Which sets of ordered pairs represent functions from A to B? (Select all that apply.)

A = {0, 1, 2, 3} and B = {−2, −1, 0, 1, 2}

A. {(0, 2), (3, 0), (1, 1)}

B. {(0, 0), (1, 0), (2, 0), (3, 0)}

C. {(0, −1), (2, 2), (1, −2), (3, 0), (1, 1)}

D. {(0, 1), (1, −2), (2, 0), (3, 2)}

Step-by-step explanation:

ab + 3c = 2x

Subtract 3c from both sides

ab = 2x - 3c

Isolate b by dividing by a

b = (2x -3c)/a

Given the ODE using Frobenius Method x²y"+x²y¹-2y = 0The Frobenius method is used to obtain the power series solution of a differential equation of the form:

xy″+p(x)y′+q(x)y=0Which is given in your question as: x²y"+x²y¹-2y = 0The general form of the Frobenius solution can be expressed as a power series of the form:y(x)=x^r ∑_(n=0)^(∞) a_n x^n+rwhere 'r' is any arbitrary constant and the 'a_n' coefficients are determined from the recurrence relation.

The Frobenius method consists of substituting this power series into the differential equation and equating the coefficient of the same powers of x to zero. This method can be used to solve any second-order differential equation having a regular singular point.

Therefore, substituting the given equation we get:$$ x^2 y'' + x^2 y' - 2y = 0 $$Let the solution of the given equation be:y(x) = ∑_(n=0)^(∞) a_n x^(n + r)Substituting this in the differential equation, we get:$$ x^2y'' + x^2y' - 2y = \sum_{n=0}^\infty a_n [(n+r)(n+r-1)x^{n+r} + (n+r)x^{n+r} - 2x^{n+r}] $$Equating the coefficient of each power of x to zero, we get:Coefficients of x^(r):$$ r(r-1)a_0 = 0 \Rightarrow r=0,1 $$Coefficients of x^(r + 1):$$ (r+1)r a_1 + (r+1)a_1 - 2a_0 = 0 $$Taking r = 0, we get:a_1 - 2a_0 = 0a_1 = 2a_0

The solution becomes:y_1(x) = a_0 [1 + 2x]Taking r = 1, we get:$$ 6a_2 + 3a_1 - 2a_0 = 0 $$a_2 = (1/6) [2a_0 - 3a_1]Substituting the value of a_1 from above, we get:a_2 = a_0/3The second solution is given by:y_2(x) = a_0 [x^2/3 - 2x/3]Therefore, the required solution of the given ODE using Frobenius method is:y(x) = c_1 y_1(x) + c_2 y_2(x)y(x) = c_1 [1 + 2x] + c_2 [x^2/3 - 2x/3]

Hence, the second and third-degree Legendre polynomials generated and the solution of the given ODE using the Frobenius method is obtained above.

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It takes Tran approximately 0.1 hours, or 6 minutes time, to travel 3 miles at a speed of 33 miles per hour.

What is the time of travels?

To find the time it takes for Tran to travel 3 miles at a speed of 33 miles per hour, we can use the formula:

time = distance / speed

Substituting the given values, we get:

time = 3 miles / 33 miles per hour

time ≈ 0.0909 hours

Rounding to the nearest tenth, we get:

time ≈ 0.1 hours

Therefore, it takes Tran approximately 0.1 hours, or 6 minutes, to travel 3 miles at a speed of 33 miles per hour.

What is speed of travel?

Speed of travel refers to how fast an object is moving relative to a reference point, usually measured in units of distance per unit of time, such as miles per hour or kilometers per hour.

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Answer:

5y = -5

Step-by-step explanation:

-2(3y+5)= -4

Divide each side by -2

-2/ -2  (3y+5)= -4/-2

3y+5 = 2

Subtract 5 from each side

3y +5 -5 = 2-5

3y = -3

Divide by 3

3y/3 = -3/3

y = -1

5y = 5*-1 = -5

Answer:

me

Step-by-step explanation:

Answer:

I can try to help whats ur question?

The share of audience for the particular show at 9:00 pm is 55.56% for 50 million households.

We need to know the number of households that watched the programme and the total number of households with televisions on at 9:00 p.m. in order to determine the proportion of audience for that programme.

In this instance, it is stated that 90 million homes had their televisions on at 9:00 p.m. in addition to 50 million households watching the programme. Consequently, the following formula can be used to determine the show's viewership share:

Share of audience is calculated as follows: (Number of households that watched the programme / Total number of households with TVs on) x 100%

= 100% x (50 million / 90 million)

= 55.56%

As a result, 55.56% of the audience watched the specific show at 9:00 p.m. This indicates that the programme was viewed by more than half of the homes with on-air televisions at the time.

The share of audience is a crucial measurement in television ratings since it aids networks and advertisers in understanding how popular a show is and how far it might be able to reach the intended audience.

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Answer:

x = 5

Step-by-step explanation:

Add the equations

x + y = 3

x - y = 7

––––––––

2x = 10

Divide both sides by2

x = 5

Note: for the equations in the question,

none of the given answers are correct.

∂g/∂u is equal to 21u⁵cos⁴(v)sin⁴(v)(cos(v) + u³cos⁴(v)sin²(v)sin(v)).

To find the indicated derivative, we need to use the chain rule. Let's differentiate step by step:

Given:

g(u, v) = f(x(u, v), y(u, v))

f(x, y) = 7x³y³

x(u, v) = ucos(v)

y(u, v) = usin(v)

To find ∂g/∂u, we differentiate g(u, v) with respect to u while treating v as a constant:

∂g/∂u = (∂f/∂x) * (∂x/∂u) + (∂f/∂y) * (∂y/∂u)

To find ∂f/∂x, we differentiate f(x, y) with respect to x:

∂f/∂x = 21x²y³

To find ∂x/∂u, we differentiate x(u, v) with respect to u:

∂x/∂u = cos(v)

To find ∂f/∂y, we differentiate f(x, y) with respect to y:

∂f/∂y = 21x³y²

To find ∂y/∂u, we differentiate y(u, v) with respect to u:

∂y/∂u = sin(v)

Now, we can substitute these partial derivatives into the equation for ∂g/∂u:

∂g/∂u = (21x²y³) * (cos(v)) + (21x³y²) * (sin(v))

To find the simplified form, we substitute the given values of x(u, v) and y(u, v) into the equation:

x(u, v) = ucos(v) = u * cos(v)

y(u, v) = usin(v) = u * sin(v)

∂g/∂u = (21(u * cos(v))²(u * sin(v))³) * (cos(v)) + (21(u * cos(v))³(u * sin(v))²) * (sin(v))

Simplifying further, we get:

∂g/∂u = 21u⁵cos⁴(v)sin⁴(v)(cos(v) + u³cos⁴(v)sin²(v)sin(v))

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In a case whereby letters in the word bubble are arranged in a row the number of unique arrangements that are there  in the letters is 120.

From the question we were given the word, bubble  which can be recognized as 6! arrangements  however we know that the  3 B’s are interchangeable, from the word which is to be arranged, and we can see that there are 6 letters all together in the word and can be arranged as;

6!/3!

= 720/6

= 120

Hence, we can conclude the arangement here is 120 unique wayas.

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Answer:

-5

Step-by-step explanation:

(18+7)-30

25-30=

-5

Answer:

its the first one

Step-by-step explanation:

Answer:

69.5 and 70.5

Step-by-step explanation:

consecutive numbers mean they are one up from the other

- e.g. 2 and 3,

- 15 and 16

if the first one is x, we can write the second consecutive number as x + 1

The info tells us the sum of these two numbers is 140, so we can write an equation and solve for x.

x + (x + 1) = 140

2x + 1 = 140

2x = 139

x = 139/2 = 69.5

(now we find the next number)

69.5 + 1 = 70.5

The solution x(t) of the equation x = rx + x', where r > 0 is fixed, approaches infinity in finite time starting from any initial condition x = 0.

We can solve the differential equation x' = rx + x using separation of variables. Rearranging the equation, we get:

x' - rx = x

This is a linear first-order differential equation with integrating factor e^(-rt). Multiplying both sides by e^(-rt), we obtain:

e^(-rt)x' - re^(-rt)x = e^(-rt)x

Using the product rule for derivatives, the left-hand side becomes:

(d/dt)[e^(-rt)x] = e^(-rt)x'

Substituting this into the equation, we get:

(d/dt)[e^(-rt)x] = e^(-rt)x

This equation can be integrated to obtain:

e^(-rt)x = C

where C is a constant of integration. Solving for x, we get:

x = Ce^(rt)

Since r > 0, the exponential function e^(rt) grows without bound as t approaches infinity. Therefore, the solution x(t) of the differential equation also grows without bound in finite time starting from any initial condition x = 0. This means that x(t) approaches infinity as t approaches a certain finite value, which depends on the value of r.


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Answer:

Step-by-step explanation:

I got you. ( It's basically just y is double x.)

y  x

2  1

4  2

6  3

8  4

10  5

Answer:

I'm pretty sure it's 13.5.

Step-by-step explanation:

Boom first let's do 108 ÷ 8

After that you should get 13.5.

13 and a half gallons per hour.

the total consumption of oil in the United States from January 1, 1980, to January 1, 1990 is approximately 596,533.7 billion barrels.

To find the total consumption of oil in the United States from January 1, 1980 to January 1, 1990, we need to integrate the given function\(C(t) = 27.08e^t\)with respect to time t, over the interval [0, 10], where t is measured in years.

The integral of the function is:
∫\((27.08e^t) dt\)

To solve this integral, we use the fact that the integral of\(e^t\) is \(e^t\)itself. Thus, we get:
27.08∫\(e^t dt = 27.08e^t\)
Now, we need to evaluate the definite integral over the interval [0, 10]:
\(27.08e^t\)| from 0 to 10 =\(27.08(e^{10} - e^0)\)

As e^0 = 1, the expression simplifies to:
\(27.08(e^{10} - 1)\)
Now, we can calculate the value of the expression:
\(27.08(e^{10} - 1) =27.08(22026.47 - 1) = 27.08 * 22025.47 =596533.7\)
Thus, the total consumption of oil in the United States from January 1, 1980, to January 1, 1990 is approximately 596,533.7 billion barrels.

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Answer:

idek

Step-by-step explanation:

jk jk its -10 :)

Answer:

c. (0,4)

Step-by-step explanation:

I recommend that Tammy create a budget to keep track of her income and expenses. She should also set up automatic payments for her International Club advisor so she doesn't miss any payments. Additionally, Tammy should create a savings plan for the trip to make sure she has enough money for it. Finally, she should start the habit of setting aside money from each paycheck for the trip, so she has a consistent source of funds when she needs them.

Answer:

= 200.811

Step-by-step explanation:

Answer:

Step-by-step explanation:

you will have to remember that -(-)=+

-102.431+59.95+38.43=-4.051

Answer: 80 is the number of cupcakes for which the profit is equal to 0

Step-by-step explanation:

The best interpretation of the number 80 in the context of the given equation will be in option A, i.e. 80 is a number of cupcakes for which the profit is equal to $0.

Profit is the amount which we earned after selling something at a price more than its cost price.

We have,

P(q) = -0.01 (q - 250) (q- 80)

Where,

P(q) = profit earned by a cupcake bakery  in dollars

q = cupcakes produced

So,

Now,

We have to find out the context of 80 in given equation,

So,

Lets substitute q = 80, in the given equation,

i.e.

P(q) = -0.01 (q - 250) (q- 80)

⇒

P(80) = -0.01 (80 - 250) (80- 80)

We get,

P(80) =  -0.01 (- 170) (0)

i.e.

P(80) = 0

So, 80 is a number of cupcakes for which the profit is equal to $0.

Hence, we can say that the best interpretation of the number 80 in the context of the given equation will be in option A, i.e. 80 is a number of cupcakes for which the profit is equal to $0.

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Answer:

36.33

Step-by-step explanation:

The given figure is pentagon

The sum of angles of polygon is (2n-4)*90 where n is number of sides of polygon

for pentagon number of sides is 5

thus, n = 5

\

sum of angles of pentagon = (2*5-4)*90 = 6*90 = 540

Given angles of pentagon

t, 149 , t+144, 3t -11 , t+40

Thus, sum of all these angles should be equal to 540

t + 149 + t+144 + 3t -11 + t+40 = 540

=> 6t + 322 = 540

=> 6t = 540 - 322 = 218

=> t = 218/6 = 36.33

Thus, t = 36.33

The p-value in a chi-square goodness of fit test for F2 data sets is used to determine the likelihood of obtaining the observed data if the true mode of inheritance is actually autosomal dominant.

To determine which F2 data set provides greater evidence for indicating the correct mode of inheritance, perform a chi-square goodness of fit test on each of the two data sets.

Follow these steps for each data set:

Calculate the expected counts for each phenotype and gender combination based on the true mode of inheritance (Autosomal Dominant). In this case, the expected ratio for Disease to Wild-Type is 1:1 for both males and females.

Calculate the chi-square statistic using the observed and expected counts. Calculate the p-value using the chi-square statistic and the appropriate degrees of freedom.

Compare the p-values of both data sets. The data set with a p-value greater than 0.05 and closer to 1 is considered to provide greater evidence for the correct mode of inheritance.

For Data Set 01:

F2 Expected Counts:
- Male: Disease: 129, Wild-Type: 129
- Female: Disease: 126, Wild-Type: 126

F2 Observed Counts:
- Male: Disease: 185, Wild-Type: 73
- Female: Disease: 183, Wild-Type: 69

Calculate the chi-square statistic and p-value for Data Set 01.

For Data Set 02:

F2 Expected Counts:
- Male: Disease: 230.5, Wild-Type: 230.5
- Female: Disease: 219, Wild-Type: 219

F2 Observed Counts:
- Male: Disease: 349, Wild-Type: 112
- Female: Disease: 323, Wild-Type: 115

Calculate the chi-square statistic and p-value for Data Set 02.

After calculating the p-values for both data sets, compare them and determine which data set provides greater evidence for indicating the correct mode of inheritance (Autosomal Dominant).

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The solution to the given system of equations is x = 2, y = -1, and z = 1.

To solve the system of equations, we can use methods such as substitution or elimination. Here, we will use the method of elimination to find the values of x, y, and z.

First, let's eliminate the variable x by multiplying equation (1) by 2 and equation (3) by -1. This gives us:

2x + 4y - 2z = -6 (4)

-x + y - z = -4 (5)

Next, we can subtract equation (5) from equation (4) to eliminate the variable x:

5y - z = 2 (6)

Now, we have a system of two equations with two variables. Let's eliminate the variable z by multiplying equation (2) by 2 and equation (6) by 1. This gives us:

4x - 2y + 2z = 10 (7)

5y - z = 2 (8)

Adding equation (7) and equation (8), we can eliminate the variable z:

4x + 5y = 12 (9)

From equation (6), we can express z in terms of y:

z = 5y - 2 (10)

Now, we have a system of two equations with two variables again. Let's substitute equation (10) into equation (1):

x + 2y - (5y - 2) = -3

x - 3y + 2 = -3

x - 3y = -5 (11)

From equations (9) and (11), we can solve for x and y:

4x + 5y = 12 (9)

x - 3y = -5 (11)

By solving this system of equations, we find x = 2 and y = -1. Substituting these values into equation (10), we can solve for z:

z = 5(-1) - 2

z = -5 - 2

z = -7

Therefore, the solution to the given system of equations is x = 2, y = -1, and z = -7.

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pls snap the picture well so that the pre information can be seen and considered

The  total distance it flies, rounded to the nearest mile is: d. 1,692 miles .

First distance= 550 miles (given)

Second distance=483 miles (given)

Now let find the third distance

Let x represent the third distance

Hence:

x/sin79 = 550/sin55

x= 659.1

Now let calculate the total distance

Total distance=550+483+659.1

Total distance= 1692.1

Total distance= 1692 miles (rounded)

Therefore the correct option is d.

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As per the distributive property, the expression -3x⁴(5x³ - 2x⁶) is equivalent to -15x⁷ + 6x¹⁰

Distributive property:

Distributive property states that the expression has been simplified when you multiply a number by a sum or difference.

Give,

Here we have the expression -3x⁴(5x³ - 2x⁶).

Now, we have to use the distributive property in order to find the equivalent expression.

Based on the distributive property, here we have to multiply the outer term with the individual inner terms, then we get,

=> -3x⁴(5x³ - 2x⁶)

=> (-3x⁴ × 5x³) + (-3x⁴ ×- 2x⁶)

Now we have to multiply the signs and the numbers then we get.

=> -15 (x⁴ × x³) + 6 (x⁴ × x⁶)

As per the rule of exponent, we have to add the exponents of the expression to find the solution,

=> -15x⁷ + 6x¹⁰

Therefore, the equivalent expression is -15x⁷ + 6x¹⁰.

Therefore, the option A is correct.

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Answer:

There are 3 feet in a yard, so a 2-yard piece of aluminum wire is 6 feet long.

To find the price per foot, we can divide the total cost by the total length:

Price per foot = Total cost / Total length

Price per foot = $15.96 / 6 feet

Price per foot ≈ $2.66

Therefore, the price per foot of the aluminum wire is approximately $2.66.