11. Separate the number 39 into two parts
so that the first number is 5 more than
the second number. What are the
numbers?

Answer:

X = 4√3

Step-by-step explanation:

Using tangent-secant theorem

So,

X² = (4)(4+8)

X² = (4)(12)

X² = (48)

Taking sqrt on both sides

X = 4√3

Given an LTI system that has an output y = 2te^-ul for the input x(t) = -(t). Here, e^-ul is the decay constant and is a real positive constant. The impulse response of the system can be found by considering the impulse input x(t) = δ(t).

The output of the system with an impulse input is given by y(t) = h(t), where h(t) is the impulse response of the system.We have,x(t) = -(t)..........(1)Applying derivative on both sides of the above equation, we get,y(t) = 2te^-ul, Applying derivative on both sides of the above equation, we get,

Plot of frequency response and Impulse response of the system Hence, the plot of frequency response and the impulse response of the LTI system is shown in the figure below:, the frequency response is given by H(jω) = (2/(-jω + ul)^2) where ω is the angular frequency. The impulse response of the system is given by h(t) = (2/ul^2)t.e^-ul.

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If we fix x = 0 and z = 0 only y coordinate can change. So triple (0, y, 0) can only represent a point in y axis.

What do you mean by a plane?

In geometry, a plane is a surface made up of all the lines that are parallel to one another and connect any two locations on it. It is, in other words, a level or flat surface.

                          A plane is defined uniquely through any of the following in a Euclidean space of any number of dimensions: with the aid of three non-collinear points.

For the triple  (x,y,z ) to represent the point on the y - axis .

    x must be 0    y must be a real number

  and z must b 0

For the triple  (x,y,z ) to represent the point on the y - axis .

    x must be 0    y must be 0

  and z must be  a real number

For the triple  (x,y,z ) to represent the point on the y - axis .

    x must be real number     y must be 0

  and z must be  a real number

For the triple  (x,y,z ) to represent the point on the y - axis .

    x must be 0     y must be real number

  and z must be  a real number

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Given:

In quadrilateral EFGH, \(FG\parallel EH,\angleE\cong \angle H,EF=4n-4,FG=3n+3, GH=2n+6\)

To find:

The length of segment GH.

Solution:

Draw a figure according to the given information as shown below.

In quadrilateral EFGH, \(FG\parallel EH,\angleE\cong \angle H\), it means the quadrilateral EFGH is an isosceles quadrilateral because base angles are equal.

Now, quadrilateral EFGH is an isosceles quadrilateral, so the sides EF and GH are equal.

\(EF=GH\)

\(4n-4=2n+6\)

\(4n-2n=4+6\)

\(2n=10\)

Divide both sides by 2.

\(n=\dfrac{10}{2}\)

\(n=5\)

Now,

\(GH=2n+6\)

\(GH=2(5)+6\)

\(GH=10+6\)

\(GH=16\)

Therefore, the correct option is C.

Answer:

the answer is C

Step-by-step explanation:

:]

Answer:

Slides

Step-by-step explanation:

Answer:

slides

Step-by-step explanation:

because sandals are better

No, there isn't any statistical proof because, according to the simulation, Audrey would sell at least 7 out of the 30 chosen tickets roughly 13.8% of the time.

What exactly is statistical proof?

A type of explanation known as statistical evidence is one that is based on information that has been gathered and then assessed using a mathematical model.

Based on the information provided, the students created the following simulation:

Choose 88 red chips and the rest 600 blue chips.

30 chips are chosen at random, with no replacements.

When choosing the 30 chips, keep track of and record the amount of red chips.

Therefore, we may say that there is no statistical proof that the occurrence happened by chance alone at = 0.05.

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The most likely reason for the boolean expression (Math.pow(x, 0.5) == Math.sqrt(x)) returning false in a student's program is due to floating-point rounding errors.

This occurs because floating-point numbers are represented using a fixed number of bits in the computer's memory, which can lead to inaccuracies in certain calculations. In particular, the computation of square roots and other transcendental functions involves a series of approximations that can amplify these errors.

While the mathematical equivalence between x^(1/2) and sqrt(x) holds true, the actual computed values of these expressions may differ slightly due to rounding errors. Therefore, when comparing these two expressions using the "==" operator, the result may be false even though they are mathematically equivalent.

To avoid this issue, it is recommended to use a tolerance or an epsilon value when comparing floating-point values for equality. This allows for a small margin of error due to rounding and other numerical issues, ensuring that the comparison is accurate even in the presence of small numerical discrepancies.

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M is the midpoint of segment LN, LM = LN / 2, N is the midpoint of segment MP, and NP = MP / 2. Since LN and MP are segments connecting the same points, we can equate their lengths: LN = MP. Substituting LN = MP in the equations from steps 1 and 2, we get LM = MP / 2 and NP = MP / 2. Therefore, using the midpoint property, LM = NP, proves that the lengths are equal.

Hence, we have proved that LM = NP using the given information about M being the midpoint of LN and N being the midpoint of MP.

Note: The complete question is:

Given: M is a midpoint of segment LN and N is a midpoint of segment MP.

Prove LM=NP.

The figure has been attached.

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We are given that there are 800 students in total, with 226 students in sixth grade and 275 students in seventh grade.  So, there are 299 eighth graders in the school.

We are given that there are 800 students in total, with 226 students in sixth grade and 275 students in seventh grade. To find the number of eighth graders, we can use the fact that the total number of students is the sum of the number of students in each grade level:

Total number of students = Number of sixth graders + Number of seventh graders + Number of eighth graders

Substituting the given values, we get:

800 = 226 + 275 + Number of eighth graders

Simplifying and solving for the number of eighth graders, we get:

800 = 501 + Number of eighth graders

Number of eighth graders = 800 - 501

Number of eighth graders = 299

Therefore, there are 299 eighth graders in the school.

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Answer:

A) 25

Step-by-step explanation:

You use x= -b/2a in order to get your maximum so x= -10/ 2(-5) and you get x=1. You plug 1 into the function as h(1)=-5(1)^2 + 10(1)+ 20 which gets you 25

A function assigns the values. The time it will take for the rocket in the air before it reached its highest height is 1 second.

A function assigns the value of each element of one set to the other specific element of another set.

A.) The maximum height of the rocket can be found by differentiating the function to get the maximum value of the height funciton.

dh/dt = -5(2t) + 10

Substitute the differentiated value with 0,

0 = -10t + 10

-10t = -10

t = 1

Therefore, the maximum height will be attained when the time is 1 second.

Now, substitute the value of t as 1 second to get the maximum height,

h(t) =- 5t²+ 10t+ 20

h(1) =- 5(1)² + 10(1)+ 20

h(1) = -5 + 10 +20

h = 25 yards

Hence, the maximum height of the rocket is 25 yards.

B.) The time it will take for the rocket in the air before it reached its highest height is 1 second.

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Based on the information provided, the plausibility of assumptions can be determined by analyzing the normal probability plot and the nature of the data.

In the given options, the first option states that the normal probability plot is reasonably straight, indicating that it is not plausible that time differences follow a normal distribution and the paired t-interval is not valid. This means that the assumption of normality is not met and the paired t-interval may not be appropriate for analysis.

The second option states that the normal probability plot is reasonably straight, suggesting that it is plausible that time differences follow a normal distribution and the paired t-interval is valid. This implies that the assumption of normality is reasonable and the paired t-interval can be used for analysis.

The third option states that the normal probability plot is not reasonably straight, indicating that it is plausible that time differences follow a normal distribution and the paired t-interval is valid. This suggests that the assumption of normality is reasonable and the paired t-interval can be used for analysis.

The fourth option states that the normal probability plot is not reasonably straight, suggesting that it is not plausible that time differences follow a normal distribution and the paired t-interval is not valid. This means that the assumption of normality is not met and the paired t-interval may not be appropriate for analysis.

In summary, the correct option based on the given information is: "The normal probability plot is reasonably straight, so it's plausible that time differences follow a normal distribution and the paired t-interval is valid."

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43 posts will be required to erect the wire fence along one side of the paddock.

If the straight section of fence is 126 meters long and the posts are to be placed 3 meters apart, we can start by calculating the number of intervals between the posts.

The length of each interval between the posts is 3 meters, so the number of intervals is given by:

Number of intervals = Length of fence / Length of interval

Number of intervals = 126 m / 3 m

Number of intervals = 42

However, we need to add one more post at the end of the fence to complete it. Therefore, the total number of posts required will be 42 + 1 = 43.

So, 43 posts will be required to erect the wire fence along one side of the paddock.

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The length of each piece of rope is 10m.

The first step is to determine the length of the rope before it was cut. In order to determine the length of the rope, multiply the length of the stick by the number of times the rope is as long as the stick.

Multiplication is the process that is used to determine the product of two or more numbers. The sign that is used to represent multiplication is x.

Length of the rope = length of the stick x 4

4 x 5 = 20m

lf the length of the rope is divided into two prices, divide the length of the rope by 2. Division is the mathematical operation that is used to determine the quotient of two or more numbers. It entails grouping a number into equal groups using another number.

Length of each piece = Length of the rope / 2

20m / 2 = 10m

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The area of the actual park is approximately 149,094 square yards.

To find the area of the actual park in square yards, we need to convert the given measurements to the same units.

Given:

Scale drawing width = 12 inches

Scale drawing length = 5 inches

Actual park length = 250 yards

First, let's convert the scale drawing measurements from inches to yards to match the units of the actual park length.

1 yard = 36 inches

Scale drawing width in yards = 12 inches / 36 inches per yard = 1/3 yard

Scale drawing length in yards = 5 inches / 36 inches per yard ≈ 0.1389 yards

Now we have the dimensions of the scale drawing in yards. We can use these dimensions to find the area of the scale drawing.

Scale drawing area = Scale drawing length * Scale drawing width

                  ≈ 0.1389 yards * 1/3 yard

                  ≈ 0.0463 square yards

Since the scale drawing represents a proportional relationship to the actual park, we can use this scale to find the area of the actual park.

Scale factor = Actual length / Scale drawing length

            = 250 yards / 0.1389 yards

            ≈ 1800

The scale factor represents the ratio of the actual length to the scale drawing length. We can use this scale factor to find the area of the actual park.

Area of actual park = Scale drawing area * Scale factor^2

                   = 0.0463 square yards * (1800)^2

                   = 149,094 square yards

Therefore, the area of the actual park is approximately 149,094 square yards.

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The evaluated integral is - ln|2 - sin(x)| + C, where C represents the constant of integration.

To evaluate the integral:

∫ cos(x) / (2 - sin(x)) dx

We can use a substitution to simplify the integral. Let's substitute u = 2 - sin(x), then

du = -cos(x) dx.

Rearranging the substitution, we have dx = -du / cos(x).

Now, we can rewrite the integral in terms of u:

∫ (-du / cos(x)) / u

Simplifying further, we get:

-∫ du / (u * cos(x))

Applying the integral, we have:

ln|u| + C

Substituting back u = 2 - sin(x), we get:

ln|2 - sin(x)| + C

Therefore, the evaluated integral is - ln|2 - sin(x)| + C, where C represents the constant of integration.

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The Gibbs-Duhem equation relates the activity coefficients of the individual components in a mixture. It states that the activity coefficients are not independent of each other but are related by a differential equation.

In the case of a binary mixture (chemical A and chemical B), the Gibbs-Duhem relation can be written as:

x1 * (∂x1/∂lnγ1)T,P = x2 * (∂x2/∂lnγ2)T,P

Here, x1 and x2 represent the mole fractions of chemical A and chemical B, respectively. The activity coefficients for chemical A and chemical B are denoted as γ1 and γ2, respectively.

The equation shows that the change in mole fraction of one component (x1) with respect to the change in the logarithm of its activity coefficient (lnγ1) is proportional to the change in mole fraction of the other component (x2) with respect to the change in the logarithm of its activity coefficient (lnγ2).

This relationship helps us understand how changes in the activity coefficients of the components affect each other in a binary mixture. By studying this relationship, we can gain insights into the behavior of the mixture and make predictions about its properties.

For example, let's consider a mixture of ethanol (chemical A) and water (chemical B). If the activity coefficient of ethanol (γ1) decreases, the Gibbs-Duhem equation tells us that the mole fraction of ethanol (x1) will also decrease. Similarly, if the activity coefficient of water (γ2) increases, the mole fraction of water (x2) will increase.

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To find the volume of all pairs of vertices (s, t) in a directed graph G using an efficient Dijkstra-like algorithm, we can adapt the Dijkstra's algorithm with some modifications.

Here is the algorithm:

Initialize all vertices' volumes as negative infinity, except for the starting vertex s, which has a volume of 0.

vol(v) = -∞ for all v in G.V

vol(s) = 0

Create a priority queue Q to store vertices based on their volumes (minimum volume first). Initially, insert vertex s into Q.

While Q is not empty, do the following:

a. Extract the vertex u with the minimum volume from Q.

b. For each neighbor v of u:

Calculate the capacity of the path from s to v via u: cap(s, v) = min(cap(s, u), w(u, v)), where w(u, v) is the weight of the arc from u to v.

If cap(s, v) > vol(v), update vol(v) with cap(s, v) and insert v into Q if it's not already present.

After the algorithm finishes, the volumes vol(s, t) will represent the maximum capacity of paths from s to t for all vertices t in G.V{s}.

This modified Dijkstra-like algorithm finds the maximum capacity (volume) from s to all other vertices by considering all possible paths and updating the volume as we encounter smaller capacities along the way. By using a priority queue to extract the minimum volume vertex efficiently, the algorithm can run in O((|V| + |E|) log |V|) time complexity, where |V| is the number of vertices and |E| is the number of edges in the graph.

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Answer:

x(x−9)

Step-by-step explanation:

x2−9x

=x(x−9)

We are given the following numbers

We are asked to arrange these numbers from least to greatest.

As you can see, the numbers are in different forms (decimal, fraction)

So, first we need to convert them into a single form then we can compare them

Let us convert all the numbers into decimals

So the order from least to greatest is

6.67, 7.111, 7.116, 7.15

Now write the numbers in their original form

Answer:

C

Step-by-step explanation:

Looking at the graph, we can see that the graph crosses the y-axis at y=2.

Hence, our y-intercept should be 2.

Therefore, we can eliminate A.

We also notice that the graph is downwards sloping.

Therefore, our slope is negative.

So, we can eliminate B.

Therefore, our answer must be C.

Answer:

C

Step-by-step explanation:

I have the same question and my answer was right

The volume of a sphere with a radius of 7 cm (or diameter of 12 cm) is 904.32 cubic centimeters.

To find the volume of a sphere with a radius of 7 cm, we can use the formula:

V = (4/3) * π * r^3

where V represents the volume and r represents the radius. However, you mentioned that the diameter of the sphere is 12 cm, so we need to adjust the radius accordingly.

The diameter of a sphere is twice the radius, so the radius of this sphere is 12 cm / 2 = 6 cm. Now we can calculate the volume using the formula:

V = (4/3) * π * (6 cm)^3

V = (4/3) * 3.14 * (6 cm)^3

V = (4/3) * 3.14 * 216 cm^3

V = 904.32 cm^3

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The correct answer to your question is: the p-value of a significance test is the probability, assuming the null hypothesis is true, that the sample would produce a result at least as extreme (meaning, as far away from expected) as was actually observed.

This means that the p-value represents the strength of evidence against the null hypothesis, with lower values indicating stronger evidence against the null hypothesis. It is important to note that the p-value does not tell us the probability that the null hypothesis is true or false, but rather the likelihood of observing a result as extreme as the one observed in the sample data, assuming the null hypothesis is true.
The p-value of a significance test is: the probability, assuming the null hypothesis is true, that the sample would produce a result at least as extreme (meaning, as far away from expected) as was actually observed.

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Answer:

10+√3=4x²

Step-by-step explanation:

Answer:

{12}

Step-by-step explanation:

isolate the radical expression

\(\sqrt{3x} = x-6\)

raise both sides to the index of the radical in this case 2

\((\sqrt{3x} )^{2} = (x-6)^2\)

\(3x = (x-6)^2\)

foil the right hand side or multiply (x-6)(x-6)

\(3x = x^{2} -6x-6x+36\)

subtract 3x from both sides and combine like terms

\(0=x^{2} -15x+36\)

factor

\(0=(x-12)(x-3)\)

set each factor equal to zero and solve for x

x - 12 = 0 and x - 3 = 0

     x = 12 and     x  = 3

Check each answer by plugging them individually into the original equation if the come out true they are a solution.

Check :

\(\sqrt{3(12)}+10=12+4\\\sqrt{36}+10 = 8\\6+10 = 16\\16=16\)           \(\sqrt{3(3)}+10=3+4\\\sqrt{9}+10=7\\3+10=7\\13\neq 7\)

So the only solution is 12.

The probability mass function of x is given as:P(x)={0.24 if x=0,0.14 if x=1,0.14 if x=2,0 otherwise}

Let the probability that device A functions correctly be denoted by pA and that device B functions correctly by pB.

We have, $p_A=0.3$ and $p_B=0.8$.

When the devices A and B fail independently, then we will get x failed devices.

Let's find the probability mass function of x.

P(x=0) represents the probability of none of the devices fail i.e. they all function correctly.

P(x=0)

=P(A works and B works)

=P(A works) * P(B works)

= 0.3*0.8

=0.24P(x=1) represents the probability of one of the devices failing while the other functions correctly.

There are two ways in which this could happen - either A fails while B works or B fails while A works.

P(x=1)=P(A fails and B works)+P(B fails and A works)

=P(A fails)*P(B works) + P(B fails)*P(A works)

= (1-P(A works)) * P(B works) + (1-P(B works)) * P(A works)

= (1-0.3)*0.8 + (1-0.8)*0.3

=0.14P(x=2) represents the probability of both the devices failing.

P(x=2)=P(A fails and B fails)

=P(A fails) * P(B fails)

= (1-P(A works))*(1-P(B works))

= 0.7*0.2=0.14

Therefore, the probability mass function of x is given as: P(x)={0.24 if x=0,0.14 if x=1,0.14 if x=2,0 otherwise}

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Using Euler's approach, the error in the estimated value of y(0.25) is approximately 0.09375 or 0.094.

Given the ODE and initial condition as:

dy/dx = (1+2x)√y, y(0) = 1

Using Euler's method, we have to evaluate the value of y(0.25) with a step size of h = 0.25.

Step 1: Calculation of f(x,y)f(x, y) = dy/dx = (1+2x)√y

Step 2: Calculation of y(0.25)

Using Euler's method, we can approximate the value of y at x=0.25 as follows:y1 = y0 + hf(x0, y0)where y0 = 1, x0 = 0 and h = 0.25f(x0, y0) = f(0, 1) = (1+2(0))√1 = 1y1 = 1 + 0.25(1) = 1.25

Therefore, y(0.25) = 1.25.

Step 3: Calculation of the exact value of y(0.25)We can find the exact value of y(0.25) by solving the ODE:

dy/dx = (1+2x)√ydy/√y = (1+2x) dxIntegrating both sides:

∫dy/√y = ∫(1+2x)dx2√y = x^2 + 2x + C, where C is athe constant of integration Since y(0) = 1,

we can solve for C as follows: 2√1 = 0^2 + 2(0) + C => C = 2

Therefore, the exact solution of the ODE is given by:2√y = x^2 + 2x + 2Solving for y, we get:y = [(x^2 + 2x + 2)/2]^2

The exact value of y(0.25) is given by:y(0.25) = [(0.25^2 + 2(0.25) + 2)/2]^2= (2.3125/2)^2= 1.15625

Step 4: Calculation of the errorError = |Exact value - Approximate value|Error = |1.15625 - 1.25| = 0.09375

Therefore, the error in the approximate value of y(0.25) using Euler's method is 0.09375 or 0.094 (approx).

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The most the salon would be willing to pay that groomer is $25×4 = $100.

The unitary method is a technique that determines the worth of a single unit from value of multiple units, as well as the quality of multiple units from value of a single unit.

Some key features regarding the unitary method are-

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Answer:

30t + 6b

Explanation:

6 x 5t = 30t

6 x 1b = 6b

There are 5 * 5 = 25 possible arrangements. Some examples include aa, bb, cc, dd, ee, ab, ac, ad, ae, ba, bb, bc, bd, be, and so on.

a. Choosing 2 objects at a time without repetition and with order counting: The ordered arrangements of 5 objects (a, b, c, d, e) taken 2 at a time without repetition and with order counting are: ab, ac, ad, ae,

ba, bc, bd, be,

ca, cb, cd, ce,

da, db, dc, de,

ea, eb, ec, ed.

b. Choosing 2 objects at a time without repetition and without order counting: The unordered arrangements of 5 objects (a, b, c, d, e) taken 2 at a time without repetition and without order counting are: ab, ac, ad, ae,

bc, bd, be,

cd, ce,

de.

c.Choosing 2 objects at a time with repetition: In this case, we can choose any of the 5 objects for the first position, and any of the 5 objects (including repetition) for the second position.

Therefore, there are 5 * 5 = 25 possible arrangements. Some examples include aa, bb, cc, dd, ee, ab, ac, ad, ae, ba, bb, bc, bd, be, and so on.

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The y-intercept of the equation of line  y = (7/9)x + 2/3 is 2/3.

The slope-intercept form is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the equation of line in the question;

y = 7/9 x + 2/3

Simplify the right hand side

y = (7/9)x + 2/3

Using the slope-intercept form, the y-intercept is 2/3.

Therefore, the y-intercept in point form is (0,2/3).

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Answer:

( 55 x .10 ) x .07