Nolan has a lot of tennis balls in his garage he has 4 green tennis balls only 5 percent of his tennis ball are green how many does does he have altogether

n(A), n(B) and n(AnB) are given and n(AUB)'s complement is asked.

Answer:

6:6=3:3=1:1=160/2=80

160/2=80 male

160/2=80 female

80 female

Answer:

  a) 625; 625; right triangle

  b) 205; 256; obtuse triangle

Step-by-step explanation:

The squares are values found in your memory or using a calculator. It is straightforward addition to find their sum.

7² +24² = 49 +576 = 625

25² = 625

The sum of the squares of the short sides is the square of the long side, so this is a right triangle.

__

6² +13² = 36 +169 = 205

16² = 256

The long side is longer than is needed to form a right triangle, so the largest angle is more than 90°. This is an obtuse triangle (as shown).

Answer:

Scalene Traingle

Step-by-step explanation:

Because a scalene triangle has no congruent sides, but can be a right angle (90 degree)!

Answer:

The answer is 13.

Step-by-step explanation:

Answer:

65 ft (which is A)

Step-by-step explanation:

A² + B² = C²

72² + B² = 97²

B² = 4225

B = √4225

B = 65 ft

We are filling an urn with two white, two black, and two red balls. P(3 white) = C(6, 3) / C(9, 3) = 20 x 84 x 5 x 21    the probability of precisely drawing one ball from each tone is 1/36.drawn two red balls, the contingent likelihood of drawing balls from the primary urn is 2/3 because P(B|A) = (1/10) * (1/4)/(3/20) = 2/3. P(A|B) = Likelihood of drawing two red balls regardless of the urn = P(A|B) * P(B)/P(A) P(A|B)

(a) Let's calculate the probabilities of each and every draw of three balls from an urn containing six white and three red balls that do not need to be replaced.

The hard and fast number of results that are possible is C(9, 3) = 84 (blends of three of the nine balls):

P(3 red) = C(3, 3)/C(9, 3) = 1/84

Likelihood of drawing 2 red and 1 white ball:

The probability of drawing two white balls and one red ball is: P(2 red, 1 white) = C(3, 2) * C(6, 1)/C(9, 3) = 3/84 = 1/28

P = C(3, 1) * C(6, 2)/C(9, 3) = 3/28 Likelihood of drawing three white balls:

In this instance, we are filling an urn with two white, two black, and two red balls. P(3 white) = C(6, 3) / C(9, 3) = 20 x 84 x 5 x 21

(b). The odds of only drawing one ball from each tone are as follows:

The all out number of potential results is 63 = 216 (each ball has 6 potential results). To precisely have one ball from each tone, use one of the accompanying mixes:

(Red, Dark, White), (White, Dark, Red, White), (Dark, White, Red), (Each mix has one great result), (Likelihood = Number of good results/Complete number of potential results = 6/216 = 1/36) In this manner, the probability of precisely drawing one ball from each tone is 1/36.

(c) For this situation, we select R red and W white balls from a urn without supplanting any of them. We must determine the likelihood that the primary red ball will be drawn at the kth draw for k = 1, 2,... The accompanying equation can be utilized to decide the probability that the principal red ball will be drawn at the kth draw:

For instance, the following condition can be used to determine the likelihood that the principal red ball will be drawn at the third draw: P(first red at kth draw) = (R-1)/(R+W-1) * (R-2)/(R+W-2) *... * 1/(R+W-k+1).

The accompanying equation can be utilized to decide the likelihood for different k qualities: P(first red at third draw) = (R-1)/(R+W-1) * (R-2)/(R+W-2) * 1/(R+W-3) There are three white and two red balls in the essential urn, and there are two white and three red balls in the ensuing urn. The fundamental urn is picked unpredictably with a probability of 1/4, and the ensuing urn is picked with a probability of 3/4. Considering that we have drawn two red balls, we should think about how conceivable it is that we have drawn balls from the primary urn since we have drawn two balls without replacement.

The drawing of the principal urn and the drawing of two red balls ought to be referred to as occasion A and occasion B, respectively.

Bayes' hypothesis can be used to determine the restrictive likelihood as follows:

Given that we have drawn two red balls, the contingent likelihood of drawing balls from the primary urn is 2/3 because P(B|A) = (1/10) * (1/4)/(3/20) = 2/3. P(A|B) = Likelihood of drawing two red balls regardless of the urn = P(A|B) * P(B)/P(A) P(A|B) = Likelihood of drawing two red balls given that we draw from the principal.

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The best mathematical model that fits the scatterplot is the logarithmic model. So, correct option is D.

To determine the best mathematical model that fits the scatterplot, we look at the coefficient of determination (R²) values for each regression model. The coefficient of determination indicates the goodness of fit of the regression model, with values closer to 1 indicating a better fit.

Given:

Linear regression R² value: 0.883

Quadratic regression R² value: 0.537

Exponential regression R² value: 0.492

Logarithmic regression R² value: 0.912

Comparing the R² values, we observe that the logarithmic regression model has the highest value of 0.912. This indicates that the logarithmic regression model provides the best fit to the scatterplot among the given options.

Therefore, correct option is D.

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Answer: 4z + 3

Step-by-step explanation:

Number of books read by Zeke = z

Michelle read twice as many book as Zeke. This will be: = 2 × z = 2z

Tay read 3 more books than Zeke. This will be: = z + 3

The expression that represents the total number of books read over the summer by Zeke, Michelle and Tay would be the addition of the books read by each person. This will be:

= z + 2z + z + 3

= 4z + 3

Designing highway drainage structures requires data such as the type of drainage system, geotechnical information, hydraulic design data, and structural design data. This information is essential for determining the dimensions of the structure and selecting suitable materials.

To determine the dimensions of highway drainage structures, the following data are required:

Type of drainage system:

The type of drainage system that is to be designed for the highway drainage structures. Different types of drainage systems are available, including subsurface, surface, and combined systems. The drainage system selected depends on the highway's characteristics and location.

Geotechnical data:

Geotechnical data, including soil type, depth to bedrock, and ground slope, is also required. This data helps to determine the appropriate structure type and its foundation design. In addition, the data helps to assess the level of erosion and sedimentation that may affect the drainage system.

Hydraulic design data:

The hydraulic design data needed to design highway drainage structures includes the maximum rainfall intensity, runoff volume, and peak flow rates. The hydraulic design calculations are used to size the drainage structure and determine the appropriate materials to be used.

Structural design data:

The structural design data required for designing highway drainage structures includes the design loadings, structural capacity, and durability requirements. This data helps to determine the dimensions of the structure, including length, width, and height. Other factors to consider during design include cost, maintenance, and environmental impact, among others.

In conclusion, designing highway drainage structures requires various data, including the type of drainage system, geotechnical data, hydraulic design data, and structural design data. The data help to determine the appropriate dimensions of the structure and the materials to be used.

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Answer:

\(x = 12 \\ x = 12 + 2 = 14 \\ x = 14 + 2 = 16 \\ x = 16 + 2 = 18 \\ 18 \geqslant 17 \\ end \: of \: loop \\ show \: 18\)

Answer

19

Step-by-step explanation:

The solution of the differential equation y′′(t) y(t) = g(t),

y(0) = 1, y′(0) = 1, for t ≥ 0 with

g(t) = (et sin(t), 0 ≤ t < π 0, t ≥ π] is:

y(t) = - t + \(c_4\) for 0 ≤ t < πy(t) = \(c_5\) for t ≥ π.

where \(c_4\) and \(c_5\) are constants of integration.

The solution of the differential equation

y′′(t) y(t) = g(t),

y(0) = 1,

y′(0) = 1, for t ≥ 0 with

g(t) = (et sin(t), 0 ≤ t < π 0, t ≥ π] is as follows:

The given differential equation is:

y′′(t) y(t) = g(t)

We can write this in the form of a second-order linear differential equation as,

y′′(t) = g(t)/y(t)

This is a separable differential equation, so we can write it as

y′dy/dt = g(t)/y(t)

Now, integrating both sides with respect to t, we get

ln|y| = ∫g(t)/y(t) dt + \(c_1\)

Where \(c_1\) is the constant of integration.

Integrating the right-hand side by parts,

let u = 1/y and dv = g(t) dt, then we get

ln|y| = - ∫(du/dt) ∫g(t)dt dt + \(c_1\)

= - ln|y| + ∫g(t)dt + \(c_1\)

⇒ 2 ln|y| = ∫g(t)dt + \(c_2\)

Where \(c_2\) is the constant of integration.

Taking exponentials on both sides,

we get |y|² = \(e^{\int g(t)}dt\ e^{c_2\)

So we can write the solution of the differential equation as

y(t) = ±\(e^{(\int g(t)dt)/ \sqrt(e^{c_2})\)

= ±\(e^{(\int g(t)}dt\)

where the constant of integration has been absorbed into the positive/negative sign depending on the boundary condition.

Using the initial conditions, we get

y(0) = 1

⇒ ±\(e^{\int g(t)}dt\) = 1y′(0) = 1

⇒ ±\(e^{\int g(t)}dt\) dy/dt + 1 = 0

The above two equations can be used to solve for the constant of integration \(c_2\).

Using the first equation, we get

±\(e^{\intg(t)\)dt = 1

⇒ ∫g(t)dt = 0,

since g(t) = 0 for t ≥ π.

So, the first equation gives us no information.

Using the second equation, we get

±\(e^{\intg(t)}dt\) dy/dt + 1 = 0

⇒ dy/dt = - 1/\(e^{\intg(t)dt\)

Now, integrating both sides with respect to t, we get

y = \(- \int1/e^{\intg(t)\)dt dt + c₃

Where c₃ is the constant of integration.

Using the second initial condition y′(0) = 1,

we get

1 = dy/dt = - 1/\(e^{\int g(t)}\)dt

⇒ \(e^{\int g(t)}\)dt = - 1

Now, substituting this value in the above equation, we get

y = - ∫1/(-1) dt + c₃

= t + c₃

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Answer: Option a.

Step-by-step explanation:

The data is:

The cost of mailing a letter is $0.37 for the first ounce.

$0.23 for each additional ounce or portion.

Then if we define the variable n, as the number of additional ounces, we can write this as:

F(n) = $0.37 + n*$0.27

This seems to be a linear relationship, but n only can take whole numbers, this means that if n is equal to 0.37, we should round it up (because we already have more than only one ounce).

Then we round up all the non-integers to the next integer.

for example, we round 1.45 to 2 and 1.876 to 2.

This means that F (1.45) = F(1.876) = F(2) = $0.37 + 2*$0.27

This is called a greastet integer function. then the correct option is a.

Answer:

Its B. Step Function, I just turned it in.

Step-by-step explanation:

Edge. 2020-21

Answer:

To complete the square and identify the curve, let's rearrange the equation as follows:

x^2 + 6x - 3y^2 + 12y = 12

Step-by-step explanation:

To complete the square for the x-terms, we need to add and subtract the square of half the coefficient of x:

x^2 + 6x + (6/2)^2 - (6/2)^2 - 3y^2 + 12y = 12

Simplifying:

x^2 + 6x + 9 - 9 - 3y^2 + 12y = 12

(x^2 + 6x + 9) - 9 - 3y^2 + 12y = 12

(x + 3)^2 - 9 - 3y^2 + 12y = 12

To complete the square for the y-terms, we need to add and subtract the square of half the coefficient of y:

(x + 3)^2 - 9 - 3(y^2 - 4y + 4) + 3(4) = 12

(x + 3)^2 - 9 - 3(y - 2)^2 + 12 = 12

(x + 3)^2 - 3(y - 2)^2 = 9

Dividing through by 9:

(x + 3)^2/9 - (y - 2)^2/3 = 1

Now we can identify the curve. The equation represents a hyperbola, since the squared terms have opposite signs.

The equation of the hyperbola is in standard form with a horizontal transverse axis, centered at the point (-3, 2). The term (x + 3)^2/9 is positive, indicating a horizontal shift to the left by 3 units. The term (y - 2)^2/3 is negative, indicating a vertical shift upwards by 2 units.

To find the critical points of the curve, we can differentiate the equation with respect to x and y and set the derivatives equal to zero.

Differentiating with respect to x:

(2/9)(x + 3) = 0

x + 3 = 0

x = -3

Differentiating with respect to y:

(-2/3)(y - 2) = 0

y - 2 = 0

y = 2

Therefore, the critical point of the curve is (-3, 2).

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The maximum magnitude of acceleration is approximately 4.085 m/s².

To find the period of the motion, we need to determine the time it takes for the peg to complete one full revolution around the circle. The period can be calculated using the formula:

T = 2πr/v

where T is the period, r is the radius of the circle, and v is the tangential speed of the peg.

Given:

r = 0.19 m

v = 0.88 m/s

Substituting these values into the formula, we have:

T = 2π(0.19 m)/(0.88 m/s)

T ≈ 0.432 s

Therefore, the period of the motion is approximately 0.432 seconds.

Part E: To find the amplitude, we can use the radius of the circle since the motion is along a circular path. The amplitude is equal to the radius of the circle:

Amplitude (A) = 0.19 m

Part F: The maximum displacement is equal to the diameter of the circle since the peg moves from one extreme point to the other:

Maximum Displacement = 2 * 0.19 m = 0.38 m

Part G: The maximum magnitude of acceleration occurs at the extreme points of the circular path. It can be calculated using the formula:

amax = v²/r

where amax is the maximum acceleration, v is the tangential speed, and r is the radius of the circle.

Substituting the given values, we have:

amax = (0.88 m/s)² / 0.19 m

amax ≈ 4.085 m/s²

Therefore, the maximum magnitude of acceleration is approximately 4.085 m/s².

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you can use Pythagoras theorem as shown in the image:

The value of x is 9 and the mistake that Maggie made is that she did use the proper operation sign when rearranging the numbers.

When any two straight lines intersect each other, then four angles are formed. The angles that are directly opposite to each other are known as opposite angles. They are also called vertical angles or vertically opposite angles.

Now, from the image attached, we see that the two given angles are opposite angles and as such they are congruent. Thus, we have;

4x + 2 = 7x - 25

Rearrange to collect like terms on same side to get;

7x - 4x = 25 + 2

3x = 27

x = 27/3

x = 9

The mistake that Maggie made is that she did use the proper operation sign when rearranging the numbers.

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The particular solution to the given ODE is:y_p(t) = (1/3)sin(t) - (1/6)sin(2t) - (1/3)θ(t)sin(t) + (1/6)θ(t)sin(2t).This solution satisfies the ODE y'' - y = sin^2(t), and it was obtained using the method of convolutions.

To construct a particular solution to the ODE y'' - y = sin^2(t), we can use the method of convolutions. The idea behind this method is to find the convolution of the forcing function, sin^2(t), with a suitable kernel function, which in this case is the Green's function for the homogeneous equation y'' - y = 0.

The Green's function for this equation is given by:

G(t, τ) = (θ(t - τ)sin(t - τ) + θ(τ - t)sin(tau - t))/W,

where θ is the Heaviside step function and W is the Wronskian of the homogeneous equation, which is 2.

Using this Green's function, we can construct the convolution of the forcing function with the kernel function as:

y_p(t) = ∫[0 to t] G(t, τ) sin^2(τ) dτ.

Substituting the expression for G(t, τ), we get:

y_p(t) = [sin(t) ∫[0 to t] sin(τ) sin^2(τ) dτ] - [θ(t) ∫[0 to t] sin(t - τ) sin^2(τ) dτ].

Evaluating the integrals, we get:

y_p(t) = (1/3)sin(t) - (1/6)sin(2t) - (1/3)θ(t)sin(t) + (1/6)θ(t)sin(2t).

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This solution satisfies the ODE y'' - y = sin^2(t), and it was obtained using the method of convolutions.

To construct a particular solution to the ODE y'' - y = sin^2(t), we can use the method of convolutions. The idea behind this method is to find the convolution of the forcing function, sin^2(t), with a suitable kernel function, which in this case is Green's function for the homogeneous equation y'' - y = 0.

The Green's function for this equation is given by:

G(t, τ) = (θ(t - τ)sin(t - τ) + θ(τ - t)sin(tau - t))/W,

where θ is the Heaviside step function and W is the Wronskian of the homogeneous equation, which is 2.

Using this Green's function, we can construct the convolution of the forcing function with the kernel function as:

y_p(t) = ∫[0 to t] G(t, τ) sin^2(τ) dτ.

Substituting the expression for G(t, τ), we get:

y_p(t) = [sin(t) ∫[0 to t] sin(τ) sin^2(τ) dτ] - [θ(t) ∫[0 to t] sin(t - τ) sin^2(τ) dτ].

Evaluating the integrals, we get:

y_p(t) = (1/3)sin(t) - (1/6)sin(2t) - (1/3)θ(t)sin(t) + (1/6)θ(t)sin(2t)

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Average waiting time for FCFS: 8.75

Average waiting time for SJF: 4.75

To solve this scheduling problem using FCFS (First-Come, First-Served) and SJF (Shortest Job First) algorithms, let's go step by step:

Schedule order for FCFS:

The FCFS algorithm schedules processes based on their arrival time. So, the schedule order for FCFS is as follows:

Pl -> P2 -> P3 -> P4

Average waiting time for FCFS:

To compute the average waiting time for FCFS, we need to calculate the waiting time for each process and then take the average.

Process | Arrival Time | Running Time | Waiting Time

Pl | 0 | 3 | 0

P2 | 3 | 10 | 3

P3 | 4 | 6 | 13

P4 | 5 | 1 | 19

Average waiting time = (0 + 3 + 13 + 19) / 4 = 8.75

Therefore, the average waiting time for FCFS is 8.75.

Schedule order for SJF:

The SJF algorithm schedules processes based on their running time. The process with the shortest running time gets executed first. If multiple processes have the same running time, the process with the earliest arrival time is selected first. The schedule order for SJF is as follows:

Pl -> P4 -> P3 -> P2

Average waiting time for SJF:

To compute the average waiting time for SJF, we need to calculate the waiting time for each process and then take the average.

Process | Arrival Time | Running Time | Waiting Time

Pl | 0 | 3 | 0

P4 | 5 | 1 | 3

P3 | 4 | 6 | 6

P2 | 3 | 10 | 10

Average waiting time = (0 + 3 + 6 + 10) / 4 = 4.75

Therefore, the average waiting time for SJF is 4.75.

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Answer:

It is A

From the x-value of 3 to the x-value of 8, the y-value goes down from 3 to -6

Uh...I have no clue. Sorry. :(

Step-by-step explanation:

oh, come on. you can just use common sense.

a local minimum is a point where the curve goes down to, and then turns around and starts to go up again. that point in the middle, where it turns around and does not go down any further, is the minimum.

for the maximum the same thing applies, just in the other direction (the curve goes up and turns around to go back down again).

a)

the local minimum values (y) are

-2, -1

b)

the values of x where it had these minimum values are

-1, +3

Answer:

$750

Step-by-step explanation:

Larger share = $450

Smaller share : Larger share :: 2 : 3

Smaller share = (larger share x 2) / 3

= (450x2)/3

= 300

Sum= larger share + smaller share

= $450 + $300 = $750

Answer:

16 inches squared

Step-by-step explanation:

We can split the figure into two rectangles. Rectangle 1 will have an area of 2*3=6. Rectangle 2 will have an area of 2*5=10

10+6=16

Answer:

95.4 yards maybe

Step-by-step explanation:

just used pythagoras theorem

Answer:

........................

Step-by-step explanation:

Probability of getting a particular number on ticket = 1/7320300

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, if we are unclear of how an event will turn out. Statistics is the study of occurrences subject to probability.

The following values of x: 100000, 1000, 500, 100, 75, 50, 20, 15, 10, 5

Their corresponding values of p(x) are 1/7320300, 1/7320300, 1/7320300, 1/7320300, 1/7320300, 1/7320300, 1/7320300, 1/7320300,

Expected Each lottery ticket's winnings are calculated as follows: (100000+1000+500+100+75+50+20+15+10+5)(1/7320300) = 101775/7320300 = 0.014 $.

But he does purchase a $5 ticket.

In other words, the Net Expected Value of Money is equal to 0.014 - 5 = -4.986 $.

due to the negative anticipation. There are therefore greater chances for failure. The predicted loss is $4.986.

Probability of getting a particular number on ticket = 1/7320300

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