help me out on this

For the first differential equation, the solution is: \(\[x(t) = \frac{52}{125}e^{5t} + \frac{78}{125}e^{-5t} -\frac{1}{25}t^2 - \frac{1}{25}t\]\) and for the second second differential equation solution is: \(\[x(t) = \frac{25}{21}e^{5t} + \frac{8}{21}e^{-5t} - \frac{1}{7}e^{2t}\]\)

Equation 1:

\(\[\begin{aligned}x'' - 25x &= t^2 + t, \quad x'(0) = 1, \quad x(0) = 2 \\\end{aligned}\]\)

Step 1: Homogeneous Solution (Yh)

The homogeneous equation is given by:

\(\[x'' - 25x = 0\]\)

The characteristic equation is:

\(\[r^2 - 25 = 0\]\)

Solving for the roots:

\(\[r^2 = 25 \implies r_1 = 5, \quad r_2 = -5\]\)

The homogeneous solution is:

\(\[Yh = c_1e^{5t} + c_2e^{-5t}\]\)

Step 2: Particular Solution (Yp)

Since the right-hand side contains polynomials, we make an educated guess for the particular solution. The form of the particular solution is the same as the right-hand side, but with undetermined coefficients:

\(\[Yp = At^2 + Bt\]\)

Taking derivatives:

\(\[Yp' = 2At + B, \quad Yp'' = 2A\]\)

Substituting these derivatives back into the original differential equation:

\(\[2A - 25(At^2 + Bt) = t^2 + t\]\)

Equating coefficients of like terms:

\(\[-25At^2 = t^2 \implies A = -\frac{1}{25}, \quad -25Bt = t \implies B = -\frac{1}{25}\]\)

The particular solution is:

\(\[Yp = -\frac{1}{25}t^2 - \frac{1}{25}t\]\)

Step 3: Complete Solution

The complete solution is the sum of the homogeneous and particular solutions:

\(\[Y = Yh + Yp = c_1e^{5t} + c_2e^{-5t} -\frac{1}{25}t^2 - \frac{1}{25}t\]\)

Step 4: Applying Initial Conditions

Using the given initial conditions:

\(\[x'(0) = 1 \implies Y'(0) = 1 \implies 5c_1 - 5c_2 - \frac{1}{25} = 1\]\[x(0) = 2 \implies Y(0) = 2 \implies c_1 + c_2 = 2\]\)

Solving these equations, we find:

\(\[c_1 = \frac{52}{125}, \quad c_2 = \frac{78}{125}\]\)

Therefore, the final solution to Equation 1 is:

\(\[x(t) = \frac{52}{125}e^{5t} + \frac{78}{125}e^{-5t} -\frac{1}{25}t^2 - \frac{1}{25}t\]\)

Now, let's move on to the second equation:

Equation 2:

\(\[\begin{aligned}x'' - 25x &= 3e^{2t}, \quad x'(0) = 1, \quad x(0) = 2 \\\end{aligned}\]\)

Step 1: Homogeneous Solution (Yh)

The homogeneous equation is given by:

\(\[x'' - 25x = 0\]\)

The characteristic equation is:

\(\[r^2 - 25 = 0\]\)

Solving for the roots:

\(\[r^2 = 25 \implies r_1 = 5, \quad r_2 = -5\]\)

The homogeneous solution is:

\(\[Yh = c_1e^{5t} + c_2e^{-5t}\]\)

Step 2: Particular Solution (Yp)

Since the right-hand side contains an exponential function, we make an educated guess for the particular solution. The form of the particular solution is the same as the right-hand side, but with undetermined coefficients:

\(\[Yp = Ae^{2t}\]\)

Taking derivatives:

\(\[Yp' = 2Ae^{2t}, \quad Yp'' = 4Ae^{2t}\]\)

Substituting these derivatives back into the original differential equation:

\(\[4Ae^{2t} - 25Ae^{2t} = 3e^{2t}\]\)

Equating coefficients of like terms:

\(\[-21Ae^{2t} = 3e^{2t} \implies A = -\frac{3}{21} = -\frac{1}{7}\]\)

The particular solution is:

\(\[Yp = -\frac{1}{7}e^{2t}\]\)

Step 3: Complete Solution

The complete solution is the sum of the homogeneous and particular solutions:

\(\[Y = Yh + Yp = c_1e^{5t} + c_2e^{-5t} - \frac{1}{7}e^{2t}\]\)

Step 4: Applying Initial Conditions

Using the given initial conditions:

\(\[x'(0) = 1 \implies Y'(0) = 1 \implies 5c_1 - 5c_2 - \frac{2}{7} = 1\]\[x(0) = 2 \implies Y(0) = 2 \implies c_1 + c_2 - \frac{1}{7} = 2\]\)

Solving these equations, we find:

\(\[c_1 = \frac{25}{21}, \quad c_2 = \frac{8}{21}\]\)

Therefore, the final solution to Equation 2 is:

\(\[x(t) = \frac{25}{21}e^{5t} + \frac{8}{21}e^{-5t} - \frac{1}{7}e^{2t}\]\)

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Answer:

1, 6.27, 2, 10.92, 3, 7.76, 4, 1.464, 5, 7.084

Step-by-step explanation:

Answer:

11% of 57= 56.89

39% of 28= 27.61

8% of 97= 96.92

6% of 24.4= 24.34

77% of 9.2= 8.43

A lovely beach resort is Data Island. Since it first became a popular tourist destination more than 80 years ago, the earliest vacation homes have been constructed just a few steps from the beach. You are a real estate agent for a company that deals in vacation rentals and sales in the Data Islands. A report was recently presented to you by one of the interns on the data science team. The age of a house affects its price, according to the linear regression model they have ran. But this is absurd because newer homes ought to be more valuable.

1.  As the coefficient of Age is positive, so the older the house, the more price it is. Sig. (or p-value) = 0.000 which implies  that the co-efficient of Age is significant.

2.  This may be that the people who live there are reluctant to sell it, so they quote a higher price or the size of old houses are large or they may be located at prime location.

3.  We would ask new interns to consider other independent variables for the regression equation like size of house, location, etc.

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Answer:

-5, -3, -1

Step-by-step explanation:

Answer:

AB=2 ft

ED=4.5 ft

BD=9 ft

m∠ABC=105°

m∠BCD=105°

m∠ADC=75°

Step-by-step explanation:

Answer:

  C.  17 units

Step-by-step explanation:

You want the hypotenuse of a right triangle with legs 8 and 15.

The Pythagorean theorem tells you the relation between the sides of a right triangle is ...

  c² = a² +b² . . . . . . where c is the hypotenuse, and a, b are the legs

  c² = 8² +15² = 64 +225 = 289

  c = √289 = 17 . . . . units

The missing side length is 17 units.

__

Additional comment

A set of integers that satisfies the Pythagorean theorem is called a "Pythagorean triple." Perhaps the first one you run across is {3, 4, 5}. Other triples commonly seen are {5, 12, 13}, and {7, 24, 25}. This one, {8, 15, 17} also shows up in algebra and trig problems. It can be worthwhile to remember a few of these.

Their multiples are also seen. For example, {6, 8, 10} is the {3, 4, 5} triple times 2.

The length and width of the larger rectangle are 9cm and 6cm, respectively.

The area of the original rectangle is 7cm x 4cm = 28cm². Let x be the amount by which both the length and the width are increased. Then, the length of the larger rectangle is 7cm + x and the width is 4cm + x. The area of the larger rectangle is (7cm + x)(4cm + x) = 28cm² + 11x + x². Since the area of the larger rectangle is increased by 42cm², we can set up the equation:

(7cm + x)(4cm + x) - 28cm² = 42cm²

Expanding the left-hand side of the equation and simplifying, we get:

11x + x² = 70

Rearranging and solving for x, we get:

x² + 11x - 70 = 0

Factoring the quadratic equation, we get:

(x + 14)(x - 3) = 0

Since the width cannot be negative, the solution is x = 3cm. Therefore, the length of the larger rectangle is 7cm + 3cm = 9cm and the width is 4cm + 3cm = 6cm.

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Answer:

119 is the value of x when y = 7

Step-by-step explanation:

Since y varies inversely with x, we can use the following equation to model this:

y = k/x, where

Step 1:  Find k by plugging in values:

Before we can find the value of x when y = k, we'll first need to find k, the constant of proportionality.  We can find k by plugging in 49 for y and 17 for x:

Plugging in the values in the inverse variation equation gives us:

49 = k/17

Solve for k by multiplying both sides by 17:

(49 = k / 17) * 17

833 = k

Thus, the constant of proportionality (k) is 833.

Step 2:  Find x when y = k by plugging in 7 for y and 833 for k in the inverse variation equation:

Plugging in the values in the inverse variation gives us:

7 = 833/x

Multiplying both sides by x gives us:

(7 = 833/x) * x

7x = 833

Dividing both sides by 7 gives us:

(7x = 833) / 7

x = 119

Thus, 119 is the value of x when y = 7.

(a) A nonzero vector orthogonal to the plane through the points P, Q, and R is (9, -17, 35). (b) The area of triangle PQR is \(\sqrt\)(811) / 2.

(a) To determine a nonzero vector orthogonal to the plane through the points P, Q, and R, we can first find two vectors in the plane and then take their cross product. Taking vectors PQ and PR, we have:

PQ = Q - P = (5, 1, -2) - (-4, 0, 0) = (9, 1, -2)

PR = R - P = (6, 4, 1) - (-4, 0, 0) = (10, 4, 1)

Taking the cross product of PQ and PR, we have:

n = PQ x PR = (9, 1, -2) x (10, 4, 1)

Evaluating the cross product gives n = (9, -17, 35). Therefore, (9, -17, 35) is a nonzero vector orthogonal to the plane through points P, Q, and R.

(b) To determine the area of triangle PQR, we can use the magnitude of the cross product of vectors PQ and PR divided by 2. The magnitude of the cross product is given by:

|n| = \(\sqrt\)((9)^2 + (-17)^2 + (35)^2)

Evaluating the magnitude gives |n| = \(\sqrt\)(811).

The area of triangle PQR is then:

Area = |n| / 2 = \(\sqrt\)(811) / 2.

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Answer:

-9.300÷30

= -310

.................. ;)

Answer:

54 square millimeters

Step-by-step explanation:

Answer:

Is a surface area a volume? Because if so its 27. And if its just the flat surface then its 9.

Answer:

The five rational numbers between -3 and -2 are : - -13/6, -14/6, -15/6, -16/6, -17/6. so, the rational numbers between -2 & -3 are -13/6, -14/6, -15/6, -16/6, -17/6.

Step-by-step explanation:

if it helped uh please mark me a BRAINLIEST :)

\( \sf{\blue{«} \: \pink{ \large{ \underline{A\orange{N} \red{S} \green{W} \purple{E} \pink{{R}}}}}}\)

1. Difference: \(\displaystyle\sf (-2) - (-3) = -2 + 3 = 1\).

2. Interval: \(\displaystyle\sf \frac{1}{6}\).

3. Rational Numbers:

a. \(\displaystyle\sf -3 + \text{Interval} = -3 + \left(\frac{1}{6}\right) = -\frac{17}{6}\).

b. \(\displaystyle\sf -3 + 2 \times \text{Interval} = -3 + 2 \times \left(\frac{1}{6}\right) = -\frac{16}{6}\).

c. \(\displaystyle\sf -3 + 3 \times \text{Interval} = -3 + 3 \times \left(\frac{1}{6}\right) = -\frac{15}{6} = -\frac{5}{2}\).

d. \(\displaystyle\sf -3 + 4 \times \text{Interval} = -3 + 4 \times \left(\frac{1}{6}\right) = -\frac{14}{6} = -\frac{7}{3}\).

e. \(\displaystyle\sf -3 + 5 \times \text{Interval} = -3 + 5 \times \left(\frac{1}{6}\right) = -\frac{13}{6}\).

Therefore, the five rational numbers between -3 and -2 are:

\(\displaystyle\sf -\frac{17}{6}, -\frac{16}{6}, -\frac{5}{2}, -\frac{7}{3}, \text{ and } -\frac{13}{6}\).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The NFAs for a+ and (c*+d).(bc)* by adding appropriate transitions. (q21) becomes the accepting state, representing the completion of the regular expression.

To draw the NFA for the given regular expressions, let's break them down step by step.

i) a*(a+b)* + abc*

NFA for a*

First, let's create the NFA for the subexpression "a*":

    ┌───┐  a   ε

-->  │ q0 │─────►(q1)

    └───┘

q0 is the initial state, and (q1) is the accepting state. The transition from q0 to (q1) is labeled with "a", and there is also an ε-transition from q0 to (q1). This allows for zero or more occurrences of "a".

NFA for (a+b)*

Next, let's create the NFA for the subexpression "(a+b)*":

        a       b        ε

  ┌───────┐  ┌─────┐  ┌─────┐

  │       │  │     │  │     │

  │  q2   ├──► q3  ├──► q4  │

  │(start)│  │     │  │     │

  └───────┘  └─────┘  └─────┘

       │        │        │

       │   a    │   b    │ε

       ▼        ▼        ▼

    ┌─────┐  ┌─────┐  ┌─────┐

    │ q5  │  │ q6  │  │ q7  │

    │(a+b)│  │(a+b)│  │(a+b)│

    └─────┘  └─────┘  └─────┘

       │        │        │

       └─────►(q8)     (q9)

                 accepting

                 state

q2 is the initial state, q5 and q6 represent the subexpression (a+b). q3 and q4 are intermediary states to allow for looping within the subexpression. The transitions labeled with "a" and "b" connect q2 to q5 and q6, respectively. There are also ε-transitions from q2 to q3 and q6 to q4 to allow for zero or more occurrences of (a+b). Finally, q8 is an accepting state, as it represents the completion of the subexpression (a+b).

NFA for abc*

Now, let's create the NFA for the subexpression "abc*":

    ┌─────┐   a   ε

-->  │ q10 │─────►(q11)

    └─────┘

      │ │

      c │ε

      │ │

      ▼ ▼

    ┌─────┐

    │ q12 │

    │  c  │

    └─────┘

q10 is the initial state, and (q11) is the accepting state. There is a transition labeled with "a" from q10 to (q11), and an ε-transition from q10 to q12. From q12, there is a transition labeled with "c", forming a loop back to q12. This allows for zero or more occurrences of "c".

Combining subexpressions

Finally, let's combine the NFAs for the subexpressions a*(a+b)* and abc*:

          a   ε

  ┌────

───┐  ┌─────┐  ε

  │       │  │     │

  │  q0   ├──►(q1) ├──► (q2)

  │(start)│  │     │

  └───────┘  └─────┘

        │        │

        │   ε    │ε

        ▼        ▼

  ┌───────┐  ┌─────┐

  │       │  │     │

  │  q3   ├──► q4  │

  │       │  │     │

  └───────┘  └─────┘

   │        │

   │   ε    │ε

   ▼        ▼

┌─────┐  ┌─────┐

│ q5  │  │ q6  │

│(a+b)│  │(a+b)│

└─────┘  └─────┘

   │        │

   └─────►(q7)

           accepting

           state

Here, we have connected the NFAs for a*(a+b)* and abc* by adding ε-transitions. q2 becomes the accepting state, representing the completion of the regular expression.

ii) a+(c*+d).(bc)*

Step 1: NFA for a+

First, let's create the NFA for the subexpression "a+":

    ┌───┐  a

-->  │ q13 │────►(q14)

    └───┘

q13 is the initial state, and (q14) is the accepting state. The transition from q13 to (q14) is labeled with "a", allowing for one or more occurrences of "a".

NFA for (c*+d)

Next, let's create the NFA for the subexpression "(c*+d)":

        c      d

  ┌───────┐  ┌─────┐

  │       │  │     │

  │  q15  ├──► q16  │

  │(start)│  │     │

  └───────┘  └─────┘

       │        │

       │   c    │   d

       ▼        ▼

    ┌─────┐  ┌─────┐

    │ q17  │  │ q18  │

    │  c*  │  │  d   │

    └─────┘  └─────┘

       │        │

       └─────►(q19)

                 accepting

                 state

q15 is the initial state, q17 represents the subexpression c*, and q18 represents the subexpression d. The transitions labeled with "c" and "d" connect q15 to q17 and q15 to q18, respectively. Finally, q19 is an accepting state, representing the completion of the subexpression (c*+d).

NFA for (bc)*

Now, let's create the NFA for the subexpression "(bc)*":

    ┌─────┐   b   ε

-->  │ q20 │─────►(q21)

    └─────┘   │ │

      │  c    │ │ε

      │  │    ▼ ▼

      ▼  │

┌─────┐

    ┌─────┐ │ q22 │

    │ q23 │ │  c  │

    │  b  │ └─────┘

    └─────┘

q20 is the initial state, and (q21) is the accepting state. There is a transition labeled with "b" from q20 to (q21), and an ε-transition from q20 to q23. From q23, there is a transition labeled with "c" back to q23, forming a loop. This allows for zero or more occurrences of "bc".

Combining subexpressions

Finally, let's combine the NFAs for the subexpressions a+ and (c*+d).(bc)*:

          a

  ┌───────┐

  │       │

  │  q13  │

  │       │

  └───────┘

      │

      │

      ▼

  ┌───────┐

  │       │

  │  q14  │

  │       │

  └───────┘

      │ │

      c │   d

      │ │

      ▼ ▼

  ┌───────┐  b   ε

  │       │─────►(q21)

  │  q15  │   │ │

  │(start)│   │ │ε

  └───────┘   ▼ ▼

       │   ┌─────┐

       │   │ q22 │

       │   │  c  │

       │   └─────┘

       │

       └────►(q19)

              accepting

              state

Here, we have connected the NFAs for a+ and (c*+d).(bc)* by adding appropriate transitions. (q21) becomes the accepting state, representing the completion of the regular expression.

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Answer:

  (c)  f^-1(x) = (x -1)/2

Step-by-step explanation:

The inverse function will give x-values when f(x) values are supplied as arguments. The function can be determined either by using table values to write the function, or by checking the offered functions against the table values.

__

We want to find f^-1(x) such that f^-1(-3) = -2, matching the first line of the table.

The equation representing f^-1(x) is ,..

  \(\boxed{f^{-1}(x)=\dfrac{x-1}{2}}\)

__

We can use the first two points in the table to determine the required inverse function:

  (x, f^-1(x)) = (-3, -2) and (-1, -1)

The slope is ...

  m = (y2 -y1)/(x2 -x1) = (-1 -(-2))/(-1 -(-3)) = 1/2

The y-intercept is ...

  b = y1 -m(x1) = -2 -(1/2)(-3) = -1/2

Then the equation of f^-1(x) is ...

  y = mx +b

  f^-1(x) = 1/2x -1/2 = (x -1)/2

10 times by the little nuber then times by 6.0

do that for them all

The formula relating the monetary multiplier and the reserve ratio shows that as the monetary multiplier increases, the reserve ratio decreases. If the monetary multiplier is 6, the reserve ratio must be 0.167.

To determine the reserve ratio given the monetary multiplier, we can use the formula:

Monetary Multiplier = 1 / Reserve Ratio

Given that the monetary multiplier is 6, we can substitute this value into the formula:

6 = 1 / Reserve Ratio

To isolate the reserve ratio, we can take the reciprocal of both sides of the equation:

1 / 6 = 1 / (1 / Reserve Ratio)

1 / 6 = Reserve Ratio

Therefore, the reserve ratio must be 1/6 or approximately 0.167.

Among the given options, b) 0.167 represents the correct answer.

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The definite integral that represents the area of the region enclosed by the polar curve r = 1 sin θ is ∫[a, b] 1/2 r^2 dθ

To determine the definite integral that represents the area of the region, we integrate the expression 1/2 r^2 with respect to θ over the interval [a, b], where a and b are the limits of the region.

In this case, the polar curve r = 1 sin θ represents a circle with radius 1 centered at the origin. As θ varies from 0 to π, the curve traces half of the circle in the positive direction. To find the area of the region enclosed by this curve, we integrate the expression 1/2 r^2 over this interval.

The expression 1/2 r^2 represents the area of a sector of the circle with radius r and central angle θ. Integrating this expression with respect to θ gives us the total area enclosed by the curve.

By evaluating the definite integral over the interval [a, b], we can find the area of the region enclosed by the polar curve r = 1 sin θ.

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The salt will acquire octahedral hole. Thus option B is correct .

Given,

\(r^{+} = 165\\ r^{-} = 297\)

Now,

Find the coordination number ,

Radius ratio = \(r^{+} / r^{-}\)

Substitute the values of radius of salt to get the coordination number .

Radius ratio = 165/297

Radius ratio = 0.556 .

If the radius ratio is between 0.414 and 0.732

Range of radius ratio : 0.414 < r < 0.732

Then coordination number is 6 . If the coordination number is 6 then it will acquire octahedral void .

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Doane's rule is used for choosing the number of histogram bins, not for determining the minimum sample size needed for a multiple regression analysis.

However, a commonly cited rule of thumb is that the sample size should be at least 10 times the number of predictors, so for a multiple regression dataset with 3 predictors, a minimum of 30 observations may be recommended.

Doane's rule is a guideline for choosing the number of histogram bins based on the sample size and skewness of the data. It suggests that the number of bins should be approximately equal to 1 + log2(N) + log2(1 + |g1|/SE(g1)), where N is the sample size and g1 is the sample skewness.

It is important to note that Doane's rule is used for determining the number of bins for a histogram, not for determining the minimum sample size needed for a multiple regression analysis.

That being said, in general, the minimum sample size needed for a multiple regression analysis depends on a variety of factors, including the number of predictors, the strength of the relationships between the predictors and the outcome variable, the desired statistical power, and the level of significance. There is no set minimum sample size that applies to all situations. However, a commonly cited rule of thumb is that the sample size should be at least 10 times the number of predictors, so for a multiple regression dataset with 3 predictors, a minimum of 30 observations may be recommended.

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Answer:

Impossible. t = 30 minutes.

Step-by-step explanation:

We are given the function.

\(\displaystyle v(t)=20000\left(1-\frac{t}{20}\right)^2, \text{ } 0 \leq t \leq 20\)

Where v(t) represents the amount of gallons remaining after t minutes.

We want to find at what time t is the instanteous rate of change from the tank 1000 gallons per minute.

Hence, find the derivative of the function with respect to time t:

\(\displaystyle \begin{aligned} \frac{d}{dt}[v(t)] &=\frac{d}{dt}\left[20000\left(1-\frac{t}{20}\right)^2\right] \\ \\ v'(t) & = 20000\frac{d}{dt}\left[\left(1-\frac{t}{20}\right)^2\right] \\ \\ & = 20000\left(2\left(1-\frac{t}{20}\right)^1\right)\left(-\frac{1}{20}\right) \\ \\ & = -2000\left(1-\frac{t}{20}\right) \\ \\ & = 100t - 2000\end{aligned}\)

To find the time at which the instanteous rate is 1000 gallons/minute, set v'(t) = 1000 and solve for t:

Hence:

\(\displaystyle \begin{aligned} 1000 &= 100t - 2000 \\ \\ 100t & = 3000 \\ \\ t &= 30\text{ minutes}\end{aligned}\)

Therefore, after 30 minutes, the instantaneous rate of change will be 1000 gallons per minute.

However, v(t) is only defined for 0 ≤ t ≤ 30.

In conclusion, it is impossible for our instantaneous rate of change to ever reach 1000 gallons per minute.

The scalar equation of the plane with vector equation (x,y,z)=(5,1,-1)+s(-4,1,0)+t(1,3,-2) is -6x + 2y + 13z = 39.

To find the scalar equation of the plane with vector equation (x,y,z)=(5,1,-1)+s(-4,1,0)+t(1,3,-2), we can use the following steps:

1. Find two vectors in the plane using the given vector equation. We can choose any two linearly independent vectors from the coefficients of s and t:

- Vector v1 = (-4,1,0)
- Vector v2 = (1,3,-2)

2. Find the cross product of the two vectors v1 and v2, which will give us a normal vector to the plane:

- n = v1 x v2 = (-6,2,13)

3. Use the point-normal form of the equation of a plane to write the scalar equation of the plane. We can choose any point on the plane, such as the point (5,1,-1) given in the vector equation:

- The equation of the plane is: -6(x-5) + 2(y-1) + 13(z+1) = 0
- Simplifying the equation, we get: -6x + 2y + 13z = 39

To find the scalar equation of the plane with the given vector equation, we first need to identify the point on the plane and the normal vector to the plane.

The given vector equation is:
(x, y, z) = (5, 1, -1) + s(-4, 1, 0) + t(1, 3, -2)

The point on the plane is the constant vector (5, 1, -1).

Now we need to find the normal vector to the plane. We can do this by taking the cross product of the direction vectors, (-4, 1, 0) and (1, 3, -2):

Normal vector N = (-4, 1, 0) x (1, 3, -2)

N = (1*0 - 3*0, -4*(-2) - 1*0, -4*3 - 1*1)
N = (0, 8, -13)

Now we have the normal vector N = (0, 8, -13) and the point on the plane P = (5, 1, -1). We can find the scalar equation of the plane using the following formula:

A(x - x0) + B(y - y0) + C(z - z0) = 0

where A, B, and C are the components of the normal vector N, and (x0, y0, z0) is the point P on the plane:

0(x - 5) + 8(y - 1) - 13(z - (-1)) = 0

Simplifying, we get the scalar equation of the plane:

8(y - 1) - 13(z + 1) = 0

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The number of individuals in Chicago that will respond positively to Program 2 is 22 out of 25.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.

Given that the chances of a positive response from Chicago residents to two government programs are 65.9% for Program 1 and 87.5%  for Program 2, the likelihood of a positive response for Program 2 given that the person is from Los Angeles must be calculated as follows:

87.5 100 = X

43.75 / 50 = X

21.875 / 25 = X

Therefore, 22 out of 25 individuals in Chicago  will respond positively to Program 2.

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By using the definition of dilation with center at the origin, the scale factor of the dilation must be equal to 5.

Herein we find the coordinates of a point and its image on a Cartesian plane. The latter is the consequence of applying a dilation with center at the origin. Therefore, the following expression defines the transformation:

H'(x, y) = k · H(x, y)

Where:

If we know that H(x, y) = (6, 4) and H'(x, y) = (30, 20), then the scale factor is:

(30, 20) = k · (6, 4)

The expression is true for k = 5.

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Answer:

true

depending on how complete the table of values is.

Answer:

36

Step-by-step explanation:

2(10)+4^2

20+4^2

20+16

36

Answer: The result of the math formula =2*10+4^2 is 28.

To calculate this formula, you first need to perform the exponentiation operation of 4^2, which is 16. Then, you multiply 2 by 10, which gives you 20. Finally, you add 20 to 16, which gives you the final answer of 28.

Answer:

D) 20.5.

Step-by-step explanation:

To find the angle of rotation, we can use the formula:

Angle of rotation = Arc length / Radius

First, we need to calculate the radius of the ferris wheel. The diameter is given as 224 feet, so the radius is half of that:

Radius = 224 feet / 2 = 112 feet

Now, we can calculate the angle of rotation:

Angle of rotation = 40 feet / 112 feet

Angle of rotation ≈ 0.3571 radians

To convert this to degrees, we multiply by 180/π:

Angle of rotation ≈ 0.3571 * (180/π) ≈ 20.4646 degrees

Rounding to the nearest tenth of a degree, the angle of rotation is approximately 20.5 degrees.

Therefore, the correct answer is option D) 20.5.

Answer:

$466.62

Step-by-step explanation:

Balance = $175 - $24.39 - $65.21 + $381.22

Use your calculator to add or subtract each new term as indicated:

$175 - $24.39 = $150.61

Next, subtract $65.21:  $150.61 - $65.21 = $85.40

Finally, add $381.22:  $85.40 + $381.22 = $466.62

on November 27 the new balance in rob's account became $466.62.

Answer:

y =  -2x + 10

Step-by-step explanation:

The equation in point slope form is expressed using the equation

y - y1 = m(x - x1) where;

m is the slope = -2

(x1, y1) is the point on the line = (4,2)

Substitute into the formula:

y - 2 = -2(x - 4)

y -2 = -2x + 8

y = -2x +8 +2

y = -2x + 10

Hence the required equation of the line is y =  -2x + 10