At a scout jamboree, dinner is served from tinned food. Each tin of soup is shared between 2 scouts. each tin of frankfurters is shared between 3 scouts and each tin of fruit is shared between 4 scouts. If 117 tins are opened to feed all the scouts, how many scouts attended the jamboree

The eccentricity for r=5/2+1sin theta and  the equation of the directrix of r=26. 4/4+4. 4 cos theta is 0.5 and x=6

To find the eccentricity of the polar equation r = 5/2 + 1sin(θ), we first need to convert it to rectangular form:

r = 5/2 + 1sin(θ)

r = 5/2 + 1y/r

r^2 = (5/2)r + y

x^2 + y^2 = (5/2)r + y

x^2 + y^2 = (5/2)√(x^2 + y^2) + y

x^2 - (5/2)√(x^2 + y^2) + y^2 = 0

We can see that this is the equation of a conic section, specifically an ellipse, since the signs of the x^2 and y^2 terms are the same. The standard form of an ellipse centered at the origin is:

x^2/a^2 + y^2/b^2 = 1

Comparing this to our equation, we can see that a^2 = (5/2) and b^2 = 1. The eccentricity of an ellipse is given by:

e = √(1 - b^2/a^2)

Plugging in our values, we get:

e = √(1 - 1/(5/2))

e = √(3/5)

e ≈ 0.5

Therefore, the answer is (A) 0.5.

To find the equation of the directrix for the polar equation r = 26.4/4 + 4.4cos(θ), we first need to convert it to rectangular form:

r = 26.4/4 + 4.4cos(θ)

r = 6.6 + 4.4x/r

r^2 = 6.6r + 4.4x

x = (r^2 - 6.6r)/4.4

We can see that this is the equation of a parabola, since the highest degree of the variable r is 2. The standard form of a parabola with its focus at (0, p) is:

y = (1/4p)x^2

Comparing this to our equation, we can see that p = -6.6/4 = -1.65. The directrix of a parabola is a line perpendicular to the axis of symmetry and located at a distance of |p| from the focus. Since the axis of symmetry is the x-axis, the equation of the directrix is:

y = 1.65

However, since the question asks for the equation of the directrix in terms of x, we can rewrite this as:

x = 0

Therefore, the answer is (C) x = 6.

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Answer:

429

Step-by-step explanation:

Answer:

2 ounces per person

Step-by-step explanation:

The remainder when f(x)=-6x^23+x^11-x^6+2x is divided by x+1 is -7.

Explanation: In this question, we can solve the problem by using the Remainder Theorem. The remainder theorem states that when we divide a polynomial f(x) by x−a then we get a remainder equal to f(a). So, here we can take a=−1 and find the remainder of f(x).

Here is the given polynomial,

()=−6^23+^11−^6+2

We are asked to find the remainder when f(x) is divided by x+1. Using the remainder theorem, we can find the remainder of f(x) by evaluating f(−1).

(−1)=−6(−1)^23+(−1)^11−(−1)^6+2(−1)=6+1+1−2=6

Now, we have the remainder as 6. However, we need the remainder when f(x) is divided by x+1. The relationship between the remainder and the divisor of a polynomial is that when we divide a polynomial f(x) by x−a, we get a remainder of r(x) such that:

()=(−)()+()

where q(x) is the quotient of the division.

So, the question asks us to divide the polynomial f(x) by x+1 and get the remainder. Here is the long division of f(x) by x+1:

The remainder is −7. Therefore, the remainder when f(x) is divided by x+1 is -7.

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Answer:

429

Step-by-step explanation:

If you spend a $5 per turn on a fair game to win $15 for each win and you lose the first round but win the next two rounds, then the net payoff is $15

Since you spend $5 per turn and play three rounds, your total cost is $5 x 3 = $15.

If you win a game, you receive $15, so winning two games will give you $15 x 2 = $30.

However, since you lost the first round, you only won two out of three rounds. Therefore, your net payoff is:

= $30 - $15

Subtract the numbers

= $15

Therefore, your net payoff is $15

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So, if we have the original coordinates of point G, we can swap the x and y values and negate the new y-value to find the coordinates of point G after a 90° counterclockwise rotation about the origin.

To perform a 90° counterclockwise rotation about the origin, we can use the following transformation:

x' = -y

y' = x

This means that the new x-coordinate (x') will be the negative of the original y-coordinate (y), and the new y-coordinate (y') will be the original x-coordinate (x).

If we have the coordinates of point G, we can apply this transformation to find the new coordinates after the rotation.

Let's say that the coordinates of point G are (x, y). Then, the new coordinates (x', y') after the rotation will be:

x' = -y

y' = x

So, the new coordinates will be (-y, x). Therefore, if we want to find the new coordinates after a 90° counterclockwise rotation, we just need to swap the x and y values and negate the new y-value. This gives us the following coordinates for point G after the rotation:

G' = (-y, x)

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Answer: To find the relative frequency for each discount, we need to divide the number of customers who received each discount by the total number of customers.

Discount           Number of customers                          Relative Frequency

10%                    70                                                            0.35

25%                   99                                                            0.495

30%                   31                                                             0.155

To determine if it is appropriate for the manager to want approximately half of the customers to receive the 25% discount, we can calculate the relative frequency for the 25% discount and compare it to 0.5 (or 50%).

Relative frequency for 25% discount = 99/200 = 0.495

Since the relative frequency for the 25% discount is already very close to 0.5, it seems like an appropriate method to achieve the manager's goal. However, it's worth noting that this method may not be the most effective in terms of maximizing profits or customer satisfaction. It's always important for businesses to carefully consider their pricing strategies and discount policies.

Step-by-step explanation:

Answer:

2.5 oz each

Step-by-step explanation:

2 boys and 2 girls

10 divided by 2 is 5, 5 is not an even number.
there would be 2 left after our calculation.
meaning that 2 in half's (hence .5)  is 4 so each child would get 2.5 oz of paint.

Hope this helps, thanks :)

Answer: 2 1/2

Step-by-step explanation:

Answer:

cubic unit eg m³

Step-by-step explanation:

Raised to power 3

Answer:

Units cubed or unit^3

Explanation:

Volume= (base)(width)(height), therefore, this would be cubed. x^3

Area=(base)(height), therefore, this would be squared. x^2

Answer:

The length of line segment CD is 10.3 units (rounded to 2 decimal places).

Step-by-step explanation:

To find the length of line segment CD, we need to use the distance formula, which is:

Distance = √[(x2 - x1)^2 + (y2 - y1)^2]

Here, (x1, y1) = (1, -5) and (x2, y2) = (6, 4).

So, substituting these values in the distance formula, we get:

Distance = √[(6 - 1)^2 + (4 - (-5))^2]

= √[5^2 + 9^2]

= √(25 + 81)

= √106

≈ 10.3 (rounded to 2 decimal places)

Therefore, the length of line segment CD is 10.3 units (rounded to 2 decimal places).

Hope this helps!

Answer: To find the equation that passes through (4, 8), we need to check which equation contains that point.

Line A has an equation of y = (2/5)x + (194/5). Plugging in x = 4, we get y = (2/5)(4) + (194/5) = 198/5, which is not equal to 8.

Line B has an equation of y = (-5/5)x + 30. Plugging in x = 4, we get y = (-5/5)(4) + 30 = 26, which is not equal to 8.

Line C has an equation of y = (13/13)x - 7. Plugging in x = 4, we get y = (13/13)(4) - 7 = -3, which is not equal to 8.

Line D has an equation of y = (-27/7)x + (491/7). Plugging in x = 4, we get y = (-27/7)(4) + (491/7) = 377/7, which is not equal to 8.

Therefore, none of the given equations has (4, 8) as its solution.

Step-by-step explanation:

Answer:  1 hour 50 minutes  

Step-by-step explanation: it took her 2 hours to get home

she left home at 11:30 am it took her 45 minutes to jog to the park by the time she got to the park it was 12:15 pm she exercised for  1 hour and 55 minutes by the time she was done her work out it is 1:10 if she finished at 3 pm it took her 1 hour 50 minutes to get home

A two-way relative frequency table, in general, is an effective instrument for analysing paired data because it offers a succinct and clear summary of the relationship between the variables, enabling us to spot patterns and conduct methodical hypothesis testing.

A tool used to display the connection between two sets of paired data is a two-way relative frequency table, which arranges the data in rows and columns. The frequency of each combination is indicated in the chart, which can also be used to determine its relative frequency, which is calculated as the frequency of the combination divided by the total number of observations.

The benefit of using a two-way relative frequency table to illustrate relationships between pairs of paired data is that it gives a more comprehensive image of the data and the interrelationships between the variables. More specifically, it enables us to:

Finding patterns and trends is simple thanks to the table's presentation of the data. We can see which combinations are more or less prevalent than others by examining the relative frequencies of each set of values, and we can spot patterns in the data that might not be obvious otherwise.

Calculate conditional probabilities: Conditional probabilities are the likelihoods of one event given the occurrence of another event, and they can be determined using the chart. We can determine the likelihood that a smoker is male or female and the likelihood that a non-smoker is male or female, for instance, if we have a two-way table illustrating the connection between gender and smoking status.

Testing hypothesis: The table can be used to evaluate theories about how the variables are related to one another. A chi-square test, for instance, can be used to determine whether gender and smoking status are significantly associated.

In general, a two-way relative frequency table is an effective tool for analysing paired data because it offers a succinct and clear summary of the relationship between the variables, enabling us to spot patterns and test theories in a methodical manner.

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Answer:

x = 1 , y = 10

Step-by-step explanation:

Given : y = 8 + 2x

by substitution,

4x + 8 + 2x = 14
6x + 8 = 14
6x = 14 - 8
6x = 6
x = 6/6 = 1


y = 8 + 2x
y = 8 + 2(1)
y= 10

Proof :
if x = 1,

4 (1) + 8 +2 (1) = 14
4 + 8 + 2 = 14
14 = 14

if y = 10 and x = 1

4 ( 1) + 10 = 14
4 + 10 = 14
14 = 14



For both equations, LHS = RHS
Therefore Proved.


hope it helps!

Answer:  B

Step-by-step explanation:

Using cross product, the vector can be proven as [a×[ob + (1-o)a] = √k is shown to be true, where k = 3 (2 - O)^2 (a · b)^6 / 4.

The vector OB can be expressed as OB = b since b is a unit vector and O is the origin.

The vector OA can be expressed as OA = 2b since the magnitude of a is twice that of b.

The angle between a and b is 60°, so we have:

|a| |b| cos 60° = a · b

2|b| · 1/2 = a · b

|b| = a · b

We can now express the vector [OB + (1 - O)A] as:

[OB + (1 - O)A] = b + (1 - O)2b

= (2 - O) b

The cross product of a and [OB + (1 - O)A] is:

a × [OB + (1 - O)A] = a × [(2 - O) b]

= (2 - O) (a × b)

The magnitude of the cross product is:

|a × [OB + (1 - O)A]| = |(2 - O) (a × b)|

= |2 - O| |a| |b| sin 60°

= √3 |2 - O| |b| |a| / 2

= √3 |2 - O| |b|^2 |b| / 2

= √3 |2 - O| |b|^3 / 2

Substituting |b| = a · b, we get:

|a × [OB + (1 - O)A]| = √3 |2 - O| (a · b)^3 / 2

Since |a × [OB + (1 - O)A]| is equal to √k for some constant k, we can set:

√k = √3 |2 - O| (a · b)^3 / 2

Squaring both sides, we get:

k = 3 (2 - O)^2 (a · b)^6 / 4

Therefore, [a×[ob + (1-o)a] = √k is shown to be true, where k = 3 (2 - O)^2 (a · b)^6 / 4.

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Sal should put the sand which is in between the amount of 3 cubic inches and 4.5 cubic inches inside the bag surrounding the base of the candle.

Base area of the bag = 4 × 2 = 8 in²

Base area of the candle = 2 × 1 = 2 in²

therefore, we know that base area to be filled with sand:

= 8 - 2 = 6 in²

now, height of sand is known to be between 1/2 and 3/4 inches,

therefore, we can make out that the volume of land is between 6 × 1/2 in³ and 6 × 3/4 in³

3 in³ and 4.5 in ³

therefore, amount of sand is between 3 cubic inches and 4.5 cubic inches, with this we know that Sal should put the sand which is in between the amount of 3 cubic inches and 4.5 cubic inches inside the bag surrounding the base of the candle.

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The cost price of the article when a profit of 22% is made after selling it for a certain price 's' can be calculated using the formula c = 0.78 * s.

Let's assume the cost price of the article is 'c'. Then, the profit made on selling the article is:

Profit = Selling price - Cost price

Since a profit of 22% was made on the selling price 's', we can express the selling price as:

Selling price = Cost price + Profit

= Cost price + 0.22 * Selling price

Rearranging this equation, we get:

0.78 * Selling price = Cost price

Substituting the given selling price 's' into this equation, we get:

0.78 * s = c

Therefore, the cost price of the article is 0.78 times the selling price. If we know the selling price 's', we can calculate the cost price 'c' using this formula. For example, if the selling price of the article is $100, then the cost price would be:

c = 0.78 * s

= 0.78 * $100

= $78

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Answer:

the answer to ur question is: 1218816

Answer:

x = 48

Step-by-step explanation:

given a line parallel to a side of a triangle and it intersects the other two sides, it divides those sides proportionally, that is

[tex]\frac{x}{18}[/tex] = [tex]\frac{56}{21}[/tex] ( cross- multiply )

21x = 18 × 56 = 1008 ( divide both sides by 21 )

x = 48

Answer:

What's your question

Step-by-step explanation:

How many customers in each tower

75 % of the college students will take more than 4.25 minutes when trying to find a parking spot in the library parking lot.

Actual experiments and sufficient documentation of the occurrence of occurrences serve as the foundation for experimental probability, sometimes referred to as empirical probability. A number of real experiments are carried out in order to ascertain the likelihood of any event. Random experiments are studies that don't have a predetermined outcome. The results of such tests are unpredictable. The chance of random experiments is calculated repeatedly. A trial is a repeating of an experiment that is performed a certain number of times.

Given that, mean of 3.5 minutes and a standard deviation of 1 minute.

Now, for 75% we have:

P(X > x) = 0.75

The z-score is given by:

0.75 = (X - μ) / σ

Substituting the formula we have:

0.75 = (X - 3.5) / 1

0.75 = X - 3.5

X = 0.75 + 3.5 = 4.25.

Hence, 75 % of the college students will take more than 4.25 minutes when trying to find a parking spot in the library parking lot.

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From the given information provided, the percent of yellow tint in the new mixture is 36.4%.

The total amount of yellow tint in the original mixture is:

0.30 × 50 liters = 15 liters

When 5 liters of yellow tint are added to the mixture, the total amount of yellow tint becomes:

15 + 5 = 20 liters

The total amount of new mixture is:

50 + 5 = 55 liters

To find the percentage of yellow tint in the new mixture, we divide the amount of yellow tint by the total amount of the mixture and multiply by 100:

(20/55) × 100 = 36.4%

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Answer: we can't see the images

Step-by-step explanation:

Answer:

Step-by-step explanation:

be can not see the pictures sir do better ni***

Therefore , the solution of the given problem of probability comes out to be the medium addition because it has the greatest expected utility (0.72).

The primary goal of the structures within a methodology expression known as criteria is to provide an indication of the probability that the assertion is true or that a specific event will occur. Any number between zero and one, at which 0 is frequently indicated as a possibility and 1 has frequently used to denote a level of confidence, can be used to represent chance. The chance that a specific event will occur is displayed in a probability diagram.

Here,

The following formula can be used to determine each option's anticipated financial value:

=> EMV of big addition =  (0.4 * $100,000) plus (0.6 * -$40,000) for a total of $16,000.

=>  EMV of the middle addition is

= (0.4 * $40,000) plus (0.6 * -$10,000) for a total of $14,000.

=>  EMV of a minor addition =  (0.4 * 10,000) plus (0.6 * 5,000), which equals $6,000

The large addition should be chosen by the physicians as it has the greatest expected financial value of $16,000.

dividing each outcome's usefulness value by its likelihood, then adding the results:

=> (0.4 * 1.0) + (0.6 * 0.0) = 0.4 is the EU of the big addition.

=> (0.4 * 0.9) + (0.6 * 0.6) = 0.72 is the EU of medium addition.

Smaller EU =  (0.4 * 0.5) +  (0.6 * 0.6) = 0.58

The doctors should choose the medium addition because it has the greatest expected utility (0.72), according to expected utility theory.

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Answer: 104

Step-by-step explanation:

If .6 or 60% of the animals in the shelter are dogs, then we can multiply .6 by 260 to get how many are dogs.

.6 times 260 is 156.

260-156=104.