Eight friends divide seven bags of apples equally between them. Enter the division represented by this situation as a fraction.

Total number of possible outcomes:

Number of ways to choose 3 numbers from 56 (56 choose 3): 56! / (3! * (56 - 3)!) = 22,957

Number of ways to choose 1 number from 49: 49

Total number of possible outcomes = 22,957 * 49 = 1,128,593

Number of favorable outcomes:

Number of ways to choose 1 number from 49: 1

Number of favorable outcomes = 1

Probability of winning the minimum award:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 1 / 1,128,593 ≈ 0.000000888, or approximately 0.0000888%

Answer:

10000

Step-by-step explanation:

100 hugs x 100 hugs

= 10,000 hugs.

Answer:

y = 3x + 20

This is an equation, in slope-intercept form, which represents a the placement of a line. The 3 in the equation represents the slope of the line, and the 20 represents the y-intercept.

9514 1404 393

Answer:

  y = -x +3

Step-by-step explanation:

The 2-point form of the equation of a line is useful when 2 points are given.

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  y = (0 -5)/(3 -(-2))(x -(-2)) +5

  y = -5/5(x +2) +5

  y = -x +3

With the help of substitution the answer to the equation is - (-9/2 , 5/2)

acc to our question -

Hence,The solution to the equation is (-9/2, 5/2) using substitution.

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The vector whose magnitude is 3 and whose components I. the I and j direction are equal is; <3√2/2i, 3√2/2j>.

It follows that the magnitude of a vector in terms of its components in the i and j direction is;

M = √(x² + y²).

On this note, since the i and j components are equal; x = y and hence, we have;

3 = √(x² + x²).

3² = 2x²

x² = 9/2

x = 3/√2

x = 3√2/2

On this note, the required vector which is as described is; <3√2/2i, 3√2/2j>.

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Using proportions, it is found that:

3. Due to the lower cost per pound, the twelve-pack is the better value.

4. Due to the lower cost per cup, the Pacific Coast Coffee is the better value.

5. Lettuce and Asparagus cost the same per pound.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

For item 3, the cost per pound is the proportion of the cost by the weight, hence:

Due to the lower cost per pound, the twelve-pack is the better value.

For item 4, we follow the same procedure, hence:

Due to the lower cost per cup, the Pacific Coast Coffee is the better value.

In item 5, we have that:

Lettuce and Asparagus cost the same per pound.

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The equivalent expression to  4√3 is  √48 or 6.928.

An equivalent expression is an expression that has equal value to the original given expression.

From the given expression, we can determine its equivalent expression as follows;

The given expression = 4√3

We can square 4 and multiply it by 3 and enclose all with the square root.

4√3 = √(4² x 3 )

= √ ( 16 x 3 )

= √ ( 48 )

= 6.928

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The initial simplex tableau is as shown below:

\(x_1\) \(x_2\) \(x_3\) \(x_4\) \(x_5\) \(x_6\)

0 3 5 2 0 0 0 0

10 3 4 5 1 0 0 10

5 1 3 10 0 1 0 5

1 1 -2 0 0 0 1 1

The problem can be rewritten using slack variables as follows:

Maximize: P = \(3x_1 + 5x_2 + 2x_3\)

Subject to:

\(3x_1 + 4x_2 + 5x_3 + x_4 = 10\\x_1 + 3x_2 + 10x_3 + x_5 = 5\\x_1 - 2x_2 + x_6 = 1\)

\(x_1\), \(x_2\), \(x_3\), \(x_4\), \(x_5\), \(x_6\) > 0

The initial simplex tableau is:

\(x_1\) \(x_2\) \(x_3\) \(x_4\) \(x_5\) \(x_6\)

0 3 5 2 0 0 0 0

10 3 4 5 1 0 0 10

5 1 3 10 0 1 0 5

1 1 -2 0 0 0 1 1

The first row represents the objective function with the coefficients of the decision variables.

The columns \(x_1, x_2,\) and \(x_3\) correspond to the decision variables, while \(x_4, x_5,\) and \(x_6\) are the slack variables.

The rightmost column represents the constant terms of the constraints. The initial values of the slack variables are set to the constants in the constraints.

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Answer:

Aquarium dimensions:

x = 3,106 m

h = 6,22 m

C(min) = 1277,62 $

Step-by-step explanation: (INCOMPLETE QUESTION)

We have to assume:

The shape of the aquarium  (square base)

Let´s call "x" the side of the base, then h ( the heigh)

V(a) = x²*h          h = V(a)/x²      

Cost of Aquarium   C(a) = cost of the base (in stones) + 4* cost of one side (in glass)

C(a) = Area of the base *120 + 4*Area of one side*30

Area of the base is x²

Area of one side  is   x*h   or  x*V(a)/x²  

Area of one side is V(a)/x

C(x) = 120*x² + 4*30*60/x

C(x) = 120*x² +  7200/x

Taking derivatives on both sides of the equation we get

C´(x) = 2*120*x  - 7200/x²

C´(x) = 0 means    240 *x  - 7200/x² = 0

240*x³ - 7200 = 0

x³ = 7200/240

x = 3,106 m   and  h = 60 /x²     h =   6,22 m

and C (min) = 120*(3,106)³ - 7200 / 3,106

C(min) =  3595,72 - 2318,1

C(min) = 1277,62

Tara kept 5 plums out of the original 9 plums she had. In fraction form, she kept 5/9 of her plums.

To solve the problem, let's break it down step by step.

Tara initially has a certain number of plums. We don't know the exact number, but we can represent it as a whole unit, let's say 9 plums for simplicity.

Tara gives 1/3 of her plums to her best friend. Since she started with 9 plums, 1/3 of that is 3 plums. So, she gives away 3 plums to her best friend.

Now, Tara has 9 - 3 = 6 plums remaining.

Next, Tara gives 2/9 of her plums to her sister. Since she now has 6 plums, 2/9 of that is (2/9) * 6 = 12/9 = 4/3 plums. However, Tara cannot give away 4/3 plums since it's more than what she has.

So, she can only give away the maximum amount possible, which is 1 plum (since 1/3 of 6 plums is 2 plums, and 2/9 of 6 plums is 2/3 plums, which leaves 1 plum remaining).

After giving 1 plum to her sister, Tara is left with 6 - 1 = 5 plums.

In summary, Tara kept 5/9 of her plums after giving 1/3 to her best friend and 2/9 to her sister.

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Answer:

here p=0.65 and n=100 hence standard error =(p*(1-.

Step-by-step explanation:

well, the tax amount is simple, it was $71 and it went up to $86.45, that's a 15.45 difference, so that IS the tax amount.

now, if we take 71(origin amount) to be the 100%, what's 15.45 off of it in percentage?

\(\begin{array}{ccll} amount&\%\\ \cline{1-2} 71 & 100\\ 15.45& x \end{array} \implies \cfrac{71}{15.45}~~=~~\cfrac{100}{x} \\\\\\ 71x=1545\implies x=\cfrac{1545}{71}\implies x\approx 21.76\)

The total amount the man had = 52,200 rupees. Out of this, he gave 21,750 rupees to his son, 13,050 rupees to his daughter, and 17,400 rupees to his wife , the total amount given away by the man = 21,750 + 13,050 + 17,400 = 52,200 rupees.

A man gave 5/12 of his money to his son, 3/7 of the remainder to his daughter, and the remaining to his wife. If his wife gets Rs. 8,700, what is the total amount?

The given problem can be solved using the concept of ratios and fractions. Let us solve the problem step-by-step.Assume the man had x rupees with him.The man gave 5/12 of his money to his son.

The remaining amount left with the man = x - 5x/12= (12x/12) - (5x/12) = (7x/12)The man gave 3/7 of the remainder to his daughter.'

Amount left with the man after giving it to his son = (7x/12)The amount given to the daughter = (3/7) x (7x/12)= (3x/4)The remaining amount left with the man = (7x/12) - (3x/4)= (7x/12) - (9x/12) = - (2x/12) = - (x/6) (As the man has given more money than what he had with him).

Therefore, the daughter's amount is (3x/4) and the remaining amount left with the man is (x/6).The man gave all the remaining amount to his wife.

Therefore, the amount given to the wife is (x/6) = 8700Let us find the value of x.x/6 = 8700 x = 6 x 8700 = 52,200

Therefore, the man had 52,200 rupees with him.He gave 5/12 of his money to his son. Therefore, the amount given to his son is (5/12) x 52,200 = 21,750 rupees.

The remaining amount left with the man = (7/12) x 52,200 = 30,450 rupees.He gave 3/7 of the remainder to his daughter. Therefore, the amount given to his daughter is (3/7) x 30,450 = 13,050 rupees.

The amount left with the man = (4/7) x 30,450 = 17,400 rupees.The man gave 17,400 rupees to his wife.
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Proportionately, the number of cups of broccoli needed for a pound of beef is B. 1 and ½ cups of broccoli per beef.

Proportion refers to the numerical quantity or relationship of one variable to another, which are set equal to each other.

Proportions, like ratios, use fractional values because they show the quantity of one variable in another.

We state proportions in fractions, decimals, or percentages.

The proportion of 3/4 pound of beef to broccoli = 9/8 cups of broccoli

3/4 pound = 0.75 pound

9/8 cups = 1.125 cups

The number of cups of broccoli for a pound of beef = 1.5 cups (1.125/0.75)

1.5 cups = 1½ cups

Thus, given the proportional relationship presented, for a pound of beef, Tyler would need 1½ cups of broccoli.

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\( \sf \longrightarrow \: 5 \bigg( \: n - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{n}{1} - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10 \times n - 1 \times 1}{1 \times 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10n - 1}{ 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: \frac{50n - 5}{ 10} = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =1(10) \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =10 \\ \)

\( \sf \longrightarrow \: \: 100n - 10=10 \\ \)

\( \sf \longrightarrow \: \: 100n =10 + 10\\ \)

\( \sf \longrightarrow \: \: 100n =20\\ \)

\( \sf \longrightarrow \: \:n = \frac{2 \cancel{0}}{10 \cancel{0}} \\ \)

\( \sf \longrightarrow \: \:n = \frac{1}{5} \\ \)

Answer:-

To solve the equation \(\sf 5(n - \frac{1}{10}) = \frac{1}{2} \\\) for \(\sf n \\\), we can follow these steps:

Step 1: Distribute the 5 on the left side:

\(\sf 5n - \frac{1}{2} = \frac{1}{2} \\\)

Step 2: Add \(\sf \frac{1}{2} \\\) to both sides of the equation:

\(\sf 5n = \frac{1}{2} + \frac{1}{2} \\\)

\(\sf 5n = 1 \\\)

Step 3: Divide both sides of the equation by 5 to isolate \(\sf n \\\):

\(\sf \frac{5n}{5} = \frac{1}{5} \\\)

\(\sf n = \frac{1}{5} \\\)

Therefore, the solution to the equation \(\sf 5(n - \frac{1}{10})\ = \frac{1}{2} \\\) is \(\sf n = \frac{1}{5} \\\), which corresponds to option (d).

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♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

Table c

Step-by-step explanation:

Required:

Which of the 4 has the greatest rate of change

For Graph (A):

We start by picking any two equivalent points on the table:

\((x_1,y_1) = (0,1)\)

\((x_2,y_2) = (2,5)\)

Next, we determine the slope, m:

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

\(m = \frac{5-1}{2-0}\)

\(m = \frac{4}{2}\)

\(m = 2\)

This represents the rate of change:

For (B): \(y = 3x + 7\)

An equation is of the form:

\(y = mx + b\)

Where

m represents slope or rate of change:

By comparison:

\(m = 3\)

For table (C):

We start by picking any two equivalent points on the table:

\((x_1,y_1) = (1,7)\)

\((x_2,y_2) = (2,12)\)

Next, we determine the slope, m:

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

\(m = \frac{12-7}{2-1}\)

\(m = \frac{5}{1}\)

\(m = 5\)

This represents the rate of change:

For (D):

The $1.00 paid every week represents the rate of change.

So:

\(m = 1\)

For A - D:

The rate of change are:

\(A = 2\)

\(B = 3\)

\(C = 5\)

\(D = 1\)

5 is the greatest.

Hence, (c) has the greatest rate of change

Using linear function you would need to cross the bridge 30 times for the costs of the two toll options to be the same.

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Answer:

30 m

Step-by-step explanation:

Answer:

it is exactly 80m it is not 30m

The simplified form of the expression is \(-32\).

To simplify the expression, we can perform the calculations written below step by step:

\(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\)\)

We follow the order of operations (PEMDAS/BODMAS):

Step 1: Simplify within parentheses:

\(\(4+6 = 10\)\).

Step 2: Perform multiplications and divisions from left to right:

\(\(-2(10) = -20\) and \(-2(4-1) = -2(3) = -6\)\).

Step 3: Evaluate the remaining additions and subtractions:

\(\(-20 + (-2) \cdot 6 = -20 - 12 = -32\)\).

Therefore, the simplified form of the expression \(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\) is \(-32\).\)

When simplifying an expression, several factors need consideration. First, apply the order of operations correctly, respecting parentheses and exponents. Next, combine like terms by adding or subtracting them. Distribute and simplify within parentheses or brackets as needed. Pay attention to negative signs and ensure their proper placement.

Finally, review the simplified expression to ensure accuracy and validity within the given context.

Note: The complete question is:

\(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\)\), calculate the simplified form of this expression.

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Step-by-step explanation:

Pythagoras theorem state that c²=a²+b²

let x represent the length of the other leg

(20cm)²=(12cm)²+x²

400cm²=144cm²+x²

400cm²-144cm²=x²

256cm²=x²

√256cm²=√x²

16cm=x

Answer:

A

Step-by-step explanation:

X's cannot have multiple outputs (y's) but y's can. The only one that prove thia is the case is A

Answer:

Step-by-step explanation:

Its 4.51

Answer:

3 square units

Step-by-step explanation:

radius r = 1 unit

area = πr² = π ≅ 3 square units

Answer:90

Step-by-step explanation:

The minimum score she needs on her next quiz is 90

The mean is the average value which can be calculated by dividing the sum of observations by the number of observations

The mean value of the data set is the ratio of sum of data set's values to number of values it has.

If the data set consists of values

Mean = Sum of observations/the number of observations

\(\overline{x} = \dfrac{x_1 + x_2 + \cdots + x_n}{n}\)

Given;

Mean of 5 weeks= 92

Mean= (week 1 + week 2 + week 3 + week 4+ week 5)/number of weeks

         let, the score of next week be x

                  Mean = (92+96+94+88+x)/5

      putting the value of mean;

                     92= (370+x)/5        

                      460=370+x

                       x=460-370

                        x=90

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Answer:15i-25/34

Step-by-step explanation:

You have to multiply by 3+5i to get rid of the i on the bottom since you can't have it.

5i/3-5i x 3+5i/3+5i

Answer:

35

Step-by-step explanation:

You can easily graph this in desmos for a visual understanding.

The slope of a line is received by (y2-y1)/(x2-x1). Assuming that Days is X and the cost is Y, we get (160-90)/(4-2), and it makes 70/2, which equates out to 35. Because the prices become more and more expensive, the slope is positive 35.

Velocity is not constant over time and can be influenced by a variety of factors. Changes in velocity can have implications for the relationship between changes in the money supply and the price level, highlighting the complexity of monetary dynamics in an economy.

According to the quantity equation (MV = PQ), changes in the money supply (M) will lead directly to changes in the price level (P) if velocity (V) and real GDP (Q) remain constant. However, velocity is not necessarily constant over time and can be influenced by various factors.

Velocity represents the rate at which money circulates in the economy, indicating how quickly money is used to facilitate transactions. It is influenced by factors such as changes in consumer and business behavior, technological advancements, financial innovation, and shifts in confidence and trust in the economy.

Changes in velocity can occur due to several reasons. For example:

Changes in Transaction Patterns: Shifts in consumer preferences or business practices can alter the frequency and speed of transactions, affecting how money circulates and influencing velocity.

Financial Innovation: Advancements in payment systems, such as the rise of electronic transactions, online banking, or mobile payments, can potentially impact the velocity of money by facilitating faster and more efficient transactions.

Confidence and Economic Stability: Changes in economic conditions, inflation expectations, or financial stability can influence people's willingness to hold money, affecting velocity.

Monetary and Fiscal Policies: Changes in monetary policy, such as interest rate adjustments or changes in the money supply, can indirectly affect velocity by influencing borrowing and spending behavior.

While changes in velocity can occur independently of changes in the money supply, they can also be related. For instance, if the money supply increases without a corresponding increase in the demand for money (velocity decreases), it can put upward pressure on prices. On the other hand, if velocity increases due to changes in transaction patterns or increased economic activity, it can offset the impact of changes in the money supply on prices.

Overall, velocity is not constant over time and can be influenced by a variety of factors. Changes in velocity can have implications for the relationship between changes in the money supply and the price level, highlighting the complexity of monetary dynamics in an economy.

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