS circuit to implement the logic function: Y(not) = A(B+C) + D + E has 5-c-mos, 5-pmos total 10 mos transistors
this can be realize by takeing three c-mos in parallel which gives ABC ,two c-mos are series which is in serires with
another c-mos whic gives D(A+B), now connect ABC and D(A+B) in series
the out put will be (ABC + D(A+B) )'
so we require total 6-mos and 6-pmos total 12mos transistors
F = AC + BD
pull down
this can be realize by takeing two c-mos in series which gives AB ,two cmos are in series
which whic gives BD, now connect AC and BD in parallel
pull up
this can be realize by takeing two c-mos in parallel which gives Ac ,two c-mos are in parallel
which whic gives BD, now connect AC and BD in series
the output is (AC+BD)'
to avoid the complement we have to connect the output to c-mos inverter then we get AC+BD
so we require 5-nmos, 5-pmos total 10 mos transistors
learn more about of circuit here
https://brainly.com/question/13128650
#SPJ4
There are 48 blue birds in a tree. There are 32 red burds in the tree. How many more bluebirds are there in the tree than red
Answer:
16 more blue birds
Step-by-step explanation:
If the total number of blue birds is 48
The total number of red birds is 32
then through simple subtraction we get to know that 16 more blue birds are present in the tree than the red birds
Extra Blue birds = 48-32
= 16
24. The average price of a new car is a function of the year it was purchased. In 1994.
the average price of a new car was $16.930. In 2002, the average price was
$19.126. Find the rate of change of the average price of a new car. Include units
in your answer.
please help me i’m struggling
The rate of change of the average price of the new car is $274.50 per year.
What is the rate of change?The rate of change of the average price of the new car is a function of the change in average price over the years and the change in the number of years.
Rate of change = change in the average price / change in the number of years
Rate of change = (price in 2002 - price in 1994) / difference in the number of years
Rate of change = (19,126 - 16,930) / (2002 - 1994)
Rate of change = 2196 / 8
Rate of change = $274.50
To learn more about prices, please check: https://brainly.com/question/22789842
#SPJ1
Consider the point of intersection where the vertical line X=2 meets the line y=7x+9
The point of intersection (x,y) is = (2,23)
Replace every x with 2 and simplify
y = 7x+9
y = 7*2 + 9
y = 14 + 9
y = 23 is the y coordinate
The vertical line x = 2 meets the diagonal line y = 7x+9 at the location (x,y) = (2,23)
What are Coordinates ?
The position of a point or points on a graph or grid is shown by its coordinates. The origin is defined as the point (0, 0). The coordinates are two units to the right in the x-direction and four units up in the y-direction according to the point (2, 4).
To know more about intersection point visit:
https://brainly.com/question/13373561
#SPJ1
PLEASE HELP
find the sum of ( 2.25 x 10^19) and ( 6.7 x 10^17) Write the answer using proper scientific notation.
A) 231.7 X 10^15
B) 2.317 X10^19
C) 231.7 X 10^17
D) 2.317 X 10^15
Answer:
Step-by-step explanation:
The sum of (2.25 x 10^19) and (6.7 x 10^17) is (2.317 x 10^19).
To find the sum of these two numbers, we first need to line up the decimal points and add the numbers as we would with any other addition problem:
2.25 x 10^19
+ 6.7 x 10^17
Then, we can carry the 1 and add the numbers:
2.25 x 10^19
6.7 x 10^17
2.317 x 10^19
The sum of these two numbers is 2.317 x 10^19, which is equal to choice B.
The ticket sales at a movie theater were $3,402. Adult tickets are $11, and senior tickets are $8. The number of senior tickets sold was 27 less than twice the number of adult tickets. Determine the number of adult tickets and senior tickets sold.
Answer:
Adults: 134
Senior: 241
Step-by-step explanation:
Known
Number of adult tickets sold: x
Revenue from adult tickets: $11x
Number of senior tickets sold: y
Revenue from senior tickets: $8y
From the problem, we found the equation [tex]y = 2x - 27[/tex] and 3,402 = 11x + 8y
Combining the two equation:
[tex]3,402 = 11x + 8(2x-27)\\3,402 = 11x + 16x - 216\\3,402 + 216 = 27x\\27x = 3,618[/tex]
Divided both side by 27
[tex]x = 134[/tex]
Since
[tex]y = 2x - 27[/tex]
Inserting the value of x,
[tex]y = 2(134) -27\\y = 268 - 27\\y = 241[/tex]
So, there are 134 adult tickets sold and 241 senior tickets sold.
Write an exponential function (1 , 10.4) and (4 , 665.6)
Answer:
[tex]f(x)=2.6(4)^x[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$f(x)=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]
Given points:
(1, 10.4)(4, 665.6)Substitute the given points into the formula to create two equations:
[tex]\implies 10.4=ab[/tex]
[tex]\implies 665.6=ab^4[/tex]
Divide the second equation by the first to eliminate a, then solve for b:
[tex]\implies \dfrac{665.6}{10.4}=\dfrac{ab^4}{ab}[/tex]
[tex]\implies 64=\dfrac{b^4}{b}[/tex]
[tex]\implies 64=b^3[/tex]
[tex]\implies b=\sqrt[3]{64}[/tex]
[tex]\implies b=4[/tex]
Substitute the found value of b into the first equation and solve for a:
[tex]\implies 10.4=4a[/tex]
[tex]\implies a=2.6[/tex]
Therefore, the exponential function is:
[tex]f(x)=2.6(4)^x[/tex]
let r be the distance from a uniformly randomly chosen point in the unit disk and the origin (0,0). find the probability density function fr(r) and cumu- lative distribution function fr(r) of r. (hint: do not attempt to use your answer from part (a)).
The probability density function fr(r) of the distance from a uniformly randomly chosen point in the unit disk to the origin is r, and the cumulative distribution function Fr(r) is (r² / 2).
To find the probability density function (PDF) and cumulative distribution function (CDF) of the distance from a uniformly randomly chosen point in the unit disk to the origin, we can first find the area of the unit disk and the area of the annulus centered at the origin and bounded by two circles with radii r and r + dr. The PDF is then the ratio of the area of the annulus to the total area of the unit disk, and the CDF is the ratio of the area of the annulus to the total area of the unit disk up to radius r.
The area of the unit disk is simply the area of a circle with radius 1, which is pi. The area of the annulus centered at the origin and bounded by two circles with radii r and r + dr is equal to the difference between the areas of the two circles, which is pi(r + dr)² - pi(r²). Therefore, the PDF of r is:
fr(r) = [pi(r + dr)² - pi(r²)] / pi = r + dr²
The CDF of r is the sum of the PDFs up to radius r, which is:
Fr(r) = ∫fr(t)dt from 0 to r = ∫(t + dt²)dt from 0 to r = (r² / 2) + (r × dt) + (dt³ / 3)
We can take the limit as dt approaches 0 to get the final expression for the CDF:
Fr(r) = (r² / 2)
Learn more about the probability density function at
https://brainly.com/question/30070005?referrer=searchResults
#SPJ4
of 649 adults selected randomly from one town, 54 of them smoke. construct a 92.5 percent n interval for the true percentage of all adults in the town that smoke.
The 92.5% of confidence interval for the percentage of adults is
(-1.176 , 1.342).
as per given in the question,
The total number of adults (n) is 649
The number of smokers (x) = 54
the probability of getting a smoker is P =x/n
=> P = 54/649
=> 0.083
not getting a smoker is
1 - P = 1-0.083
=> 0.916
At 92.5% confidence level the Z critical value is ,
[tex]\alpha[/tex] = 1 - 92.5%
=> 1 - 0.925
=> 0.075
[tex]\alpha[/tex] / 2 = 0.075/ 2
=> 0.0375
now,
for the two tail test
Z[tex]\alpha[/tex]/2
= Z(0.0375)
= 1.7805
Margin of error
E = [tex]Z\alpha / 2 * \sqrt{( p * (1 - p) / n)}[/tex]
= 1.780 [tex]\times (\sqrt{((0.083 \times 0.916 ) / 649)}[/tex]
= 1.2596
A 92.5 % confidence interval for population proportion p is ,
P- E < P < P + E
0.083- 1.259 < P < 0.083 + 1.259
-1.176 < p < 1.342
(-1.176 , 1.342) is the interval
To learn more about Z critical value :
https://brainly.com/question/3605192
#SPJ4
Please help me. It's only 1 question :(
Answer:
5/12 of a pizza
Step-by-step explanation:
a small island is 3 miles from the nearest point p on the straight shoreline of a large lake. if a woman on the island can row a boat 3 miles per hour and can walk 4 miles per hour, where should the boat be landed in order to arrive at a town 7 miles down the shore from p in the least time? let x be the distance (in miles) between point p and where the boat lands on the lakeshore.
The point where the boat should be landed is the point 3.4 miles from point P towards the town.
The point where the boat should be landed can be found by expressing
the distance traveled on the boat and walking as a function of time.
Given that x represents the distance from point P to the boat landing point.
Therefore, distance of rowing the boat = √((12 - x)² + 3²)
The total time, t, is, therefore;
[tex]t=\frac{12-x}{4} +\frac{\sqrt{x^2+3^2} }{3}-----------(1)[/tex]
differentiate the above equation we get:
[tex]\frac{dt}{dx} =\frac{d}{dx} (\frac{12-x}{4} +\frac{\sqrt{x^2+3^2} }{3} )\\\\\\=\frac{12.(-3+4*\frac{2x}{2*\sqrt{x^2+9} } )}{144} \\\\\\=\frac{12(-3+4*\frac{2x}{2*\sqrt{x^2+9} }) }{144}\\\\=-\frac{1}{4} +\frac{x}{3*\sqrt{x^2+9} } \\\\\frac{x}{3*\sqrt{x^2+9} }=\frac{1}{4} \\\\cross multiplying both terms we get:\\\\4x=3*\sqrt{x^2+9}[/tex]
squaring on both sides we get:
16x^2=9(X^2+9)
16x^2=9x^2+81
7x^2=81
[tex]x=\frac{9*\sqrt{x} }{7}[/tex]
Approximately,x=3.4 miles.
To know more about the Distance of points:
https://brainly.com/question/23848540
#SPJ4
The lifetime X of a certain brand of sixty-watt light bulb is exponentially distributed with population mean 1000 hours, that is, 5.23 1 e/1000 1000 f(x) x > 0. If 30 light bulbs having this lifetime distribution are placed on test, find the probability that 10 or fewer of these light bulbs survive to time 1200 by (a) writing a mathematical expression, (b) giving an R statement that will compute the probability.
The function given by f(x) = 1/1000×e^(-x/1000) is the expression that represents the function that 10 or fewer of the bulbs survive to time 1200.
Given, the lifetime X of a certain brand of sixty-watt light bulb is exponentially distributed with population mean 1000 hours.
That is, 5.231(e/1000)f(x) x > 0. I
f 30 light bulbs having this lifetime distribution are placed on test.
we have to find the probability that 10 or fewer of these light bulbs survive to time 1200.
as, we have to find the expression for the function f(x) so that 10 or fewer of the given light bulbs survive to time 1200.
f(x) = 1/1000×e^(-x/1000)
So, the function given by f(x) = 1/1000×e^(-x/1000) is the expression that represents the function that 10 or fewer of the bulbs survive to time 1200.
Hence, the function given by f(x) = 1/1000×e^(-x/1000) is the expression that represents the function that 10 or fewer of the bulbs survive to time 1200.
Learn more about Exponential Distribution here https://brainly.com/question/11843641
#SPJ4
is y=-2x - 4 proportional?
Answer:
It does not represent a proportional relationship
Step-by-step explanation:
Answer:
It does not represent a proportional relationship
Step-by-step explanation For a line, the constant of proportionality is a fancy way to say the slope. It makes more sense without the intercept: y=2xclearly, the constant of proportionality is 2.
PLEASE HELP WILL MARK BARINLIEST
Answer:
<CYZ = 60 degrees
Step-by-step explanation:
CY = CZ ==> both segments are radiuses of the circle since they both have
a CenterPoint at Point C and a point touching the edge of the
circle
CY = YZ ==> Since CY=CZ and YZ=CZ, CY also equal YZ. In addition, this
means that CY, YZ, and CZ are all radiuses of the circle
Hence, CY = YZ = CZ.
Since all sides of the triangle are equal, that means that all angles of the triangle are equal as well:
<CYZ + <CZY + <YCZ = 180 ==> 180 is the total degrees in a triangle
<CYZ + <CYZ + <CYZ = 180 ==> all angles have the same measure
3 * <CYZ = 180 ==> solve for <CYZ
(3 * <CYZ)/3 = 180/3 ==> divide by 3 on both sides to isolate <CYZ
<CYZ = 60 degrees
Answer: [tex]\angle CYZ=60^{\circ}[/tex]
Step-by-step explanation:
[tex]\overline{CZ}=\overline{CY}[/tex] (radii of a circle)
[tex]\implies \overline{YZ}=\overline{CZ}=\overline{CY}[/tex]
[tex]\therefore \angle CYZ=60^{\circ}[/tex] (equilateral triangle)
yolanda will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $70 and costs and costs and additional $0.30 per mile driven. The second plane has no initial fee but costs $0.80 per mile driven. How many miles would Yolanda need to drive for the two plans to cost the same?
The two plans will cost the same when Yolanda has driven 233 miles distance. That is, $70 + (0.30 x 233) = $233 = 0.80 x 233.
To find out how many miles Yolanda needs to drive for the two plans to cost the same, we need to set up an equation. The equation should calculate the total cost of each plan. For the first plan, the total cost is the initial fee plus the cost of the miles driven. For the second plan, the total cost is just the cost of the miles driven. We can then set the two equations equal to each other and solve for the number of miles distance driven. The final result is that Yolanda needs to drive 233 miles for the two plans to cost the same.
Plan 1: C = F + (D × CPM)
Plan 2: C = (D × CPM)
Plan 1 = Plan 2
F + (D × CPM) = (D × CPM)
F = 0
D × CPM = D × CPM
D = 233
Therefore, Yolanda needs to drive 233 miles for the two plans to cost the same.
Learn more about distance here
https://brainly.com/question/28956738
#SPJ4