Please help with this, write an equation of the ellipse 18th a vertex at (-8,0) and a co-vertex at (0,4) and a center at (0, 0)

The angle of intersecting arc theorem indicates that the angle marked ? in the drawing is 190°

The angle of intersecting chords theorem states that the angle formed by two chords when they intersect in a circle is equivalent to half the sum of the arcs they intercept on the circumference of the circle.

The angle of intersecting chords theorem states that we get;

The angle QPR formed = (1/2) × ((Arc QR) + (Arc NS))

Therefore, we get;

m∠QPR = 125° = (1/2) × ((Arc QR) + 60°)

2 × 125° = ((Arc QR) + 60°)

250° = (Arc QR) + 60°

(Arc QR) = 250° - 60° = 190°

The measure of the arc QR = 190°

m[tex]\widehat{QR}[/tex] = 190°

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The art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper for proper distribution.

To determine the largest number of identical kits the art teacher can make using all the crayons and drawing paper, we need to find the greatest common divisor (GCD) of the quantities.

The GCD represents the largest number that can divide all the quantities without leaving a remainder.

The GCD of the quantities of crayons can be found by considering the prime factorization:

72 = 2³ × 3²

48 = 2⁴ × 3

48 = 2⁴ × 3

48 = 2⁴ × 3

The GCD of the crayons is 2³ × 3 , which is 24.

Now, we need to find the GCD of the quantity of drawing paper:

120 = 2³ × 3 × 5

The GCD of the drawing paper is also 2³ × 3 , which is 24.

Since the GCD of both the crayons and drawing paper is 24, the art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper.

Each kit would contain an equal distribution of crayons and drawing paper.

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Itamar had a relatively more impressive day in terms of his performance compared to the average performance in the 400-meter race

A positive z-score indicates that the data point is above the mean, while a negative z-score indicates that it is below the mean.

Itamar had a z-score of 2.3 for the 400-meter race, while Eleanor had a z-score of 1.2 for the SAT.

A z-score of 2.3 for Itamar suggests that his performance in the 400-meter race was 2.3 standard deviations above the mean performance in that event.

Similarly, Eleanor's z-score of 1.2 for the SAT implies that her SAT score was 1.2 standard deviations above the mean SAT score.

Comparing the z-scores, Itamar's z-score of 2.3 is larger than Eleanor's z-score of 1.2.

Therefore, Itamar had a relatively more impressive day in terms of his performance compared to the average performance in the 400-meter race, while Eleanor had a relatively more impressive performance on the SAT compared to the average SAT score.

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The price of a ticket should be $1.20 to make the lottery a fair game.

To find the expected gain from one ticket, we first need to calculate the total amount of money won by all the tickets. The winning ticket receives $5000, while the five tickets that each win $1000 collectively receive $5000.

Similarly, the ten tickets that each win $200 collectively receive $2000. Therefore, the total amount of money won by all the tickets is $12,000.

To find the expected gain from one ticket, we divide the total amount of money won by the number of tickets sold. So, the expected gain from one ticket is $1.20.

To make the lottery a fair game, the price of a ticket should be equal to the expected gain from one ticket. However, in reality, the price of a ticket is usually higher to cover the cost of organizing and running the lottery.

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Using proportional reasoning, we can predict that there will be 40 red candies in the large bag.

Using proportional reasoning, we can set up and solve the following equation to determine the number of red candies in the large bag:

P = Proportion of red candies in the large bag

R = Red candies in the small bag

R × (33/9) = P

12 × (33/9) = P

P = 40 red candies in the large bag

Therefore, using proportional reasoning, we can predict that there will be 40 red candies in the large bag.

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The statement that  best compares the graph of function  g(x) with the graph of f(x) is option B which is  The graph of g(x) is shifted 2 units to the right.

Let compare the  f(x) = x2 and g(x) = (2x)²

The function of f(x) = x² represents a basic quadratic function, where the input x is squared. The graph of f(x) is a parabola that opens upwards with its vertex at the origin (0,0).

The function of  g(x) = (2x)² can be simplified to g(x) =4x². In this case, the function g(x) is the same as f(x), except that the inout x is multiplied by 2 before being squared. Multiplying x by 2 stretches that graph horizontally. The resulting graph of g(x) is also parabola that opens upwards, but it is narrower than the graph of f(x) because the x values are doubled.

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In order to ensure that depositors would get their money back in the event of a bank run, the Federal Reserve can support the bank by lending money to the bank. Option C

When a bank faces a bank run and experiences a sudden and significant increase in withdrawals, it may face a liquidity crisis, meaning it may not have enough cash on hand to meet the withdrawal demands of depositors.

To address this, the Federal Reserve can step in and provide loans or emergency funding to the bank to help it meet its obligations to depositors. This lending can help stabilize the bank's liquidity position and ensure that depositors are able to access their funds.

It is important to note that this support from the Federal Reserve is typically done on a temporary basis and is intended to help address the immediate liquidity needs of the bank during a crisis

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The value of y in this linear system as per the given data, the value of y in the linear system is 18.

To find the value of y inside the linear device, we are able to use the given equations:

Equation 1: x + y + z = 62

Equation 2: x - y = 12

Equation three: 2x + y + z = ninety two

To remedy this gadget, we can dispose of the variable x via subtracting Equation 2 from Equation 1:

(x + y + z) - (x - y) = 62 - 12

Simplifying, we get:

2y + z = 50

Next, we can subtract Equation 2 from Equation 3 to eliminate the variable x once more:

(2x + y + z) - (x - y) = 92 - 12

Simplifying, we get:

x + 2y + z = 80

(x + 2y + z) - (2y + z) = 80 - 50

Simplifying, we get:

x = 30

30 - y = 12

Solving for y, we get:

y = 18

Thus, the correct option is B.

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Answer:

2,-3

Step-by-step explanation:

The correct answer is 2 and -3 .

Given ,

Equation : x²+x-6=0

Now to find the value of x we need to find the roots/ solutions of the equation by either factor method or by quadratic formula.

So,

x² + x - 6 = 0

By factor method,

x² + 3x - 2x - 6 = 0

Take the common terms ,

x(x + 3) -2(x + 3) = 0

(x-2)(x + 3) = 0

Thus the roots of x are 2 and -3 .

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The derivative is f'(x) = (4x - 1) / (2x² - x).

To find the derivative of the function f(x) = ln(2x² - x), we can use the chain rule.

Begin by identifying the function to be differentiated, which is f(x) = ln(2x² - x).

Apply the chain rule, which states that if we have a composition of functions, f(g(x)), the derivative is given by (f'(g(x))) g'(x).

Let's consider the inner function g(x) = 2x² - x.

To differentiate g(x), we need to apply the power rule and the constant rule. The derivative of 2x² is 4x, and the derivative of -x is -1.

Now, we differentiate the outer function f'(g(x)). The derivative of ln(x) is 1/x.

Finally, we multiply the derivatives obtained in steps 3 and 4. Thus, the derivative of f(x) = ln(2x² - x) is:

f'(x) = (1 / (2x² - x)) * (4x - 1)

Simplifying further, we have:

f'(x) = (4x - 1) / (2x² - x)

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k, a, f, and c are the exterior angles of the given figure.

In a figure, an exterior angle refers to an angle formed by one side of the trapezium and the extension of an adjacent side.

In other words, an exterior angle is formed when you extend one of the sides of the trapezium and look at the angle it creates with the adjacent side.

The angle b degrees, g , d and 70 degrees are interior angles.

k, a, f, and c are the exterior angles of the given figure.

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Answer:

Step-by-step explanation:

That's 6th grade math but the answer is -5 3/5, this is because subtracting a positive number from a negative adding them together and adding a negative sign.

The volume of the cuboctahedron is approximately [tex]32768 cm^3 - 512 * sqrt(3) cm^3.[/tex]

By using the clue provided, we may determine the volume of the original cube and then deduct the volume of the cut corners.

All of the edges of the original cube measure 32 cm. As a result, its volume can be determined as follows:

[tex]Volume of cube = (Edge length)^3 = (32 cm)^3 = 32^3 cm^3 = 32768 cm^3[/tex]

Let's now determine the volume of the corners that were eliminated. Each corner has a similar equilateral triangle with sides that are 16 cm long.

The volume of one equilateral triangle can be calculated using the formula:

Volume of equilateral triangle =[tex](sqrt(3) / 4) * (Side length)^2[/tex]

Plugging in the values, we have:

Volume of one corner [tex]= (sqrt(3) / 4) * (16 cm)^2[/tex]

Since there are 8 corners that are removed, we multiply the volume of one corner by 8 to get the total volume of the removed corners:

Total volume of corners = [tex]8 * [(sqrt(3) / 4) * (16 cm)^2][/tex]

Simplifying the expression:

Total volume of corners = [tex]8 * (sqrt(3) / 4) * (16 cm)^2[/tex]

=[tex]2 * sqrt(3) * (16 cm)^2[/tex]

Now, we can subtract the volume of the corners from the volume of the original cube to find the volume of the cuboctahedron:

Volume of cuboctahedron = Volume of cube - Total volume of corners

[tex]= 32768 cm^3 - 2 * sqrt(3) * (16 cm)^2[/tex]

Calculating the expression:

Volume of cuboctahedron ≈ [tex]32768 cm^3 - 2 * sqrt(3) * (16 cm)^2[/tex]

≈ [tex]32768 cm^3 - 2 * sqrt(3) * 256 cm^2[/tex]

≈ [tex]32768 cm^3 - 512 * sqrt(3) cm^3[/tex]

Therefore, the volume of the cuboctahedron is approximately[tex]32768 cm^3 - 512 * sqrt(3) cm^3.[/tex]

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The term "100 points" usually indicates a high level of achievement or success in a particular area.

The term "100 points" can refer to a number of different things depending on the context. For example, in sports, it could refer to a team scoring 100 points in a game.

In wine tasting, it could refer to a perfect score given to a wine by a critic or judge. In school, it could refer to receiving a perfect score on an exam or assignment worth 100 points.

It's important to note that while a perfect score of 100 points is often seen as the ultimate goal, it's not always necessary or even possible in some situations. In many cases, simply doing your best and striving for improvement is enough to be considered successful.

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Mean:

Bus: 17.5

Walking: 20.5

Median:

Bus: 15

Walking: 21

Mode:

Bus: 15 and 14

Walking: 21 and 20

Range:

Bus: 17

Walking: 3

According to the given table,

Bus: 16, 14, 15, 14, 31, 15     number of observations = 6

Walking: 22, 19, 21, 20, 21, 20  number of observations = 6

Now mean of bus = (16 + 14 + 15 + 14 + 31 + 15)/6

                              = 17.5

Now mean of walking = (22 + 19 + 21 + 20 + 21 + 20)/6

                                     = 20.5

To find the median,

Arranging these into ascending order:

Bus: 14, 14, 15, 15, 16, 31

Walking: 19, 20, 20, 21, 21, 22

Since 6 is an even number thus median is

For Bus:

⇒ (6/2th term  +  (6/2 + 1)term)/2

⇒ (15 + 15)/2

⇒ 15

For walking:

⇒(20+21)/2

Hence median is 21

Now mode for Bus is  14 and 15 as it is repeating more times

And mode for walking is 20 and 21.

Since we know that

Range = largest observation - lowest observation

Therefore,

Range of bus   =  31 - 14

                         = 17

Range of Walking = 22 - 19

                              = 3

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The values of the other trigonometric functions for the given values of sin(Ф) and cos(Ф) are as follows, cos(Ф) = -5/4, sec(Ф) = -4/5, tan(Ф) = 16/25, cot(Ф) = 25/16.

To find the values of the other trigonometric functions of Ф, we can use the given information of sin(Ф) and cos(Ф).

We know that sin(Ф) = -4/5 and cos(Ф) = -5/4.

Recall that cos(Ф) is the reciprocal of sin(Ф), so we can determine cos(Ф) by finding the reciprocal of sin(Ф):

cos(Ф) = 1/sin(Ф) = 1/(-4/5) = -5/4

Similarly, we can find sec(Ф) by taking the reciprocal of cos(Ф):

sec(Ф) = 1/cos(Ф) = 1/(-5/4) = -4/5

To find tan(Ф), we can use the identities tan(Ф) = sin(Ф)/cos(Ф):

tan(Ф) = sin(Ф)/cos(Ф) = (-4/5)/(-5/4) = 16/25

Next, we can find cot(Ф) by taking the reciprocal of tan(Ф):

cot(Ф) = 1/tan(Ф) = 1/(16/25) = 25/16

Finally, we can find sec(Ф) by taking the reciprocal of csc(Ф):

cot(Ф) = 1/csc(Ф) = 1/(-5/4) = -4/5

Therefore, the values of the other trigonometric functions for the given values of sin(Ф) and cos(Ф) are as follows:

cos(Ф) = -5/4

sec(Ф) = -4/5

tan(Ф) = 16/25

cot(Ф) = 25/16

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Answer:

  C. reflected in the x-axis, shifted right 4

Step-by-step explanation:

You want to know the effect on f(x) of the transformation -f(x -4).

Multiplying the function value by -1 causes it to be reflected across the x-axis. The image point will be as far from one side of the x-axis as the preimage point is from the other side.

Replacing x with (x-4) in the function argument means the value of x must be larger by 4 units to get the same function value. This shifts the graph to the right by 4 units.

Together, the transformations reflect the graph in the x-axis and shift it right by 4 units, moving the vertex to (2, 2).

__

Additional comment

In the attachment, the blue graph is the one that has the given transformation. As you can see, it opens downward.

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Using the pattern, the next 4 numbers in the sequence would be

3.2; 4.0; 4.8; 5.6

The given sequence seems to follow a pattern where each term is obtained by adding 0.8 to the previous term.

hence this is an AP sequence, with a common difference of 0.8, adding 0.8 to each term gives the next consecutive term

2.4 + 0.8 = 3.2

3.2 + 0.8 = 4.0

4.0 + 0.8 = 4.8

4.8 + 0.8 = 5.6

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The battery life of the latest model after 7 months would be approximately 828.402 minutes.

The battery life increment is 4% longer than the previous model.

To calculate the battery life for each month, we can multiply the battery life by 1.04.

Starting with the initial battery life of 697.0 minutes, we can calculate the battery life after 7 months as follows:

697.0 * (1.04)^7

Using a calculator, we can evaluate this expression:

697.0 * (1.04)^7 ≈ 828.402.

Therefore, the battery life of the latest model after 7 months would be approximately 828.402 minutes.

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Answer:

35/36

Step-by-step explanation:

5/9 + 5/12 =

We need to get a common denominator of 9 and 12, which is 36.

5/9 * 4/4 = 20/36

5/12 * 3/3 = 15/36

20/36 + 15/36

35/36

Answer:

What do you need help with?

Step-by-step explanation:

Step-by-step explanation:

The correct answer is none of the options given. The given sequence is a geometric sequence with a common ratio of 7. The general form of a geometric sequence is g(x) = ar^(x-1), where a is the first term and r is the common ratio. In this case, a = 5 and r = 7, so the correct form of the geometric sequence is g(x) = 5(7^(x-1)).

Answer:

Step-by-step explanation:

a>b

1≤b,a≤25

smallest value of b=1

Answer:

Step-by-step explanation:

Answer:

Therefore, the 4-point DFT of the signal [3, 2, -5, 4] is [4, 5 - 9i, 0, -1 + i].

Step-by-step explanation:

To find the 4-point Discrete Fourier Transform (DFT) of the given signal [3, 2, -5, 4], we can use the formula for DFT:

X(k) = Σ[n=0 to N-1] x(n) * exp(-j * 2π * k * n / N)

where X(k) is the DFT coefficient at frequency index k, x(n) is the input signal, N is the length of the signal, and j is the imaginary unit.

For the given signal [3, 2, -5, 4], with N = 4, the 4-point DFT coefficients can be calculated as follows:

For k = 0:

X(0) = (3 * exp(-j * 2π * 0 * 0 / 4)) + (2 * exp(-j * 2π * 0 * 1 / 4)) + (-5 * exp(-j * 2π * 0 * 2 / 4)) + (4 * exp(-j * 2π * 0 * 3 / 4))

= 3 + 2 - 5 + 4

= 4

For k = 1:

X(1) = (3 * exp(-j * 2π * 1 * 0 / 4)) + (2 * exp(-j * 2π * 1 * 1 / 4)) + (-5 * exp(-j * 2π * 1 * 2 / 4)) + (4 * exp(-j * 2π * 1 * 3 / 4))

= 3 + 2 - 5i - 4i

= 5 - 9i

For k = 2:

X(2) = (3 * exp(-j * 2π * 2 * 0 / 4)) + (2 * exp(-j * 2π * 2 * 1 / 4)) + (-5 * exp(-j * 2π * 2 * 2 / 4)) + (4 * exp(-j * 2π * 2 * 3 / 4))

= 3 - 2 - 5 + 4

= 0

For k = 3:

X(3) = (3 * exp(-j * 2π * 3 * 0 / 4)) + (2 * exp(-j * 2π * 3 * 1 / 4)) + (-5 * exp(-j * 2π * 3 * 2 / 4)) + (4 * exp(-j * 2π * 3 * 3 / 4))

= 3 - 2 + 5i - 4i

= -1 + i

Therefore, the 4-point DFT of the signal [3, 2, -5, 4] is [4, 5 - 9i, 0, -1 + i].

Answer:

Step-by-step explanation:

The output value of f(0) include the following: 3.

In Mathematics and Geometry, a piecewise-defined function simply refers to a type of function that is defined by two (2) or more mathematical expressions over a specific domain.

Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains.

Since the value of x is 0, the output value of this piecewise-defined function can be calculated by using the third function as follows;

f(x) = x² + 3

f(0) = 0² + 3

f(0) = 3

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[tex]16+15+14=45[/tex] - the total number of balls

[tex]|\Omega|=45\cdot44=1980[/tex]

a)

[tex]A[/tex] - blue, then yellow is selected

[tex]|A|=15\cdot14=210\\\\P(A)=\dfrac{210}{1980}=\dfrac{7}{66}\approx10.6\%[/tex]

b)

 A - red, then red is selected

[tex]|A|=16\cdot15=240\\\\P(A)=\dfrac{240}{1980}=\dfrac{4}{33}\approx12.1\%[/tex]

Answer:

169

Step-by-step explanation:

To apply the Laws of Exponents and write an equivalent expression for (-9-4)², we need to simplify the expression step by step.

First, let's simplify the expression (-9-4)²:

(-9-4)² = (-13)²

Next, we apply the exponent rule for a negative base. According to the rule, when a negative number is raised to an even exponent, the result is positive. So, we have:

(-13)² = 13²

Now, we can simplify 13² using the exponent rule for multiplication:

13² = 13 * 13 = 169

Therefore, the equivalent expression for (-9-4)² is 169.