in a dependency matrix, when a2 must be completed before a4, then the activities are

Answer:

b^4 / a

Step-by-step explanation:

I have attached the explanation above. hopefully this will help

Answer:

Therefore, the exact value of cos 30 degrees is written as 0.8660 approx. √3/2 is the value of Cos 30° which is a trigonometric ratio or trigonometric function of a particular angle

The type directions that lie in the (110) plane are Crystal planes are equivalent planes that represent a group of crystal planes with a common set of atomic indexes.

Crystallographers use Miller indices to identify crystallographic planes. A crystal is a three-dimensional structure with a repeating pattern of atoms or ions.In a crystal, planes of atoms, ions, or molecules are stacked in a consistent, repeating pattern. Miller indices are a mathematical way of representing these crystal planes.

Miller indices are the inverses of the fractional intercepts of a crystal plane on the three axes of a Cartesian coordinate system.Let us now determine which of the type directions lie in the (110) plane.[101] is not in the (110) plane because it has an x-intercept of 1, a y-intercept of 0, and a z-intercept of 1. So, this direction does not lie in the (110) plane.[110] is in the (110) plane since it has an x-intercept of 1, a y-intercept of 1, and a z-intercept of 0.

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To find the volume of the solid obtained by rotating the region under the curve over the interval [4, 7] about the x-axis, we can use the method of cylindrical shells.

The formula for the volume of a solid generated by rotating a curve f(x) about the x-axis, over an interval [a, b], is given by:

V = ∫[a, b] 2πx * f(x) * dx

In this case, the interval is [4, 7], so we need to evaluate the integral:

V = ∫[4, 7] 2πx * f(x) * dx

To find the function f(x), we need the equation of the curve. Unfortunately, you haven't provided the equation of the curve. If you can provide the equation of the curve, I will be able to help you further by calculating the integral and finding the volume.

Please provide the equation of the curve so that I can assist you in finding the volume of the solid.

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Answer:

260

Step-by-step explanation:

The variance of the reaction times is approximately 0.02596.

To find the variance, you need to follow these steps:

1. Calculate the mean of the reaction times.

  mean = (0.74 + 0.71 + 0.41 + 0.82 + 0.74 + 0.85 + 0.99 + 0.71 + 0.57 + 0.85 + 0.57 + 0.55) / 12

       = 8.54 / 12

       = 0.7125

2. Subtract the mean from each individual value, and square the result.

  (0.74 - 0.7125)^2 = 0.000525625

  (0.71 - 0.7125)^2 = 2.50625e-06

  (0.41 - 0.7125)^2 = 0.09100625

  (0.82 - 0.7125)^2 = 0.01150625

  (0.74 - 0.7125)^2 = 0.000525625

  (0.85 - 0.7125)^2 = 0.02000625

  (0.99 - 0.7125)^2 = 0.07800625

  (0.71 - 0.7125)^2 = 2.50625e-06

  (0.57 - 0.7125)^2 = 0.02000625

  (0.85 - 0.7125)^2 = 0.02000625

  (0.57 - 0.7125)^2 = 0.02000625

  (0.55 - 0.7125)^2 = 0.02400625

3. Calculate the sum of the squared differences.

  sum = 0.000525625 + 2.50625e-06 + 0.09100625 + 0.01150625 + 0.000525625 + 0.02000625 + 0.07800625 + 2.50625e-06 + 0.02000625 + 0.02000625 + 0.02000625 + 0.02400625

      = 0.285625

4. Divide the sum by the number of values minus 1 (n-1).

  variance = sum / (12 - 1)

           = 0.285625 / 11

           ≈ 0.02596

Therefore, the variance of the reaction times is approximately 0.02596.

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Answer: The cosine of angle C is -0.0168.

Step-by-step explanation: To find the cosine of the angle opposite the side of length 2.92 meters, you can use the cosine law which states that:

c^2 = a^2 + b^2 - 2ab * cos(C)

where c is the length of the hypotenuse (the longest side), a and b are the lengths of the other two sides, and C is the angle opposite side c.

So in this case,

c = 8.82 m

a = 2.92 m

b = 7.67 m

then we can substitute the values into the equation and solve for cos(C):

(8.82)^2 = (2.92)^2 + (7.67)^2 - 2(2.92)(7.67) * cos(C)

cos(C) = (a^2 + b^2 - c^2) / (-2ab)

cos(C) = (2.92^2 + 7.67^2 - 8.82^2) / (-22.927.67)

cos(C) = -0.0168

Answer:

41.1 cm

Step-by-step explanation:

1) Find the perimeter of the visible rectangle...

1) Find the perimeter of semicircles

We can put the semicircles together to make a whole circle so instead of finding the perimeter of both semicircles separately we can find the perimeter of a whole circle with radius 4.

3) Add the results

Have a lovely day :)

Total Perimeter of the figure is 41.13274 cm

Given that,

Length of a side = 4 cm

Now,

There are two semi circles being formed in the figure. If we add both it will form a circle.

The perimeter of the circle = Circumference of the circle

Circumference = 2 π r                         ( r  = 4 cm i.e. a side)

                         = 2 π * 4

                         = 8 π cm

and the four sides of the figure that are left, form a square,

so, the perimeter of the square = 4 * side

                                                     = 4 * 4 = 16 cm

Total Perimeter = 8π +16

                          = 41.13274 cm

Therefore, Total Perimeter of the figure is 41.13274 cm

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Answer:

I would say about 5 times but I am not sure so if it is wrong am sorry.

Answer:

61 degrees

Step-by-step explanation:

The THREE angles in the diagram sum to 180 degrees ( straight line = flat wall)

3x+1     +   58   +   4x-19     = 180

solve for x = 20     then A = 3x+1 = 61 degrees

Answer:

hi

7.6×7.6= 57.76

so it has to be bigger than √55

gud luck

Answer:

if you want you can keep simplifying

Step-by-step explanation:

Step-by-step explanation:

\(x = - \frac{33}{8} \)

not sure about that

Answer:

-8

Step-by-step explanation:

m∠3 + m∠5 = 180 (interior angles are supplementary)

-4x + 5 + (-13x + 39) = 180

-4x + 5 -13x +39 = 180

-17x = 180 - 5 - 39

-17x = 136

x = 136/(-17) = -8

Answer:

degree 3  zeros -1 and 1

Step-by-step explanation:

This is a third degree polynomial

f(x)=(x-1)^2(x+1)

It has an x^2 from the first term and an x from the second term for x^3

The zeros are x-1 =0  which means x=1

x+1 = 0  x=-1

Answer:

Step-by-step explanation:

(x-1)²(x+1) = x³-2x²+x+x²-2x+1

                 = x³-x²-x+1

                 = x²(x-1)-x+1

                 = x²(x-1)-(x-1)

                 = (x²-1) (x-1)

She can select one freshman and one sophomore in 72 ways.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is Phyllis who wants to select one freshman and one sophomore to attend a conference. She teaches 8 freshman and 9 sophomores

Total number of possible combinations are -

C[8,1] x C[9,1]

8!/(7! x 1!) x 9!/(8! x 1!)

8 x 9

72

Therefore, she can select one freshman and one sophomore in 72 ways.

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(f-1)'(1) = 1 / (2 - sin(2)).

Given that f(x)=2x + cos(2) is one-to-one, we can use the formula (f-1)'(x) = 1 /(f'( f-1)(x))) to find (f-1)'(1).

First, we need to find f'(x). The derivative of f(x) is f'(x) = 2 - sin(2).

Next, we need to find f-1(x). Since f(x) is one-to-one, we can switch x and y and solve for y to find the inverse function. So we have:

x = 2y + cos(2)

x - cos(2) = 2y

y = (x - cos(2))/2

Therefore, f-1(x) = (x - cos(2))/2.

Now we can plug in f'(x) and f-1(x) into the formula (f-1)'(x) = 1 /(f'( f-1)(x))) to find (f-1)'(1):

(f-1)'(1) = 1 / (f'( f-1)(1))

(f-1)'(1) = 1 / (2 - sin(2))

Therefore, (f-1)'(1) = 1 / (2 - sin(2)).

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The value of f(1) is 81

Recursive Function is a function that repeats or uses its own previous term to calculate subsequent terms and thus forms a sequence of terms

Given:

f(n + 1) = 1/3* f(n)

f(3) = 9

let n=0

f(0+1) = 1/3 * f(0)

f(1) = 1/3 * f(0)

Let n=1

f(1+1) = 1/3 * 1/3*f(0)

f(2) = 1/9 * f(0)

let n=2

f(2+1) = 1/3 * 1/9* f(0)

f(3) = 1/27 * f(0)

Also, f(3) =9

So,

9 = 1/27 * f(0)

f(0) = 27 * 9

f(0) = 243

Now,

f(1) = 1/3 * f(0)

f(1) = 1/3/ 243

f(1) = 81

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A subclass refers to a class that can inherit properties of another class called a superclass. The subclass will have all the characteristics and behavior of the superclass, and it can be modified to meet the unique needs of a specific class. Therefore, if a program uses two classes, airplane, and jumbojet, then the most likely subclass is the jumbojet.

Suppose that the airplane is the superclass that will have all the characteristics and behavior of an airplane. On the other hand, the jumbojet will be the subclass that inherits the features of an airplane. As the subclass, the jumbojet can be modified to have additional features unique to it.

The inheritance concept in programming ensures that there is efficient use of code. It makes it easy to reuse code for creating new classes. When using inheritance, developers avoid copying and pasting code, which can lead to errors and repetition.

Suppose that the airplane and jumbojet are classes representing vehicles in a flight system.

Airplane is the superclass representing all the aircraft, while jumbojet is the subclass representing a specific type of airplane, which is a large passenger aircraft. Therefore, the jumbojet, being a specific type of airplane, is the most likely subclass.

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The simplified expression is \(21x^2 - 25x - 28\) in the given case.

An expression in mathematics is a combination of numbers, symbols, and operators (such as +, -, x, ÷) that represents a mathematical phrase or idea. Expressions can be simple or complex, and they can contain variables, constants, and functions.

"Expression" generally refers to a combination of numbers, symbols, and/or operations that represents a mathematical, logical, or linguistic relationship or concept. The meaning of an expression depends on the context in which it is used, as well as the specific definitions and rules that apply to the symbols and operations involved. For example, in the expression "2 + 3", the plus sign represents addition and the meaning of the expression is "the sum of 2 and 3", which is equal to 5.

To simplify the expression, first distribute the -3x and (3x + 4) terms:

\(-3x(4 - 5x) + (3x + 4)(2x - 7) = -12x + 15x^2 + (6x^2 - 21x + 8x - 28)\)

Next, combine like terms:

\(-12x + 15x^2 + (6x^2 - 21x + 8x - 28) = 21x^2 - 25x - 28\)

Therefore, the simplified expression is \(21x^2 - 25x - 28.\)

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Answer:

Step-by-step explanation:

Use Pythagorean theorem to find the length of the square.

Length of the square = a

a² +a² = diagonal²

2a² = 12²

2a² = 144

a² = 144 ÷ 2

a² = 72

\(a =\sqrt{72}\\\\ = \sqrt{2*2*2*3*3}\\\\ = 2*3\sqrt{2}\\\\a = 6\sqrt{2}\\\\\\\\Perimeter= 4a\\\\ = 4*6\sqrt{2}\\\\= 24\sqrt{2} cm\)

The line integral ∫[C] (Pdx + Qdy) over the given curve C consisting of the arc of the parabola y = x² from (0,0) to (1, 1), and the line segment from (1,1) to (0,1) is equal to 2/5.

What is integral?

The value obtained after integrating or adding the terms of a function that is divided into an infinite number of terms is generally referred to as an integral value.

To evaluate the line integral using Green's theorem, we need to find a vector field F = (P, Q) such that ∇ × F = Qₓ - Pᵧ, where Qₓ represents the partial derivative of Q with respect to x, and Pᵧ represents the partial derivative of P with respect to y.

Let's consider F = (P, Q) = (x²y², xy).

Now, let's calculate the partial derivatives:

Qₓ = ∂Q/∂x = ∂(xy)/∂x = y

Pᵧ = ∂P/∂y = ∂(x²y²)/∂y = 2x²y

The curl of F is given by ∇ × F = Qₓ - Pᵧ = y - 2x²y = (1 - 2x²)y.

Now, let's find the line integral using Green's theorem:

∫[C] (Pdx + Qdy) = ∫∫[R] (1 - 2x²)y dA,

where [R] represents the region enclosed by the curve C.

To evaluate the line integral, we need to parameterize the curve C.

The arc of the parabola y = x² from (0, 0) to (1, 1) can be parameterized as r(t) = (t, t²) for t ∈ [0, 1].

The line segment from (1, 1) to (0, 1) can be parameterized as r(t) = (1 - t, 1) for t ∈ [0, 1].

Using these parameterizations, the region R is bounded by the curves r(t) = (t, t²) and r(t) = (1 - t, 1).

Now, let's calculate the line integral:

∫∫[R] (1 - 2x²)y dA = ∫[0,1] ∫[t²,1] (1 - 2t²)y dy dx + ∫[0,1] ∫[0,t²] (1 - 2t²)y dy dx.

Integrating with respect to y first:

∫[0,1] [(1 - 2t²)(1 - t²) - (1 - 2t²)t²] dt.

Simplifying:

∫[0,1] [1 - 3t² + 2t⁴] dt.

Integrating with respect to t:

[t - t³ + (2/5)t⁵]_[0,1] = 1 - 1 + (2/5) = 2/5.

Therefore, the line integral ∫[C] (Pdx + Qdy) over the given curve C consisting of the arc of the parabola y = x² from (0,0) to (1,1), and the line segment from (1,1) to (0,1) is equal to 2/5.

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We would randomly select 37 individuals from the population and calculate their mean, which would provide an estimate of the population mean with a margin of error of 3 at a 90% level of confidence.

To calculate the sample size needed to estimate the population mean with a margin of error of 3 and a 90% level of confidence, we can use the formula:
n = [(zα/2 * σ) / E]^2

Where:
n = sample size
zα/2 = z-value for the desired level of confidence (90% in this case) and is found using a z-table or calculator, which gives a value of 1.645
σ = standard deviation of the population (11 in this case)
E = margin of error (3 in this case)

Substituting the values into the formula, we get:

n = [(1.645 * 11) / 3]^2
n = (18.095 / 3)^2
n = 6.031^2
n ≈ 36.373

Rounding up, we need a sample size of at least 37 to estimate the population mean with a margin of error of 3 and a 90% level of confidence, assuming the population standard deviation is 11.

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A person who placed a $5 bet on a horse with 11 to 2 odds and that horse won the Preakness race would win $27.50 in addition to having their $5 wager returned.

when odds are expressed in a ratio such as 11 to 2, it means that for every 11 chances the horse will lose, there are 2 chances it will win. This can also be expressed as a probability of 2/13 (2 chances out of a total of 13 possible outcomes).

To calculate the potential payout, you simply multiply the amount of the bet by the odds ratio and then add the original bet back in. In this case, $5 multiplied by 11/2 equals $27.50, which is the amount the person would win if the horse they bet on won the race.

understanding odds and how to calculate potential payouts can help individuals make informed bets and potentially win money at horse races and other betting events.

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Answer:

A 26

Step-by-step explanation:

4(x - y) + 2                     x = 7 and y = 1

4(7 - 1) + 2

= 4(6) + 2

= 24 + 2

= 26

So, the answer is A 26

Answer:

Step-by-step explanation:

lisa is 26 because 13+26=36

Answer:

  y +3 = 5(x +2)

Step-by-step explanation:

You want the equation of a line with slope 5 through the point (-2, -3).

The point-slope form of the equation for a line is ...

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

  y +3 = 5(x +2) . . . . . . line with slope 5 through point (-2, -3)

__

Additional comment

This can also be written as ...

  y = 5x +7 . . . . . . . . . subtract 3 and simplify

<95141404393>

Based on both the p-value method and the critical value method, we fail to reject the null hypothesis and cannot infer that the two groups differ in the mean number of pictures printed.

To determine if the two groups (digital camera owners and standard camera owners) differ in the mean number of pictures printed, we can conduct a hypothesis test using both the p-value method and the critical value method.

Let's define our hypotheses:

Null Hypothesis (\(H_0\)): The mean number of pictures printed is the same for both groups.

Alternative Hypothesis (\(H_1\)): The mean number of pictures printed differs between the two groups.

We'll use a significance level of 0.05 (5%).

First, let's calculate the test statistic for the two-sample t-test using the provided summary statistics:

Digital:

Mean = 18.25

Standard Deviation = 6.5

Sample Size = 8

Standard:

Mean = 16.5

Standard Deviation = 19.2

Sample Size = 8

Using the formula for the two-sample t-test, the test statistic (t) is given by:

\(t = (mean_1 - mean_2) / \sqrt{(s_1^2/n_1) + (s_2^2/n_2)}\)

Substituting the values, we have:

\(t = (18.25 - 16.5) / \sqrt{(6.5^2/8) + (19.2^2/8)}\)

t ≈ 0.75

Now, let's perform the hypothesis test using both methods:

1) P-value Method:

Using the t-distribution with \((n_1 + n_2 - 2)\) degrees of freedom, we can calculate the p-value associated with the test statistic.

The p-value is the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true.

Using a t-table or statistical software, we find that the p-value corresponding to t ≈ 0.75 is approximately 0.47.

Since the p-value (0.47) is greater than the significance level (0.05), we fail to reject the null hypothesis. There is not enough evidence to conclude that the mean number of pictures printed differs between the two groups.

2) Critical Value Method:

Using the t-distribution with \((n_1 + n_2 - 2)\) degrees of freedom and a significance level of 0.05, we can find the critical value.

The critical value is the value beyond which we would reject the null hypothesis.

For a two-tailed test at a 5% significance level and 14 degrees of freedom (8 + 8 - 2), the critical value is approximately ±2.145.

Since the test statistic (0.75) does not exceed the critical value (±2.145), we fail to reject the null hypothesis. There is not enough evidence to conclude that the mean number of pictures printed differs between the two groups.

In conclusion, based on both the p-value method and the critical value method, we do not have sufficient evidence to infer that the two groups differ in the mean number of pictures printed.

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Answer:

\(x + 0.05x = 15\), solution is $14.29

Step-by-step explanation:

We can create an equation for this scenario to try and solve it.

Assuming the cost of the CD is x, it’s sale tax will be 0.05x (as that is 5% of x, 0.05.)

We can write the equation in two ways:

\(x + 0.05x = 15\) or \(1.05x = 15\).

Assuming we take the second one (easier to work with), we can divide both sides by 1.05. The equation simplifies to x = 14.289... which rounds to x = 14.29.

Therefore, the equation is \(x + 0.05x = 15\) and the solution is $14.29.

Hope this helped!

Answer:

x + 0.05x = 15; x = $14.29

Step-by-step explanation: