Answer:
For a sample size of n = 609.
Step-by-step explanation:
Central limit theorem for proportions:
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
We have that p = 0.58.
We have to find n for which s = 0.02. So
[tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
[tex]0.02 = \sqrt{\frac{0.58*0.42}{n}}[/tex]
[tex]0.02\sqrt{n} = \sqrt{0.58*0.42}[/tex]
[tex]\sqrt{n} = \frac{\sqrt{0.58*0.42}}{0.02}[/tex]
[tex](\sqrt{n})^{2} = (\frac{\sqrt{0.58*0.42}}{0.02})^{2}[/tex]
[tex]n = 609[/tex]
For a sample size of n = 609.
The measurement of the circumference of a circle is found to be 64 centimeters, with a possible error of 0.9 centimeter. (a) Approximate the percent error in computing the area of the circle. (Round your answer to two decimal places.) 2.81 Correct: Your answer is correct. % (b) Estimate the maximum allowable percent error in measuring the circumference if the error in computing the area cannot exceed 1%. (Round your answer to one decimal place.)
Answer:
(a) 2.81%
(b) 0.5%
Step-by-step explanation:
We have the following information from the statement:
P = 64 + - 0.9
(a) We know that the perimeter is:
P = 2 * pi * r
if we solve for r, we have to:
r = P / 2 * pi
We have that the formula of the area is:
A = pi * r ^ 2
we replace r and we are left with:
A = pi * (P / 2 * pi) ^ 2
A = (P ^ 2) / (4 * pi)
We derive with respect to P, and we are left with:
dA = 2 * P / 4 * pi * dP
We know that P = 64 and dP = 0.9, we replace:
dA = 2 * 64/4 * 3.14 * 0.9
dA = 9.17
The error would come being:
dA / A = 9.17 / (64 ^ 2/4 * 3.14) = 0.02811
In other words, the error would be 2.81%
(b) tell us that dA / A <= 0.01
we replace:
[P * dP / 2 * pi] / [P ^ 2/4 * pi] <= 0.01
solving we have:
2 * dP / P <= 0.01
dP / P <= 0.01 / 2
dP / P <= 0.005
Which means that the answer is 0.5%
Use reduction of order (NOT the integral formula we developed) to find the general solution of the nonhomogeneous linear DE, showing all work. Also clearly state the particular solution yp that you obtain using the reduction of order process and show a clear check that your particular solution yp satisfies the original nonhomogeneous DE. [Do NOT use the Method of Undetermined Coefficients here!]
''y + 6y' + 9y + 4e^x
Note: Use the characteristic polynomial to find a first solution yi of the associated homogencous DE.)
Answer:
[tex]y = (e^{4x}{4} + kx+d) \cdot c_1e^{-3x} = \frac{e^{x}}{4} + Ae^{-3x}+Bxe^{-3x}[/tex] where A,B are constants.
Step-by-step explanation:
Consider the differential equation [tex]y''+6y'+9y = 4e^{x}[/tex]. To find the homogeneus solution, we assume that [tex]y = Ae^{rt}[/tex] and replace it in the equation [tex]y''+6y'+9y = 0[/tex]. If we do so, after using some properties of derivatives and the properties of the exponential function we end up with the equation
[tex]r^2+6r+9 = 0 = (r+3)^2[/tex]
which leads to r = -3. So, one solution of the homogeneus equation is [tex]y_h = c_1e^{-3x}[/tex], where c_1 is a constant.
To use the order reduction method, assume
[tex] y = v(x)y_h(x)[/tex]
where v(x) is an appropiate function. Using this, we get
[tex]y'= v'y+y'v[/tex]
[tex]y''=v''y+y'v'+y''v+v'y'=v''y+2v'y'+y''v[/tex]
Plugging this in the original equation we get
[tex]v''y+2v'y'+y''v + 6(v'y+y'v) +9vy=4e^{x}[/tex]
re arranging the left side we get
[tex]v''y+2v'y'+6v'y+v(y''+6y'+9y)=4e^{x}[/tex]
Since y is a solution of the homogeneus equation, we get that [tex]y''+6y'+9y=0[/tex]. Then we get the equation
[tex]yv''+(2y'+6y)v' = 4e^{x}[/tex]
We can change the variable as w = v' and w' = v'', and replacing y with y_h, we get that the final equation to be solved is
[tex] e^{-3x}w'+(6e^{-3x}-6e^{-3x})w =4e^{x}[/tex]
Or equivalently
[tex]w' = 4e^{4x}[/tex]
By integration on both sides, we get that w = e^{4x}+ k[/tex] where k is a constant.
So by integration we get that v = [tex]e^{4x}{4} + kx+d[/tex] where d is another constant.
Then, the final solution is
[tex]y = (e^{4x}{4} + kx+d) \cdot c_1e^{-3x} = \frac{e^{x}}{4} + Ae^{-3x}+Bxe^{-3x}[/tex] where A,B are constants
Graph g(x)=-2|x-5|-4
Answer:
Step-by-step explanation:
s the last book a person in City Upper A read a discrete random variable, continuous random variable, or not a random variable? A. It is a continuous random variable. B. It is a discrete random variable.
Answer:
Not a random variable
Step-by-step explanation:
The last book a person read in City A is not a random variable because it is not a number as there is no numerical description for the outcome of this experiment.
Thus, the last book read by someone in City A is not a random variable.
Answer:
not random
Step-by-step explanation:
in a classroom 5/8 of the students are wearing blue shirts and 1/4 for wearing white shirts there are 24 students in the classroom how many are wearing shirts other than blue shirts and
Answer:
3
Step-by-step explanation:
Those wearing a shirt of another color are ...
1 - 5/8 -1/4 = 8/8 -5/8 -2/8 = 1/8
of the total number of students in the classroom
(1/8)×(24 students) = 3 students . . . . wearing another color
_____
Alternate solution
With the given information, you know ...
(5/8)(24) = 15 . . . students wear blue
(1/4)(24) = 6 . . . . students wear white
24 -15 -6 = 3 . . . students wear another color
What is the slope of the line represented by the equation y = 4/5x - 3?
in
Answer:
[tex]\boxed{\sf \ \ \ \dfrac{4}{5} \ \ \ }[/tex]
Step-by-step explanation:
when the equation is like y = ax + b
the slope is a
in this case we have
[tex]y \ = \ \dfrac{4}{5}x\ \ - \ 3[/tex]
so the slope is
[tex]\dfrac{4}{5}[/tex]
Please answer this correctly
Answer:
20-39 ⇒ 5
40-59 ⇒ 3
60-79 ⇒ 5
80-99 ⇒ 10
Answer:
20-39: 5
40-59: 3
60-79: 5
80-99: 10
Step-by-step explanation:
If you just added up, you can find all the values.
Change 3.2t into kilograms please help me
Let's think:
1 ton ------------ 1000 kilograms
3.2 tons ----------- x kilograms
Multiply in cross
1 . x = 1000 . 3.2
x = 3200
So 3.2t = 3200 kilograms
Answer:
It is 2902.99 to be exact
Step-by-step explanation:
Choose the ratio that you would use to convert 1.5 feet to miles. Remember
that there are 5,280 feet in one mile.
Answer: B, 1 mile / 5280 ft.
Step-by-step explanation: If you need to convert feet to miles the unit multiplier (ratio) that you use should have miles on top and feet on the bottom so that the feet cancel when you multiply, leaving miles as the unit. B is the only answer that has miles on top and feet on the bottom as well as the correct amounts (1 mile and 5280 ft).
A real estate agent is showing homes to a prospective buyer. There are ten homes in the desired price range listed in the area. The buyer has time to visit only four of them. If four of the homes are new and six have previously been occupied and if the four homes to visit are randomly chosen, what is the probability that all four are new
Answer:
0.48% probability that all four are new
Step-by-step explanation:
The homes are chosen "without replacement", which means that after a home is visited, it is not elegible to be visited again. So we use the hypergeometric distribution to solve this question.
Hypergeometric distribution:
The probability of x sucesses is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[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]
In this question:
Total of 10 homes, so N = 10.
We want 4 new, so x = 4.
In total, there are 4 new, so k = 4.
Sample of four homes, so n = 4.
Then
[tex]P(X = 4) = h(4,10,4,4) = \frac{C_{4,4}*C_{6,0}}{C_{10,4}} = 0.0048[/tex]
0.48% probability that all four are new
The calculated probability is "0.0048".
Probability calculation:From a total of [tex]N=10\ \ \text{homes},\ r=4[/tex] are completely new while 6 are not.
Let X indicate the series of innovative dwellings in a sample of[tex]n=4[/tex] homes.
X is the next step. Algebraic distribution for parameters[tex]N=10, r=4, \ \ and\ \ n = 4[/tex] Only integer values in this range: can be given to a hypergeometric random variable.
[tex]\to [ \max {(0,\,n+r-N)}, \min {(n,\,r)} ] = [ 0, 4 ] \\\\ \to P( X = 4) \\\\ \to N=10\\\\ \to r=4\\\\ \to n = 4[/tex]
[tex]\to \bold{P(X=k) = \dfrac{\binom{r }{ k}{\binom{N-r} {n-k}}}{\binom{N}{n}}} \\\\\to P(X =4 ) = \dfrac{\binom{r }{ 4}{\binom{N-r} {n-4}}}{\binom{N}{n}} \\\\[/tex]
[tex]= \dfrac{\binom{4 }{ 4}{\binom{10-4} {4-4}}}{\binom{10}{4}}\\\\= \dfrac{\binom{4 }{ 4}{\binom{6} {0}}}{\binom{10}{4}} \\\\= \dfrac{ 1 \times 1}{210} \\\\= \dfrac{ 1}{210} \\\\= \dfrac{1}{210} \\\\= 0.004762[/tex]
Using the excel function:
[tex]\text{HYPGEOM.DIST( k, n, r, N. cumulative)}[/tex] for calculating the [tex]P_{X} (4)[/tex]:
[tex]\to \text{HYPGEOM.DIST( 4, 4, 4, 10, FALSE) = 0.0047619047619}[/tex]
[tex]\to P(X= 4 ) = \frac{1}{210} = { 0.0048 }[/tex]
Find out more information about the probability here:
brainly.com/question/2321387
Rectangle is 5ft in length and 3 ft in height. What is the area of the rectangle
Answer: 15
Step-by-step explanation:
to find the area multiply the length by height
in this case it’s 5ft and 3ft
5 • 3 = 15
A=15
Use the given probability value to determine whether the sample results could easily occur by chance, then form a conclusion. A study of the effect of seatbelt use in head-on passenger car collisions found that drivers using a seatbelt had a 64.1% survival rate, while drivers not using a seatbelt had a 41.5% survival rate. If seatbelts have no effect on survival rate, there is less than a 0.0001 chance of getting these results. What do you conclude?
Answer:
As the P-value is very low, we can conclude that there is enough evidence to support the claim that the survival rate is significantly higher when the seatbelt is used.
Step-by-step explanation:
We have a hypothesis test that compares the survival rate using the seatbelt versus the survival rate not using it.
The claim is that the survival rate (proportion) is significantly higher when the seatbelt is used.
Then, the null hypothesis is that the seatbelts have no effect (both survival rates are not significantly different).
The P-value is the probabilty of the sample we have, given that the null hypothesis is true. In this case, this value is 0.0001.
This is very low, what gives enough evidence to claim that the survival rate is significantly higher when the seatbelt is used.
The city of Oakdale wishes to see if there is a linear relationship between the temperature and the amount of electricity used (in kilowatts). Using the estimated regression equation found by using Temperature as the predictor variable, find a point estimate Kilowatt usage when the Temperature is 90 degrees outside?
The question is incomplete. The complete question is as follows.
The city of Oakdale wishes to see if there is a linear relantionship between the temperature and the amount of electricity used (in kilowatts). Using the estimated regression equation found by using Temperature as the predictor variable, find a pont estimate Kilowatt usage when the Temperature is 90 degrees outside?
Temperature(x) Kilowatts(y)
73 680
78 760
85 910
98 1510
93 1170
83 888
92 923
81 837
76 600
105 1800
Answer: The point estimate is 1132.5 Kilowatts
Step-by-step explanation: Regression analysis is used to find an equation that fits the data. Once this equation is found, it's used to make predictions. One of the regressions is linear regression.
To find the linear regression model:
1) Create a table with the following: ∑y; ∑x; ∑xy; ∑x²; ∑y²;
2) Use these equations to find coefficients a and b:
a = (∑y)(∑x²) - (∑x)(∑yx) / n(∑x²) - (∑x)²
b = n(∑xy) - (∑x)(∑y) / n(∑x²) - (∑x)²
3) Substitute the coefficients into the equation of form: y = a + bx
For the table above, the linear regression equation is:
y = - 2004 + 34.85x
When Temperature is 90, i.e. x = 90:
y = - 2004 + 34.85*90
y = 1132.5
The estimate Kilowatt is 1132.5.
The populations and areas of four states are shown.Which statement regarding these four states is true?
Heidi looks at the donkeys and
tourists. She counts 50 heads
and 114 legs.
How many donkeys are there?
o
ANSWER:
O The retired question
Answer:
7 donkeys
Step-by-step explanation:
Given
A system consisting of donkeys and tourists
Heads = 50
Legs = 114
Required
Calculate number of donkeys.
Represent donkeys with D and tourists with T.
By means of identification; donkeys and tourists (human) both have 1 head.
This implies that
Number of Heads = D + T
50 = D + T ----- Equation 1
While each donkey have 4 legs, each tourists have 2 legs.
This implies that
Number of legs = 4D + 2T
114 = 4D + 2T ---- Multiply both sides by ½
114 * ½ = (4D + 2T) * ½
57 = 4D * ½ + 2T * ½
57 = 2D + T ----- Equation 2
Subtract equation 1 from 2
57 = 2D + T
- (50 = D + T)
---------------------
57 - 50 = 2D - D + T - T
7 = D
Recall that D represents the number of donkeys.
So, D = 7 implies that
The total number of donkeys are 7
To solve the system given below using substitution, it is best to start by
solving the second equation for y.
5x + 2y = 33
6y + x = 3
true or false
Answer:
False, it is easier to isolate x.
Step-by-step explanation:
6y+x=3
x=3-6y
Could you please help me with this problem.
Answer:
x=6√2please see the attached picture for full solution...
Hope it helps...
Good luck on your assignment....
A game require rolling a six sided die numbered fro 1 to 6. What is the probability of rolling a 1 or a 2?
Answer:
1/3
Step-by-step explanation:
hello,
probability of 1 = 1/6
probability of 2 = 1/6
probability of 1 or 2 = 1/6+1/6 as probability of 1 and 2 = 0
so the answer is 2/6=1/3
Which equation represents the line that passes through and left-parenthesis 4, StartFraction 7 Over 2 right-parenthesis.?
Answer:
We want a line that passes through the point (4, 7/2)
and we have no other information of this line, so we can not fully find it, but we can find a general line.
We know that a line can be written as:
y = a*x + b.
Now we want that, when x = 4, we must have y = 7/2.
7/2 = a*4 + b
b = -a*4 + 7/2
Then we can write this line as:
y = a*x - a*4 + 7/2.
Where a can take any value, and it is the slope of our line.
Answer:
A
Step-by-step explanation:
Can someone please help me?
Answer:
''0 is neither a rational number nor an irrational number.''
Step-by-step explanation:
Zero is a rational number. Zero can be written as a fraction, where p/q = 0, where p = 0 and q is any non-zero integer. Hence, 0 is a rational number.
Nolan is using substitution to determine if 23 is a solution to the equation. Complete the statements.
j – 16 = 7 for j = 23
First, Nolan must substitute
for
.
To simplify, Nolan must subtract
from
.
23
a solution of the equation.
Answer:
Step-by-step explanation:
Given the equation j – 16 = 7, If Nolan is using substitution to determine if 23 is a solution to the equation, then Nolan need to make j the subject of the formula from the equation. The following statements must therefore be made by Nolan.
First, Nolan must substitute for the value of j in the equation.
To simplify, Nolan must subtract the value of 7 from both sides to have;
j – 16 - 7= 7 - 7
j – 23 = 0
Then Nolan must add 23 to both sides of the equation to get the value of j as shown;
j – 23 + 23 = 0+23
j = 23
23 is therefore a solution to the equation
Answer:First, Nolan must substitute 23 for j.To simplify, Nolan must subtract 16 from 23. 23 is a solution of the equation.
Step-by-step explanation:
I got it right on Edge
The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 2 sin(πt) + 5 cos(πt), where t is measured in seconds.
A) Find the average velocity during each time period.
1) [1, 2]
2) [1, 1.1]
3) [1, 1.01]
4) [1, 1.001]
B) Estimate the instantaneous velocity of the particle when t = 1. cm/s
Answer:
A) 10, -3.73, -6.035, -6.259 . . . cm/s
B) -6.2832 cm/s
Step-by-step explanation:
A) For problems like this, where repeated evaluation of a function is required, I find a graphing calculator or spreadsheet to be an appropriate tool. The attached shows that we defined the position function ...
p(t) = 2sin(πt) +5cos(πt)
and a function for computing the average velocity from t=1. For some time interval ending at t2, the average velocity is ...
Va(t2) = Δp/Δt = (p(t2) -p(1))/(t2 -1)
Then, for example, for t2 = 2, the average velocity on the interval [1, 2] is ...
Va(2) = (p(2) -p(1))/(2 -1) = ((2sin(2π) +5cos(2π)) -(2sin(π) +5cos(π)))/(1)
= (2·0+5·1 -(2·0 +5·(-1)) = 10 . . . . matches the table value for x1 = 2.
Then the average velocity values for the intervals of interest are ...
1) [1, 2] Va = 10
2) [1, 1.1] Va = -3.73
3) [1, 1.01] Va = -6.035
4) [1, 1.001] Va = -6.259
__
B) Sometimes a better estimate is obtained when the interval is centered on the point of interest. Here, we can compute the average velocity on the interval [0.999, 1.001] as a better approximation of the instantaneous velocity at t=1. That value is ...
[0.999, 1.001] Va = -6.283175*
Our estimate of V(1) is -6.2832 cm/s.
The exact value is -2π ≈ -6.2831853... cm/s
__
* This is the average of the Va(0.999) and Va(1.001) values in the table.
The computer hardware company requires all of its chips purchased from its supplier of computer chips to meet specifications of 1.2 cm with the margins of error of plus and minus 0.1 cm. Based on the computer chip supplied last month, the mean length of a computer chip was 0.9 cm. What are the elements that the production manager should consider in determining his company's ability to produce chips that meet specifications
Answer:
Step-by-step explanation:
The computer hardware company requires all of the chips purchased from its supplier of computer chips to meet the specification of 1.2 centimeters, with error margins of -0.1cm and +0.1cm
This means that the required length of computer chips is between 1.1cm - 1.3cm
Where 1.1cm = [1.2 - 0.1]
1.3cm = [1.2 + 0.1]
Based on the computer chips supplied last month, mean length was 0.9cm. This means that most of the chips were (in length) less than the lower boundary of 1.1cm.
The element that the production manager should consider in determining his company's ability to produce chips that meet specification is:
- The length of the chips.
The length of the chips his production team produces should be tailored to meet the length specification of his client.
Solve the equation.
5x + 8 - 3x = -10
x = -1
x=1
x=9
Answer:
x=-9solution,
[tex]5x + 8 - 3x = - 10 \\ or \: 5x - 3x + 8 = -10 \\ or \: 2x + 8 = -10 \\ or \: 2x = -10 - 8 \\ or \: 2x = -18\\ or \: x = \frac{-18}{2 } \\ x = -9[/tex]
hope this helps..
Good luck on your assignment
Answer:
x = -9
Step-by-step explanation:
5x + 8 - 3x = -10
Rearrange.
5x - 3x + 8 = -10
Subtract like terms.
2x + 8 = -10
Subtract 8 on both sides.
2x = -10 - 8
2x = -18
Divide 2 into both sides.
x = -18/2
x = -9
Please answer this correctly
Answer:
0| 2
1| 2
2| 0 0 3 9
3| 2 4 4 4 8 8
4| 2 2 4 5 5 6 7
Step-by-step explanation:
Same as the other similar questions
hope this helps!
Let's list the elements of these sets and write whether thoy are empty
(null), singleton, finite or Infinito sots.
a) A = {prime number between 6 and 7)
b) B = {multiples of 2 less than 20}
Answer:
a. They are empty set.
b. they are finite set.
Solution,
a. A={ prime number between 6 and 7}
There are not any number between 6 and 7.
So there will be no Elements.
A={ }
It is empty set.
Empty set are those set which doesn't contain any Element.
b.B={multiples of 2 less than 20}
B={2,4,6,8,10,12,14,16,18}
It is a finite set.
Finite set are those set which we can count easily.
Hope this helps...
Good luck on your assignment...
Please answer this correctly
Answer:
Pillows:
Blankets:
Pet Beds:
Step-by-step explanation:
18 + 45 + 27 = 90 (there are 90 students)
18 out of 90 = 20%
45 out of 90 = 50%
27 out of 90 = 30%
Hope this helps!
Which statement is true about the polynomial 3j4k−2jk3+jk3−2j4k+jk3 after it has been fully simplified?
Answer:
[tex]j^4k[/tex]
Step-by-step explanation:
[tex]3j^4k-2jk^3+jk^3-2j^4k+jk^2\\2j^4k-2j^4k-2jk^3+jk^3+jk^3\\j^4k[/tex]
Answer:
4
Step-by-step explanation:
give me brainliest
we nendndhdhebdbdbdd
Step-by-step explanation:
Joe mama
If the volume of a cube is
64 cubic feet, what is the
surface area of the cube in
square feet?
Answer:
96 ft^2
Step-by-step explanation:
volume=l^3
l=4
4x4x4=64
Surface area (4x4)=16
16x6=96
Answer:
SA =96 ft^2
Step-by-step explanation:
The volume of a cube is given by
V = s^3
64 = s^3
Take the cube root of each side
64 ^ 1/3 = s^3 ^ 1/3
4 =s
The side length si 4
The surface area of a cube is
SA = 6 s^2
SA = 6 * 4^2
SA = 6 * 16
SA =96 ft^2