In a class of 30 students, 6 play an instrument and 17 play a sport. There are 9
students who do not play an instrument or a sport. What is the probability that a
student chosen randomly from the class plays neither a sport nor an instrument?

To prove the statement, let's assume that a and b are integers such that a is divisible by n and b is divisible by a.

Since a is divisible by n, we can write a = kn for some integer k.

Similarly, since b is divisible by a, we can write b = am for some integer m.Now, let's find the difference a - b:

a - b = kn - am

Factoring out common terms, we get:

a - b = n(k - m)

Since k and m are integers, their difference (k - m) is also an integer.

Therefore, we have expressed a - b as the product of n and an integer (k - m), which means that a - b is divisible by n.

Hence, we have proved that if a and b are integers such that a is divisible by n and b is divisible by a, then a - b is divisible by n, without using any specific theorem from a book.

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Answer:

A) 90°

Step-by-step explanation:

if lines b and c are perpendicular then all 8 angles measure 90 degrees

Answer: The number of hens are 4 and number of sheeps are 6

Step-by-step explanation:

Given : Total animals = 10

Total number of legs = 32

Let number of hens = h  and number of sheep = s

Thus h+s = 10    (1)

Now each hen has two legs and each sheep has 4 legs :[tex]2\times h+4\times s=32[/tex]   (2)

Solving for h and s we get:

s = 6 , h =4

Thus number of hens are 4 and number of sheeps are 6

The requried, there are 495 possible combination lineups with eight bands out of twelve for the benefit concert.

To determine the number of possible lineups with eight out of twelve bands performing, we need to calculate the combination.

The number of ways to choose eight bands out of twelve without considering the order is given by the combination formula:

[tex]C(n, r) = \dfrac{n!}{ (r! * (n-r)!)}[/tex]

where n is the total number of bands (12 in this case) and r is the number of bands to be chosen (8 in this case).

Let's calculate it:

[tex]C(12, 8) =\dfrac {12!}{(8! * (12-8)!)}[/tex]

            [tex]= \dfrac{12!} {(8! * 4!)}[/tex]

            = (12 * 11 * 10 * 9) / (4 * 3 * 2 * 1)
            = 495

Thus, there are 495 possible combination lineups with eight bands out of twelve for the benefit concert.

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Step-by-step explanation:

the beginning number is the beginning of your range the last number is the end of your range

Answer:

First term = 12

Step-by-step explanation:

A4 = 24

A12 = 56

An = A1 + (n-1)d; this defines the formula of an arithmetic series

A4 = 24 = A1 + (4-1)d

A4 = 24 = A1 + 3d

A12 = 56 = A1 + (12-1)d

A12 = 56 = A1 + 11d

Subtract A4 from A12 to get d (distance)

(56 = A1 + 11d) - (24 = A1 +3d)

32 = 8d

d = 4

Substitute d = 4 into A4

A4 = 24 = A1 + 3(d)

24 = A1 + 3(4)

24 = A1 + 12

24 - 12 = A1

12 = A1

(a) The complete graph [tex]K_n[/tex] has an Euler cycle if and only if n is an even number greater than or equal to 2.

(b) There are no complete graphs [tex]K_n[/tex] that have Euler trails but not Euler cycles. A complete graph always has an Euler cycle if it has an Euler trail.

(c) The bipartite graph [tex]K_r[/tex],s has an Euler cycle if and only if both r and s are even numbers greater than or equal to 2.

(a) To determine the values of n for which the complete graph [tex]K_n[/tex] has an Euler cycle, we need to understand the conditions for an Euler cycle to exist in a graph.

An Euler cycle is a closed walk in a graph that visits every edge exactly once and starts and ends at the same vertex. In order for a graph to have an Euler cycle, it must satisfy the following conditions:

All vertices in the graph have even degrees (an even number of edges incident to them).

The graph is connected, meaning there is a path between any two vertices.

Now let's apply these conditions to the complete graph [tex]K_n[/tex].

Degree of Vertices: In a complete graph [tex]K_n[/tex], each vertex is connected to every other vertex. Therefore, each vertex has a degree of n-1, as it is connected to n-1 other vertices. Since n-1 is always an odd number, it means that all vertices in [tex]K_n[/tex] have odd degrees. Hence, [tex]K_n[/tex] does not have an Euler cycle for any value of n.

Connectivity: A complete graph [tex]K_n[/tex] is always fully connected, meaning there is a direct edge between every pair of vertices. Therefore, the connectivity condition is satisfied for any value of n.

Based on these conditions, we can conclude that the complete graph [tex]K_n[/tex] does not have an Euler cycle for any value of n.

(b) since [tex]K_n[/tex] does not have an Euler cycle for any value of n, it also implies that there are no [tex]K_n[/tex] graphs that have Euler trails but not Euler cycles.

(c) The bipartite graph [tex]K_r[/tex],s is a complete bipartite graph with two sets of vertices, one with r vertices and the other with s vertices. To have an Euler cycle in this bipartite graph, the following conditions must be met:

All vertices in each set have even degrees.

The number of vertices in each set must be equal.

Since the complete bipartite graph [tex]K_r[/tex],s has all vertices with degree s in one set and degree r in the other set, it means that both r and s must be even numbers for all vertices to have even degrees. Additionally, the number of vertices in each set must be equal for the graph to be bipartite. Therefore, an Euler cycle exists in the bipartite graph [tex]K_r[/tex],s if and only if both r and s are even numbers.

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The probability of selecting  a girl to read the poem out loud in her class is 46.4% .

To calculate the probability of selecting a girl to read a poem out loud in a class of 28 students, we can use the formula:

Probability = Number of Desirable Outcomes / Total Number of Outcomes

Here, the desirable outcome is selecting a girl to read the poem, and the total outcomes are all the students in the class.

Number of Desirable Outcomes:

Mrs. Avery has 13 girls in her class, so there are 13 desirable outcomes.

Total Number of Outcomes:

Mrs. Avery has 28 students in her class, so there are 28 total outcomes.

Probability = Number of Desirable Outcomes / Total Number of Outcomes

Probability = 13 / 28

Probability = 0.464 or 46.4%

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Note: The complete question is -Mrs. Avery is planning to have one student read a poem out loud in class. She has a class of 28 students, consisting of 15 boys and 13 girls. What is the probability that she will select a girl to read the poem out loud?

Answer:

4=3  5=10 6= YOu would add more dots accordingly 7=4

Step-by-step explanation:

hoped this helped!

Answer: 84π √(17) (rounded to 3 significant figures)

a) To find the arc length of the given curve we need to first evaluate the derivative of y w.r.t. x:dy/dx = 4. The arclength of the curve is given by L = ∫√(1+(dy/dx)^2) dx The value of dy/dx is already given and hence we can substitute the value and integrate .L = ∫√(1+(4)^2) dx = ∫√(17) dx Between the limits z = 1 and 2, x varies from 9 to 13. We need to substitute these values in the integral. L = ∫√(17) dx = √(17) * [x]9^13= √(17) * [13 - 9]= 4 √(17)Answer: 4√17 (rounded to 3 significant figures)

b) The area of the surface of revolution, A, that is obtained when the curve is rotated by 2 radians about the a-axis is given by:A = ∫2π * y √(1+(dy/dx)^2) dx We know that dy/dx = 4 and the value of y is given by 4x+5.A = ∫2π * (4x+5) √(1+(4)^2) dx= ∫2π * (4x+5) √(17) dx Between the limits z = 1 and 2, x varies from 9 to 13. We need to substitute these values in the integral. A = ∫2π * (4x+5) √(17) dx = 2π * √(17) * ∫(4x+5) dx= 2π * √(17) * [2x^2/2 + 5x]9^13= 2π * √(17) * [(26 + 60) - (18 + 20)]= 84π √(17)

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The value of the F-statistic for the test of overall significance of this regression relationship is approximately 11.245.

Given:SST = 2326.9523 SSR = 1632.8843 Independent variables = 7

Observations = 66Formula used:F = (SSR/K) / (SSE / (n-K-1))

Where SSR = Regression sum of squares SSE = Error sum of squaresK = Number of independent variables n = Number of observations

To calculate the F-statistic, we first need to calculate SSE which is given by:SSE = SST - SSR = 2326.9523 - 1632.8843 = 693.068

The degrees of freedom for the regression are K and the degrees of freedom for the error term are n - K - 1 = 66 - 7 - 1 = 58

The value of the F-statistic is given by:F = (SSR/K) / (SSE / (n-K-1))= (1632.8843/7) / (693.068 / 58)= 11.245

Therefore, the value of the F-statistic for the test of overall significance of this regression relationship is approximately 11.245.

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The given initial value problem using the method of undetermined coefficients. The final solution to the initial value problem is y = cos(2x) + x - (1/9)*sin(3x).

To solve the given initial value problem, we begin by finding the general solution to the associated homogeneous equation. The homogeneous equation is given by y'' + 4y = 0. The characteristic equation is obtained by substituting y = e^(mx) into the equation, resulting in the quadratic equation m^2 + 4 = 0. Solving this equation yields two distinct roots: m_1 = 2i and m_2 = -2i. Thus, the general solution to the homogeneous equation is y_h = c_1cos(2x) + c_2sin(2x), where c_1 and c_2 are arbitrary constants.

Next, we assume a particular solution in the form of y_p = Ax + B + Csin(3x) + Dcos(3x), where A, B, C, and D are undetermined coefficients. We substitute this particular solution into the given differential equation and solve for the coefficients. Comparing the coefficients of like terms, we find A = 0, B = 1, C = -1/9, and D = 0.

The particular solution is y_p = x - (1/9)*sin(3x), and the complete solution is obtained by adding the particular solution to the homogeneous solution: y = y_h + y_p. Applying the initial condition y(0) = 1, we find that c_1 = 1 and c_2 = 0. Therefore, the final solution to the initial value problem is y = cos(2x) + x - (1/9)*sin(3x).

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Step-by-step explanation:

36 is your answer

I hope.it helps mate

have a nice day

#Captainpower

Answer:

10*5 or 25*2

Step-by-step explanation:

There are other answers but those involve decimals and I'm assuming they want whole numbers.

Answer:

C) 5x-70=105

Step-by-step explanation:

As marked in the graph, angle 105 and angle (5x-70) equal to each other because they are vertically opposite angles therefore we have equation C)

Answer:

-18+ 13

-6 + 1

-20 + 15

-7 + 2

Step-by-step explanation:

Answer:

2.07x2.4=4.968

Step-by-step explanation:

Answer:

4.968

Step-by-step explanation:

I'm on my school computer so the picture is blocked sorry :(

Answer:

the answer is in the photo hope it help

Answer: The horizontal extent of the graph is -3 to 1, so the domain of f is (-3,1]

Step-by-step explanation:

The range is [-4,0]

Answer:

45

Step-by-step explanation:

x = -30/2(-5)

x = -30/(-10)

x = 3 sec

.

Plug above into equation to find height:

h=-5t^2 + 30t

h=-5*3^2 + 30(3)

h=-5*9 + 30(3)

h=-45 + 90

h=45

Assuming the profit of one airport is regulated by a rate-of-return (ROR) based regulation of 2% and the estimated airport asset for 2020 is about $100 million, the maximum profit the airport can generate is $2 million.

The maximum profit of the airport is a function of the multiplication of the estimated asset and the allowed maximum rate of return.

The rate of return is the percentage of total returns expressed as a quotient of the total assets multiplied by 100.

The allowed maximum rate of return = 2%

Estimated asset of the airport for 2020 = $100 million

The maximum profit = $2 million ($100 million x 2%)

Thus, the airport's maximum profit for 2020 is $2 million.

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Answer:

[tex]\sqrt{53}[/tex]

Step-by-step explanation:

Use the distance formula:

[tex]\sqrt{(x1-x2)^2+(y1-y2)^2}[/tex]

plug in (-5,6) for (x1,y1) and (-3,-1) for (x2,y2)

[tex]\sqrt{(-5-(-3))^2+(6-(-1))^2}[/tex]

[tex]\sqrt{4+49}[/tex]

[tex]\sqrt{53}[/tex]

Hope that helps :)

Answer:

80 percent of 70 is 56, so you were 20% wrong?

The percent error is 20%

let me know if you need anything else :)

Answer:

x intercept=2

y intercept=6

Step-by-step explanation:

to find x and y intercepts, plug in 0 for x and y

x intercept-

6x+2(0)=12

6x=12

x=2

y intercept-

6(0)+2y=12

2y=12

y=6

What is the LCM of 64 and 72?

Find the prime factorization of 64.

Find the prime factorization of 72. 72 = 2 × 2 × 2 × 3 × 3.

Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM: LCM = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3.

LCM = 576.

What is the GCF of 64 and 72?

Find the prime factorization of 64. 64 = 2 × 2 × 2 × 2 × 2 × 2.

Find the prime factorization of 72. 72 = 2 × 2 × 2 × 3 × 3.

To find the GCF, multiply all the prime factors common to both numbers: Therefore, GCF = 2 × 2 × 2.

GCF = 8.

Answer:

8x8 and 8x9

Step-by-step explanation:

because 8x8 is 64 and 8x9 is 72

Answer: (4+1)*5=25; (25+1)*5=130; (130+1)*5=655.

Step-by-step explanation:

As per the given values, the after-tax salvage value is $435,200.

Amount required = $3,200,000

Time = 6 years

Calculating the accumulated depreciation -

Amount/ Number of years

=  $3,200,000 / 6

= $533,333.3.

Calculating the accumulated depreciation at project end -

= 6 x $533,333.33

= $3,200,000.

Calculating the book value of the fixed assets -

Book value = Cost of fixed assets - Accumulated depreciation

= $3,200,000 - $3,200,000

= $0

Calculating the taxable gain or loss on the sale of the fixed assets -

Taxable gain/loss = Selling price - Book value

= $640,000 - $0

= $640,000

Calculating the tax liability -

Tax liability = Tax rate x Taxable gain

= 0.32 x $640,000

= $204,800

Calculating the after-tax salvage value -

After-tax salvage value = Selling price - Tax liability

= $640,000 - $204,800

= $435,200

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