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No S with sum greater than 61 is possible and 61 is indeed the maximum.

By using the greedy algorithm, we obtain 61, with S={15,14,13,11,8}.

We must now prove that no such set has sum greater than 61. Suppose such a set [tex]$S$[/tex] existed. Then [tex]$S$[/tex] must have more than 4 elements, otherwise its sum would be at most 15+14+13+12=54.

S can't have more than 5 elements. To see why, note that at least.

[tex]$\left(\begin{array}{l}6 \\ 0\end{array}\right)+\left(\begin{array}{l}6 \\ 1\end{array}\right)+\left(\begin{array}{l}6 \\ 2\end{array}\right)+\left(\begin{array}{l}6 \\ 3\end{array}\right)+\left(\begin{array}{l}6 \\ 4\end{array}\right)=57$[/tex] of its subsets have at most four elements (the number of subsets with no elements plus the number of subsets with one element and so on), and each of them have sum at most 54. By the Pigeonhole Principle, two of these subsets would have the same sum. If those subsets were disjoint, we would directly arrive at a contradiction; if not, we could remove the common elements to get two disjoint subsets.

Thus, [tex]$S$[/tex] would have to have 5 elements. [tex]$S$[/tex] contains both 15 and 14 (otherwise its sum is at most 10+11+12+13+15=61.

It follows that [tex]$S[/tex] cannot contain both a and a-1 for any [tex]$a \leq 13$[/tex], or the subsets {a,14} and {a-1, 15} would have the same sum. So now [tex]$S$[/tex] must contain 13 (otherwise its sum is at most 15+14+12+10+8=59, and S cannot contain 12, or the subsets, {12,15} and {13,14} would have the same sum.

Now the only way [tex]$S$[/tex] could have sum at least 62=15+14+13+11+9

would be if S={15,14.13,11.9}. But the subsets {9,15} and {11,13} have the same sum, so this set does not work.

Therefore, no S with sum greater than 61 is possible and 61 is indeed the maximum.

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a. The representation of 1 inch in the model is 30 feet.

ii. The scale is 1:30.

b. The scale factor of the model is 1:360.

A scale factor is also referred to as a representation fraction which is the rate of length on drawing to that of the original length.

i.e. scale factor = length on drawing/ original length

Given that Washington space Needle is 20 inches tall. And the actual space Needle is approximately 600 feet tall, then;

a. 1 inch in the model = 600 feet/ 20 inch

                                = 30 feet / inch

i. The representation of 1 inch in the model is 30 feet.

ii. The scale is 1:30 i.e. 1 inch on the drawing is equal to 30 feet on the actual model.

b. The scale factor of the model is;

1 feet = 12 inches

   600 feet = x

x = 7200 inches

scale factor = 20 / 7200

                    = 1/ 360

The scale factor is 1:360. i.e. 1 inch on the drawing is equivalent to 360 inches on the actual model.

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Answer:

9π inches

Step-by-step explanation:

we know clock start from 12 o'clock to 9 o'clock, it will be 270 degree. Then we convert it to radian is 3π/2. We get the radian and the radius. So we can apply the formula of the lenghth of an arc.

l = rθ

l=6*3π/2=9π inches

The amount he will be able to depreciate using the class recovery period for a residential rental property each year is D. $10,909.09.

The term depreciation defines as an accounting method used to allocate the cost of a tangible or physical asset over its useful life.

It also represents how much of an asset's value has been used, and allows companies to earn revenue from the assets they own by paying for them over a certain period of time.

Using this formula:

Depreciation=Rental unit amount/ MACRS residential rental property recovery period

Where:

Rental unit amount=$300,000

MACRS Residential rental property recovery period=27.5 years

Let's plug in the formula

Depreciation=$300,000/27.5

Depreciation=$10,909.09

In conclusion, the amount he will be able to depreciate  using the class recovery period for a residential rental property each year is: D. $10,909.09

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Here to solve the probability of this sum, it is difficult to say that the probability without no information.

(a)The probability that the team wins the debate with a junior giving the closing argument is 0.083.

(b) To design a simulation to estimate the probability that a sophomore is never selected to give the closing argument in the next 3 debates, one could randomly assign a closing argument speaker for each debate using a table of random digits. The table would have two columns: one for sophomores and one for juniors and seniors. The probability of a sophomore being selected would be 20%, and the probability of a junior or senior being selected would be 80%. The simulation would be run for 3 debates and the number of times a sophomore is never selected would be recorded. This process would be repeated a number of times to estimate the probability of a sophomore never being selected. (e) Based on the dot plot, it appears that there is some evidence that the sophomores were purposely ignored, as there are several simulated sets of 5 debates where a sophomore was not selected to give the closing argument. However, without more information, it is difficult to say for certain if this is enough evidence to support the claim that the sophomores were purposely ignored.

A larger sample size or a more detailed analysis of the simulation results may be needed to make a more convincing determination.

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The probability that a teenage boy has a cholesterol level greater than 200 is 0.33: Option D

It is the chance of occurrence of an event E

To solve this problem you must first find the z-score associated with a cholesterol level greater than 200.

The general formula for a z score is:

z = (x-µ)/σ

Where z is the z score, x is the data point, µ is the mean, and σ is the standard deviation. With your numbers that would become:

z = (200-170)/30

z = 1.833

If you are using a graphing calculator, such as the TI-83 Plus, you can then go to 2nd vars, and the second option is normalcdf

To use normalalcdf enter normalcdf (lower z score, upper z score) in your case normalcdf (1.833, 1E99) to get the probability that a teenage boy has a cholesterol level greater than 200 Which will give you .0337.

If you are using a z table, find the probability associated with your z score of 1.83, and subtract that from 1. You subtract from 1 because a z table gives you the probability of a score being below the one you obtained.  

This implies therefore that the probability is 0.337

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Country B is more efficient than Country A when it comes to producing cars and tanks.

Country A takes twice as long to produce a car (30 minutes) than Country B (12 minutes). However, Country A takes 20 minutes to produce a tank while Country B takes 10 minutes, cutting the amount of time in half.

We can measure the efficiency of each country by calculating the number of cars and tanks each country can produce in an hour. We can do this using the following formula:

Cars per hour = (60 minutes/minutes to produce car)

Tanks per hour = (60 minutes/minutes to produce tank)

For Country A, the number of cars produced in an hour is (60 minutes/30 minutes) = 2 cars per hour and the number of tanks produced in an hour is (60 minutes/20 minutes) = 3 tanks per hour.

For Country B, the number of cars produced in an hour is (60 minutes/12 minutes) = 5 cars per hour and the number of tanks produced in an hour is (60 minutes/10 minutes) = 6 tanks per hour.

Therefore, Country B is more efficient than Country A when it comes to producing cars and tanks.

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Answer:

$705

Step-by-step explanation:

($3400)(0.075) = $255 commission earned

Total wage for that week = $450 + $255 = $705

note:  this answer assumes that $450 is the weekly basic wage, not daily

21 = 3 · 7

33 = 3 · 11

If 21 and 33 are two divisors, then so are 3, 7, 11, and 77.  And 1 and the number itself are always divisors.

So, we have 1, 3, 7, 11, 21, 33, 77, and the number. That's eight divisors.

So the number is 3·7·11 = 231, the product of only the prime divisors of the number.

6 coach tickets and 9 first-class tickets were bought, totaling the number of tickets purchased.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

A mix of operators, constants, and variables make up an expression. An expression can yield a value by using one or more operands and one or more operators.

An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases.

The algebraic expression that results from multiplying two variables, x and y, is xy.

Let's say that x coach tickets were purchased.

And y is the total number of first-class tickets bought.

Now,

15 people in total, including Sarah, made the journey.

Thus,

x + y = 15(1)

Coach and first-class tickets are priced at $200 and $1290, respectively.

The trip's total spending for air travel is $11,720.

Therefore,

200x + 1290y = 11720

20x + 129y = 1172

We obtain by resolving both equations.

x = 6

y = 9

Consequently, 6 coach tickets and 9 first-class tickets were acquired, making up the total number of tickets.

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The length of the chalk outline is 19 feet.

The field is circular and the line drawn by chalk is the length of the rim of the circular field and is called the circumference. It can be calculated from the radius(or diameter) of the circle.

The formula of the circumference of a circle:

Circumference of circle [tex]= 2 * \pi * r = \pi * d[/tex]

where r means the radius of the circle and d means the diameter of the circle.

The diameter d = 2 times of radius

Thus, we have:

Length of a chalk outline [tex]= \pi * d = \pi * 6 = 3.14 * 6 = 18.84 = 19 feet[/tex]

So,  the length of the chalk outline is 19 feet.

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The inequality -x+3y < 6 passes through the points (-6, 0) and (0, 2).

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

We have an inequality,

-x+3y < 6.

The graph of the inequality is given in the attached image.

And inequality passes through the points (-6, 0) and (0, 2).

Therefore, the graph of the inequality is given in the attached image.

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a. 9 quarts of sparkling water

b. 1 quart of grape juice

c. 50 quarts of sparkling water and 50 quarts of grape juice

The rationale behind the values above are as explained below:

a. If the recipe calls for 1 quart of sparkling water to be mixed with 1 quart of grape juice, then to mix with 9 quarts of grape juice, you would need 9 quarts of sparkling water.

b. If the recipe calls for 1 quart of sparkling water to be mixed with 1 quart of grape juice, then to mix with 1 quart of sparkling water, you would need 1 quart of grape juice.

c. To make 100 quarts of sparkling grape juice, using the 1:1 ratio in the recipe, you would need 50 quarts of sparkling water and 50 quarts of grape juice.

Therefore, the correct answers are as given above

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Answer:

I don't know????????....................

Answer: plane a is faster than plane b because it has more speed than plane b

Step-by-step explanation:

Answer:

Step-by-step explanation:

a)
Because if you visualize the formation of it size x will fit perfectly on the 6cm side therefore x = 6cm

b)
6 x 9 = 54cm

Answer: If each of the s swimmers on the relay team swam an equal number of the 8 laps in a race, the expression that shows how many laps each swimmer swam would be 8/s.

This expression shows that each swimmer swam 8 laps, divided by the total number of swimmers on the team, s.

So, if there are 's' swimmers on the relay team, each swimmer swam 8/s laps.

Step-by-step explanation:

The equivalent ratio where the amount of stock is 100 mL is 80 mL

An equivalent ratio is a ratio that is equal to another ratio, but with the terms in a different order or with different values.

Since the recipe calls for 350 mL of Dashi in order to make a smaller batch using 280 mL of Dashi. Thus, we can say:

equivalent ratio = 280/350

Thus, an equivalent ratio where the amount of stock is 100 mL will be:

280/350 = x/100

0.8  = x/100

x = 0.8 × 100

x = 80 mL

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The value of k that makes the equation true is given as follows:

a. 6.

The equation for this problem is defined as follows:

12a + 9b = k(2a + 3/2b).

The equation will be true is both sides are equal.

Applying the distributive property to the right side, we have that:

12a + 9b = 2ak + 3kb/2.

Taking one of the terms, the value of k is obtained as follows:

2ak = 12a

k = 12a/2a

k = 6.

Meaning that the correct option is given by option A.

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The height of the wall decal when my actual height is 5.5 inches, is equals to the 110 inches.

We have, My height in the portrait measures = 3 1/2 inches = 7/2 = 3.5 inches

According to the scale used by company,

one inch measurement on portrait = 20 inches on the wall decal. That is portrait measurement / wall decal = 1/20 ( in inches) . We have to determine the height on the wall decal if my actual height is 5.5 inches. Let the height of wall decal be "h inches" when my actual height is 5.5 inches. Write the proportion like this to calculate the value of h , 1/20 = 5.5/ h

Cross multiply we get,

=> 1× h = 5.5 × 20

=> h = 110.0

Hence, the required height of the decal is 110 inches.

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Complete question:

Your height in the portrait measures 3 1/2 inches, if the company uses a scale where 1 inch on the portrait represents 20 inches on the wall decal, find the height on the wall decal if your actual height is 5.5 inche?

When compared to my actual height of 5.5 inches, the wall decal's height is 110 inches.

We've got My height in the image is 3 1/2 inches plus 7/2, which is 3.5 inches.

On the basis of the scale:

20 inches are equal to one inch in a portrait on the wall decal. That is a portrait measurement divided by a 20-inch wall decal. If my real height is 5.5 inches, we must determine the height on the wall decal. Let the wall decal's height be "h inches" even though my height is 5.5 inches. To compute the value of h, write the ratio as 1/20 = 5.5/h.

When we cross multiply,

1× h = 5.5 × 20

h = 110.0

Therefore, 110 inches is the minimum height for the decal.

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Note: The complete question would be as bellow,

Your height in the portrait measures 3 1/2 inches, if the company uses a scale where 1 inch on the portrait represents 20 inches on the wall decal, find the height on the wall decal if your actual height is 5.5 inche?

As per the given ratio between distance, The Train ride from Chicago to Port Huron is 304.375 miles.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given, A train ride from Chicago to Emeryville, California, is 2,438 miles.

Since It is about 8 times as long as a train ride from Chicago to Port Huron, Michigan.

Thus,

The train ride from Chicago to Port Huron = 2438/8

The Train ride from Chicago to Port Huron = 304.375 miles

Therefore, The Train ride from Chicago to Port Huron is 304.375 miles.

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The range of the function (f+g)(x) = x² - 1 will be ( -1, ∞ ). The correct option is B.

The range of values that we are permitted to enter into our function is known as the domain of a function.

The x values for a function like f make up this set (x). A function's range is the set of values it can take as input. After we enter an x value, the function outputs this set of values.

Given that the function is f(x) = x²+2x-5. The function g(x) will be calculated by the data given in the table.

x           -6    -3     -1    4

g(x)       16    10    6   -4

The function g(x) will be:-

g(x) = mx + c

m = ( 10 - 16 ) / ( -3 + 6 )

m = -6 / 3

m = -2

c = y - mx

c = 10 - 6

c = 4

g(x) = -2x + 4

The function ( f + g)(x) will be:-

( f + g)(x) = f(x) + g(x)

( f + g)(x) = x²+ 2x - 5 - 2x + 4

( f + g)(x) = x² - 1

At x = 0, the value ( f + g)(x) is -1. The range of the function is ( -1, ∞).

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Answer:

x 23 y 60

Step-by-step explanation:

The answer is -1(x - 5)(x + 1)

To simplify the rational expression x^2 - 5x + 5 - x - 5, we can combine like terms and factor out the greatest common factor of the numerator and denominator.

Step 1: First, we can combine like terms in the numerator to get x^2 - x - 5

Step 2: Next, we can factor out the greatest common factor of -1 from the numerator to get -1(x^2 - x - 5)

Step 3: Now we can factor the expression in the parenthesis:

-1(x - 5)(x + 1)

So the simplified form of the given rational expression is: -1(x - 5)(x + 1)

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Answer:

-6x+x^2

Step-by-step explanation:

To start off the equation you want to make everything have the same symbol:

x^2+-5x+5+-x+-5

next, you can rearrange the symbols to combine terms:

5+-5+-x+-5x+x^2

Now we combine:

-6x+x^2

the 5 cancels out. The -x plus the -5x gets you -6x. and the x^2 can not be combined.

Your answer:

-6x+x^2

The value of x, y, and z in the rhombus are -114, 7 and 59 respectively

Since the opposite angles of a rhombus are equal to each other. We can write:

(-x-10)° = 104°

-x-10 = 104

-x = 104 + 10

x = -114

Since the adjacent angles in rhombus are supplementary. We have:

114 + (z + 7) = 180

121 + z = 180

z = 180 -121

z = 59

104  + (10y + 6) = 180

110 + 10y = 180

10y = 180 - 110

10y = 70

y = 70/10

y = 7

Thus, the value of x, y, and z are -114, 7 and 59

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The value of cosθ = 0.5

The correct option is (A).

Now, According to the question:

Basic Trigonometric Function Formulas:

By using a right-angled triangle as a reference, the trigonometric functions and identities are derived: sin θ = Opposite Side/Hypotenuse. cos θ = Adjacent Side/Hypotenuse. tan θ = Opposite Side/Adjacent Side.

Remember that in a right triangle, we have that:

cos(θ) = (adjacent cathetus)/(hypotenuse)

Here we have:

Replacing all that in the equation we get:

cos(60°) = 1/2 = 0.5

Hence, the value of cosθ = 0.5

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The height of the utility pole casting a shadow 10 ft is 32 feet.

A ratio is simply the relation between two amounts showing how many times a value is contained within another value.

Given that;

Ratio of height of utility pole and its shadow  = x / 10

Ratio of height of sign post and its shadow  = 8/2.5

Equate to determine the height of the utility pole.

x/10 = 8/2.5

Solve for x

x × 2.5 = 8 × 10

2.5x = 80

x = 80 / 2.5

x = 32 ft

Therefore, the height of the utility pole is 32 ft.

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Answer

60%

Step-by-step explanation:

Answer: 75% of students are girls.

Step-by-step explanation: First, you divide 960 by 100 to get 9.6. Then you do 960-240 to get the amount of girls (720), then you divide 720 by 9.6 to get 75.