When there is a _____ relationship, as values of variable X (e.g., elevation) increase, values of variable Y (e.g., temperature) decrease.Answers:a. positiveb. negativec. curvilineard. zerozero

The Bernoulli differential equation is a nonlinear ordinary differential equation of the form:

dy/dx + P(x)y = Q(x)y^n, where n ≠ 0, 1.

For n = 0 or n = 1, the equation is linear. For other values of n, a common technique to linearize the equation is to make the substitution y = v^(-1/n-1). The resulting equation is:

dv/dx + (P(x) + Q(x)/v^(1/n-1)) * (1/n-1) * v^(1/n-2) * dv/dx = 0.

For the initial value problem given, we have P(x) = -1/x, Q(x) = -5, and n = 2.

We make the substitution y = v^(-1), so v = y^(-1), and dv/dx = -y^(-2)dy/dx. The equation becomes:

-y^(-2)dy/dx + (-1/x - 5y^2) = 0.

We have the initial condition y(1) = 1/5. In terms of v, the initial condition becomes v(1) = 1/(1/5)^2 = 25.

Now, the differential equation is linear, and we can solve it using standard methods, such as separation of variables. To find the solution that satisfies the initial condition, we may use numerical methods such as the Euler method or Runge-Kutta method.

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Answer:To calculate the annual percentage rate (APR) and effective annual rate of interest on Aruna's investment, we can use the following formula:

APR = (FV/PV)^(1/n) - 1

Where FV is the Future Value, PV is the Present Value, and n is the number of periods.

In this case, FV = 168,925, PV = 150,000, and n = 1.5 (since the investment was held for 18 months).

Therefore, the APR = (168,925/150,000)^(1/1.5) - 1

APR = 6.66%

The effective annual rate of interest (EAR) can be calculated using the following formula:

EAR = (1 + APR/m)^m - 1

Where m is the number of compounding periods in one year.

In this case, m = 4 (since interest is paid every 3 months).

Therefore, the EAR = (1 + 6.66%/4)^4 - 1

EAR = 8.24%

Based on the Alternate Exterior Angles Theorem, the measure of angle 7 is 65 degrees.

The Alternate Exterior Angles Theorem states that if two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent (equal in measure). In other words, the angles on the outside of the lines, on opposite sides of the transversal, have the same measure

Angles 1 and 7 are exterior angles, therefore:

m<7 = m<1

Substitute

m<7 = 65 degrees.

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The linear function whose graph has slope -4 and passes through the point (5, 2) is f(x) = -4x + 22

Let us assume that f(x) be a required linear function.

We know that an equation of the line passing through point (x₀, y₀) and having slope m is:

(y -  y₀) = m(x - x₀)

Let  (x₀, y₀) = (5, 2) and slope m = -4

So, the equation of the line would be,

(y -  y₀) = m(x - x₀)

(y - 2) = -4(x - 5)

y - 2 = -4x + 20

y -2 + 2 = -4x + 20 + 2

y = -4x + 22

Let y = f(x)

f(x) = -4x + 22

So, the linear function is: f(x) = -4x + 22

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Answer: y = 4 and LH = 16

Step-by-step explanation:

because of the fact that HJK is bisected by LJ, we know that LH and LK are equal. with that, we can equal 3y + 4 and 6y - 8.

3y + 4 = 6y - 8

3y + 12 = 6y

12 = 3y

y = 4

with that, we can now plug in 4 for y in 6y - 8.

6(4) - 8

24 - 8

16

Therefore, y = 4 and LH = 16.

Consider the continuous random variable x that has a uniform distribution over the interval from 40 to 44. The variance of 'x' is approximately C: 1.155.

The variance of a continuous uniform distribution over the interval [a, b] is determined by the formula given as follows:

Var(x) = (b-a)^2 / 12

For the given distribution, a = 40 and b = 44, so the variance is calculated by putting these values into the above formula:

Var(x) = (44 - 40)^2 / 12 = 1.155

Therefore, the variance of 'x' is approximately 1.155

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Answer:

2 units

Step-by-step explanation:

vertical distance will be the magnitude of the difference in the 'y' coordinates

| -.8 - 1.2| = 2 units

A hydrogen donor and acceptor must both be present for a hydrogen bond to form.

The key concepts in hydrogen bonding are;

Typically, a strongly electronegative element like N, O, that is covalently connected to a hydrogen bond serves as the donor in a hydrogen bond.

Given that the information is incomplete, the above information shows adequate information about hydrogen bonds.

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The function rules are (a) f(x) = x - 10, (b) g(x) = 0.85x, (c) g (f(x)) = 0.85x - 8.5 and (d) f (g(x)) = 0.85x - 10

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Let x be the original price of the item.

(a) You have $10 coupon.

Price of the item after applying coupon = x - 10

f(x) = x - 10

(b) There is a 15% discount.

Discounted price of the item = x - (15% × x)

                                               = x - (0.15x)

                                               = 0.85x

g(x) = 0.85x

(c) We have f(x) = x - 10 and g(x) = 0.85x

Price of the item when applied $10 coupon first and then taking the 15% discount is,

g (f(x)) = g(x - 10) = 0.85(x - 10) = 0.85x - 8.5

(d) Price of the item when applied 15% discount first and then taking the $10 coupon is,

f (g(x)) = f(0.85x) = 0.85x - 10

(e) We have  g (f(x)) = 0.85x - 8.5 and f (g(x)) = 0.85x - 10

The price will be lower for the composite function f (g(x)) = 0.85x - 10, since there is a $10 decrease in the 0.85x.

Hence the rules for the functions are f(x) = x - 10 and g(x) = 0.85x. The composite functions are g (f(x)) = 0.85x - 8.5 and f (g(x)) = 0.85x - 10.

The price will be lower when we first apply the discount and then the coupon.

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Answer:

The logistic equation is a differential equation that describes the growth of a population over time. The solution of this equation can be found using separation of variables or other methods of solving differential equations. The general solution for the logistic equation is given by:

y(t) = y_0 * e^(rt) / (1 + (y_0 - 1)e^(rt))

Where y_0 is the initial population size, r is the growth rate, and t is time.

For the specific case given in the question, we have the initial conditions y1(0)=14 and y2(0)=-3. We can use these to find the specific solution for each case.

1(0)=14 => y1(t) = 14e^(rt) / (1 + (14 - 1)e^(rt))

2(0)=−3 => y2(t) = -3e^(rt) / (1 + (-3 - 1)e^(rt))

It is important to note that we can not find the exact value of r without additional information.

Answer:

y(t) = 1 / (1 + (-4e^(-t))

Step-by-step explanation:

The logistic equation is a nonlinear differential equation that describes how a population grows. The solution for the logistic equation is given by y(t) = 1 / (1 + (Ce^(-t)) where C is the constant of integration, which can be determined by the initial conditions.

For the first initial condition, 1(0)=14, we can substitute the initial condition into the solution to get:

y(0) = 1 / (1 + (Ce^(0)) = 1 / (1 + C) = 14

Solving for C, we get C = 13.

So the solution for the first initial condition is:

y(t) = 1 / (1 + (13e^(-t))

For the second initial condition, 2(0)=-3, we can substitute the initial condition into the solution to get:

y(0) = 1 / (1 + (Ce^(0)) = 1 / (1 + C) = -3

Solving for C, we get C = -4.

So the solution for the second initial condition is:

y(t) = 1 / (1 + (-4e^(-t))

Answer:

$270

Step-by-step explanation:

0.12 x 750 = 90

90 x 3 = 270

Ashley makes house calls. For each, she is paid a base amount and makes additional money for each hour she works. The graph below shows her pay (in dollars) versus the number of hours worked.

A) Ashley’s pay for a course call if she doesn’t work any hours is $60

B) her pay is she works 1 hour is: $90

C) her pay increases for each hour worked is: $30

D)  No. Because if she works 1 hour it becomes $90 as at 0 hours her pay becomes $60.

And her pay increases for each hour is $30.

Correct option: D

The amount of U.S dollars that would be produced if the appropriate foreign currency were converted into US dollars.

Currency rates, Treasury bills, and foreign exchange reserves are the three metrics used to determine the value of the US dollar. The fact is that you need to be familiar with all three in order to make informed predictions about where the dollar could go next, even if the most popular technique is through exchange rates.

This simply indicates that her set compensation (at 0 hours, even before she begins working), is $60, and that she earns $30 for each subsequent hour worked, or a $30 rise in pay overall.

Thus, correct option: D

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The length of each edge of the cube : C : 2∛12

Three-dimensional space is quantified by volume.

V= a³ => 96 = a³ => a= ∛96 =2∛12

The length of each edge of the cube : C : 2∛12

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Answer:

21 IAMOOOOOOOO

Step-by-step explanation:

Answer:

w = 64

Step-by-step explanation:

A = 6016[tex]m^2[/tex]

l = 94m

A = lw

Sub in all the known values

6016 = (94)(w)

w = [tex]\frac{6016}{94}[/tex]

w = 64

By algebra properties, the four general equations represents the standard form of the equation of the sphere.

In this problem we find four general equations that must be checked if it represent spheres, this can be done by completing the square, an application of algebra properties, and obtaining the standard form of the formula. The standard form of a sphere is shown below:

(x - h)² + (y - k)² + (z - m)² = r²

Where:

Now we proceed to determine if each equation represents a sphere:

Case 15:

x² + y² + z² - 2 · x - 4 · y + 8 · z = 15

(x² - 2 · x) + (y² - 4 · y) + (z² + 8 · z) = 15

(x² - 2 · x + 1) + (y² - 4 · y + 4) + (z² + 8 · z + 16) = 15 + 1 + 4 + 16

(x - 1)² + (y - 2)² + (z + 4)² = 6²

Case 16:

x² + y² + z² + 8 · x - 6 · y + 2 · z + 17 = 0

x² + y² + z² + 8 · x - 6 · y + 2 · z = - 17

(x² + 8 · y) + (y² - 6 · y) + (z² + 2 · z) = - 17

(x² + 8 · y + 16) + (y² - 6 · y + 9) + (z² + 2 · z + 1) = - 17 + 16 + 9 + 1

(x + 4)² + (y - 3)² + (z + 1)² = 3²

Case 17:

2 · x² + 2 · y² + 2 · z² = 8 · x - 24 · z + 1

x² + y² + z² = 4 · x - 12 · z + 1 / 2

(x² - 4 · x) + y² + (z² + 12 · z) = 1 / 2

(x² - 4 · x + 4)² + y² + (z² + 12 · z + 36) = 1 / 2 + 4 + 36

(x - 2)² + y² + (z + 6)² = 81 / 2

(x - 2)² + y² + (z + 6)² = (9√2 / 2)²

Case 18:

3 · x² + 3 · y² + 3 · z² = 10 + 6 · y + 12 · z

x² + y² + z² = 2 · y + 4 · z + 10 / 3

x² + (y² - 2 · y) + (z² - 4 · z) = 10 / 3

x² + (y² - 2 · y + 1) + (z² - 4 · z + 4) = 10 / 3 + 1 + 4

x² + (y - 1)² + (z - 2)² = 25 / 3

x² + (y - 1)² + (z - 2)² = (5√3 / 3)²

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A simple way to depict sets visually is with a Venn diagram, also called an Euler-Venn diagram. A circle is used for the sets that are being considered, and a rectangle is used as the standard representation.

Consequently, we'll talk about issues with variables two and three in this post.

Let's look at some fundamental Venn diagram formulas for two and three members.

n (A ∪ B) = n (A + B) - n (A ∪ B)

n (A ∪ B ∪ C ) = n(A) + n (B) + n (C) - n (A ∩ B) - n (B  ∩ C) - n (C ∩  A) + n (A  ∩ B  ∩ C)

Then, where n(A) is the quantity of elements in set A, goes on.

You won't need to memorize these formulas once you've understood the notion of a Venn diagram using diagrams.

In this scenario, X is the number of elements that only belong to set A, Y is the number of elements that only belong to set B, and Z is the number of elements that both sets A and B (A + B) contain.

W is the number of objects that are not part of either set A or set B.

n(A) = x + z; n(B) = y + z; n(A B) = z; and n (A B) = x + y + z are all easily deduced from the above diagram.

w = total number of elements = x + y + z.

The Complete Question.

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The ball reaches a maximum height of 35.375 ft.

s(t) = -16t^2 + 28t + 5

To find the time at which the ball reaches its maximum height, we can take the derivative of the height function with respect to time:

s'(t) = -32t + 28

And then set the derivative equal to zero and solve for t:

-32t + 28 = 0

32t = 28

t = 28/32 = 7/8 sec

So, the ball reaches its maximum height 7/8 seconds after it was thrown.

Next, we can plug this value of t back into the height function to find the maximum height:

s(7/8) = -16 * (7/8)^2 + 28 * (7/8) + 5 = 9.375 + 21 + 5 = 35.375 ft

Therefore, The ball reaches a maximum height of 35.375 ft.

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Answer:

(-18±[tex]\sqrt{204}[/tex])÷6

Step-by-step explanation:

Answer:

Step-by-step explanation:

To determine the minimum number of students needed, we need to first determine how many newspapers and magazines each student can deliver in total (over 8 hours).

Each student can deliver 35 newspapers + 50 magazines = 85 newspapers + magazines per hour.

In 8 hours, each student can deliver 85 newspapers + magazines/hour * 8 hours = 680 newspapers + magazines.

Now, we can divide the total number of newspapers and magazines to be delivered by the number of newspapers and magazines each student can deliver in 8 hours:

875 newspapers + 1200 magazines = 2075 newspapers + magazines

2075 newspapers + magazines / 680 newspapers + magazines/student = 3 students.

Therefore, the minimum number of students needed to deliver 875 newspapers and 1200 magazines is 3 students.

The required diameter of the spherical gasoline tank is given as 50 feet.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

Here,
The volume of the cylinder = 4/3πr³
4/3πr³ = 65450
r³ = 15625
r = 25 feet

Diameter = 2 × r
              = 2 × 25
              = 50 feet

Thus, the required diameter of the spherical gasoline tank is given as 50 feet.

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The 15 terms are: 2, -12, 7, -2, 20, -30, 42, -56, 72, -90, 110, -132, 156, -182, 210.

Arithmetic Progression (AP) is a numerical series in which the differences between any two successive integers is a fixed value. Arithmetic Sequence is another name for it. We will come across various key terminologies in AP, which are designated as: The first term (a), Common distinction (d), nth Term (an),The total of the first n terms (Sn).

A progression is a sort of sequence in which a formula for the nth term may be found. The Arithmetic Progression is the most often used sequence in mathematics, using simple formulae. There are three types of progressions in mathematics. They are as follows: Arithmetic Progression (AP), Geometric Progression (GP), and Harmonic Progression (HP).

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The equation of the line passing through the point (0, 8), and having a slope of m = 4 is y = 4x + 8.

The slope of the line and a point on the line can be used to create the equation of a line. To better comprehend how the equation for a line is formed, let's learn more about the line's slope and the necessary point on the line. The slope of the line, which can be stated as a numeric integer, fraction, or the tangent of the angle it forms with the positive x-axis, is the line's inclination with respect to the positive x-axis. The coordinate system's point with the x coordinate and the y coordinate is referred to as the point.

The equation of the line passing through the points (x1, y1), with a slope of m is given by the formula:

(y - y1) = m (x - x1)

Given that the point is (0, 8) and the slope, m = 4.

Substituting the values we have:

(y - y1) = m (x - x1)

y - 8 = 4 (x - 0)

y - 8 = 4x

y = 4x + 8

Hence, the equation of the line passing through the point (0, 8), and having a slope of m = 4 is y = 4x + 8.

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The four main principles of randomized experiments are:

True, True, False, True, and True

1. True: Confounding variables can make it harder to draw conclusions from a study because they can obscure the effect of the treatment being studied. Confounding variables are extraneous factors that can affect the outcome of the study and mimic or mask the effect of the treatment being studied.

2. True: In a randomized experiment, the treatment and control groups are designed to be as similar as possible in terms of all relevant factors, except for the treatment itself. This helps to ensure that any observed differences between the groups can be attributed to the treatment being studied, rather than to other factors that might affect the outcome.

3. False: Observational studies are generally considered to be less reliable than randomized experiments because they are subject to a number of biases that can affect the results. For example, observational studies often involve selection bias, in which certain groups are more likely to be included in the study, and measurement bias, in which the measurements used in the study are not accurate or reliable.

4. True: The four main principles of randomized experiments are:  

5. True: In a double-blind study, neither the investigators nor the subjects know who is receiving which treatment. This helps to reduce the potential for bias and increase the reliability of the results, by ensuring that neither the investigators nor the subjects can influence the outcome of the study based on their knowledge of the treatment assignments.

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Answer:

p = - 4

Step-by-step explanation:

- 0.9p + 3.2 = - 1.7p ( add 1.7 to both sides )

0.8p + 3.2 = 0 ( subtract 3.2 from both sides )

0.8p = - 3.2 ( divide both sides by 0.8 )

p = [tex]\frac{-3.2}{0.8}[/tex] = - 4

Answer: p=-4

Step-by-step explanation:

-0.9p+3.2=-1.7p

+0.9p          +0.9p

3.2=-0.8p

32=-8p

p=-4

Answer:

below

Step-by-step explanation:

The direct distance, d, from starting point is the hypotenuse of a right triangle with two legs of 25 mi and 15 mi

Pythagorean Theorem

d^2 = 25^2 + 15^2

   show d = sqrt(850) = 29.15 mi

Answer:

I believe it is -0.2

Step-by-step explanation:

Because all your doing is simplifying the equation, Tell me if im wrong that way other people know  

Answer:

Step-by-step explanation:

The revenue can be modeled by the polynomial function

R

(

t

)

=

−

0.037

t

4

+

1.414

t

3

−

19.777

t

2

+

118.696

t

−

205.332

where R represents the revenue in millions of dollars and t represents the year, with t = 6 corresponding to 2006. Over which intervals is the revenue for the company increasing? Over which intervals is the revenue for the company decreasing? These questions, along with many others, can be answered by examining the graph of the polynomial function. We have already explored the local behavior of quadratics, a special case of polynomials. In this section we will explore the local behavior of polynomials in general.

Multiplicity and Turning Points

Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.

Suppose, for example, we graph the function

f

(

x

)

=

(

x

+

3

)

(

x

−

2

)

2

(

x

+

1

)

3

.

Notice in the figure below that the behavior of the function at each of the x-intercepts is different.

Graph of h(x)=x^3+4x^2+x-6.

The behavior of a graph at an x-intercept can be determined by examining the multiplicity of the zero.

The x-intercept

x

=

−

3

is the solution to the equation

(

x

+

3

)

=

0

. The graph passes directly through the x-intercept at

x

=

−

3

. The factor is linear (has a degree of 1), so the behavior near the intercept is like that of a line; it passes directly through the intercept. We call this a single zero because the zero corresponds to a single factor of the function.

The x-intercept x=2

is the repeated solution to the equation  (x−2)2=0

. The graph touches the axis at the intercept and changes direction. The factor is quadratic (degree 2), so the behavior near the intercept is like that of a quadratic—it bounces off of the horizontal axis at the intercept.

(x−2)2=(x−2)(x−2)

The answer is cos CAB = 5 × √(10² + h²) in terms of x.

"h" denotes the parallelogram's height.

We know that the base of parallelogram A and B is 10, so the area of parallelogram A and B can be found by:

Area = base * height = 10 * h

Since parallelogram A and B make up a hexagon, their combined area must equal the area of the hexagon:

2 * (10 * h) = 6 * h * a/2

Where a is the length of one of the sides of the hexagon.

Solving for a, we get:

a = 5 * h

Next, let's find the length of DE, which is equal to BC.

We know that the height of parallelogram A is h, and the base is 10.

So, the diagonal of parallelogram A can be found using the Pythagorean theorem:

DA = √(10² + h²)

Since DE = DA, we can substitute DA with DE:

DE = √(10² + h²)

Now we can find cos CAB using the Law of Cosines:

cos CAB = (AB² + BC² - AC²) / 2 * AB * BC

AB = 10

BC = DE = √(10²+ h²)

AC = 10

So,

cos CAB = (10² + (√(10² + h²))² - 10²) / 2 * 10 * √(10² + h²)

= (√(10² + h²))² / 2 * 10 * √(10² + h²)

= 5 × √(10² + h²)

Since h is a variable, we cannot simplify the expression further.

Therefore, cos CAB = 5 × √(10² + h²) in terms of x.

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Answer:

16x + 5

Step-by-step explanation:

2(5x + 4) + 3(2x - 1) ← distribute both parenthesis

= 10x + 8 + 6x - 3 ← collect like terms

= (10x + 6x) + (8 - 3)

= 16x + 5