Find the y intercept slope and equation
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Answer:

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2a=a+10+44°[exterior angle of a triangle is equal to the sum of two opposite interior angle]

2a-a=54°

a=54°

.so

exterior angle=2×54°=108°is your answer

Answer:

A) Is correct

Step-by-step explanation:

Answer:

The only real difference between producing on Broadway or Off-Broadway is the cost. The professional union that represents the stage managers on Broadway is the International Alliance of Theatrical Stage Employees (IATSE).

Answer:

  a(n) = 10 -3n

Step-by-step explanation:

You want the explicit formula for the sequence recursively defined by a(1)=7, a(n)=a(n-1) -3.

The recursion relation tells you that each term is 3 less than the one before. That is, the common difference between terms is -3.

A sequence with a common difference is an arithmetic sequence. The formula for the n-th term is ...

  a(n) = a(1) +d(n -1)

where a(1) is the first term and d is the common difference.

The first term is given by the recursive definition as 7. Then the explicit formula is ...

  a(n) = 7 -3(n -1)

This can be simplified to ...

  a(n) = 10 -3n

Answer:

It would be 8p+4

Step-by-step explanation:

dividing (48p + 24) by 6 involves factoring and simplifying the expression to obtain the result of 8p + 4

To divide (48p + 24) by 6, you first factor out the common factor of 6 from the expression, which yields

(48p + 24) = 6(8p + 4).

Then, you can further simplify by dividing each term by 6.

The result is 8p + 4.

This process of division distributes the division operation across all terms in the expression, and as a result, each term's coefficient is divided by 6.

In this case, it simplifies the original expression to 8p + 4.

In summary, dividing (48p + 24) by 6 involves factoring and simplifying the expression to obtain the result of 8p + 4

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Answer:

1.03 hours

Step-by-step explanation:

Let x be the time taken to travel from office to seashore at 62mph

Distance traveled = speed x time = 62x miles

Since both trips together took 2 hours, the time taken for the same distance from seashore to office = 2 - x hours

At a speed of 66 mph, the distance traveled = 66(2-x) = 132 - 66x

Since the distances on each trip are equal:
62x = 132 - 66x

Add 66x to both sides => 62x + 66x = 132 =-66x + 66x

128x = 132

x = 132/128 = 1.03125 hours = 1.03 hours rounded to 2 decimal places

When the height is 38 cm and the base is 32 cm, the rate at which the area of the triangle changes is 10 cm²/min.

The rate at which the area of a triangle changes can be found by multiplying the rate at which the base is shrinking by the rate at which the height is increasing.

Given:

Rate of shrinking of the base = -2 cm/min

Rate of increasing of the height = 3 cm/min

Height of the triangle = 38 cm

Base of the triangle = 32 cm

To find the rate at which the area of the triangle changes, we use the formula for the area of a triangle:

Area = (1/2) * base * height

Differentiating the area formula with respect to time gives us:

dA/dt = (1/2) * (db/dt) * height + (1/2) * base * (dh/dt)

Substituting the given values, we have:

dA/dt = (1/2) * (-2) * 38 + (1/2) * 32 * 3

Simplifying, we get:

dA/dt = -38 + 48

dA/dt = 10 cm²/min

Therefore, when the height is 38 cm and the base is 32 cm, the rate at which the area of the triangle changes is 10 cm²/min.

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The sum of the series converges to 7 / (1 + 2z), and the domain for which it converges is -1/2 < z < 1/2.

To find the sum of the given geometric series\(7−14z+28z^2−56z^3+\)⋯, we need to first identify the first term (a) and the common ratio (r).
Step 1: Identify the first term (a)
The first term is 7.
Step 2: Identify the common ratio (r)
Observe the series and find the ratio between consecutive terms:
-14z / 7 = -2z
\(28z^2 / -14z = -2z\)
\(-56z^3 / 28z^2 = -2z\)
The common ratio is -2z.
Step 3: Determine the convergence of the series
A geometric series converges when the absolute value of the common ratio (|r|) is less than 1:
| -2z | < 1
To solve for the domain of z, we need to find the values for which this inequality holds:
-1 < -2z < 1
Divide all parts of the inequality by -2, and remember to reverse the inequality signs when dividing by a negative number:
1/2 > z > -1/2
Step 4: Find the sum of the converging series
For a converging geometric series, the sum can be calculated using the formula:
sum = a / (1 - r)
Plug in the values of a and r:
sum = 7 / (1 - (-2z))

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Putting it all together, we get:

A:

[-3 0 0]

[ 0 1 0]

[ 0 0 -1]

which is an orthogonal matrix with the first row being a multiple of (3, 3, 0).

An orthogonal matrix is a square matrix whose columns and rows are orthonormal vectors, i.e., each column and row has unit length and is orthogonal to the other columns and rows.

Let's start by finding a vector that is orthogonal to (3, 3, 0). We can take the cross product of (3, 3, 0) and (0, 0, 1) to get such a vector:

(3, 3, 0) x (0, 0, 1) = (3*(-1), 3*(0), 3*(0)) = (-3, 0, 0)

Note that this vector has length 3, so we can divide it by 3 to get a unit vector:

(-3/3, 0/3, 0/3) = (-1, 0, 0)

So, the first row of the orthogonal matrix A can be (-3, 0, 0) or a multiple of it. For simplicity, we'll take it to be (-3, 0, 0).

To find the remaining two rows, we need to find two more orthonormal vectors that are orthogonal to each other and to (-3, 0, 0). One way to do this is to use the Gram-Schmidt process.

Let's start with the vector (0, 1, 0). We subtract its projection onto (-3, 0, 0) to get a vector that is orthogonal to (-3, 0, 0):

v1 = (0, 1, 0) - ((0, 1, 0) dot (-3, 0, 0)) / ||(-3, 0, 0)||^2 * (-3, 0, 0)

= (0, 1, 0) - 0 / 9 * (-3, 0, 0)

= (0, 1, 0)

We can then normalize this vector to get a unit vector:

v1' = (0, 1, 0) / ||(0, 1, 0)|| = (0, 1, 0)

So, the second row of the orthogonal matrix A is (0, 1, 0).

To find the third row, we take the cross product of (-3, 0, 0) and (0, 1, 0) to get a vector that is orthogonal to both:

(-3, 0, 0) x (0, 1, 0) = (0, 0, -3)

We normalize this vector to get a unit vector:

v2' = (0, 0, -3) / ||(0, 0, -3)|| = (0, 0, -1)

So, the third row of the orthogonal matrix A is (0, 0, -1).

Putting it all together, we get:

A:

[-3 0 0]

[ 0 1 0]

[ 0 0 -1]

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By analyzing the given values, we can identify the appropriate rate of change.  Therefore, option A, $8.75 per hour worked, represents the correct rate of change.

The table provides information on the number of hours worked and the corresponding total earnings. By comparing the total earnings for different hour values, we can calculate the rate of change.

Calculating the rate of change between consecutive hour values:

(63.75 - 20) / (5 - 0) = 43.75 / 5 = 8.75

(151.25 - 63.75) / (15 - 5) = 87.5 / 10 = 8.75

(238.75 - 151.25) / (25 - 15) = 87.5 / 10 = 8.75

(326.25 - 238.75) / (35 - 25) = 87.5 / 10 = 8.75

(370 - 326.25) / (40 - 35) = 43.75 / 5 = 8.75

As we can see, the rate of change of the contractor's total earnings in dollars with respect to the number of hours worked is consistently 8.75 dollars per hour. Therefore, option A, $8.75 per hour worked, represents the correct rate of change.

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An equation that can  can be used to find the number of sales Luke made this week is; 191 + 16.55x = ¹/₃(573 + 49.65x)

We are told to represent the number of sales as x.

Now, Luke works at a store and earns a fixed amount of $191 plus $16.55 per sale. This is represented as; 191 + 16.55x

Noah works at a different store and earns a fixed amount of $573 plus $49.65 per sale. This is represented as; 573 + 49.65x

We are told that they both made the same number of sales but Luke earned a third of what Noah earned. Thus;

191 + 16.55x = ¹/₃(573 + 49.65x)

An equation that can  can be used to find the number of sales Luke made this week is;

191 + 16.55x = ¹/₃(573 + 49.65x)

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Answer:

Writing the inequality, we have;

the solution to the inequality is;

Explanation:

Given that Natalie has $680 to spend at a bicycle store for some new gear and biking outfits.

Total spending must not exceed $680

She buys a new bicycle for $383.33.

• She buys 2 bicycle reflectors for $7.61 each and a pair of bike gloves for $22.01.

She plans to spend some or all of the money she has left to buy new biking outfits

for $32.43 each.

let x represent the number of biking outfits she can buy.

Total spending is;

Writing the inequality, we have;

we can now solve the inequality;

Therefore, the solution to the inequality is;

Answer:

Step-by-step explanation:

I'm pretty sure it's the first answer, translating left 4, up 5.

Answer:

Step-by-step explanation:

numbers of students = n

party decoration charge = 60

per child cost = 6

so, therefore

f(n) = 60 + 6n

Answer: A. f(n) 60 + 6n

60 is constant

6 per child is variable

Let c = number of children

total cost = 60 +6c

Step-by-step explanation: i got it from somebody else's brainly

If there are n children, and each additional child who joins will add another $6 to the cost, then the cost due to the number of children will be 6n. We also have the fixed cost of $60, no matter how many children join. Therefore, we add up these costs to get Cost = f(n) = 60 + 6n.

We can determine coordinates if point t is between points u and v by checking if u < t < v or v < t < u.

To determine if point t is between points u and v, we need to compare their coordinates. If u < v, then point t is between points u and v if and only if u < t < v. On the other hand, if v < u, then point t is between points u and v if and only if v < t < u.

Whether or not point t is between points u and v depends on the relationship between the coordinates of u and v. If u < v, t must fall between them, and if v < u, t must also fall between them.

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Explanation

In this case as the factor of dilation is 2.5 and the point (0,0) each coordinate is multiplied by 2.5.

Answer

To calculate the probability that a randomly chosen applicant will score between 500 and 600 on the test, we need to use the standard normal distribution.

We'll convert the given scores into z-scores and then find the corresponding probabilities using a standard normal distribution table or a statistical calculator. First, let's calculate the z-score for the lower boundary of 500: z1 = (500 - 560) / 90 = -0.667

Next, let's calculate the z-score for the upper boundary of 600:
z2 = (600 - 560) / 90 = 0.444. Now, we can find the probability associated with each z-score. Using a standard normal distribution table or a calculator, we find that the probability corresponding to z1 is approximately 0.2525, and the probability corresponding to z2 is approximately 0.6700.

To find the probability between these two boundaries, we subtract the lower probability from the upper probability:
P(500 < X < 600) = P(z1 < Z < z2) = P(Z < z2) - P(Z < z1) = 0.6700 - 0.2525 = 0.4175 Therefore, the probability that a randomly chosen applicant will score between 500 and 600 on the test is approximately 0.4175, or 41.75%.

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d. It is impossible to determine how the Gini coefficient will change as it will depend on the original income distribution.

The Gini coefficient is a measure of income inequality in a society. It takes into account the entire income distribution, not just the average or total increase in income. The change in the Gini coefficient depends on how the income increase is distributed among different income groups.

If the income increase is distributed equally among all households, then the Gini coefficient would stay the same because the relative income differences between households remain unchanged. However, if the income increase is concentrated among higher-income households, it is likely that the Gini coefficient would increase, indicating a higher level of income inequality.

On the other hand, if the income increase is disproportionately distributed to lower-income households, it is possible for the Gini coefficient to decrease, indicating a reduction in income inequality.

Therefore, without knowing the initial income distribution and how the income increase is distributed across households, it is impossible to determine how the Gini coefficient will change over the 10-year period.

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The system of equations does not have a solution that satisfies all three equations simultaneously.

To solve this problem, we need to isolate the variable "x" in each equation, and then find the value of "x" that satisfies all three equations simultaneously.

Let's start with the first equation:

2x + 3 = 5x + 9

Subtracting 2x from both sides, we get:

3 = 3x + 9

Subtracting 9 from both sides, we get:

-6 = 3x

Dividing both sides by 3, we get:

-2 = x

So the solution to the first equation is x = -2.

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

3x + 2 = 20

Subtracting 2 from both sides, we get:

3x = 18

Dividing both sides by 3, we get:

x = 6

So the solution to the second equation is x = 6.

Finally, let's look at the third equation:

5x + 5 = ?

This equation cannot be solved because there is no value of "x" that will make it true. However, we can use the solutions we found from the first two equations to check if a value of "x" makes the equation true.

If we plug in x = -2, we get:

5(-2) + 5 = -5

This does not satisfy the equation.

If we plug in x = 6, we get:

5(6) + 5 = 35

This also does not satisfy the equation.

Therefore, the system of equations does not have a solution that satisfies all three equations simultaneously.

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The complete question is :

Isolate the variable "x" in each equation, and then find the value of "x" that satisfies all three equations simultaneously then Find the value of "x" that satisfies all three equations simultaneously .

2x+3=5x+9=3x+2=205x+5=  ?

Ck = (1/2) * ∫ 0^2 (2 + e^(-T) - e^(-2T)) * e^(-j2πkt/2) dT is the Fourier coefficients for the exponential form for the signals.

To find the Fourier coefficients for the exponential form of the signals in Figure P4.7 using formula (4.23), which is the complex Fourier series coefficients formula, we need to substitute the given signal x(T) into the formula and integrate over one period T0. The formula for the complex Fourier coefficients is given as:
Ck = (1/T0) * ∫ T0 x(T) * e^(-j2πkt/T0) dT

where k is an integer representing the harmonic frequency, and T0 is the period of the signal. The exponential form of the signal is given as:
x(T) = 2 + e^(-T) - e^(-2T)

We can see that the period of the signal is T0 = 2, so we need to integrate the signal over one period from T = 0 to T = 2. Substituting the signal into the formula, we get:
Ck = (1/2) * ∫ 0^2 (2 + e^(-T) - e^(-2T)) * e^(-j2πkt/2) dT

Now, we need to simplify and solve the integral using integration by parts or other methods. After some algebraic manipulation, we can find the Fourier coefficients for each harmonic frequency k. The final answer will be a complex number, with a real and imaginary part representing the amplitude and phase of the harmonic frequency in the Fourier series.

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Answer:

A.  {-4, 2, 3, 8}

Step-by-step explanation:

The range of a function is the set of all possible output values (y-values).

From inspection of the graph, the coordinates of the points are:

Therefore, the set of y-values is {-4, 2, 3, 8}.  This is the range of the graphed function.

Answer:

The Probability is 63.7%

Step-by-step explanation:

We need to calculate the area of the circle and the area of the square

From the question, we can see that the square is of side 4 √2 cm

The area of the square is simply the square of its side length

We have this as 4√2 * 4√2 = 16 * 2 = 32 cm^2

The area of the circle can be calculated using the formula for the area of a circle, with the radius being 4 cm

So, we have the area of the circle as;

Pi * r^2

= 22/7 * 4 * 4 = 50.3 cm^2

so, to find the probability, we need to divide the area of the circle by the area of the square

we have this as;

32/50.3 = 0.6366

In percentage, we simply multiply by 100% to give

0.6366 * 100% = 63.66%

To the nearest tenth, this is 63.7%

Answer:

b

Step-by-step explanation:

Answer:

it is D) 25

Step-by-step explanation:

Answer:

f(x)=3^x

Step-by-step explanation:

assuming the n-1 is the exponent,

f(x)=3^x

the -1 is removed due to a graph starting at 0

Answer:

yes

Step-by-step explanation:

becasue yes