A sum of money is to be divided between Alyah, Byron and Cecil. Alyah receives $1 plus one-third of what is left. Byron then receives $6 plus one-third of what remains. Cecil receives the rest, which amounts to $40. How much did Byron receive? (A) $26 (B) $28 (C) $30 (D) $32 (E) $34​

Answer:

B

Step-by-step explanation:

Convert from mixed numbers to improper fractions:

\(\sf area=90 \frac{3}{10}=\dfrac{90 \cdot 10+3}{10}=\dfrac{903}{10}\)

\(\sf length=10\frac12=\dfrac{10 \cdot 2+1}{2}=\dfrac{21}{2}\)

Area of a rectangle = length x width

⇒ width = area ÷ length

\(\sf \implies width=\dfrac{903}{10} \div \dfrac{21}{2}\)

\(\sf \implies width=\dfrac{903}{10} \times \dfrac{2}{21}\)

\(\sf \implies width=\dfrac{1806}{210}\)

\(\sf \implies width=\dfrac{1806 \div 42}{210 \div 42}\)

\(\sf \implies width=\dfrac{43}{5}\)

\(\sf \implies width=8\frac35\)

\( \pink{ \text{Given:}}\)

\( \\ \)

\( \star \sf{}Area =90 \dfrac{3}{10} \)

\( \\ \)

\( \star \sf{}Length =10 \dfrac{1}{2} \)

\( \\ \\ \)

\( \purple{ \text{To~Find:}}\)

\( \\ \\ \)

\( \star \sf Width \: of \: rectangle\)

\( \\ \\ \)

\( \orange{ \text{Solution:}}\)

\( \\ \\ \)

So first convert length and area from fraction form to decible.

\( \leadsto\sf{}Area =90 \dfrac{3}{10} \)

\( \\ \)

\( \leadsto\sf{}Area = \dfrac{903}{10} \)

\( \\ \)

\( \leadsto\sf{}Area =90.3\)

\( \\ \)

Now convert value length into decibel .

\( \\ \)

\( \leadsto\sf{}Length =10 \dfrac{1}{2} \)

\( \\ \)

\( \leadsto\sf{}Length = \dfrac{21}{2} \)

\( \\ \)

\( \leadsto\sf{}Length = 10.5\)

\( \\ \)

We know :-

\(\bigstar\boxed{\rm Area~of~rectangle= length \times width}\)

\( \\ \\ \)

So:-

\( \\ \)

\(: \implies\sf Area~of~rectangle= length \times width \\ \\ \\ : \implies\sf 90.3= 10.5 \times width \\ \\ \\: \implies\sf 90.3 \div 10.5=width \\ \\ \\: \implies\sf \dfrac{ 90.3}{10.5}=width \\ \\ \\: \implies\sf \dfrac{ 90 \cancel.3}{10 \cancel.5}=width \\ \\ \\: \implies\sf \dfrac{ 903}{105}=width \\ \\ \\: \implies\sf width = \dfrac{ 903}{105} \\ \\ \\: \implies \underline{\boxed{\sf width = 8.6}} \pink\bigstar\)

\(\\\\\\\)

\(\begin{lgathered}\small\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin {array}{cc}\\ \dag\quad \Large\underline{\bf \small{Formulas\:of\:Areas:-}}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Base\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}d\sqrt {4a^2-d^2}\\ \\ \star\sf Parallelogram =Base\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}\end{gathered}\end{gathered}\end{lgathered}\)

The statement "Every connected undirected graph having degree sequence 2, 2, 4, 4, 6 has a Hamilton cycle" is false.

The statement "Every connected undirected graph having degree sequence 2, 2, 4, 4, 6 has a Hamilton cycle" is false.

To determine if a graph has a Hamilton cycle, we need to analyze the given degree sequence and the connectivity of the graph.

In this case, the degree sequence 2, 2, 4, 4, 6 implies that there are five vertices in the graph, each having a specific number of edges connected to them.

However, the degree sequence alone does not guarantee the existence of a Hamilton cycle.

To disprove the statement, we can provide a counterexample by constructing a connected undirected graph with the given degree sequence (2, 2, 4, 4, 6) that does not have a Hamilton cycle.

By carefully arranging the edges between the vertices, it is possible to create a graph where a Hamilton cycle cannot be formed.

Therefore, the statement claiming that every connected undirected graph with degree sequence 2, 2, 4, 4, 6 has a Hamilton cycle is false.

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Answer:

the answer is D have a good day

Each piece is 24 inches long. One yard is equal to 36 inches, so two yards are equal to 72 inches.

To solve this problem, we need to convert the length of the board from yards to inches and then divide it into 3 equal parts.

First, we convert 2 yards to inches by multiplying by 36 (since there are 36 inches in a yard):

2 yards × 36 inches/yard = 72 inches

So, the board is 72 inches long.

Next, we divide 72 inches by 3 to find the length of each piece:

72 inches / 3 = 24 inches

Therefore, each piece is 24 inches long. In summary, to find the length of each piece of a board that is 2 yards long and cut into 3 equal pieces, we convert 2 yards to inches by multiplying by 36 and then divide by 3 to get each piece's length, which is 24 inches.

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Given the expression :

The expression will be equal:

so, the answer is option 4)

The required rate of return (or minimum acceptable rate of return) is 20 percent. If the net cash flows are $15,000 per year for ten years, the total cash flow is $150,000. The project's cost is $47,500. We can now apply the net present value formula to determine whether or not the project is feasible.

Net Present Value (NPV) = Cash flow / (1 + r)^n - Cost Where, r is the discount rate, n is the number of years, and Cost is the initial outlay.

Net Present Value = 150000 / (1 + 0.20)^10 - 47500

Net Present Value = $67,482.22

Since the NPV is positive, the project is feasible. When calculating net present value, it's important to remember that a positive NPV implies that the project is expected to generate a return that exceeds the cost of capital, whereas a negative NPV indicates that the project is expected to generate a return that is less than the cost of capital, and as a result, it should be avoided.

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Answer:

XD   \(\frac{1}{12}\) is the answer.

Step-by-step explanation:

So, to divide a fraction with a whole number you'll have to multiply the denominator with the whole number.

Hopes This Helps

The Presence and Absence (PandA) representation is a discrete form of representing a phenomenon or logic. In this representation, there are two distinct states: presence and absence. It simplifies the representation by categorizing the phenomenon as either existing or not existing, or the logic being true or false.

Unlike continuous representations that allow for gradations or varying levels, the PandA representation does not consider any intermediate states. It focuses on the binary distinction between presence and absence, which can be useful in certain contexts where discrete categorization is sufficient.

By utilizing the PandA representation, we can effectively analyze and interpret data or information based on the clear distinction of the phenomenon being present or absent, providing a straightforward and simplified approach for decision-making and analysis.

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Answer:

Step-by-step explanation:

Using the equation of motion S = ut + 1/2at² where;

S is the distance travelled = 20m

u is the initial velocity = 0m/s (car starts from rest)

a is the acceleration = ?

t is the time taken = 4s

To get the acceleration of the car, we will substitute the given parameters into the given equation.

S = ut + 1/2at²

20 = 0(4)+1/2a(4)²

20 = 0+ a/2*16

20 = 8a

divide both sides by 8

20/8 = 8a/8

20/8 = a

a = 20/8

a = 2.5m/s²

Hence the acceleration of the car is 2.5m/s²

Answer:

1 4 3 4 4 = ilyvm

1 4 3 3 = ilyt

Step-by-step explanation:

1. Perimeter is 3 + 3 +3 +4 +5 = 18 feet

 Area = 3*3 = 9, 1/2*3*4 = 6, 9 + 6 =15 square feet

2. perimeter = 2.5 +2.5+ 2.5+2.5+0.5+0.5 = 11 meters

  Area = 3*.5 = 1.5, 3*2=6,  6+1.5 = 7.5 square meters

3. perimeter = 3.14*2*3 = 18.84 +8 = 26.8 inches

  Area = 6*4 = 24 + 3.14*3^2 = 28.26 = 28.26 +24 = 52.3 inches  

4. surface area = 2*π*6*20+2*π*6^2= 980.2 yards

Volume = π*6^2*20 = 2261.9 cubic yards

5.surface area = 2*(9*7+2*2+2*9) = 190 cm

Volume = 2*7*9 = 126 cubic cm

6. surface area = 2*(11*11+11*11+11*11) = 726 mm

 Volume = 11 *11*11 = 1331 cubic cm

Answer:

12 the probability that both mark and jennifer win

Answer: it’s A

Step-by-step explanation:

Answer:

Well, the answer is 0.

Step-by-step explanation:

Answer: 0

Step-by-step explanation: the answer will be zero because since -456 and 456 are both the opposite the answer will be zero I hope this helps :)

The rate of change is meaning the slope. The slope of A is 8, therefore, the answer would be 7.

hope this helps :)

To write the equation in proper form, we can divide the entire equation by \(t^9\):

\[y^{(5)} - \frac{t^{-6}}{t^{-12}}y'' + 6t^{-9}y = 0\]

Simplifying further, we can multiply the equation by \(t^{12}\):

\[t^{12}y^{(5)} - t^3y'' + 6y = 0\]

Therefore, the given differential equation is:

\[t^{12}y^{(5)} - t^3y'' + 6y = 0\]

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Answer:

1/2 (14) ( 3x - 4 ) > 56

14/2 (3x-4) > 56

7 (3x-4) > 56

21x - 28 > 56

21x > 56+28

21x > 84

x < 4

Answer:

Step-by-step explanation:

The area of the triangle is

Given

Then

If A > 56, then solving inequation:

Answer:

a) Pop

b) 30

c) 230

Step-by-step explanation:

Answer:

It would be $35

Step-by-step explanation:

hope this helps

15 percent of 45 is 6.75

45- 6.75 is 38.25

The price after a 15% discount is $38.25

Answer:

9= coefficient

4= degree

-6m= term

-5= constant

Step-by-step explanation: I hope this helps ;)

Answer:

The answer to your question is −2v+1v

The number of wild bears the naturalist can relocate per month is 2 wild bears.

Number of wild bears relocated by the naturalist = 12 wild bears

Time taken by the naturalist to relocate these wild bears = 6 months

Thus the number of bears the naturalist can relocate in 1 month can be found out by using unitary method

This implies that the number of bears relocated by the naturalist in 1 month or per month = 12 / 6 = 2 wild bears

Thus the number of wild bears the naturalist can relocate per month is 2 wild bears .

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Answer:

15

Step-by-step explanation:

500/35 approx 14.28

Always round up otherwise there won’t be enough

14.28 rounded up = 15

(a) $$(4.7 \times 10^5) \cdot (2.9 \times 10^4)$$

To multiply these numbers, we multiply the coefficients and add the exponents:

$$(4.7 \cdot 2.9) \times 10^{5+4} = 13.63 \times 10^9$$

The answer in scientific notation is $$1.363 \times 10^{10}$$.\(\)

(b) $$\frac{5.8 \times 10^3}{2 \times 10^8}$$

To divide these numbers, we divide the coefficients and subtract the exponents:

$$\frac{5.8}{2} \times 10^{3-8} = 2.9 \times 10^{-5}$$

The answer in scientific notation is $$2.9 \times 10^{-5}$$.

(c) $$(1.5 \times 10^3) + 2491$$

To add these numbers, we keep the larger exponent and add the coefficients:

$$1.5 \times 10^3 + 2491 = 1.5 \times 10^3 + 2.491 \times 10^3 = 3.991 \times 10^3$$

The answer in scientific notation is $$3.991 \times 10^3$$.

(d) $$0.0005 - 1.5 \times 10^{-4}$$

To subtract these numbers, we keep the larger exponent and subtract the coefficients:

$$0.0005 - 1.5 \times 10^{-4} = 0.0005 - 0.00015 = 0.00035$$

The answer is $0.00035$

To find the minimum value of the average cost over the given intervals, we need to calculate the average cost function and evaluate it at the endpoints of each interval.

a) For the interval 1 ≤ x ≤ 10, the average cost function is given by C_avg = (C(10) - C(1))/(10 - 1), where C(x) = x + 30x + 128. Evaluating C(10) and C(1), we get C(10) = 10 + 30(10) + 128 = 388 and C(1) = 1 + 30(1) + 128 = 159. Plugging these values into the average cost function, we have C_avg = (388 - 159)/(10 - 1) = 229/9 ≈ 25.4. Therefore, the minimum value of the average cost over the interval 1 ≤ x ≤ 10 is approximately 25.4.

b) Similarly, for the interval 10 ≤ x ≤ 20, we calculate the average cost function C_avg = (C(20) - C(10))/(20 - 10). Evaluating C(20) and C(10), we get C(20) = 20 + 30(20) + 128 = 748 and C(10) = 10 + 30(10) + 128 = 388. Plugging these values into the average cost function, we have C_avg = (748 - 388)/(20 - 10) = 36. Therefore, the minimum value of the average cost over the interval 10 ≤ x ≤ 20 is 36.

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Answer: 12

Step-by-step explanation:

Answer:

Now that the values of m (slope) and b (y-intercept) are known, substitute them into y=mx+b . to find the equation of the line.

y=5/4x+9/4

Step-by-step explanation:

Use y=mx+b to calculate the equation of the line, where m represents the slope and b represents the y-intercept.

To calculate the equation of the line, use the y=mx+b format.

Slope is equal to the change in y over the change in x , or rise over run.

m=(change in y)/(change in x)

The change in x

is equal to the difference in x-coordinates (also called run), and the change in y is equal to the difference in y-coordinates (also called rise).

m=(y2−y1)/(x2−x1)

Substitute in the values of x and y into the equation to find the slope.

m=1−(6)/−1−(3)

Finding the slope m.

m=5/4

Find the value of b

using the formula for the equation of a line.

b=9/4

The formula to calculate the coefficient of variation is given as the ratio of the standard deviation to the mean. Coefficient of Variation = Standard Deviation / Mean.

It is represented as a percentage to make comparisons between sets of data with different units of measurement.Let's calculate the coefficient of variation for the above-given data. Coefficient of variation= Standard Deviation / MeanWe can calculate the standard deviation by using the following formula: σ = √ ∑ (Pᵢ (Xᵢ – μ)²).

For our given data, the calculation of standard deviation is shown below:σ = √ (.30(70-100)² + .30(90-100)² + .40(150-100)²)σ = √ (63,000)σ = 251.97We can calculate the mean by using the following formula: Mean = ∑ (Pᵢ Xᵢ)For our given data, the calculation of Mean is shown below:Mean = (.30 x 70) + (.30 x 90) + (.40 x 150)Mean = 25 + 27 + 60Mean = 112Coefficient of variation= Standard Deviation / Mean Coefficient of variation= 251.97 / 112Coefficient of variation = 2.247 rounded to 3 decimal places. Therefore, the coefficient of variation is 2.247.

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Answer:

recessions

Step-by-step explanation: