Christopher drives the concert speak to his friends house which is 12 miles away it takes him 36 minutes to get there what is Christophers constant speed Write a literal equation in two variables to represent Christopher's Constant speed

The power set of {a, b}, or P({a, b}), is {{}, {a}, {b}, {a, b}}.P({a, b}) and P({0, 1}) are different sets.

The set of P({a,b}), also denoted as 2^{a,b}, represents the power set of the set {a, b}. The power set of a set is the set that contains all possible subsets of the original set, including the empty set and the set itself.

In this case, we have the set {a, b}, where a and b are elements of the set.

The power set of {a, b} is obtained by considering all possible combinations of elements from the original set.

The possible subsets of {a, b} are:

- The empty set: {}

- Individual elements: {a}, {b}

- The set itself: {a, b}

Therefore, the power set of {a, b}, or P({a, b}), is {{}, {a}, {b}, {a, b}}.

Now, let's consider P({0, 1}). Following the same process, we obtain the power set of {0, 1} as {{}, {0}, {1}, {0, 1}}.

Hence, P({a, b}) and P({0, 1}) are different sets.

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1. The equation of the perpendicular line is: y = -x + 4

2. The equation of the parallel line is: y = -x + 4

The equations of two lines that are parallel to each other will have the slope (m), while the equations of two lines that are perpendicular to each other will have slope values that are negative reciprocals of each other.

The slope-intercept form for the equation of a line is, y = mx + b, where b is the y-intercept and m is the slope of the line.

1. The slope (m) of y = x - 4 is 1. The line that is perpendicular to y = x - 4 would have a slope (m) of -1.

Substitute (a, b) = (1, 3) and m = -1 into y - b = m(x - a):

y - 3 = -1(x - 1)

Rewrite in slope-intercept form:

y - 3 = -x + 1

y = -x + 1 + 3

y = -x + 4

2. The slope (m) of y = -x - 4 is -1. The line that is parallel to y = -x - 4 would have a slope (m) of -1.

Substitute (a, b) = (3, 1) and m = -1 into y - b = m(x - a):

y - 1 = -1(x - 3)

Rewrite in slope-intercept form:

y - 1 = -x + 3

y = -x + 3 + 1

y = -x + 4

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Answer:

w = 20

Step-by-step explanation:

a) Flip the equation.

-3/4 w = -15

b) Multiply both sides by 4/(-3).

(4/-3) * (-3/4 w) = (4/-3) * (-15)

w = 20

The paperclip is a typical example of something with a mass of about a gram.  The other items are significantly more massive.   I'm in the US so I remember there are 28 grams in an ounce and 454 grams in a pound.  

Answer: paperclip

Answer:

Japan = $17.95

Switzerland = $13.41

Step-by-step explanation:

Let x be the cost of a Japanese ticket and y be the cost of a Switzerland ticket

We can set up a system of equations:

3x+2y=80.67

2x+3y=76.13

We can multiply the first equation by 2 and the second equation by 3

6x+4y=161.34

6x+9y=228.39

Subtract the first equation from the second equation to remove x

5y=67.05

Divide 5 from both sides

y=13.41

Plug this back into any of the equations

2x+3(13.41)=76.13

2x+40.23=76.13

2x=35.9

x=17.95

Japan = $17.95

Switzerland = $13.41

Answer:

(4, -2)

Step-by-step explanation:

When rotating a point 180° about the origin, the coordinates of the image are the negatives of the coordinates of the preimage.

Answer:

X =8

Step-by-step explanation:

779.50 - 275.75 = 503.75

503.75 - 42 = 461.75

3 * 7.25 = 21.75 = 440

440 / 55 = 8

The answer in the form of x,y is -7x + 10y  = 118.

A Cartesian plane (named after French mathematician Rene Descartes, who formalized its use in mathematics) is defined by two perpendicular number lines: the x-axis, which is horizontal, and the y-axis, which is vertical. Using these axes, we can describe any point in the plane using an ordered pair of numbers.

from given conditions, we get,

(-4, 9) and  10  left  7 down  puts her at  (  -4 - 10 , 9  - 7)  = ( -14, 2)

So,  the points  ( -4, 9)  and (-14,2)  are on the  line

Slope of this line  =   [ 2 - 9] / [ -14 - -4 ]  =  [ -7] / [ -10]  =  7/10

Equation of the line

y  = (7/10)(x - - 4)  + 9

y  = (7/10) ( x + 4)  + 9     multiply through by 10

10y = 7 (x + 4)  + 90

10y = 7x + 28  + 90

-7x + 10y  = 118

Therefore, the answer in the form of (x , y) is -7x + 10y  = 118

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Step-by-step explanation:

the area of :

1) inside surface = (3.14× 1.25²)+(3.14×2.5×1.5)

= 4.90625 + 11.775 = 16.68125 m²

2) upper side surface= (3.14 × (1.35²-1.25²))

= 3.14× (1.8225-1.5625)= 3.14×0.26=0.8164m²

3) lateral surface= 3.14×2.7×1.6=13.5648m²

the total amount of vinyl required for the spa =

16.68125+0.8164+13.5648 = 31.06245 m²

The reflection across the x-axis of (-85, 40) is (-85, -40).

A reflection over a given axis, just translates the point to the other side of the axis, in such a way that the distance between the point and the axis does not change.

Then, for a point (x, y), a reflection across the x-axis gives the point:

(x, -y).

So only the sign of the y-component changes.

Now we can apply that to our point, the reflection across the x-axis of (-85, 40) is just (-85, -40).

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Answer: Your answer is (-85 -40)

Step-by-step explanation: I did the test here's proof

Hope it helped :D

one real eigenvalue. find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace.

What is eigenvalue?

In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that, when the linear transformation is applied to it, changes at most by a scalar factor. The factor by which the eigenvector is scaled is known as the associated eigenvalue, frequently denoted by lambda.

a) -4

b) 1

c) 1

Step-by-step explanation:

a) The matrix A is given by:

\(A=\left[\begin{array}{ccc}-3 & 0 & 1 \\2 & -4 & 2 \\-3 & -2 & 1\end{array}\right]\\\)

where lambda are the eigenvalues and I is the identity matrix. By replacing you obtain:

\(A-\lambda I=\left[\begin{array}{ccc}-3-\lambda & 0 & 1 \\2 & -4-\lambda & 2 \\-3 & -2 & 1-\lambda\end{array}\right]\)

and by taking the determinant:\(\begin{aligned}& {[(-3-\lambda)(-4-\lambda)(1-\lambda)+(0)(2)(-3)+(2)(-2)(1)]-[(1)(-4-\lambda)(-3)+(0)(2)(1-} \\& \lambda)+(2)(-2)(-3-\lambda)]=0 \\& -\lambda^3-6 \lambda^2-12 \lambda-16=0\end{aligned}\)

and the roots of this polynomial is:

\(\begin{aligned}& \lambda_1=-4 \\& \lambda_2=-1+i \sqrt{3} \\& \lambda_3=-1-i \sqrt{3}\end{aligned}\)

hence, the real eigenvalue of the matrix A is -4.

b) The multiplicity of the eigenvalue is 1.

c) The dimension of the eigenspace is 1 (because the multiplicity determines the dimension of the eigenspace)

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Complete Quetion

The matrix A= (−3 0 1, 2 −4 2, −3 −2 1) has one real eigenvalue. Find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace. The eigen value = has multiplicity = and the dimension of the corresponding eigenspace is:_______.

Answer:

780

Step-by-step explanation:

☞ To find the solution, divide 39 by 5% and multiply by 10

P = 39 * 5%(0.5) = 78

P = 78 * 10 = 780

a. The measure of angle 7 is 47°. It is is a vertical angle to angle 5

b. If the measure of ∠6 is represented by (2x - 5), the equation used to solve for x is 42 + 2x = 180

c. The value of x is 69

Vertically opposite angles are defined as those angles that are opposite one another at a vertex and are formed by the intersection of two straight lines.

Vertical opposite angles are known to be congruent.

From the information given, we have;

a. ∠5 ≅ ∠7, they are vertical angles

Therefore, angles 5 and 7 are congruent to each other.

∠7 = 47°

b. Suppose ∠6 = 2x - 5

To determine the value of x, we have

∠5 + ∠6 = 180

Then, we have the equation as;

47 + 2x - 5 = 180

collect the like terns

2x = 180 - 42

2x = 138

Divide both sides by 2

x = 138 / 2

x = 69

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Answer:

665280

Step-by-step explanation:

12x11x10x9x8x7=665280

There are 665280 ways in which 6 policemen can be appointed in 12 coaches of a passenger train if they are to ride in a separate coach.

Probability is defined as the branch of mathematics that deals with the numerical description of how likely an event is to occur, or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, roughly where 0 indicates the improbability of the event and 1 indicates certainty.

It is based on the probable probability of something happening while the theoretical probability is based on the logic behind the probability. For example, if a coin is tossed, the theoretical probability of getting a head is ½.

In above example,

There are 6 policemen

Number of coaches assigned are 12

So, the number of ways are 12x11x10x9x8x7=665280 ways

Thus, there are 665280 ways in which 6 policemen can be appointed in 12 coaches of a passenger train if they are to ride in a separate coach.

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a) If two points on a line are A(-5,7) and B(-2,1), the rise -6, the run is of 3, and then the slope is of -2.

b) If two points on a line are A(10,-3) and B(12,9), the rise 12, the run is of 2, and then the slope is of 6.

c) If two points on a line are A(4,6) and B(8,-8), the rise -14, the run is of 4, and then the slope is of -3.5.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the parameters are given as follows:

As the slope represents the rate of change of the output relative to the input, it is calculated as the change in the output y divided by the change in the input x, that is, the rise divided by the run.

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The equation of g(x) include the following: D. g(x) = 4x² + 2

In Mathematics and Geometry, the translation of a graph to the right simply means a digit would be added to the numerical value on the x-coordinate of the pre-image:

g(x) = f(x - N)

Conversely, the translation of a graph downward simply means a digit would be subtracted from the numerical value on the y-coordinate (y-axis) of the pre-image:

g(x) = f(x) - N

In this context, we can logically deduce that the parent function f(x) = x² was translated 2 units up and vertically stretched by 4 units in order to produce the graph of the image g(x), we have:

g(x) = 4f(x) + 2

g(x) = 4x² + 2

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Option C: At margin of error of 0.44, we are 90% confident that the true proportion of seniors who will attend homecoming is within 0.044 of the sample proportion.

The formula for confidence interval of proportions is;

CI = p^ ± z√((p^(1 - p^)/n)

where;

CI is confidence interval

p^ is sample proportion

z is test statistic at confidence level

n is sample size

We are given;

n = 95

x = 88

Thus;

p^ = 88/95 = 0.9263

z at CL of 90% = 1.645

Now, margin of error is;

E = z√((p^(1 - p^)/n)

Thus;

E = 1.645√((0.9263(1 - 0.9263)/95)

E ≈ 0.044

Thus, at margin of error of 0.44, we are 90% confident that the true proportion of seniors who will attend homecoming is within 0.044 of the sample proportion.

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Answer:

35 degrees

Step-by-step explanation:

Sum of angles inside a triangle is 180 degrees.

Right angle is 90 degrees.

180 = 90 + (x + 46) + (x + 66) = 2x + 202

x = -11

A = x + 46 = -11 + 46 = 35

Finding simple interest rate:

I = PRT    

I= interest

P= principal amount

R= rate

T= time

Equation:

I = PRT

I = (500)(0.06)(18)

I= 540

yes

Final Statements:

Therefore the interest rate is $540 after 18 months (answer is yes)

Reasoning: In this question it asked to determine whether the answer our friend provided was wrong or right using the information presented. In order to prove that they were correct I took the equation and checked it again myself and also looked for any errors that might of been there. Everything checked out including the rate which is where things are usually messed up considering it's a percentage.

Answer:

48 cubic inches

Step-by-step explanation:

Answer:

192π

and or \(603in^{3}\)

Step-by-step explanation:

Answer:

X and y answer is 45 degrees

Answer:

x = 20, y = 70 degrees.

Step-by-step explanation:

x + y = 90 degrees  ( As the large triangle is right-angled).

Now x is the base angle of an isosceles triangle so the small angle that is part of the right angle = x. Call this angle z.

Consider the small triangle which includes 40 degrees:

y + 40 + 90 - z = 180     But as  z = x:

y + 130 - x = 180

y - x = 50

Adding the equation to the highlighted equation above we have:

2y = 90 + 50

2y = 140

y = 70 degrees.

So x + 70 = 90

giving x = 20 degrees.

The lateral surface area of given square pyramid is 120 cm².

In the given square pyramid:

lateral height = l = 10mm

With = 6mm

Length =  6 mm

A square pyramid's lateral area is defined as the area covered by its slant of lateral faces.

A pyramid is a three-dimensional object with any polygon as its base and any congruent triangles as its side faces.

Each of these triangles has one side that corresponds to one side of the basic polygon.

Pyramids are called by the shape of their bases. A square pyramid is a pyramid with a square base.

The formula for the lateral surface area of a square pyramid is

L = (Perimeter of base) x (slant height) / 2

Perimeter of base = 6x4

                              = 24 cm

Now put the values into formula;

L = 24 x 10 / 2

  = 120 cm²

The lateral surface area = 120 cm².

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( - ∞ , + ∞) is  the possible domain and range for this situation.

What is the domain function?

Because C(s) = 8s + 15  one off function.

So,   s ∈ R

80 the domain is defined as ( - ∞ , + ∞)

b)  because s ∈ R

So ,  C(s) ∈   ( - ∞ , + ∞)

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The complete question is -

Consider the U.S. Shirts function, C(s) = 8s + 15. What expression in the function equation represents: a. the domain of the function? b. the range of the function? 5. Describe the possible domain and range for this situation.

Since 80 out of 100 free throws were successful, the standard deviation of the success rate would be 8, and the standard deviation of a binomial distribution is the square root of (p*q)/n, where p is the probability of success, q is the probability of failure (1-p), and n is the total number of trials.

Standard deviation is calculated as follows:

p*q/n = 0.8*0.2/100 = 0.0016 = 0.04 = 8

Since 80% of 100 equals 80 successful free throws, the standard deviation of the successes from 100 free throws would be 8. The dispersion in a set of data is measured by standard deviation. A binomial distribution's standard deviation is equal to the square root of (p*q)/n, where p is the success probability, q is the failure probability (1-p), and n is the number of trials. Since the success rate in this instance is 80%, p = 0.8, q = 0.2, and n = 100. The standard deviation is then equal to the square root of (p*q/n): (0.8*0.2/100) = (0.0016) = (0.04), which equals 8. Therefore, the standard deviation of the successes from 100 free throws for a basketball player who makes 80% of them would be 8.

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Answer:

50+-50+0

Step-by-step explanation:

adding 50 to -50 and add 0 =0

The formula for the nth term of the series is an = -14n + 68 for n>1 and the nth term an of the series for n > 1 is an = -67.

To find an for n>1, we need to first find the formula for the nth term of the series. We can do this by taking the difference between successive partial sums:
sn - sn-1 = (5n-72n+7) - (5(n-1)-7(2(n-1)+7))
         = 5 - 7(2n-9)
         = -14n + 68
We know that the nth term of the series is given by the difference between the nth partial sum and the (n-1)th partial sum, so we can set this expression equal to an:
an = sn - sn-1
  = -14n + 68
Therefore, the formula for the nth term of the series is an = -14n + 68 for n>1.
To find the nth term an of the series, we need to consider the difference between the (n+1)th and nth partial sums. Using the given formula for the partial sum sn:
s(n+1) = 5(n+1) - 72(n+1) + 7
sn = 5n - 72n + 7
Now, subtract sn from s(n+1):
an = s(n+1) - sn = [5(n+1) - 72(n+1) + 7] - [5n - 72n + 7]
Simplify the expression:
an = 5n + 5 - 72n - 72 + 7 - 5n + 72n - 7
Combine the like terms:
an = 5 - 72
So, the nth term an of the series for n > 1 is an = -67.

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i. Paola's taxable income is $40,675.

From the table, as she is married but filing taxes jointly, her withheld tax should be,

But she had $4,654 withheld.

Therefore, Paola would be getting a refund of $4654 - $4486 = $168

ii. Pedro's taxable income however is $38,802

From the table, since he is married and files taxes jointly, his withheld tax should be,

But he had $4345 withheld.

Therefore, Pedro would be getting a refund of $4345 - $3544 = $801

Answer:

Both Paola and Pedro would get refunds.

Paola would get $168 while Pedro would get $801