This differential equation is separable:
(1 + y²) dx + (1 + x²) dy = 0
(1 + y²) dx = - (1 + x²) dy
dy/(1 + y²) = -dx/(1 + x²)
Integrating both sides gives
arctan(y) = -arctan(x) + C
and solving for y gives (over an appropriate domain)
y = tan(C - arctan(x))
(the domain being -1 ≤ y ≤ 1).
Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to thegiven statistics and confidence level. Round the margin of error to four decimal places.1)99% confidence; n
Answer:
[tex]E = 0.0158[/tex]
Step-by-step explanation:
Given
[tex]n = 5900[/tex]
[tex]x = 1770[/tex]
[tex]CI = 99\%[/tex]
Required
The margin of error (E)
First, calculate proportion p
[tex]p = x/n[/tex]
[tex]p = 1770/5900[/tex]
[tex]p = 0.3[/tex]
Given that:
[tex]CI = 99\%[/tex]
Calculate the alpha leve;
[tex]\alpha = 1 - CI[/tex]
[tex]\alpha = 1- 0.99[/tex]
[tex]\alpha= 0.01[/tex]
Divide by 2
[tex]\alpha/2= 0.01/2[/tex]
Subtract from 1
[tex]1 - \alpha/2= 1 - 0.01/2[/tex]
[tex]1 - \alpha/2= 0.995[/tex]
The corresponding z value is:
[tex]z =2.576[/tex]
So, the margin of error is:
[tex]E = z * \sqrt{p * (1 - p)/n}[/tex]
So, we have:
[tex]E = 2.576 * \sqrt{0.3 * (1 - 0.3)/5600}[/tex]
Using a calculator, we have:
[tex]E = 0.01577471394[/tex]
Approximate
[tex]E = 0.0158[/tex]
help with 27 please. thanks
Answer:
See Below.
Step-by-step explanation:
We are given the function:
[tex]\displaystyle y=\sqrt{\sin x}[/tex]
And we want to show that:
[tex]\displaystyle 4y^3\frac{d^2y}{dx^2}+y^4+1=0[/tex]
Find the first derivative of y using the chain rule:
[tex]\displaystyle \frac{dy}{dx} = \frac{1}{2\sqrt{\sin x}}\cdot \cos x = \frac{\cos x}{2\sqrt{\sin x}}[/tex]
And find the second derivative using the quotient and chain rules:
[tex]\displaystyle \begin{aligned} \frac{d^2y}{dx^2} &= \frac{1}{2}\left(\frac{(\cos x)'(\sqrt{\sin x})-(\cos x)(\sqrt{\sin x})'}{(\sqrt{\sin x})^2}\right) \\ \\ &=\frac{1}{2}\left(\frac{-\sin x\sqrt{\sin x} - \left(\cos x\right) \left (\dfrac{\cos x}{2\sqrt{\sin x}}\right)}{\sin x}\right) \\ \\ & = \frac{1}{2}\left(\frac{ -\sin x(2\sin x) -\cos x(\cos x) }{\sin x \left(2\sqrt{\sin x}\right) }\right) \\ \\ &= -\frac{1}{2} \left(\frac{2\sin^2 x + \cos^2 x}{2\sin^{{}^{3}\!/\! {}_{2}}x}\right)\end{aligned}[/tex]
Find y³:
[tex]\displaystyle y^3 = \left((\sin x)^{{}^{1}\!/\!{}_{2}}\right) ^3= \sin^{{}^{3}\! / \! {}_{2} }x[/tex]
And find y⁴:
[tex]\displaystyle y^4 = \left((\sin x)^{{}^{1}\!/\!{}_{2}}\right)^4 = \sin^2 x[/tex]
Substitute:
[tex]\displaystyle 4\left( \sin^{{}^{3}\! / \! {}_{2} }x\right)\left(-\frac{1}{2}\left(\frac{2\sin ^2x + \cos ^2 x}{2\sin^{{}^{3}\!/ \! {}_{2}}x}\right)\right)+\left(\sin ^2 x\right) + 1= 0[/tex]
Simplify:
[tex]-\left(2\sin^2 x + \cos^2 x\right) + \sin ^2 x + 1=0[/tex]
Distribute:
[tex]-2\sin ^2 x - \cos^2 x + \sin ^2 x + 1=0[/tex]
Simplify:
[tex]-\sin ^2 x - \cos^2 x + 1= 0[/tex]
Factor:
[tex]-(\sin ^2 x + \cos^2 x ) + 1=0[/tex]
Pythagorean Identity:
[tex]-(1)+1=0\stackrel{\checkmark}{=}0[/tex]
Q.E.D.
a) Show that 4x² -6x+9 is positive for all values real numbers x.
Answer:
(4x² -6x+1.5²) +9-1.5²= (2x-1.5)²+9-2.25= (2x-1.5)²+6.75
(2x-1.5)² is greater or equal to 0 , 6.75>0 so expression is positive for all real numbers x
Step-by-step explanation:
a) Use the formula a²-2ab+b²= (a-b)² (You need to make squared expression because it is always positive)
Consider 4x² as a² and -6x=-2ab
4x²=a² a=2x ab=3x 2x*b=3x
b=1.5
Express 4x² -6x+9= (4x² -6x+1.5²) +9-1.5²= (2x-1.5)²+9-2.25= (2x-1.5)²+6.75
(2x-1.5)² is greater or equal to 0 , 6.75>0 so expression is positive for all real numbers x
El valor de "x" que es solución de la ecuación 5x + 22 = 2x + 29 es:
Answer:
x =7/ 3
Step-by-step explanation:
5x+ 22= 2x+ 29
⇔5x - 2x= 29 - 22
⇔3x = 7
⇔x = 7/3
5765865876+5737555586=
Answer:
5765865876+5737555586=11503421462
father of economics
If a 0.05 significance level is to be used to test the claim that p1< p2 , what confidence level should be used?
Using test hypothesis and confidence interval concepts, it is found that a 95% confidence level should be used.
A confidence interval can be used to make a hypothesis test.For a significance level of [tex]\alpha[/tex], the confidence level is of [tex]1 - \alpha[/tex]In this problem, there is a significance level of 0.05, hence the confidence level is of 1 - 0.05 = 0.95 = 95%.
A similar problem, also involving a confidence interval and an hypothesis test, is given at https://brainly.com/question/14740644
Starting with a fresh bar of soap, you weigh the bar each day after you take a shower. Then you find the regression line for predicting weight from number of days elapsed. The slope of this line will be:__________.
Answer:
The slope will be negative
Step-by-step explanation:
The slope of the regression line tells us about the relationship or behavior of the dependent and independent variables. In the scenario above, where the weight is being compared with the number of days elapsed. What is expected of the weight and quantity of a bar soap each time it is used for a shower is that it will decrease in weight. Therefore, as the number of days increases, and hence, number of showers rise, the weight of soap will decrease. Hence, we'll obtain a negative slope, one in which the increase in a variable leads to decrease in the other.
Suppose that it takes 12 units of carbohydrates and 8 units of protein to satisfy Jacob's minimum weekly requirements. A particular type of meat contains 2 units of carbohydrates and 2 units of protein per pound. A particular cheese contains 3 units of carbohydrates and 1 unit of protein per pound. The meat costs $3.70 per pound and the cheese costs $2.60 per pound. How many pounds of each are needed in order to minimize the cost and still meet the minimum requirements? What is the minimum cost?
Answer:
a. The number of pounds of the meat required is 3 pounds and the number of pounds of cheese required is 2 pounds.
b. $ 16.7
Step-by-step explanation:
a. How many pounds of each are needed in order to minimize the cost and still meet the minimum requirements?
Let c represent the carbohydrate units and p the protein units.
For the meat portion M, we have 2 units of carbohydrates and 2 units of protein per pound. So, M = 2c + 2p
For the cheese portion K, we have 3 units of carbohydrates and 1 units of protein per pound. So, K = 3c + p.
Let x be the number of pounds of meat required and y be the number of cheese pounds required. The total number of pounds required is T
So, we have xM + yK = x(2c + 2p) + y(3c + p)
= 2xc + 2xp + 3yc + yp
= 2xc + 3yc + 2xp + yp
= (2x + 3y)c + (2x + y)p
Since the required number of units, R is 12 units of carbohydrates and 8 units of protein, we have R = 12c + 8p
Since T = R, we have
(2x + 3y)c + (2x + y)p = 12c + 8p
Equating coefficients, we have
2x + 3y = 12 (1) and 2x + y = 8 (2)
Subtracting (2) from (1), we have
2x + 3y = 12 (1)
-
2x + y = 8 (2)
2y = 4
y = 4/2
y = 2
Substituting y = 2 into (2), we have
2x + y = 8
2x + 2 = 8
2x = 8 - 2
2x = 6
x = 6/2
x = 3
Since x = 3 and y = 2
The number of pounds of the meat required is 3 pounds and the number of pounds of cheese required is 2 pounds.
What is the minimum cost?
Since meat costs $3.70 per pound and the cheese costs $2.60 per pound and we have 3 pounds of meat and 2 pounds of cheese, the total cost of meat is C = $3.70/pound × 3 pounds = $ 11.1.
The total cost of cheese is C' = $2.60/pound × 2 pounds = $ 5.2.
So, the minimum cost C" = C + C' = $ 11.1 + $ 5.2 = $ 16.7
Answer:
Step-by-step explanation:
Compose an expression to find the 20th term of any arithmetic sequence in terms of just a and d. Look at the pattern in
part A with the first three terms to help you.
20th term:
Answer:
Hello,
Step-by-step explanation:
u(i) is the ith term of the a.s
a is the first term and d the common difference
for n in {1,2,3...}: u(n)=a+(n-1)*d
u(1)=a+0*d=a
u(2)=u(1)+d=a+d=a+1*d
u(3)=u(2)+d=a+1*d+d=a+2*d
...
u(20)=a+19*d
Answer:
a+19d
Step-by-step explanation:
edmentum
Write each of the following equations in general form.
a. 1 − 2x = y
b. 9y + 7x = 16 − 3y + x
c. x = 3
d. 2y − 4x − 1 = 7
Answer:
a)2x+y=1
b) 6x+12y=16
c) y=-x+3 (I was a bit confused on this one but I believe this is correct)
d) 4x-2y=-8
Answer:
a. -2x - y + 1 = 0
b. 6x + 12y -16 = 0
c. x - 3 = 0
d. -4x + 2y - 8 = 0
Step-by-step explanation:
If you double then triple a number, this is the same as cutting the number in half. What is the number?
9514 1404 393
Answer:
zero
Step-by-step explanation:
3(2x) = x/2
5.5x = 0 . . . . subtract x/2
x = 0 . . . . . . . divide by 5.5
The number is zero.
A cylinder with a base diameter of x units has a volume of excubic units.
Which statements about the cylinder are true,Select
two options.
1)The radius of the cylinder is 2x units.
2)The area of the cylinder's base is 1/4 piex^2square units.
3)The area of the cylinder's base is 1/2 piex^2 square units.
4)The height of the cylinder is 2x units.
5)The height of the cylinder is 4x units.
Answer:3 and 4
Step-by-step explanation:
2^17+2^14 chia hết cho 9
Answer:
ABC
Step-by-step explanation:
= 2^14.2^3 + 2^14
= 2^14. (2^3 +1)
= 2^14 . 9
Vì 2^14.9 chia hết cho 9 nên 2^17 + 2^14 chia hết cho 9
(. là dấu nhân)
Answer:
đúng
Step-by-step explanation:
PLEASE I NEED HELP RIGHT NOW
Select the graph that correctly translates ƒ(x) = |x| 4 units in the negative x-direction and 3 units in the positive y-direction.
answers are the pictures
Answer:
The third graph
Step-by-step explanation:
What the translation is saying is that for each value of f(x) = |x|, the graph is translated 4 units in the negative x direction and 3 units for the positive y direction. Another way to say this is that for each f(x), we can add (-4) (or subtract 4) to its x value and add 3 to its y value.
One way to find which graph works is to take a point, figure out where it should be, and work from there.
One example of this is (-1,1). If x=-1, |x| is 1, so in the original graph, our point is (-1, 1). In our translated graph, we need to subtract 4 from the x component (the first number, which is -1 in this case) and add 3 to the y component (the second number, or 1 in this case). Our new point comes to
(-1-4 , 1+3)
= (-5, 4)
Therefore, one point on the resulting graph is (-5, 4). We can look through each graph and see if it has the point.
Looking at each graph, it is clear that the graph in the bottom left, or the third graph, contains the point.
The equation of the translated function will be f(x) = |x + 4| + 3. Then the correct option is C.
What is an absolute function?The absolute function is also known as the mode function. The value of the absolute function is always positive.
The absolute function is given as
f(x) = | x – h | + k
The function is given below.
f(x) = |x|
Then the function is translated 4 units in the negative x-direction and 3 units in the positive y-direction. Then the vertex will be at (-4, 3). Then the equation of the function will be
f(x) = |x + 4| + 3
Then the graph is given below.
Then the correct option is C.
More about the absolute function link is given below.
https://brainly.com/question/10664936
#SPJ2
Can anyone please help me out?
If a cube has an edge of length e, then the lateral surface area is:
Answer:
The total lateral surface of this cube is 4*e^2
Step-by-step explanation:
A cube is a figure with all the sides of the same length, so each face of a cube is a square.
Remember that the area of a square of sidelength L is:
A = L^2
Now, when we want to find the lateral surface of a figure, we ignore the bases of the figure.
So, if a cube has 6 faces, if we ignore the two bases, we are left with 4 square faces.
And if the edge length is e, then each one of these four faces has an area:
A = e^2
So the total lateral surface is 4 times that:
S = 4*e^2
The total lateral surface of this cube is 4*e^2
Answer:
4e2
Step-by-step explanation:
I got it correct on founders edtell
How many ways are there to rearrange the letters of the word: COMBINATION?
Answer: 4,989,600 different ways
Step-by-step explanation:
There are 11 students on a committee. To decide which 4 of these students will attend a conference, 4 names are chosen at random by pulling names one at a time from a hat. What is the probability that Sarah, Jamal, Kate, and Mai are chosen in any order
Answer:
0.003 = 0.3% probability that Sarah, Jamal, Kate, and Mai are chosen in any order.
Step-by-step explanation:
The students are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes 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 successes.
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:
11 students means that [tex]N = 11[/tex]
4 are Sarah, Jamal, Kate, and Mai, so [tex]k = 4[/tex]
4 are chosen, which means that [tex]n = 4[/tex]
What is the probability that Sarah, Jamal, Kate, and Mai are chosen in any order?
This is P(X = 4). So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 4) = h(4,11,4,4) = \frac{C_{4,4}*C_{7,0}}{C_{11,4}} = 0.003[/tex]
0.003 = 0.3% probability that Sarah, Jamal, Kate, and Mai are chosen in any order.
Which of the following choices is equivalent to the equation below?
5(2x−1) = 5(5x−14)
A 2x − 1 = 5x − 14
B 5(2x − 1) = 5x − 14
C 2x − 1 = 5
D None of these choices are correct.
Answer:
2x-1 = 5x-14
Step-by-step explanation:
5(2x−1) = 5(5x−14)
Divide each side by 5
5/5(2x−1) = 5/5(5x−14)
2x-1 = 5x-14
Answer:
A.
Step-by-step explanation:
5(2x−1) = 5(5x−14)
10x - 5 = 25x - 70
65 = 15x
x = 13/3.
Take Option A.
2x - 1 = 5x - 14
3x = 13
x = 13/3 so its this one.
B: 10x - 5 = 5x - 14
5x = -9
x = -9/5 so NOT B.
C. simplifies to x = 3. so NOT C.
o the area of a rhombus is 24m²
and one of its diagonals 18cm find
the side of the rhombus
Area of rhombus = 1/2 × d1 × d2
Let the other diagonal be x
ATQ
1/2 × 18 × x = 24
9 × x = 24
x = 24/9
x = 8/3
Now half each diagonal = 9 and 4/3
Now side = b² + p² = h²
9²+(4/3)² = h²
81 + 16/9 = h²
729/9 + 16/9 = h²
745/9 = h²
√(745/9) = h
Therefore the side of the rhombus is √(745/9)cm
Answered by Gauthmath must click thanks and mark brainliest
find range,domains, intercepts, interval of increase decrease and asymptotes of graphs
Answer:
Product of the zeroes of polynomial 3x²-2x-4 is ?
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Want accurate answers ✔
Two boats are travelling at 30 miles/hr, the first going north and the second going east. The second crosses the path of the first 10 minutes after the first one was there. At what rate is their distance increasing when the second has gone 10 miles beyond the crossing point
Answer:
their distance is increasing at the rate of 41.6 miles/hr
Step-by-step explanation:
Given the data in the question;
first we determine the distance travelled by the first boat in 10 min when the second boat was crossing its path;
⇒ ( 30/60 ) × 10 = 5 miles
so as illustrated in the diagram below;
y² = x² + ( x + 5 )²
2y[tex]\frac{dy}{dt}[/tex] = 2x[tex]\frac{dx}{dt}[/tex] + 2(x+5)[tex]\frac{dx}{dt}[/tex]
y[tex]\frac{dy}{dt}[/tex] = ( 2x + 5 ) ][tex]\frac{dx}{dt}[/tex]
[tex]\frac{dy}{dt}[/tex] = [( 2x + 5 )/y ][tex]\frac{dx}{dt}[/tex] ------ let this be equation 1
Now, given that, [tex]\frac{dx}{dt}[/tex] = 30 miles/hr, when x = 10
so
y = √( 10² + 15² ) = √325
so from equation 1
[tex]\frac{dy}{dt}[/tex] = [( 2x + 5 )/y ][tex]\frac{dx}{dt}[/tex]
we substitute
[tex]\frac{dy}{dt}[/tex] = [( 2(10) + 5 ) / √325 ]30
[tex]\frac{dy}{dt}[/tex] = [ 25 / √325 ] × 30
[tex]\frac{dy}{dt}[/tex] = 41.6 miles/hr
Therefore, their distance is increasing at the rate of 41.6 miles/hr
(a) Express the prime number 3 as the difference of two squares? 3=
Answer:
2^2 - 1^2
Step-by-step explanation:
1^1 = 1
2^2 = 4
4-1 =3
2^2 - 1^1 = 3
I need help completing this problem ASAP
Answer:
7x sqrt(2) - 2 sqrt(2)
Step-by-step explanation:
5x sqrt(2) - 2 sqrt(2) + 2x sqrt(2)
Combine like terms
5x sqrt(2) + 2x sqrt(2) - 2 sqrt(2)
7x sqrt(2) - 2 sqrt(2)
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
18x + 3y = -18
Answer:
y = -6x -6
Step-by-step explanation:
The general form of the equation of a line in the slope-intercept form may be given as
y = mx + c where
m is the slope and c is the intercept
Hence given the equation
18x + 3y = -18
subtract 18x from both sides
3y = -18x - 18
Divide both sides of the equation by 3
y = -6x -6
This is the equation in the slope - intercept form with -6 as the slope and -6 as the intercept
Describe what is the most difficult part of solving equations, for you personally.
What do you personaly feel like is most dificult.
For me its rembering minus signs
Complete the coordinate table for the given equation.
Xy=-4
Step-by-step explanation:
X= -4,-2,2,4 (respectively)
Y=4,-4 (respectively)
hope it helps
1000 randomly selected Americans were asked if they believed the minimum
wage should be raised. 600 said "yes." What is the 99% confidence interval
for the proportion of Americans who believe that the minimum wage should
be raised?
Answer:i dont now
Step-by-step explanation:
What steps are included in the construction of a perpendicular line through a point on a line
Answer:
A perpendicular line from a given point
Place your compass on the given point (point P).
From each arc on the line, draw another arc on the opposite side of the line from the given point (P).
Use your ruler to join the given point (P) to the point where the arcs intersect (Q).
Answer:
get the slope of original line
take the inverse of the slope and multiply by -1 (2/3 becomes - 3/2)
y = -b/a x + b
plug on y & x using the given point
calculate the "B"
go back to the y = -b/ax + calculated "B"
that is your answer
Step-by-step explanation:
