The ratio of the number of roses to the number of lilies in a flower shop is 3:5. One-sixth of the roses and half of the lilies are white. If there are a total of 24 white flowers, how many lilies are in the flower shop?
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Answer:

Option D is the right option.

Solution,

\( \frac{6x}{7} - \frac{2x}{7} \\ = \frac{6x - 2x}{7} \\ = \frac{4x}{7} \)

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Answer:

\(= \frac{4x}{7} \\ \\ \)

Step-by-step explanation:

\( \frac{6x}{7} - \frac{2x}{7} \\ \frac{6x - 2x}{7} \\ = \frac{4x}{7} \)

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Final result is: a. 1010111012 + 001101012

In the given calculation, we first start with the least significant bit. 1+1 = 0 and carry = 1 (since 1+1 can’t be expressed as 1 in binary).Similarly, moving leftward:0+0+1 = 1, 1+0+1 = 0 and carry = 1,1+0+0+1 = 0 and carry = 1,1+1+0+1 = 1 and carry = 1,1+0+1+1 = 1 and carry = 1,0+0+0+1 = 1 and carry = 0.The sequence of carry bits are: 11110112Final result is: 1100001112b. 10110111112 + 110101012:

In this given calculation, we start with the least significant bit.1+0 = 1, 1+1 = 0 and carry = 1,1+0+1 = 0 and carry = 1,1+1+0+1 = 1 and carry = 1,0+1+1+1 = 1 and carry = 0,1+1+0+1 = 1 and carry = 1,1+1+1+1 = 0 and carry = 1,1+1+1 = 0 and carry = 1,1+1+1 = 0 and carry = 1.

The sequence of carry bits are: 111110112Final result is: 10001100102c. 10101000112 - 101110102:In this given calculation, we start with the least significant bit.1-0 = 1, 0-0 = 0,1-1 = 0 and borrow = 1,1-1 = 0 and borrow = 1,0-1 = 1 and borrow = 1,0-0 = 0,1-1 = 0 and borrow = 1,1-1 = 0,0-1 = 1 and borrow = 1.

The sequence of borrow bits are: 111110112Final result is: 1110010102d. 10001000112 - 1110102:In this given calculation, we start with the least significant bit.1-0 = 1, 0-1 = 1 and borrow = 1,1-0 = 1,0-1 = 1 and borrow = 1,0-0 = 0,0-1 = 1 and borrow = 1,0-1 = 1 and borrow = 1,1-1 = 0.The sequence of borrow bits are: 1111112Final result is: 1111100112

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Answer:

-x^2-2x+3

Step-by-step explanation:

3 - (2x² + 3) + (x² - 2x + 3)

Distribute the minus sign

3 - 2x² - 3 + x² - 2x + 3

Combine like terms

- 2x²  + x² - 2x + 3-3+3

-x^2-2x+3

The solution to the inequality graphed below is a point that lies in the dark region of the graph. The point (4, 4) is a solution to the graph.

An equation is an expression that shows the relationship between two or more numbers and variables.

The solution to the inequality graphed below is a point that lies in the dark region of the graph. The point (4, 4) is a solution to the graph.

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Answer:

3=-2x-14+5x+12-8x

3+14-12=-2x+5x-8x

5=-5x

x=(-1)

Answer: 1/3

Step-by-step explanation:

If you enter 1/3 into a calculator, you should get something around .3333336

The fraction form of the decimal expansion 0.3 repeating is 1/3.

To express the decimal expansion 0.3 repeating as a fraction, we can use the concept of a geometric series.

Let's represent the repeating decimal as x:

x = 0.333...

To eliminate the repeating part, we can multiply x by 10 to shift the repeating part one decimal place to the left:

10x = 3.333...

Now, we can subtract x from 10x to eliminate the repeating part:

10x - x = 3.333... - 0.333...

9x = 3

To express x as a fraction, we divide both sides of the equation by 9:

9x / 9 = 3 / 9

x = 1 / 3

Therefore, the fraction form of the decimal expansion 0.3 repeating is 1/3.

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Answer:

40-5x

Step-by-step explanation:

Sahai starts with 40 and loses 5 times the entrance fee, which is represented by x. So, 40-5x is the expression

Answer:

Step-by-step explanation:

Given sequence:

This is AP with:

The rule for the nth term of the sequence is:

Substitute values:

The Laplace domain equation X(s) is found to be X(s) = (s + 2)/(s^2 + 5s + 6). The time domain equation x(t) can be obtained by applying the inverse Laplace transform to X(s), resulting in x(t) = e^(-t) - e^(-2t).

Given the Laplace domain equation X(s), we need to substitute the given parameters and find its expression in terms of s. The equation provided is X(s) = (s + 2)/(s^2 + 5s + 6).

To obtain the time domain equation x(t), we need to apply the inverse Laplace transform to X(s). The inverse Laplace transform of X(s) will give us x(t) in terms of t.

Applying the inverse Laplace transform to X(s) involves finding the inverse transform of each term separately. The inverse Laplace transform of (s + 2) is simply 1, representing the unit step function. The inverse Laplace transform of (s^2 + 5s + 6) is e^(-t) - e^(-2t), which can be obtained through partial fraction decomposition.

Therefore, the time domain equation x(t) is given by x(t) = e^(-t) - e^(-2t), where t represents time.

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The mean value of the radius (r) at which you would find the electron, given the H atom wave function is 100(r), is 0.

The wave function of an electron in the hydrogen atom, denoted by Ψ, describes the probability distribution of finding the electron at different positions around the nucleus. In this case, the given wave function is 100(r), where r represents the radius.

To calculate the mean value of the radius, we need to evaluate the integral of r multiplied by the absolute square of the wave function, integrated over all possible values of r. However, the wave function 100(r) does not provide a valid description of the hydrogen atom's electron distribution. The wave function should be normalized, meaning that the integral of the absolute square of the wave function over all space should equal 1. In this case, the given wave function lacks normalization.

Since the wave function is not properly normalized, we cannot accurately calculate the mean value of the radius. Without normalization, the probability distribution described by the wave function does not provide meaningful information about the electron's position.

In summary, based on the given wave function, the mean value of the radius cannot be determined without proper normalization of the wave function. A properly normalized wave function is necessary to obtain accurate information about the electron's position.

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D. because its a straight line

Answer:

1) 14 dimes

2) 5 quarters 3 nickels

3) 140 pennies

4) 28 nickels

5) 4 quarters 4 dimes

6) 10 dimes 4 nickels

Step-by-step explanation:

140% = $1.40

Answer:

9 times as many, the answer would be number 4

Step-by-step explanation:

Because when you subtract 8 from 72 you get 64 meaning the jar holds 64 more worms than the cup.

Answer:

the best is equations is 72:8=1

Step-by-step explanation:

Answer:

LCM(24,30,40)=120.The Least common multiple for three numbers 24,30 and 40 is 120

Step-by-step explanation:

Answer:

16x+6

Step-by-step explanation:

5x+2+3x+1+5x+2+3x+1 =

16x+6

Answer:

16x + 2

Step-by-step explanation:

\(\boxed{\begin{minipage}{4 cm}\underline{Perimeter of a rectangle}\\\\$P=2(w+l)$\\\\where:\\ \phantom{ww}$\bullet$ $w$ is the width. \\\phantom{ww}$\bullet$ $l$ is the length.\\\end{minipage}}\)

Given expressions:

To write an expression for the perimeter of the rectangle, substitute the given expressions for the width and length into the perimeter formula:

\(\begin{aligned}\implies \textsf{Perimeter} &=2\left(5x+2+3x-1 \right)\\ &= 2(5x+3x+2-1)\\&=2(8x+1)\\&=16x+2\end{aligned}\)

Polygon pairs are dissimilar because their proportions are not equal.So,

\(\frac{8}{5}\neq \frac{15}{12}\)

Congruent polygons are exactly the same size and fit perfectly because all corresponding parts are congruent (equal). Conversely, similar polygons have the same shape but not the same size (that is, one larger than the other).

That is, if two polygons are similar, their corresponding angles are congruent and their corresponding sides are proportional.

So if we find that the corresponding angles here match, we know if the corresponding sides are proportional. The angles are coincident, but the sides are not proportional.

how \(\frac{17}{13}\) , \(\frac{15}{12}\) , \(\frac{8}{5}\)

You can see that the ratios are not equal. Therefore, polygon pairs are dissimilar. 

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The answer is option A) similar; the corresponding angles are congruent and 8/5 = 17/13.

What is meant by congruent angles?

Congruent angles are two angles that have the same measure in degrees or radians. In other words, if two angles are congruent, they have the same angle measurement and can be superimposed on each other. When two angles are congruent, they will look exactly the same and will have the same degree or radian value.

We can see that the given polygons are right angled triangles.

To check if the two right triangles are similar, we can use the Pythagorean theorem to confirm that the ratio of the sides is consistent between the two triangles.

For Triangle 1:

Base = 8

Height = 15

Hypotenuse = 17

For Triangle 2:

Base = 5

Height = 12

Hypotenuse = 13

Using the Pythagorean theorem, we can find that the length of the missing side (the side perpendicular to the hypotenuse) for Triangle 1 is:

\(\sqrt{(17^2 - 8^2)\) = \(\sqrt{(225)\) = 15

Using the Pythagorean theorem, we can find that the length of the missing side (the side perpendicular to the hypotenuse) for Triangle 2 is:

\(\sqrt{(13^2 - 5^2)\) = \(\sqrt{(144)\) = 12

Now we can compare the ratios of the corresponding sides:

Triangle 1:

Base/Height = 8/15

Height/Hypotenuse = 15/17

Base/Hypotenuse = 8/17

Triangle 2:

Base/Height = 5/12

Height/Hypotenuse = 12/13

Base/Hypotenuse = 5/13

We can see that the ratios of the corresponding sides in the two triangles are equal:

Base/Height: 8/15 = 5/12

Height/Hypotenuse: 15/17 = 12/13

Base/Hypotenuse: 8/17 = 5/13

Therefore, the two triangles are similar and the answer is A) similar; the corresponding angles are congruent and 8/5 = 17/13.

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To find the maximum profit, we can look for the vertex of the parabolic function representing the profit.

The given profit function is:

\(Z = -3x^2 + 12x + 25\)

We can see that the coefficient of the \(x^2\) term is negative, which means the parabola opens downwards. This indicates that the vertex of the parabola represents the maximum point.

The x-coordinate of the vertex can be found using the formula:

\(x = \frac{-b}{2a}\)

In our case, a = -3 and b = 12. Plugging these values into the formula, we get:

\(x = \frac{-12}{2 \cdot (-3)}\\\\x = \frac{-12}{-6}\\\\x = 2\)

To find the maximum profit, we substitute the x-coordinate of the vertex into the profit function:

\(Z = -3(2)^2 + 12(2) + 25\\\\Z = -12 + 24 + 25\\\\Z = 37\)

Therefore, the maximum profit is 37.

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The required solution of the given expression is given as x = 5 and x = -3.

Given that,
To solve x² - 2x=15,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
x² - 2x - 15 = 0
x² -5x + 3x - 15 = 0
x (x - 5) + 3 (x - 5) = 0
(x + 3)(x - 5) = 0
So,
x = -3 and x = 5

Thus, the required solution of the given expression is given as x = 5 and x = -3.

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The correct statement is that Ursula has incurred the finance charge of 46.17% about for the loan amounting to $6400. So, the correct option matching the statement is not as quoted in the options above.

Finance charge can be calculated by summarizing and comparing the principal amount with the annuity amount derived by the formula of compound interest.

Hence, the correct option is that Ursula has borne the financial charge as 46.17% of her principal.

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The area of a circle can be found using the formula A = πr^2, where r is the radius of the circle. Since the diameter is given as 18 units, the radius would be half of that, which is 9 units. Now, substitute the value of the radius into the formula: A = π(9^2) = 81π units^2. Therefore, the correct answer is option b) 81π units^2.


1. Use the formula A = πr^2, where A is the area and r is the radius of the circle.
2. The diameter is given as 18 units, so the radius would be half of that, which is 9 units.
3. Substitute the value of the radius into the formula: A = π(9^2) = 81π units^2.

Therefore, the area of the circle with a diameter of 18 units is 81π units^2.

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Answer:

208 mm

Step-by-step explanation:

A = Area. P = Perimeter. B = base.

Let's say H = Height

P = 2B + 2H

Now we already know the perimeter is 68 mm, so P = 68:

68 = 2B + 2H

In addition, we know that the base is 26 mm, so B = 26:

68 = 2(26) + 2H

68 = 52 + 2H

16 = 2H ==> subtract 52 on both sides

H = 8  ==> the height of the rectangle is 8 mm

A = B * H  

A = 26 * 8  ==> plugin B=26 and H=8 into the Area formula

A = 208  ==> simplified

Hence, the area is 208 mm.

Answer:

XXXXXXXXXXXXXXXXXXXX Ion know

Answer:

Step-by-step explanation:

1)

white (w) marble

yellow (y) marble

green (g) marble

red (r) marble

Pw+Pw+Pg+Pr=1 (Eq. 1 )

w+y+g+r=12 (Eq. 2)

Answer: There are 12 marbles in the bag. SInce the question says the bag contains 12 marbles.

2)

a) Pw+Py = Pg

w + y = g (Eq. 3)

b) Pw = 10/40 = 1/4

If P = 1/4, if we have 12 marbles, P=3/12

Then, we know that we have 3 white marbles

Answer: There are 3 white marbles in the bag.

3) Pr = 1/5. Considering that 2 marbles were removed, we have 10 markles. The Pr=2/10.

Answer: Thus, we have 2 balls red.

4) From 12 marbles, we already know that 3 are white and 2 are red.

Then: 12-3-2= 7

Answer: 7 marbles are green or yellow.

5)

From question 4 , we know that;

y + g = 7

y = 7 - g (Eq. 4)

And from Eq. 3

w + y = g

3 + y = g

Substituing Eq. 4 in Eq. 3:

3 + 7 - g = g

10 = 2g

10/2 = g

g = 5

And:

y = 7 - g

y = 7-5

y = 2

The numeratiors are:

3 (Pw), 2 (Py), 5 (Pg)

5) 2 = yellow marbles

5 = green marbles

The function represents the frog population after x years is f(x) = 1200 × (0.97)ˣ which is correct option (C)

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

Given as:

The average rate  decreasing = 3% per year

Determine the reduction rate.

So, net rate = (100 - 3) %

⇒ 97 %

The frog population at 1,200

Determine the frog population after 1 year.

f(1) = 97% of 1200

f(1) = (0.97) × 1200

f(1) = 1200 × (0.97)

Determine the frog population after 2 years.

f(2) = (0.97) ×  1200 × (0.97)

f(2) = 1200 × (0.97)²

Determine the frog population after 3 years.

f(3) = (0.97) ×  1200 × (0.97)²

f(3) = 1200 × (0.97)³

Determine the frog population after x year.

f(x) = 1200 × (0.97)ˣ

Hence, the function represents the frog population after x years is f(x) = 1200 × (0.97)ˣ

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The solution is of the form y = tr where r = 5/14 for the given differential equation.

Given differential equation:

t²y''- 10ty' + 28y = 0

Let's assume the solution is of the form y = tr. We need to find the values of r for which this form of the solution holds.Let's differentiate the solution y = tr with respect to t in order to solve for the first and second derivatives of y as follows:

y = tr.....(1)

First derivative of y w.r.t t is given by:

y' = r.....(2)

Second derivative of y w.r.t t is given by:

y'' = 0.....(3)

Substituting equations (1), (2), and (3) in the given differential equation, we get:

(t² * 0) - 10t * r + 28(tr) = 0

Simplifying, we get:

(28r - 10) * t = 0

Since t > 0, then the coefficient of t must be zero. Thus,

28r - 10 = 0

=> 28r = 10

=> r = 10/28 (reduced)

=> r = 5/14

So, the value of r is 5/14 when the given differential equation has solutions of the form y = tr for t > 0.

In summary, the solution is of the form y = tr where r = 5/14 for the given differential equation.

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