Choose the rate of change (slope) to match the line. The graph with the X-coordinate marks -4, -2, 0, 2, and 4. The Y-coordinate mark -4, -2, 0, 2, and 4. There is line which intersects x-axis at (0.5, 0) and y-axis at (0, 1), and passes through point (2, -2). A. –2 B. –32 C. –1 D. –23

Answer:

To solve the Bernoulli equation t^2y' + 9ty − y^3 = 0, we use the substitution v = y^(1−2) = y^−1.

Differentiating v with respect to t, we get:

dv/dt = −y^−2 dy/dt

Using the chain rule, we have:

dy/dt = −y^2 dv/dt

Substituting y^−1 for v and −y^2 dv/dt for dy/dt, we get:

t^2 (−y^2 dv/dt) + 9t (1/y) y^2 − (1/v)^3 = 0

Simplifying and multiplying through by v^3, we get:

−t^2v^3 dv/dt − 9tv^2 + 1 = 0

This is now a separable differential equation. We can move the dv term to the left and the t term to the right, and then integrate both sides:

−v^−3 dv = 9t^−1 dt

Integrating both sides, we get:

v^−2/−2 = 9 ln|t| + C

Substituting v = y^−1, we get:

y^2/2 = (−1/2C) − 9 ln|t|

where C is the constant of integration.

Therefore, the solution to the given Bernoulli equation is:

y = [2/(−1/2C − 18 ln|t|)]^(1/2)

give thanks for more! your welcome!

Step-by-step explanation:

A z-score of -2 indicates that the sample mean does not occur very often by chance in the sampling distribution of means and probably did not come from the given population.

To answer this question, we need to calculate the z-score of the sample mean. The formula for the z-score is (sample mean - population mean) / standard error.

Plugging in the values given, we get:

z = (80 - 100) / 10 = -2

A z-score of -2 indicates that the sample mean is 2 standard errors below the population mean.

Based on this information, we can conclude that the sample mean does not occur very often by chance in the sampling distribution of means, and probably did not come from the given population.

This is because the z-score is beyond the typical range of values we would expect to see if the sample mean came from the population.

In this case, you have a random sample with a mean of 80, while the population mean is 100, and the standard error is 10.

To calculate the z-score, use the formula: (sample mean - population mean) / standard error, which is (80-100)/10 = -20/10 = -2.

Visit here to learn more about Standard Error:

brainly.com/question/1191244

#SPJ11

A. The required vectors to component form as:  -7(u • v) = -21√(6).

B. u and w are neither parallel nor orthogonal.

Part A:

The vectors are given as:

u = −2(cos 30°i + sin30°j),

v = 6(cos 225°i + sin225°j),

w = 8(cos 120°i + sin120°j)

So we have:

u = -2(√(3)/2 i + 1/2 j) = -√(3) i - j

v = 6(-√(2)/2 i - sqrt(2)/2 j) = -√(2) i - √(2) j

w = 8(-1/2 i + √(3)/2 j) = -4i + √(3) j

To find -7(u • v), we first need to find the dot product of u and v:

u • v = (-√(3))( -√(2) ) + (-1)(-√(2)) = √(6)

Then, we can multiply by -7:

-7(u • v) = -7(√(6)) = -√(6)

Therefore, -7(u • v) = -21√(6).

Part B:

To determine if u and w are parallel, orthogonal, or neither, we can use the dot product:

u • w = (-√(3))(-4) + (-1)(4√(3)) = -8√(3)

Since the dot product is not equal to 0, we know that u and w are not orthogonal. To determine if they are parallel, we can compare their direction vectors:

The direction vector of u is < -√(3), -1 >, and the direction vector of w is < -4, 4√(3) >.

If u and w are parallel, then their direction vectors will be scalar multiples of each other.

So we need to check if there exists a scalar k such that:

< -√(3), -1 > = k < -4, 4√(3) >

This is equivalent to the system of equations:

-k × 4 = -√(3)

k × 4√(3) = -1

Solving for k, we get:

k = √(3)/12

Since k is not a real number, we know that u and w are not parallel.

Therefore, u and w are neither parallel nor orthogonal.

Learn more about the vectors here :

brainly.com/question/17254148

#SPJ1

The line integral is approximately equal to 0.2675 or 6/5, depending on the method used.

To evaluate the line integral y³ds along the curve C given by x=t³, y=t, 0<=t<=2, we can use either the parameterization method or the line integral formula.

Using the parameterization method, we first find the parametric equations for C:

x = t³
y = t

Then, we can express ds in terms of dt:

ds = √((dx/dt)² + (dy/dt)²) dt
  = √((3t²)² + (1)²) dt
  = √(9t⁴ + 1) dt

Therefore, the line integral can be written as:

integral(y³ ds) = integral(y³ √(9t⁴ + 1) dt)
                 = integral(t³ √(9t⁴ + 1) dt)
                 = 0.2675 (approx.)

Alternatively, we can use the line integral formula:

integral(y³ ds) = integral(y³ dx) - integral(y'² dx)
                 = integral(t³ 3t² dt) - integral(1 9t⁴ dt)
                 = 2 - 32/5
                 = 6/5

Therefore, the line integral is approximately equal to 0.2675 or 6/5, depending on the method used.

To learn more about integral here:

brainly.com/question/18125359#

#SPJ11

The difference in the account balances at the end of the loan terms is given as follows:

$1,686.87.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

The parameters for the offer 2 are given as follows:

P = 75000, r = 0.035, n = 12, t = 62/12.

Hence the balance of the offer 2 is given as follows:

B = 75000 x (1 + 0.035/12)^(12 x 62/12)

B = $89,842.51.

The balance of Offer 1 is of $91,529.38, hence the difference in the balances is given as follows:

91529.38 - 89842.51 = $1,686.87.

More can be learned about compound interest at https://brainly.com/question/24274034

#SPJ1

The Area of R in terms of a is 288a.

first we need to understand what R represents. R is the region bounded by the x-axis, the graph of f(x), and the lines x=6 and x=-6. To find the area of R in terms of a, we need to integrate f(x) from -6 to 6.

∫f(x)dx = ∫a(36-x^2)dx = a∫(36-x^2)dx

To integrate (36-x^2), we can use the power rule: ∫x^n dx = (x^(n+1))/(n+1) + C, where C is the constant of integration. So:

a∫(36-x^2)dx = a(36x - (x^3)/3) + C

Now we need to evaluate the definite integral from -6 to 6:

Area of R = ∫(-6)^6 f(x)dx = a(36(6) - (6^3)/3) - a(36(-6) - ((-6)^3)/3)
= 432a - 432a/3
= 288a

Therefore, the area of R in terms of a is 288a.

To Learn More About Area

https://brainly.com/question/2607596

#SPJ11

The Master Theorem is a powerful tool for solving divide-and-conquer recurrences. It provides a way to quickly determine the asymptotic behavior of algorithms by analyzing their running time.

Case 1 of the Master Theorem applies to algorithms that split the problem into smaller subproblems of equal size and combine their solutions in constant time. In this case, the running time can be expressed as T(n) = aT(n/b) + f(n), where a is the number of subproblems, b is the size of each subproblem, and f(n) is the time to combine the subproblem solutions. The solution to this recurrence is T(n) = Θ(nlogba) if f(n) = Θ(nlogka) for some constant k < log(ba).

Case 2 of the Master Theorem applies to algorithms that split the problem into smaller subproblems of equal size and combine their solutions in linear time. In this case, the running time can be expressed as T(n) = aT(n/b) + f(n), where a is the number of subproblems, b is the size of each subproblem, and f(n) is the time to combine the subproblem solutions. The solution to this recurrence is T(n) = Θ(nlogba logn) if f(n) = Θ(nlogba) .

If the recurrence cannot be expressed in either of these forms, then the Master Theorem does not apply. In this case, other techniques such as substitution or recursion trees may be used to solve the recurrence.

Learn more about Theorem:

brainly.com/question/29196697

#SPJ11

Step-by-step explanation:

Calculate the unit rate as follows

2.4 kg  / 20 bag =   .12 kg per bag

The area of the shaded region is 70.65 ft² and length of arc ADB is 260.

We have,

The radius of the circle is 9 ft.

The measure of ∠AOB is 100°.

So, The measure of ∠ADB

= 360 - <AOB

= 360 - 100

= 260

So, The area of the shaded region

A = ([tex]\theta[/tex]/360) πr²

A = (100/360) (3.14) (9)²

A = 70.65 ft²

Learn more about Area of Sector here:

https://brainly.com/question/7512468

#SPJ1

If you said that fold f2 was a plunging fold, the direction of plunge is NorthEast. Option a is correct.

A plunging fold is a type of fold in which the fold axis has an inclined orientation with respect to the horizontal plane. When describing a plunging fold, the direction of plunge is important as it indicates the orientation of the axis.

In this case, it has been determined that fold f2 is a plunging fold and the direction of plunge is towards the northeast (NE). This means that the fold axis has an inclined orientation towards the NE direction. Understanding the direction of plunge is important for interpreting the deformation history of the rock formation and can also be useful in predicting the location of mineral deposits or hydrocarbons. Hence option a is correct.

To know more about plunging fold, here

brainly.com/question/28173288

#SPJ4

Therefore, the solutions to the equation x² + 3x = 3 are x = -3/2 + √(21)/2 and x = -3/2 - √(21)/2.

An equation is a mathematical statement that shows the equality of two expressions. It usually consists of two sides separated by an equal sign (=). The expressions on both sides of the equal sign can include numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

Here,

To complete the square for the expression x² + 3x, we need to add and subtract (3/2)² = 9/4 inside the parentheses, as follows:

x² + 3x = x² + 3x + 9/4 - 9/4

= (x + 3/2)² - 9/4

Now the left-hand side can be written as:

(x + 3/2)² - 9/4 = 3

Adding 9/4 to both sides, we get:

(x + 3/2)² = 3 + 9/4

= 21/4

Taking the square root of both sides, we get:

x + 3/2 = ±√(21)/2

Subtracting 3/2 from both sides, we get the two solutions:

x = -3/2 ± √(21)/2

To know more about equation,

https://brainly.com/question/649785

#SPJ1

So there are 6,442,752 different license plates that can be issued under these restrictions.

There are a few different restrictions to consider when calculating the number of possible license plates that can be issued. Let's break it down step by step:

The first symbol must be a letter: There are 24 letters to choose from (all except o and i).

The second symbol must be a digit: There are 8 digits to choose from (all except 0 and 1).

The final three symbols can be either letters or digits: For each of the final three symbols, there are 24 letters and 8 digits to choose from (the same restrictions as above).

All five symbols must be chosen: We can multiply the number of choices for each symbol together to get the total number of possible license plates:

24 (choices for first symbol) * 8 (choices for second symbol) * 32,768 (choices for final three symbols, since there are 32 choices for each of the final three symbols) = 6,442,752

To know more about different license plates,

https://brainly.com/question/31544322

#SPJ11

The average increase in first-year GPA per one-point increase in ACT score is different for MSU students than it is for UM students.

Null hypothesis (H0): The relationship between ACT scores and GPA is the same for both UM and MSU students. The average increase in first-year GPA per one-point increase in ACT score is the same for both UM and MSU students.

Alternative hypothesis (Ha): The relationship between ACT scores and GPA is different for MSU students than it is for UM students. The average increase in first-year GPA per one-point increase in ACT score is different for MSU students than it is for UM students.

To learn more about MSU students visit:  https://brainly.com/question/30402013

#SPJ11

We can rewrite the given expression as follows:
$\sqrt{5} \frac{1}{\sqrt{5}} \sqrt{7} \frac{1}{\sqrt{7}} = \frac{\sqrt{5}}{\sqrt{5}} \cdot \frac{\sqrt{7}}{\sqrt{7}} = \frac{5}{\sqrt{5}\sqrt{5}} \cdot \frac{7}{\sqrt{7}\sqrt{7}}$

Now, we simplify further:
$= \frac{5}{5} \cdot \frac{7}{7} = \frac{1 \cdot 1}{1}$

So, in the form $\dfrac{a\sqrt{5}  b\sqrt{7}}{c}$, we have $a = 0$, $b = 0$, and $c = 1$. Therefore, the product $abc = 0 \cdot 0 \cdot 1 = 0$.

First, let's simplify the expression:
$\sqrt{5} \frac{1}{\sqrt{5}} \sqrt{7} \frac{1}{\sqrt{7}} = \frac{\sqrt{5}}{\sqrt{5}} \cdot \frac{\sqrt{7}}{\sqrt{7}} = 1$

So now we want to write $1$ in the form $\dfrac{a\sqrt{5}  b\sqrt{7}}{c}$ with positive integers $a$, $b$, and $c$, and $c$ as small as possible.

We can do this by setting $a=b=c=1$ since $1\cdot 1\cdot 1 = 1$ and $1$ is the smallest possible value for $c$. So we have:
$1 = \dfrac{1\sqrt{5}\cdot 1\sqrt{7}}{1}$

Therefore, $a=1$, $b=1$, and $c=1$, so $abc=1$.

Learn more about Expression:

brainly.com/question/14083225

#SPJ11

Answer:

Step-by-step explanation:

not for help but for points

Therefore , the solution of the given problem of percentage comes out to be Chong is the correct answer in (b).

In statistics, a figure or quantity that may be stated as a percent of 100 is denoted by the abbreviation "a%." Other odd spellings include "pct," "pct," and "pc." The percentage symbol ("%") is the technique that is most usually used for this. Also unknown are any clues or any fixed ratio of any part to the whole. Numbers are effectively integers since they frequently add up to 100. If a figure comprises a percentage, the expression "fraction" or simply the shorthand for % (%) must appear first.

Here,

We must first compute each person's commission earnings before comparing the results to see who received the highest commission payments.

On sales of $549.50, Janice received a 15% commission, which is:

commission:

=>  $82.425 ($0.15 x $549.50)

On sales of $343.25, Chong received a 25% commission, which is:

=>  commission = 0.25 * $343.25%, or $85.7125.

On sales of $418.75, Adrienne received a 20% commission, which is:

=> commission: $83.75 ($0.20 * $418.75)

On sales of $625.75, Luke received a 10% commission, which is:

=> commission: $62.575 = 0.10 * $625.75

By comparing the figures, it is clear that Chong, with $85.8125, earned the most through commission, followed closely by Adrienne, with $83.75,

Janice, with $82.425, and Luke, with $62.575.

So Chong is the correct answer in (b).

To know more about percentage visit:

https://brainly.com/question/28269290

#SPJ1

A segment that joins the other two sides of a triangle and runs parallel to its base is divided in half by a median line drawn from the vertex.

Consider a triangle ABC, where AB is the base, and CD is a segment parallel to AB, connecting sides AC and BC. Let E be the midpoint of CD and M be the midpoint of AB. We want to prove that CM is the median from vertex C and that it bisects CD.

To prove that CM is the median, we need to show that it passes through the midpoint of the third side, which is ED. First, we note that triangles CED and CMB are similar by angle-angle similarity. Therefore, we have CE/CB = DE/AB. Substituting this into the previous equation, we get CE/CB = DE/2MB. Rearranging, we have DE/CE = 2MB/CB. But DE/CE = 1 (because E is the midpoint of CD), so we have 1 = 2MB/CB, which implies that MB = CB/2. Thus, M is indeed the midpoint of CB.

Now, to prove that CM bisects CD, we need to show that EM = MD. Since E is the midpoint of CD, we have CE = DE. Also, since M is the midpoint of AB, we have AM = MB. Therefore, we have AE = AC/2 and BM = BC/2. But triangles AEC and BMC are similar by angle-angle similarity, so we have AE/AC = BM/BC, which implies that AE = BM. Substituting this into the previous equation, we get AC/2 = BC/4, which implies that BC = 2AC. Thus, BM = AC, and so we have MD = AC/2 = BM = AC. Therefore, CM bisects CD.

Therefore, we have shown that if a segment is parallel to the base of a triangle and connects the other two sides, then it is bisected by the median drawn from the vertex.

To learn more about Segments here:

brainly.com/question/17107345#

#SPJ11

If A is any n x n matrix,

(i) Proved that A + A^T is symmetric.

(ii) Proved that A - A^T is skew symmetric.

To show that A + A^T is symmetric, we need to show that (A + A^T)^T = A + A^T.

Now, (A + A^T)^T = A^T + (A^T)^T = A^T + A

Therefore, if we add A + A^T, we get

(A + A^T) + (A^T + A) = 2A^T + 2A

Which is clearly equal to 2(A + A^T). Therefore,

(A + A^T)^T = A + A^T

So, A + A^T is symmetric.

To show that A - A^T is skew symmetric, we need to show that (A - A^T)^T = -(A - A^T).

Now, (A - A^T)^T = A^T - (A^T)^T = A^T - A

Therefore, if we negate A - A^T, we get:

-(A - A^T) = -A + A^T

And we see that (A - A^T)^T = -(A - A^T) holds true.

Thus, we have shown that A + A^T is symmetric, and A - A^T is skew symmetric for any nxn matrix A.

Learn more about matrix here

brainly.com/question/14405062

#SPJ4

The circumference of the gasket when in service is 6.4 cm, which is twice the original circumference of 3.2 cm, consistent with the scale factor of 2.

When we say that the rubber gasket expands by a scale factor of 2, we mean that all of its linear dimensions, such as its length, width, and circumference, double in size.

Let's focus on the circumference, which is the distance around the outside of a circle. The circumference of a circle is calculated using the formula:

Circumference = 2 x π x radius

In this case, we don't know the radius of the gasket, but we do know its circumference, which is given as 3.2 cm. We can rearrange the formula to solve for the radius:

radius = Circumference / (2 x π)

Plugging in the given circumference, we get:

radius = 3.2 cm / (2 x π) ≈ 0.509 cm

Now that we know the radius, we can calculate the circumference of the gasket when in service. Since the scale factor is 2, we know that the new radius will be:

new radius = old radius x scale factor = 0.509 cm x 2 = 1.018 cm

Using the same formula as before, but with the new radius, we get:

Circumference in service = 2 x π x new radius

Circumference in service = 2 x π x 1.018 cm ≈ 6.4 cm

Therefore, the circumference of the gasket when in service is 6.4 cm, which is twice the original circumference of 3.2 cm, consistent with the scale factor of 2.

To learn more about consistent  visit:  https://brainly.com/question/3935025

#SPJ11

We can solve this problem by using the formula for the number of elements in the union of two sets:

n(A U B) = n(A) + n(B) - n(A ∩ B)

where n(A) represents the number of elements in set A, n(B) represents the number of elements in set B, and n(A ∩ B) represents the number of elements in the intersection of sets A and B.

In this case, we have:

n(A) = 250

n(B) = 250

n(A U B) = 500 - 20 = 480

Substituting these values into the formula, we get:

480 = 250 + 250 - n(A ∩ B)

Solving for n(A ∩ B), we get:

n(A ∩ B) = 250 + 250 - 480 = 20

So, the number of customers who regularly buy both products A and B is 20.

To find the number of customers who regularly buy only product A, we can subtract the number of customers who regularly buy both products A and B from the total number of customers who regularly buy product A:

n(A) - n(A ∩ B) = 250 - 20 = 230

Therefore, the number of customers who regularly buy only product A is 230.

Answer:

2

Step-by-step explanation:

To determine whether the sequence is bounded, we can consider its behavior as n gets larger and larger. As n increases, 2^n grows exponentially, which means that a_n will also grow exponentially. However, no matter how large n gets, there will always be a constant term of 8 added to the result, which means that the sequence will never become unbounded. In other words, the sequence is both monotonic and bounded.

To determine the boundedness and monotonicity of the sequence a_n = 2^n + 8, n≥1, we can start by considering its first few terms:
a_1 = 2^1 + 8 = 10
a_2 = 2^2 + 8 = 12
a_3 = 2^3 + 8 = 16
a_4 = 2^4 + 8 = 24
From this, we can see that the sequence is increasing, as each term is larger than the one before it. This means that the sequence is monotonic.

Learn more about monotonicity of the sequence here, https://brainly.com/question/31405095

#SPJ11

The balance in the account after 5 years with quarterly compounding at a 3% annual interest rate, starting with an initial investment of $750, would be $859.43.

To calculate the balance in the account after 5 years with quarterly compounding at a 3% annual interest rate, we can use the formula for compound interest:

[tex]A = P (1 + r/n)^(^n^t^)[/tex]

where:

A is the final amount or balance in the account

P is the initial investment or principal amount

r is the annual interest rate expressed as a decimal (3% = 0.03)

n is the number of times the interest is compounded per year (4 for quarterly)

t is the time in years

Plugging in the given values, we get:

A = $750 (1 + 0.03/4)²⁰

= $750(1.0075)²⁰

=$750×1.161

=$870.75

Hence,  the balance in the account after 5 years with quarterly compounding at a 3% annual interest rate, starting with an initial investment of $750, would be $870.75

To learn more on Percentage click:

https://brainly.com/question/24159063

#SPJ1

The correct option is b. h0: π = 0.50, where π represents the probability of observing a positive difference.

The null hypothesis for a two-tailed sign test is that there is no difference between the two populations being compared.

Specifically, the null hypothesis is that the proportion of positive differences is equal to the proportion of negative differences, which is equivalent to stating that the median difference between the two populations is zero.

Therefore, the correct option is b. h0: π = 0.50, where π represents the probability of observing a positive difference.

Learn more about null hypothesis

brainly.com/question/28920252

#SPJ11

The dimensions of the rectangle is D. 7 units by 6 units

Go 2 units to the right, and then 3 units up

5(d + 1) = 5d + 5 .

A vertex (plural: vertices) is a point where two or more lines, edges, or curves meet in a geometric shape. In graph theory, a vertex refers to a node in a graph, which can be connected to other vertices by edges.

For example, in a triangle, each of the three points where the sides of the triangle meet is a vertex. In a cube, each of the eight points where the edges of the cube meet is a vertex. In a graph, each point representing a person or object would be a vertex, and the connections between them would be edges.

The term vertex is commonly used in mathematics, geometry, computer science, and other fields where shapes or networks are analyzed and studied.

Read more about vertices here:

https://brainly.com/question/29660530

#SPJ1

Answer:

51.84 gigabytes

Step-by-step explanation:

Answer: A

Step-by-step explanation:

Answer:  (x+3)^2+(y+10)^2=4

Step-by-step explanation:

The standard form of the equation of a circle is:

(x−x1)2+(y−y1)2=r2

In order to place the center of the circle at point (3, 10), simply replace x1 with 3 and y1 with 10

(x+3)^2+(y+10)^2=r2

Finally, replace r with the radius of the circle.

The final equation is:

(x+3)^2+(y+10)^2=4

The likelihood of randomly selecting a chocolate chip cookie is (c) equally likely and unlikely

From the question, we have the following parameters that can be used in our computation:

P(chocolate chip) = 50%

When a probability is at 50% ot 0.5, then it means that

The probability is equally likely and unlikely

Hence, the true statement is (c) equally likely and unlikely

Read more about probability at

https://brainly.com/question/24756209

#SPJ1

The flux of the smooth vector field ~f leaving an infinitesimal cube of volume dv is given by (~∇· ~f) dv. This is derived by finding the divergence of the vector field (~∇· ~f) and multiplying it by the volume of the cube (dv).

=
1. Consider an infinitesimal cube with sides dx, dy, and dz, and volume dv = dx * dy * dz.

2. Calculate the flux through each face of the cube.

3. For the x-faces, the flux is given by (f_x(x+dx, y, z) - f_x(x, y, z)) dy dz.

4. For the y-faces, the flux is given by (f_y(x, y+dy, z) - f_y(x, y, z)) dx dz.

5. For the z-faces, the flux is given by (f_z(x, y, z+dz) - f_z(x, y, z)) dx dy.

6. Add up the fluxes through all faces of the cube.

7. Divide the sum by dv to obtain the average flux per unit volume.

8. Use the definition of the divergence: ~∇· ~f = (∂f_x/∂x) + (∂f_y/∂y) + (∂f_z/∂z).

9. Multiply the divergence by dv to find the total flux leaving the cube: (~∇· ~f) dv.

To know more about divergence click on below link:

https://brainly.com/question/29757201#

#SPJ11