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The formula to find the number of subsets with at least k elements is given by nCk+1 − 1.So, the number of subsets with at least 5 elements the set of cardinality 7 has is: nC5+1 − 1 = 7C6 − 1 = 7 − 1 = 6.

The formula to find the number of subsets with at least k elements is given by nCk+1 − 1, where n is the number of elements in the set. The derivation is given below:Let S be a set with n elements.We want to find the number of subsets of S with at least k elements. For this, we can use the complement of the event "subset with at least k elements". The complement is "subset with less than k elements".Now, a subset of S can have 0 elements, 1 element, 2 elements, ..., n elements. Hence, the total number of subsets of S is 2n.Let's count the number of subsets of S with less than k elements. A subset of S with less than k elements can have 0 elements, 1 element, 2 elements, ..., k-1 elements. Hence, the total number of subsets of S with less than k elements is:  2^0 + 2^1 + 2^2 + ... + 2^(k-1) = 2^k − 1 (using the formula for sum of geometric series) Therefore, the number of subsets of S with at least k elements is given by the complement: 2n − (2^k − 1) = 2n − 2^k + 1 = nCk+1 − 1 (using the formula for sum of binomial series).Hence, the number of subsets with at least 5 elements the set of cardinality 7 has is: nC5+1 − 1 = 7C6 − 1 = 7 − 1 = 6.

Therefore, the number of subsets with at least 5 elements the set of cardinality 7 has is 6. In the binomial expansion of (2x-1)11, the term containing x7 is -4624x7. The coefficient of x7 is -4624. Option D is correct. The binomial expansion of (2x-1)11 is given by: (2x-1)11 = 1(2x)11 − 11(2x)10 + 55(2x)9 − 165(2x)8 + 330(2x)7 − 462(2x)6 + 462(2x)5 − 330(2x)4 + 165(2x)3 − 55(2x)2 + 11(2x) − 1 The general term in the binomial expansion is given by: T(r+1) = nCr prqn-r Here, n = 11, p = 2x, q = -1 For the term containing x7, r+1 = 8. Therefore, r = 7. T(8) = 11C7 (2x)7 (-1)^4 = 330x7 Thus, the coefficient of x7 is 330. But the coefficient of -x7 is -330.So, the term containing x7 is -330x7. Hence, the coefficient of x7 is -330 × -1 = 330.

Therefore, the coefficient of the term containing x7 in the binomial expansion of (2x-1)11 is 330.

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Answer:

Not a parallelogram.

Step-by-step explanation:

By the midpoint formula, the midpoint of a segment between \((x_{0},\, y_{0})\) and \((x_{1},\, y_{1})\) is:

\(\begin{aligned} \left(\frac{x_{0} + x_{1}}{2},\, \frac{y_{0} + y_{1}}{2}\right)\end{aligned}\).

A quadrilateral is a parallelogram if and only if the midpoints of the two diagonals are the same.

The two diagonals of quadrilateral \({\sf ABCD}\) are segment \(\sf{AC}\) and segment \({\sf BD}\), respectively.

Using the midpoint formula, the midpoint of segment \({\sf AC}\) (between \({\sf A}\; (3,\, 3)\) and \({\sf C}\; (-3,\, 1)\)) would be:

\(\begin{aligned} & \left(\frac{3 + (-3)}{2},\, \frac{3 + 1}{2}\right) \\ =\; & (0,\, 2)\end{aligned}\).

Likewise, the midpoint of segment \({\sf BD}\) (between \({\sf B}\; (1,\, 2)\) and \({\sf D}\; (-1,\, 4)\) would be \((0,\, 3)\).

Thus, quadrilateral \({\sf ABCD}\) would not be a parallelogram since the midpoints of its two diagonals are not the same.

Answer:

We have to:

"All of the plots are the same length, x"

L = x

"and the width of each plot is 5 yards less than the length"

W = x-5

"The total number of plots Liam owns is 20 more than the length of a plot"

20 + x

"the total area of all the plots Liam owns is 2,688 square yards"

A = (20 + x) * (x) * (x-5)

A = (20x - 100 + x ^ 2 -5x) * (x)

A = (x ^ 2 + 15x - 100) * (x)

2688 = (x ^ 3 + 15x ^ 2 - 100x)

x ^ 3 + 15x ^ 2 - 100x = 2688

x ^ 3 + 15x ^ 2 - 100x - 2688 = 0

Answer:

*** The equation x3 + 15x2 - 100x - 2.688 = 0 can be used to find the length of each plot.

Answer:x^3+15x^2-100x-2,688=0

Step-by-step explanation:

Answer:

$10

Step-by-step explanation:

200*0.05=10

Answer:

$10

Step-by-step explanation:

90% = 0.95

200×0.95= 190

200-190=10

2)Main Answer: a)1,8,27,64,125,216,343,512

                        b)I,II,III,IV,V,VI,VII,VIII,IX,X,XI                                    

Concept and definitions should be there:

A conjecture is an educated guess that is based on known information. Example. If we are given information about the quantity and formation of section 1, 2 and 3 of stars our conjecture would be as follows.

Given data

a)Next five terms 1,8,27,64

b)Next five terms I,II,III,IV,V

Solving part

using conjecture

a)Next five terms 1,8,27,64,125,216,343,512

Notice that the difference between consecutive terms is 7.

Conjecture: n3, n=1,2,3...

Final Answer:1,8,27,64,125,216,343,512

b))Next five terms I,II,III,IV,V,VI,VII,VIII,IX,X,XI

Conjecture: n, n=i,ii,iii,...

Final Answe:I,II,III,IV,V,VI,VII,VIII,IX,X,XI

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3)Quastion incompleted

4)Main answer :The number 14 is even and therefore is divisible by 2. This is the correct statement.

Given data

The statement which uses deductive reasoning to draw the conclusion is C. The number 14 is even and therefore is divisible by 2.

Solving part

The number 14 is even and therefore is divisible by 2. This is the correct statement.

Final Answer:The number 14 is even and therefore is divisible by 2. This is the correct statement.

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5)Main Answer:X = -2

Concept and definitions should be there:This solution deals with linear equations with one unknown.

Given data

18x-2(3x+1)=5x-16

Solving part

We simplify the equation first:

18x−2(3x+1)=5x−16

18x+(−2)(3x)+(−2)(1)=5x+−16 (Distribute)

18x+−6x+−2=5x+−16

(18x+−6x)+(−2)=5x−16 (Combine Like Terms)

12x+−2=5x−16

12x−2=5x−16

Then we cancel out:

12x−2−5x=5x−16−5x

7x−2=−16

7x−2+2=−16+2

7x=−14

7x/7 = −14/7

x = -2

Final Answer:x = -2

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Answer:

y = 1/3x

Step-by-step explanation:

use a slope that is the opposite and reciprocal of -3, which would be 1/3

The correct answer is A. The selling price of a bond is affected by the coupon rate and the market interest rate.

If the coupon rate is less than the market interest rate, investors will not be interested in buying the bond because they can get a higher return elsewhere. This results in the selling price of the bond being less than its face value of $10,000.
The selling price of a $10,000 5-year bond will be less than $10,000 if the:
A. Coupon rate is less than the market interest rate

This is because when the coupon rate (the interest paid by the bond) is lower than the market interest rate, investors would prefer to invest in other options that offer a higher return. Therefore, to attract buyers, the bond's selling price would be discounted to compensate for the lower coupon rate.

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Answer:

u=1

v = 10

Step-by-step explanation:

For the triangles to be congruent

IG = PR

50 = u+49

50 - 49 = u

1 = u

GH = RQ

v+6 = 16

v = 16-6

v = 10

Answer:

see below

Step-by-step explanation:

$178 x .05 = $8.90 discount nearest hundredth

$178 - $8.90 = $169.10 sale price nearest hundredth

(a) After 4500 years, the sample will remain 3.9 mg.

(b) The sample will remain 15 mg after 1369 years.

The result is obtained by using the exponential decay equation.

The exponential decay equation can be used to calculate radioactive decay for the activity, the nuclei, and also the mass. The exponential decay equation for the mass is

\(m = m_{o} e^{-\lambda t}\)

Where

The half-life of radium-226 is 1600 years and the mass of a sample is 27 mg.

(a) What is the remaining mass after 4500 years?

(b) What is the decay time if the remaining mass is 15 mg?

First, let's calculate the decay constant.

λ = 0.693/T½

λ = 0.693/1600

λ = 0,000433

After 4500 years, the remaining mass is

\(m = m_{o} e^{-\lambda t}\)

\(m = 27 e^{-0.000433 \times 4500}\)

m = 27 × 0.142

m = 3.8 mg

If the remaining mass is 15 mg, the decay time is

\(m = m_{o} e^{-\lambda t}\)

\(15 = 27 e^{-0.000433 t}\)

\(ln \frac{15}{27} = ln (e^{-0.000433 t})\)

\(ln \frac{15}{27} = -0.000433 t\)

-0.588 = - 0.000433t

t = 1357.9 years

Hence,

(a) After 4500 years, the sample will remain 3.9 mg.

(b) The sample will remain 15 mg after 1369 years.

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Answer:

Decimal version: 71%

Percentage version: 0.71

Step-by-step explanation:

You can build a two-way relative frequency table to represent the data:

These are the columns and rows:

              Car         No car      Total

Boys

Girl

Total

Fill the table

30% of the children at the school are boys

            Car         No car      Total

Boys                                       30%

Girl

Total

60% of the boys at the school arrive by car

That is 60% of 30% = 0.6 × 30% = 18%

            Car         No car      Total

Boys      18%                         30%

Girls

Total

By difference you can fill the cell of Boy and No car: 30% - 18% = 12%

            Car         No car      Total

Boy       18%           12%         30%

Girl

Total

Also, you know that the grand total is 100%

            Car         No car      Total

Boy       18%           12%         30%

Girl

Total                                     100%

By difference you fill the total of Girls: 100% - 30% = 70%

            Car         No car      Total

Boy       18%           12%         30%

Girl                                         70%

Total                                     100%

80% of the girls at the school arrive by car

That is 80% of  70% = 0.8 × 70% = 56%

            Car         No car      Total

Boy       18%           12%         30%

Girl       56%                         70%

Total                                     100%

Now you can finish filling in the whole table calculating the differences:

            Car         No car      Total

Boy       18%           12%         30%

Girl        56%         14%         70%

Total     74%          26%      100%

Having the table completed you can find any relevant probability.

The probability that a child chosen at random from the school arrives by car is the total of the column Car: 74%.

That is because that column represents the percent of boys and girls that that  arrive by car: 18% of the boys, 56% of the girls, and 74% of all the the children.

Answer:

-16r^2 - 10r

Step-by-step explanation:

To simplify the expression -2r(8r+5), you can use the distributive property of multiplication over addition.

-2r(8r+5) = -2r * 8r - 2r * 5

First, let's simplify -2r * 8r:

-2r * 8r = -16r^2

Next, let's simplify -2r * 5:

-2r * 5 = -10r

Putting it all together, the simplified expression is:

-2r(8r+5) = -16r^2 - 10r

A displacement vector is a vector that represents the overall change in position of an object, taking into account both the direction and magnitude of the change. It is a measurement of the distance and direction from an object's initial position to its final position.

Distance, on the other hand, is a scalar quantity that refers to the total amount of ground covered by an object, regardless of its direction. It is simply a numerical value indicating the length of the path traveled by an object.

When considering velocity vs speed, velocity is also a vector quantity that includes both the speed and direction of an object's motion. Average velocity is calculated by dividing the total displacement of an object by the time it took to travel that distance.

Average speed, however, is calculated by dividing the total distance traveled by the time it took to travel that distance.

Instantaneous velocity refers to the velocity of an object at a specific point in time, while instantaneous speed refers to the speed of an object at a specific point in time.

Both of these values can be calculated by taking the derivative of the object's position vs time graph. Overall, the difference between displacement and distance is that displacement takes direction into account, while distance does not. And when considering velocity vs speed, velocity includes both direction and speed, while speed only includes the numerical value of the distance traveled over time.

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Answer:

x=3/2

Step-by-step explanation:

2x-3=0

2x=0+3

2x=3

x=3/2

Hi there!

you can use the Pythageron Therom for this one.

Basically you just need to apply this formula: a^2 + b^2 = c^2

And then find the root of the hypotenuse.

So, 15^2 + 8^2 = the hypotenuse^2

Which equals, 225 + 64 = 289

Square root of 289 = 17

17 is the answer you are looking for!

Please mark me brainliest if this helps!

Have a wonderful day!

Answer:

C

Step-by-step explanation:

y=mx+b m=slope b=y-intercept, y-int: 4 slope: 3/1 but can just be put as 3. y=3x+4 bc it's a positive slope with a positive y-int.

Answer:

1st option

Step-by-step explanation:

3z and 2z are adjacent angles on a straight line and sum to 180° , that is

3z + 2z = 180

5z = 180 ( divide both sides by 5 )

z = 36

Then

3z = 3 × 36 = 108°

2z = 2 × 36 = 72°

The general integral is provided by y = C1e-t + C2te-t + (1/2)(t2)e-t.

(m + 1)2 =0 is the characteristic polynomial for the differential equation y" +2y' + y = e-t.

Roots -1, -1. yh = C1e-t + C2te-t is the answer to the homogeneous equation at that point.

Use the method of variation of parameters, taking into account the independent integrals y1 = e-t, y2 = te-t, and Wronskian

W(t) = e-2t, to derive the specific integral related to f(t) = e-t.

Then, use the conventional formula yp = - y1(t)(Integral of Y2(t)f(t)dt/W(t)) +y

Obtain yp = (1/2)(t2)e-t for the given situation.

As a result, the general integral is provided by

y = C1e-t + C2te-t + (1/2)(t2)e-t.

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Answer:

5.

Step-by-Step explanation:

Distance = √ [(6-3)^2 + (8-4)^2) ]

= √(9 + 16)

= √25

= 5.

The range of the function f(x) = 2x^2 - 3x + 5 is (5/8, ∞).

To find the range of the function f(x) = 2x^2 - 3x + 5, we need to determine the set of all possible output values (y-values) for the corresponding input values (x-values). The range represents the set of all possible y-values.

One way to approach this is by considering the graph of the function, which is a parabola that opens upward since the coefficient of the x^2 term is positive. Since there is no restriction on the x-values, the parabola extends infinitely in both directions. Therefore, the range of the function is also infinite.

Mathematically, we can confirm this by considering the vertex of the parabola. The x-coordinate of the vertex can be found using the formula x = -b/2a, where a and b are the coefficients of the quadratic terms. In this case, a = 2 and b = -3, so x = -(-3)/(2*2) = 3/4. Substituting this value back into the function, we find that f(3/4) = 5/8.

Since the function is a parabola that opens upward, the y-values increase without bound as x approaches infinity. Therefore, the range of the function is (5/8, ∞).

Complete question should be  What is the range of the function f(x) = 2x^2 - 3x + 5?

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Answer:

Slope: -5 Y-intercept: 3

Step-by-step explanation:

the slope intercept of a linear equation is:

y=mx+b

were m is slope. and b is the y intercept

therfore the problem is:

y=-5x+3

m=-5 so the slope is -5

b=3 so the y-intrercept is 3

Answer:

-5

Step-by-step explanation:

The slope is always in front of the x

Answer:

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is know as the "constant of proportionality".

The two requirements for a proportional relationship are: The ratio of the two variables maintain the same ratio.

Answer:

A. tan A = sin A / sin C

Step-by-step explanation:

Answer:

tan A = sin A / sin C

Step-by-step explanation:

Answer:

(-1,-2) is the correct one but they all are the same

The work done by the force field F along the line segment from (0, 0, 1) to (2, 1, 0) is 1/3.

The work done by a force field F along a curve C is given by the line integral:

W = ∫C F · dr

where dr is the differential of the position vector r(t) along the curve, and the dot (·) represents the dot product.

In this case, the curve C is the line segment from (0, 0, 1) to (2, 1, 0), which we can parameterize as:

r(t) = <2t, t, 1 - t> for 0 ≤ t ≤ 1.

The differential of r(t) is:

dr = <2, 1, -1> dt

The force field F(x, y, z) = <yz, xz, xy>, so we can evaluate F at each point along the curve to obtain:

F(r(t)) = <t, 2t(1 - t), t>

Finally, we can compute the dot product F · dr:

F · dr = <t, 2t(1 - t), t> · <2, 1, -1> dt

= 2t + 2t(1 - t) - t dt

= 2t - 2t^2 dt

Integrating this expression over the interval [0, 1], we get:

∫C F · dr = ∫0^1 (2t - 2t^2) dt

= [t^2 - (2/3)t^3]0^1

= 1 - (2/3)

= 1/3

Therefore, the work done by the force field F along the line segment from (0, 0, 1) to (2, 1, 0) is 1/3.

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a) A symbol with a frequency of at least 0.4 will never be encoded with two or more bits. - True

b) A symbol with a frequency of at least 0.5 will never be encoded with two or more bits. - False

c) If all symbol frequencies are less than 0.33, all symbols will be encoded with at least two bits. - False

d) If all symbol frequencies are less than 0.5, all symbols will be encoded with at least two bits. - True

a) The Huffman greedy algorithm assigns shorter codes to symbols with higher frequencies. Therefore, a symbol with a frequency of at least 0.4 will never be encoded with two or more bits because it has a higher frequency and will be assigned a shorter code.

b) This statement is false. The Huffman greedy algorithm does not guarantee that a symbol with a frequency of at least 0.5 will always be encoded with a single bit. The encoding depends on the distribution of frequencies and the construction of the Huffman tree.

c) This statement is false. If all symbol frequencies are less than 0.33, it is possible that some symbols will be encoded with a single bit if they have a high frequency, while others may be encoded with more than two bits depending on their frequencies.

d) This statement is true. If all symbol frequencies are less than 0.5, the Huffman greedy algorithm guarantees that all symbols will be encoded with at least two bits. This is because the algorithm assigns shorter codes to symbols with higher frequencies, and since all frequencies are less than 0.5, none of the symbols will have a high enough frequency to be encoded with a single bit.

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This graph represent a system of equation with one solution. The blue point is the solution.

Hope this helps ^◇^