solve the given initial-value problem. Dy dx + y = f(x), y(0) = 1, where f(x) = 1, 0 ≤ x ≤ 1; -1 , x ≥ 1

The solution to the equation is given as option C

The equation says [tex]\frac{6}{5}+\frac{3}{5}x[/tex]

we have to add the fractions

[tex]\frac{1 *6 +1*3x}{5}[/tex]

= 6 + 3x / 5

Hence the correct solution to the question here is option C because[tex]\frac{6+3x}{5} = \frac{3}{5}(2+x)[/tex]

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Answer:

slope-5\7 is the answer

If Sandy used a virtual coin toss app to show the results of flipping a coin 100 times, 500 times, and 1,000 times. The things that most likely happened in Sandy's experiment is: C. Sandy's experimental probability was closest to the theoretical probability in the experiment with 1,000 flips.

Sandy's experimental probability was closest to the theoretical probability in the experiment with 1,000 flips.

This is because as the number of trials increases, the experimental probability tends to as well  approach the theoretical probability. The theoretical probability of getting heads or tails in a fair coin flip is always 0.5 or 50%. The larger the sample size, the more likely the experimental probability will be close to the theoretical probability.

Therefore the correct option is C.

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Inserting plus or minus signs in Web Assign can be done in the following way Log into your Web Assign account.

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A statement which best describes the area of Triangle ABC shown above include the following: D. It is one-half the area of a rectangle of length 2 units and width 4 units.

Mathematically, the area of a triangle can be calculated by using this mathematical expression:

Area of a triangle = 1/2 × b × h

Where:

Mathematically, the area of a rectangle can be calculated by using this formula:

Area of a rectangle = LW or bh

Where:

In this context, we can reasonably infer and logically deduce that the area of a triangle ABC is half the of a rectangle i.e A = (bh)/2.

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The area of the folded napkin is 81 square inches.

Square inch is a unit of area, equal to the area of a square with sides of one inch.

A square with an area of 324 square inches can be folded in half to form a rectangle with half the area, or 162 square inches.

Folding the rectangle in half again will result in a smaller square with a side length equal to half the shorter side of the rectangle. The area of this smaller square is (1/2)^2 * 162 square inches = 81 square inches.

So, the area of the folded napkin is 81 square inches.

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Answer:

Interest = $720

Balance = $9,720

Step-by-step explanation:

P = $9,000, the principal

r = 8% = 0.08, the interest rate

n = 2, semiannual compounding

After 6 months, the interest is

9000 * 0.08 = $720

The balance after 6 months is

9000 + 720 = $9720

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The surface area of the cone with a slant height of 10ft and radius of 7ft is 373.7 ft²,

A cone is simply a 3-dimensional geometric shape with a flat base and a curved surface pointed towards the top.

The surface area of a cone is expressed as;

A = πrl + πr²

Where r is radius of the base, l is the slant height of the cone and π is constant pi ( π = 3.14 )

From the diagram;

Plug the given values into the above formula

A = πrl + πr²

A = ( 3.14 × 7 × 10 ) + ( 3.14 × (7)² )

A = ( 219.8 ) + ( 153.86 )

A = 373.7 ft²

Therefore, the surface area is 373.7 ft²

Option B) 373.7 ft² is the correct answer.

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The algebraic expression of the sum of 4 consecutive even numbers is 4y + 12.

An algebraic expression is an expression which is made up of variables and constants, along with algebraic operations such as addition, subtraction, multiplications, division etc.

Therefore, let's represent the algebraic expression for the sum of 4 consecutive even numbers.

Even numbers are numbers which when divide by 2 has no remainders.

Therefore,

let

y = first even number

Hence, the expression is as follows;

y + y + 2 + y + 4 + y + 6

y + y + y + y + 2 + 4 + 6

4y + 12

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Answer:

Both Rachel and Erik are trying to estimate the area of the circular rug with a diameter of 8 ft. Rachel's estimate using the formula A = πr^2 is correct and is the standard way to find the area of a circle. Erik's method of dividing the circle into 12 parts and forming a parallelogram is also a creative way to estimate the area, but it may not be as accurate as Rachel's formula-based approach.

Step-by-step explanation:

The area of a circle can be calculated using the formula A = πr^2, where r is the radius of the circle. In this case, the diameter of the circle is 8 ft, so the radius can be calculated as r = 8/2 = 4 ft. Substituting the radius into the formula gives A = π x 4^2 = 16π.

Erik's approach of dividing the circle into 12 parts and forming a parallelogram is an estimation method that could be used to find the area of a circle. The idea is to divide the circle into equal parts, arrange them into a parallelogram shape, and find the area of the parallelogram. This will give an estimate of the area of the circle, but it may not be as accurate as using the formula A = πr^2.

Step-by-step explanation:

-x² + 4x + 8 = (x + 2)² = x² + 4x + 4

-x² + 8 = x² + 4

4 = 2x²

2 = x²

x = ±sqrt(2)

trinomial just means "3 terms".

binomial just means "2 terms".

(x + 2) is therefore a binomial. its square is (x + 2)².

the question is for what x are the trinomial and the square of the binomial equal.

so, we just set both expressions as equal and solve for the variable x.

there are 2 solutions :

+sqrt(2)

-sqrt(2)

The equation of the circle can be written as:

(x - 3)^2 + (y + 2)^2 = 16

We know that for a circle of radius R and the center is (a, b) can be written as:

(x - a)^2 + (y - b)^2  = R^2

Here we want to find the equation for a circle of radius of 4 units and a center at (3, -2), then the equation is:

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

Now we can simplify that equation to get:

(x - 3)^2 + (y + 2)^2 = 16

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x = 2.67 is the solution to the equation -6x + (3)(2x) = 16.

What is the Algebraic Equations?

Algebraic equations are mathematical statements that describe a relationship between two or more variables, where one variable is expressed in terms of the others.

To solve the equation -6x + (3)(2x) = 16, we can simplify the expression on the left-hand side first:

-6x + (3)(2x) = -6x + 6x = 0x = 0

Next, we isolate the x term on one side of the equation by subtracting 16 from both sides:

0x = 0 - 16 = -16

Finally, we can solve for x by dividing both sides of the equation by -6:

x = -16 / -6 = 2.67 (rounded to two decimal places).

So, x = 2.67 is the solution to the equation -6x + (3)(2x) = 16.

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Option D is correct, the differentiate of the equation of x³+y³=1 is dy/dx=-x²/y²

A differential equation is an equation that contains one or more functions with its derivatives.

We have to differentiate the equation of x³+y³=1

Differentiate both sides

3x²+3y²dy/dx=0

3y²dy/dx=-3x²

Divide both sides by 3y²

dy/dx=-x²/y²

Hence, option D is correct, the differentiate of the equation of x³+y³=1 is dy/dx=-x²/y²

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The probability that all have type B​+ blood is 0.000286 The probability that none of the have type B​+ blood is 0.572898.

Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.

Then, suppose we want to find the probability of an event E.

Then, its probability is given as

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]

where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.

Given;

The probability that a person in the United States has type B​+ blood is 13​%.

Since four unrelated people in the United States are selected at random, we can say that each person is independent of the other to have B+ blood group;

Let X be the number of persons who have blood group B+ in the group of 4 persons;

X is Binomial with p = 0.13;

a) P(X = 4) = (0.13)4 = 0.000286

b) P(x =0) = (1 -0.13)¹ = 0.572898

Therefore, the probabilities will be 0.000286 and 0.572898

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a) The total amount that you will have into the account is given as follows: $360,211.

b) The amount of money inserted into the account is of: $84,000.

c) The amount of interest earned is given as follows: $276,211.

The balance of an account is given as follows:

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

The meaning of each parameter is given as follows:

The parameters for this problem are given as follows:

P = 200, r = 0.07, n = 12, t = 35.

Hence the balance will be given as follows:

[tex]B = \frac{200\left(\left(1 + \frac{0.07}{12}\right)^{420}-1\right)}{\frac{0.07}{12}}[/tex]

B = $360,211.

The amount inserted into the bank account is given as follows:

200 x 12 x 35 = $84,000.

Then the amount of interest is given as follows:

360211 - 84000 = $276,211.

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Answer: I understand that you're feeling overwhelmed. Let's try to solve this problem together.

To evaluate the function f(x) = -3x + 5 at a specific value of x, we substitute that value into the expression and simplify. For example, if we want to evaluate the function at x = 2:

f(2) = -3 * 2 + 5 = -6 + 5 = -1

So f(2) = -1. This means that the value of the function when x = 2 is -1.

If you have any other questions or concerns, I'm here to help!

Step-by-step explanation:

Answer: A and C

Step-by-step explanation: They both get longer by 3 blocks (X is 3 blocks long, 1 block tall) and 1 block tall per every 3 blocks added length wise.

The approximation for the population of the bacteria 5 minutes from now is 3506 organisms.

Let's call the current time "t", and the population of the bacteria at time "t" be "P(t)".

So, we have two points on the curve:

(t, P(t)) = (0, 1661), and (t + 9, P(t + 9)) = (9, 3 * 1661) = (9, 4983).

The equation of the line that passes through these two points can be found using the point-slope form of the line:

y - y1 = m(x - x1)

Substituting the points into the equation, we get:

4983 - 1661 = m(9 - 0)

m = (4983 - 1661) / (9 - 0) = 3322 / 9 = 369

So, we have

y = 369x + 1661

For the next 5 minutes, we have

P(t + 5) ≈ y = 369 * 5 + 1661 = 3506 (rounded to the nearest whole number)

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Answer:

i hope this help

Step-by-step explanation:

Statement Reason

Points A, B, and C form a triangle. Given

Let be a line passing through B and parallel to . Definition of parallel lines

∠3 ≅ ∠5 and ∠1 ≅ ∠4 Definition of corresponding angles in parallel lines

m∠1 = m∠4 and m∠3 = m∠5 Substitution of corresponding angles

m∠4 + m∠2 + m∠5 = 180° Angle addition and definition of a straight line

m∠1 + m∠2 + m∠3 = 180° Substitution.

The length of AB is 10 cm.

What is the Pythagorean Theorem?

The Pythagorean theorem is a mathematical theorem that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. It can be expressed as c² = a² + b².

The length of AB can be found using the Pythagorean theorem. The theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides equals the square of the length of the hypotenuse (the longest side). In this case, we can form two right triangles, one with sides AD and AC and another with sides BC and AB.

Using the Pythagorean theorem, we have:

AB² = AC² + AD²

AB² = (8²) + (6²)

AB² = 64 + 36

AB² = 100

AB = √(100) = 10

Hence, AB is 10 cm.

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a) -32.06 (To the nearest hundredth)

b) -37.7 (To the nearest tenth)

c) 3.1 (To the nearest tenth)

d) 5.86  (To the nearest hundredth)

f) -4.33  (To the nearest hundredth)

g) 11.44  (To the nearest hundredth)

h) 62x + 45 = 38x + 79

i) 46y - 18 = -37y

An equation is a mathematical statement that asserts the equality of two expressions. It consists of two expressions separated by an equal sign (=), and shows the relationship between the variables present in the equation. Equations are used to model real-world problems and find solutions to various mathematical problems.

They can be solved for a specific variable by using various mathematical methods and techniques.

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[A] Under the present cash-only sales policy, the firm's net cash flow every three weeks is:

2,548 units x RM35/unit = RM89,180

2,548 units x RM20/unit = RM50,960

= RM38,220

[B] The firm's immediate (now) net cash flow from adoption of the proposed 3-week credit sales policy is:

0

[C] The firm's net cash flow every 3 weeks from adopting the proposed credit policy is:

2,912 units x RM36/unit = RM105,312

2,912 units x RM22/unit = RM63,904

= RM41,408

[D] The incremental cash flow every 3 weeks arising from switching from the present cash to the proposed credit policy is:

RM41,408 - RM38,220 = RM3,188

[E] The firm's effective 3-week required rate of return from receivables is:

7%/4 = 1.75%

[F] The present value of the perpetual incremental 3-week cash flows arising from switching from the cash to credit policy is:

RM3,188 / (1 + 1.75%) = RM3,147.65

[G] The present value of the costs of switching from cash to credit policy is:

0

[H] The net present value of switching from cash to credit policy is:

RM3,147.65 - 0 = RM3,147.65

[I] The firm should switch from the cash to credit policy as the net present value is positive. The increase in revenue from the increased sales volume outweighs the increased cost of goods sold.

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Answer

We have, 6% × x = 24 or, 6 100 × x = 24

Step-by-step explanation:

Multiplying both sides by 100 and dividing both sides by 6,

Answer:

24 % of that number is 4

Step-by-step explanation:

First solution:

If 6% of a number is 1, then 1% is 1/6 which is a repeating decimal, so we can just take it as 1/6. Then, to find 24% of that number we would have to do 1/6 x 24 which is equal to 24/6. 6 can evenly divide 24 which is 4.

Second solution:

We can see that since 24 is evenly divided by 6, to find 24%, we can multiply 1 by 4 because 6% x 4 = 24%

Therefore, 24% of that number is 4.

The circumferance of the circle is 131.88 inches.

The circumferance of a circle is the length of the one - dimensional curve that encloses the circle's area. Mathematically -

C = 2πr

C = πd                                  ..... Eq { 1 }

Given is a circle with diameter of 42 inches.

We can write the circumferance as -

C = 3.14 x 42

C = 131.88 inches.

Therefore, the circumferance of the circle is 131.88 inches.

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Work Shown:

Complementary angles add to 90 degrees.

A+B = 90

(3x+18)+(2x+17) = 90

5x+35 = 90

5x = 90-35

5x = 55

x = 55/5

x = 11

Then we can determine each angle:

As a check: A+B = 51+39 = 90 to confirm the answer.

Answer: a) No existe un tipo específico de arroz que aporte más vitamina B1. La cantidad de vitamina B1 varía dependiendo del cultivo y la forma de preparación.

b) El arroz fortificado con yodo es el que proporciona una mayor cantidad de yodo al organismo.

c) El arroz integral o de grano entero proporciona una mayor cantidad de fibra en comparación con el arroz refinado.

d) No se puede determinar la cantidad exacta de complejo B que aporta el arroz refinado, ya que depende de varios factores como el tipo de cultivo, la forma de preparación y el método de almacenamiento.

e) El arroz integral o de grano entero es preferible para consumo por una persona que desea obtener una mayor cantidad de potasio, ya que es una fuente rica en este nutriente.

f) El arroz integral o de grano entero es preferible porque es una fuente de nutrientes más completa que el arroz refinado. Sin embargo, esto depende de las necesidades individuales y objetivos nutricionales. Algunas personas pueden necesitar más arroz refinado por motivos de digestibilidad, mientras que otras pueden preferir el arroz integral para obtener una mayor cantidad de fibra, vitaminas y minerales.

Step-by-step explanation:

The required domain of the function is all real numbers. Option A is correct.

The domain is defined as the values of the independent variable for which there is a certain value of the dependent variable exists in the range of the function.

here,
Given function,
f(x) = 2x³ + 8

Since the domain of the given function is all real numbers, and also the range of the function is all real numbers.

Put x = 0,
f(0) = 8

the y-intercept of the function is (0, 8)

Thus, the required domain of the function is all real numbers. Option A is correct.

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