WN
1. Paula compro cuatro docenas de margaritas. Piensa regalare
la mitad a su mamá, de la mitad que le quede le va a dar
mitad a su tia Irene: y de las que queden, le dará la mitad as
hermana y ella se quedará con la otra parte.
a) ¿Con cuántas margaritas se quedará Paula?
12
b) ¿Qué parte del total de flores recibirá su tía Irene?
c) ¿Qué parte del total le dará a su hermana?
d) ¿Qué fracción del total representa la cantidad de flores
que se quedará Paula?​

Answer:

3x^3 − x^2 − 10x

Step-by-step explanation:

V= l*w*h

V= x * (x-2) * (3x+5)

V= (x(x−2)) (3x+5)

= (x(x−2)) (3x) + (x(x−2)) (5)

= 3x^3 − 6x^2 + 5x^2 − 10x

=3x^3 − x^2 − 10x

The radius of the given circle is 7.5 units.

So, use the Pythagorean theorem:

Now, calculate as follows:

So, the diameter is 15 units.

Then the radius is:

Therefore, the radius of the given circle is 7.5 units.

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Answer: a= (4x-1)(6x+9)

Step-by-step explanation:

area= length x width

Answer:

below

Step-by-step explanation:

24 x 2 + 30 x − 9

Answer:

A

Step-by-step explanation:

2 + 12 = 14 = 4 + 10

Answer:

A or 12

Step-by-step explanation:

2 + z = 4 + 10

2 + z = 14

z = 12

A

to eliminate the variable y

we have steps are,

1) Divide the second equation by 2. then add the result to the first equation

or

2) Multiply the first equation by 2. then add the result to the second equation

or

3) Multiply the first equation by 4 and the second equation by 6, then subtract the resulting equations.

so the answer is the first three options.

Jeffrey has a fish tank that holds 8 liters of water. He already has the tank filled with 1 liter of water. Thus, to fill the fish tank completely with water, Jeffrey needs 7000 milliliters of water.

This is because 1 liter is equal to 1000 milliliters. Thus, 8 liters are equal to 8 × 1000 = 8000 milliliters.

Therefore, the amount of water Jeffrey needs to completely fill the fish tank is 8000 - 1000 = 7000 milliliters of water.

Jeffrey has a fish tank of 8 liters of water that already has 1 liter of water in it.

The amount of water Jeffrey needs to completely fill the fish tank is calculated by subtracting the liters of water already present in the tank from the total liters of water the tank can hold.To completely fill the fish tank, Jeffrey needs to fill the remaining 7 liters with water. One liter of water is equivalent to 1000 milliliters. Thus, Jeffrey needs to multiply the remaining liters of water he needs to fill by 1000 milliliters.

7 × 1000 = 7000

Therefore, Jeffrey needs 7000 milliliters of water to completely fill the fish tank with water.

To completely fill the fish tank, Jeffrey needs 7000 milliliters of water because he has already filled it with 1 liter of water, and the fish tank can hold 8 liters of water.

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Let:

After a reflection across the line y = x:

Answer: 20%

Step-by-step explanation:

Answer:

13.5

Step-by-step explanation:

look at the bottom and line it up to the top

The equivalence classes are [1] = {1} and [2] = [3] = {2, 3}.

The equivalence classes of the set R, which defines an equivalence relation on the set {1, 2, 3}, are as follows:

1. Identify the elements of the set: {1, 2, 3}
2. Group elements according to the equivalence relation R = {(1, 1), (2, 2), (3, 3), (2, 3), (3, 2)}
3. Create equivalence classes based on R:
  - [1] = {1} (since only (1, 1) ∈ R)
  - [2] = {2, 3} (since (2, 2), (2, 3), and (3, 2) ∈ R)
  - [3] = {2, 3} (since (3, 3), (2, 3), and (3, 2) ∈ R)

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To find the inverse Laplace transform of ℒ{e^(-s) / [s(s + 1)]}, we can use partial fraction decomposition and known Laplace transforms.

First, let's express the given function in partial fraction form:

e^(-s) / [s(s + 1)] = A/s + B/(s + 1)

To find A and B, we multiply both sides by s(s + 1) and then substitute appropriate values of s to simplify and solve for the coefficients:

e^(-s) = A(s + 1) + Bs

Setting s = 0, we get:

1 = A(0 + 1)

A = 1

Setting s = -1, we get:

e = B(-1)

B = -e

Therefore, the partial fraction decomposition is:

e^(-s) / [s(s + 1)] = 1/s - e/(s + 1)

Now, we can use the known Laplace transforms to find the inverse transform:

ℒ^(-1){1/s} = 1

ℒ^(-1){-e/(s + 1)} = -e^(-t)

Finally, we combine the inverse transforms:

f(t) = ℒ^(-1){e^(-s) / [s(s + 1)]} = ℒ^(-1){1/s} - ℒ^(-1){e/(s + 1)} = 1 - e^(-t)

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A speedup of 2 suggests that the program is efficiently utilizing the additional computational resources provided by the second computer, resulting in a significant reduction in computation time.

A speedup of 2 indicates that the program running on two computers in parallel is approximately twice as fast as running it on a single computer. In other words, the distributed computing techniques and parallel processing allow the mathematician to solve the systems of linear equations in half the time compared to running the program on a single computer.

Speedup is a measure of the improvement achieved by using parallel computing techniques. It quantifies the ratio of the time required to execute a task sequentially (on a single computer) to the time required to execute the same task in parallel (using multiple computers). A speedup of 2 suggests that the program is efficiently utilizing the additional computational resources provided by the second computer, resulting in a significant reduction in computation time.

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Answer:

The perimeter of triangle ABC is 33.

Explanation:

AY = 7 is half of the line of XY so we would then multiply 7 by 2:

7 x 2 = 14

and we would then do this to all of our numbers:

8 x 2 = 16

18 x 2 = 36

now we make a full equation for the answer of the perimeter of triangle XYZ:

14 + 16 + 36 = 66

66 is the perimeter of triangle XYZ.

We would then divide this answer by 2 to find the perimeter of ABC because it is half of XYZ:

66 ÷ 2 = 33

The perimeter of triangle ABC is 33

Hope this helps! :)

Answer:

Answer:

If this cycle continued indefinitely, how much money that eventually resulted from the initial deposit is

500,000 (C is the answer)

Answer:

  $200,000

Step-by-step explanation:

The total amount deposited is the sum of an infinite geometric series. The first term of the series is $12,000, and the common ratio is 1 -0.06 = 0.94.

That is, 0.94 times $12,000 is loaned after the first deposit. When that loan amount is all deposited, 6% is kept in reserve, and $12,000×0.94² is loaned after that deposit.

The formula for the sum of an infinite geometric series is ...

  S = a/(1 -r)

where 'a' is the first term, and r is the common ratio..

For the given series, a=12000, and r=0.94 so the sum is ...

  S = 12000/(1 -0.94) = 12000/0.06 = 200,000

The result of the initial deposit will eventually be $200,000.

__

Additional comment

In economics, the inverse of the reserve ratio is called the "deposit multiplier."

The more variable the data, the less accurate the sample mean will be as an estimate of the population mean. In statistical analysis, accuracy is important. Statistical analysis is a method of gathering and examining data to uncover useful information.

A sample mean is a numerical estimate that represents a data set's central tendency. The population mean, on the other hand, is a statistical measure that represents the mean value of the entire population. The difference between the two lies in the fact that sample mean is computed on a subset of the population whereas population mean is calculated for the entire population. If the variability of the sample data is large, the sample mean becomes less accurate as an estimate of the population mean.

As a result, the more variable the data, the less accurate the sample mean will be as an estimate of the population mean.Therefore, it is essential to examine the variability of the data in order to better estimate the population mean. The greater the variability in the data, the more difficult it becomes to identify the true population mean and the less accurate the sample mean is as an estimator of the population mean.

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Answer:

12.649

Step-by-step explanation:

we can use Pythagoras to solve this; simply by forming a triangle of the difference between the x and y values. (I added a lil-sketch of it).

So, we just need to find the length of the two sides:

Vertical side: 12

Horizontal side: 4

Thus;

\(4^{2} + 12^{2} = c^{2} \\160 = c^{2}\\Side c is equal to 12.649 (in whatever unit given)\)

Based on fractional values, if Susan originally has 7 yards of fabric, after making 3 aprons consuming 5⁵/₈ yards, the quantity of fabric left is 1³/₈ yards.

Fractional values are the results of fractional computations.

Fractions may be proper, improper, and complex fractions, depending on the values of the denominators and the numerators.

Algebraic expressions that have fractions are stated as fractional values.

The original quantity of fabric that Susan has = 7 yards

The quantity of fabric used for the front of each apron = 1¹/₄ yards

The quantity of fabric used for the tie of each apron = ⁵/₈ yards

The total quantity of fabric used for each apron = 1⁷/₈ yards (1¹/₄ + ⁵/₈)

The total quantity of fabric used for the 3 aprons made = 5⁵/₈ yards (1⁷/₈ x 3)

Therefore, the remaining quantity of fabric that Susan has after making the 3 aprons = 1³/₈ yards (7 - 5⁵/₈).

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Susan first made 3 aprons using 1¹/₄ yards for the front and ⁵/₈ yards for the tie.

Solution

Question 1:

Question 2:

Final Answer

Question 1:

The exponential function to model the scenario is

Question 2:

The number of rabbits that will hop out of the hat on the 13th Day is 12,288 rabbits

The trigonometric values for a right triangle can be obtained through the measurements of the different sides,

this can be found in a triangle like this,

then, identify the measurements in the given triangle

then,

Answer: 18oz

Step-by-step explanation:

Answer:

\(x=2\\x=-\frac{1}{2}\)

Step-by-step explanation:

1) Move terms to the left side.

\(3x=2x^{2} -2\\3x-(2x^{2}-2)=0\)

2) Distribute.

\(3x-(2x^{2} -2)=0\\3x-2x^{2} +2=0\)

3) Rearrange terms.

\(3x-2x^{2} +2=0\\-2x^{2} +3x+2=0\)

4) Common factor.

\(-2x^{2} +3x+2=0\\-(2x^{2} -3x-2)=0\)

5) Divide both sides of the equation by the same term.

\(-(2x^{2} -3x-2)=0\\2x^{2} -3x-2=0\)

6) Use the quadratic formula.

\(x=\frac{-b+\sqrt{b^{2}-4ac } }{2a}\)

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

\(2x^{2} -3x-2=0\\a=2\\b=-3\\c=-2\)

\(x=\frac{-(-3)+\sqrt{(-3)^{2} -4*2(-2)} }{2*2}\)

7) Simplify.

Evaluate the exponent

\(x=\frac{3+\sqrt{(-3)^{2}-4*2(-2) } }{2*2}\)

\(x=\frac{3+\sqrt{9-4*2(-2)} }{2*2}\)

Multiply the numbers

\(x=\frac{3+\sqrt{9-4*2(-2)} }{2*2}\)

\(x=\frac{3+\sqrt{9+16} }{2*2}\)

Add the numbers

\(x=\frac{3+\sqrt{9+16} }{2*2}\)

\(x=\frac{3+\sqrt{25} }{2*2}\)

Evaluate the square root

\(x=\frac{3+\sqrt{25} }{2*2} \\x=\frac{3+5}{2*2}\)

Multiply the numbers

\(x=\frac{3+5}{2*2}\)

\(x=\frac{3+5}{4}\)

8) Seperate the equations.

To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.

\(x=\frac{3+5}{4}\)

\(x=\frac{3-5}{4}\)

9) Solve.

Rearrange and isolate the variable to find each solution.

\(x=2\\x=-\frac{1}{2}\)

The inequality that correctly describes the number of ounces of water, w, that tom drinks each day is d. 64<w.

Amount of water that the bottle can hold = 32 ounces

Bottles of water consumed = 2

A mathematical comparison and representation of the connection between two expressions is known as an inequality. It can be regarded as a generalisation of an equation and is denoted by signs such as <, > and =.

Tom consumes more than two complete bottles of water every day. Since each bottle can carry up to 32 ounces of water, we can describe Tom's daily water consumption as -

= w > 2 × 32

Therefore,

Simplifying the right side of the inequality:

w > 64

Complete Question:

Toms water bottle can hold up to 32 ounces of water. each day he drinks more than 2 full bottles of water. which inequality correctly describes the number of ounces of water, w, that tom drinks each day?

a. w>2

b. 32<w

c. w = 64

d. 64<w

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Answer:

x=2, y=4. (2, 4).

Step-by-step explanation:

3x-3y=-6 implies 3(x-y)=3(-2), so x-y=-2.

-----------------------------

x-y=-2

3x+y=10

---------------

4x=8

x=8/4=2

2-y=-2

y=2-(-2)=2+2=4

11

Step-by-step explanation:

2 times 5 +1=11

Answer:

2n+1=-5

2n=-5-1

2n=-6

n=-6÷2

n=-3

Given statement :- 5y = 8x does not represent direct variation.

K= the coefficient is 8/5 instead of a single constant value.

In the equation 5y = 8x, we can determine whether it represents direct variation by comparing it to the general form of a direct variation equation: y = kx, where k is the constant of variation.

If we rewrite the given equation in the form y = kx, we divide both sides by 5 to isolate y:

y = (8/5)x

Comparing this to the general form, we can see that the given equation is not in the direct variation form. In a direct variation equation, the coefficient of x (the constant of variation, k) should remain constant, but in this case, the coefficient is 8/5 instead of a single constant value.

Therefore, the given equation does not represent direct variation.

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The numeric value of the expression 1/α + 1/β is given as follows:

-3/7.

The quadratic function in this problem is given as follows:

4x² + 3x + 7 = 0.

The coefficients of the quadratic function are given as follows:

a = 4, b = 3, c = 7.

The sum of the roots is given as follows:

α + β = -b/a.

Hence:

α + β = -3/4

The product of the roots is given as follows

αβ = c/a

Hence:

αβ =7/4.

These values are used to obtain the numeric value of the expression, as follows:

1/α + 1/β = (α + β)/αβ = (-3/4)/(7/4) = -3/7.

(the least common multiple of α and β is αβ, and then the least common factor is used to solve the expression).

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