Which of the following is equivalent to the complex number i51?
Choose 1 answer:
A.1
B.i
C.-1
D.-i

The penny will fall from distance of 232 feet during the 8th second only, as it falls 960 feet in the first 8 seconds, but 728 feet in the first 8 seconds.

The distance the penny falls each second is increasing by 32 feet (16 feet + 32 feet = 48 feet, 48 feet + 32 feet = 80 feet, and so on). Therefore, during the 8th second, the distance it will fall is:

16 + 48 + 80 + ... + (8 - 1) * 32 feet

Using the formula for the sum of an arithmetic sequence, we get:

(8 / 2) * (16 + (8 - 1) * 32) feet

= 4 * (16 + 7 * 32) feet

= 4 * 240 feet

= 960 feet

So the penny will fall 960 feet during the first 8 seconds. However, we need to subtract the distance it fell during the first 7 seconds to find the distance it fell during the 8th second only. The total distance it fell during the first 7 seconds is:

16 + 48 + 80 + ... + (7 - 1) * 32 feet

= (7 / 2) * (16 + (7 - 1) * 32) feet

= 3.5 * (16 + 6 * 32) feet

= 3.5 * 208 feet

= 728 feet

Therefore, the penny will fall 960 - 728 = 232 feet during the 8th second only.

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Answer:

135 is the distance

Step-by-step explanation:

I subtracted the numbers.

I hope this helped and have a great day!

(please vote this brainliest)

Answer:

135

Step-by-step explanation:

Take 313 and subtract 178 from it to get your answer.

Answer:

0.375

Step-by-step explanation:

The probability of having at least one girl out of 3 children can be calculated as;

P(1 girl, 2 boys) or P(2 girls, 1 boy) or P(3 girls)

Since the P(b) = P(g) = 1/2

Then the probability at any point in time is 1/2 * 1/2 * 1/2 = 1/8

So we have ;

1/8 + 1/8 + 1/8 = 3/8 = 0.375

Answer:

25/70=red cubes

15/70=green cubes

12/70=blue cubes

8/70=yellow cubes

Step-by-step explanation:

you have to add up all the cubes together and get 70 so you have to see the possibility of getting each cube from the bag.

sorry if you get this wrong

Answer:

Step-by-step explanation: Alright so first add up how many cubes there are in total - 25 + 15 + 12+ 8 = 60. Then, each color cube is its number out of 60. So, for example, for 25 red cubes, it would be 25/60 as a fraction and that’s the probability as a fraction for the red cubes. So:

red = 25/60

green = 15/60

blue = 12/60

yellow = 8/60

then simply the fractions.

25/60 —> 5/12

15/60 —> 1/4

12/60 —> 1/5

8/60 —> 2/15

I hope that helped!

Answer:

-3231a-5326b

Step-by-step explanation:

I subtracted the a's but you can't subtract the b with anything so .....yea

The angles between the edges of the resulting pieces are approximately \($56.1^\circ$ and $42.5^\circ$.\)

We know that the rectangle has sides of length 4 ft and 5.5 ft, so we can use the Pythagorean Theorem to find the length of the diagonal \($BD$\):

\($$ BD^2 = 4^2 + 5.5^2 $$\)

\($$ BD^2 = 16 + 30.25 $$\)

\($$ BD^2 = 46.25 $$\)

\($$ BD = \sqrt{46.25} $$\)

\($$ BD = 6.8 \text{ ft (rounded to one decimal place)} $$\)

Now, we can use the Law of Cosines to find the angle between sides \($AB$\)and \($AD$\) in triangle \($ABD$\):

\($$ \cos(A) = \frac{BD^2 + AB^2 - AD^2}{2 \cdot BD \cdot AB} $$\)

\($$ \cos(A) = \frac{6.8^2 + 4^2 - 5.5^2}{2 \cdot 6.8 \cdot 4} $$\)

\($$ \cos(A) = 0.5471 $$\)

\($$ A = \cos^{-1}(0.5471) $$\)

\($$ A = 56.1^\circ \text{ (rounded to one decimal place)} $$\)

Similarly, we can use the Law of Cosines to find the angle between sides \($BC$\) and \($CD$\) in triangle:

\($$ \cos(B) = \frac{BD^2 + BC^2 - CD^2}{2 \cdot BD \cdot BC} $$\)

\($$ \cos(B) = \frac{6.8^2 + 5.5^2 - 4^2}{2 \cdot 6.8 \cdot 5.5} $$\)

\($$ \cos(B) = 0.7416 $$\)

\($$ B = \cos^{-1}(0.7416) $$\)

\($$ B = 42.5^\circ \text{ (rounded to one decimal place)} $$\)

Therefore, the angles between the edges of the resulting pieces are approximately \($56.1^\circ$ and $42.5^\circ$.\)

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Answer:

nfw

Step-by-sntep explanation:

fwjfba

Answer:

  45

Step-by-step explanation:

You want the area of triangle RST using the area formula A=1/2bh, given the points R(-2, 7), S(-5, 1), and T(7, -5).

A plot of the points is shown in the first attachment. By counting grid squares, you can see that segment RS has a "rise" of 2 grid squares for each 1 to the right. The total (run, rise) is ...

  R -S = (-2, 7) -(-5, 1) = (-2 +5, 7 -1) = (3, 6)

The length of RS is found using the Pythagorean theorem (distance formula). It is ...

  RS = √(3² +6²) = √45 = 3√5

Similarly the length of segment ST is ...

  T -S = (7, -5) -(-5, 1) = (7 +5, -5 -1) = (12, -6)

  ST = √(12² +(-6)²) = √180 = 6√5

We note that the slopes of these segments are opposite inverses of each other:

  slope RS = 6/3 = 2

  slope ST = -6/12 = -1/2

This means the segments are at right angles. One of them can be considered to be the "base" and the other the "height" of the triangle.

Using the area formula, we find the area to be ...

  A = 1/2bh

  A = 1/2(6√5)(3√5) = (1/2·6·3)(√(5·5)) = 9·5 = 45

The area of ∆RST is 45 square units.

__

Alternate solution

When the coordinates of a polygon are given, there are several other ways to find its area. One of these is illustrated in the second attachment.

The method illustrated here computes successive "determinants", then finds the area as half the absolute value of their sum. (The sign of the sum will depend on the order in which the points are listed around the figure. Here, it is counterclockwise.) As you can see, we get the same result. You can also see that a spreadsheet is useful for doing the repetitive math.

  Area ∆RST = 45 square units

__

Additional comment

The distance formula for the length of the segment between two points is ...

  d = √((x2-x1)² +(y2-y1)²)

Above, we calculated the differences (x2-x1, y2-y1) separately, then used the "root sum squares" formula for the distance. This has the advantage that (y2-y1)/(x2-x1) is the slope of the segment, and we needed to make sure the segments were perpendicular.

As per the given data, r'(t) · r''(t) = \(108e^{(2t)} - 72e^{(-2t)} + 72te^{(2t)\).

To discover t(zero), we want to alternative 0 for t inside the given feature r(t). This offers us:

\(r(0) = 3e^{(2(0)}), 3e^{(-2(0)}), 3(0)e^{(2(0)})\\\\= 3e^0, 3e^0, 0\\\\= 3(1), 3(1), 0\\\\= 3, 3, 0\)

Therefore, t(0) = (3, 3, 0).

To find r''(0), we need to locate the second one derivative of the given feature r(t). Taking the by-product two times, we get:

\(r''(t) = (3e^{(2t)})'', (3e^{(-2t)})'', (3te^{(2t)})''= 12e^{(2t)}, 12e^{(-2t)}, 12te^{(2t)} + 12e^{(2t)}\)

Substituting 0 for t in r''(t), we have:

\(r''(0) = 12e^{(2(0)}), 12e^{(-2(0)}), 12(0)e^{(2(0)}) + 12e^{(2(0)})\\\\= 12e^0, 12e^0, 12(0)e^0 + 12e^0\\\\= 12(1), 12(1), 0 + 12(1)\\\\= 12, 12, 12\)

Therefore, r''(0) = (12, 12, 12).

Finally, to discover r'(t) · r''(t), we need to calculate the dot made of the first derivative of r(t) and the second spinoff r''(t). The first spinoff of r(t) is given by using:

\(r'(t) = (3e^{(2t)})', (3e^{(-2t)})', (3te^{(2t)})'\\\\= 6e^{(2t)}, -6e^{(-2t)}, 3e^{(2t)} + 6te^{(2t)\)

\(r'(t) · r''(t) = (6e^{(2t)}, -6e^{(-2t)}, 3e^{(2t)} + 6te^{(2t)}) · (12, 12, 12)\\\\= 6e^{(2t)} * 12 + (-6e^{(-2t)}) * 12 + (3e^{(2t)} + 6te^{(2t)}) * 12\\\\= 72e^{(2t)} - 72e^{(-2t)} + 36e^{(2t)} + 72te^{(2t)\)

Thus, r'(t) · r''(t) = \(108e^{(2t)} - 72e^{(-2t)} + 72te^{(2t)\).

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96 eight-bit strings either begin with 100 or have the fourth bit 1 or both.

In our case, we need the number of 8-bit strings to either begin with 100 or have the fourth bit 1 or both.

Case1: For our purpose, the first three digits are fixed with 100. We know that the non-decided position will take the numbers 0 or 1. We have 5 such positions. So, the number of possibilities = 2*2*2*2*2 = 32.

Case2: For our purpose, the fourth digit is fixed with 1. The first position can be only 1. We know that the non-decided position will take the numbers 0 or 1. We have 6 such positions. So, the number of possibilities = 1*2*2*2*2*2*2 = 64.

64 + 32 = 96.

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Answer:

Step-by-step explanation:

Maximum :)

For the given graph,

Axis of symmetry : x = 1

Vertex : (1, 4)

Domain : Set of all real numbers or (-∞, ∞)

Range : {y : y ≤ 4, y ∈ R}

Behavior :

Given a graph of a quadratic function which is a parabola.

The axis of symmetry of a quadratic graph is the line which divides the two parts of the parabola symmetrically.

Here the line x = 1 divides the parabola symmetrically.

So axis of symmetry : x = 1

The x coordinate of the vertex is 1, which is same as axis of symmetry.

From the graph, y coordinate = 4

So vertex is (1, 4).

Domain is the set of all the input values or in this case the x values for which the function is defined.

Here x values range from -∞ to ∞, which is the set of all real numbers.

Range is the set of all y values for the given x values in the domain.

Here y values are all the y values which are less than or equal to 4.

So range is y ≤ 4.

End behavior of the function is that as x tends to positive or negative infinity, y tends to negative infinity.

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answer=0.58

Step-by-step explanation:

24/7= 3.42 ,so you subtract this from 4 to get 0.58

Answer: We can use the equation to find the number of dimes in Kendall's pocket:

25g + 10d = 150

25 * 4 + 10d = 150

100 + 10d = 150

10d = 50

d = 5

So Kendall has 5 dimes in her pocket.

Step-by-step explanation:

Answer:

Neither

Step-by-step explanation:

This function isn't even, because

\(f(x) = f( - x)\)

Basically this mean for every x opposites the y value should be the same.

Here, 6 and -6 doesn't share the same y value, nor as -3,and 3.

This function isn't odd because

\(f( - x) = - f(x)\)

Basically, this means our y values should be reflected about the orgin,

here, the y values does not switch signs for every x value and it's opposite itself , so this function isn't odd.

So The answer is neither

Answer = 320.05 (to 2 d.p)

In a self-selection problem, the explanatory variables can be endogenous.

Endogenous variables are those that are determined within the system, meaning they are affected by other variables in the model. In self-selection problems, individuals or units choose whether to participate in a particular group or program based on their own characteristics.

As a result, the explanatory variables that influence the decision to participate can be correlated with unobservable factors that also affect the outcome of interest. This correlation creates endogeneity, which can lead to biased estimates if not properly addressed in the analysis.

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(A) Circular orbits of stable particles are possible at radii greater than three times the Schwarzschild radius for the non-rotating spherically symmetric mass.

This represents the radius of a black hole's event horizon, within which nothing can escape. The Schwarzschild radius is the event horizon radius of a black hole with mass M.

M can be calculated using the formula: r+ = 2Mwhere r+ is the radius of the event horizon.

(B)  1/2 M -1/2 3M (²) ¹² (1-³) dT = R³ R. This is the required expression.

Tau is the proper time of the particle moving around a circular orbit. Hence, by making use of the formula given above:1/2 M -1/2 3M (²) ¹² (1-³) dT = R³ dt.

(C) Time passes differently in different gravitational fields, and it follows that the period as measured at infinity should be larger than that measured by the particle.

The principle of equivalence can be defined as the connection between gravitational forces and the forces we observe in non-inertial frames of reference. It's basically the idea that an accelerating reference frame feels identical to a gravitational force.

(D) The period of the orbit as measured by an observer at infinity is 16π M^(1/2) and the period of the orbit as measured by the particle is 16π M^(1/2)(1 + 9/64 M²).

The period of orbit as measured by an observer at infinity can be calculated using the formula: T = 2π R³/2/√(M). Substitute the given values in the above formula: T = 2π (8M)³/2/√(M)= 16π M^(1/2).The period of the orbit as measured by the particle can be calculated using the formula: T = 2π R/√(1-3M/R).

Substitute the given values in the above formula: T = 2π (8M)/√(1-3M/(8M))= 16π M^(1/2)(1 + 9/64 M²).

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Answer:

$270,000

Step-by-step explanation:

1. 3/10 = 30% and 30% of 3,000,000 is equal to 900,000

2. 900,000 divided by 1,000 is 90,000

Then, to calculate the dollar amount we do:

3. 90,000 x 3.00 = 270,000

In step 1, we found 3/10 of her total streams. In step 2, we found how many streams were monetized. And, in step 3 we found the amount of money she made off of those streams.

Hope this helps!

Final answer: 3\(b^{2}\) + 8b + 2

12(3y + 6) = 12 x 3(y + 2) // Factor out 12 = 36(y + 2) // Simplify the multiplication Final answer: 36(y + 2)

An equation is a statement that two mathematical expressions are equal. It consists of two expressions separated by an equal sign (=), where one expression is on the left side and the other expression is on the right side of the equal sign. An equation represents a balance or equivalence between the two expressions, and it can be solved for the unknown variable(s) by applying mathematical operations to both sides of the equation.

Given by the question.

3b (b+4) - 4 (b-5)

= 3\(b^{2}\) + 12b - 4b + 20 // Distribute the terms.

= 3\(b^{2}\) + 8b + 20 // Simplify the like terms.

Final answer: 3\(b^{2}\)+ 8b + 20

12(3y + 6)

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Answer:

471 cm^3

(none of the answers above are correct)

Step-by-step explanation:

Volume of cylinder = πr^2 × h

= 3.14 × 5^2 × 6

= 3.14 × 25 × 6

= 471 cm^3

Cosine distance is used in the k-means clustering algorithm to remove outliers. It is a metric used to determine the similarity between two documents. In k-means clustering, cosine distance is used to calculate the distance between data points.

Cosine distance is used to normalize the data so that it is not affected by the length of the data vectors or the scale of the data. The cosine distance is calculated as follows:

Cosine distance = 1 - Cosine similarity,

where Cosine similarity = dot product of two vectors/ product of the magnitude of two vectors.

To remove the outliers from the k-means clustering algorithm, we can set a threshold value for the cosine distance. If the cosine distance between two data points is greater than the threshold value, then those data points are considered outliers and they are not included in the cluster. This helps to ensure that the clustering algorithm only groups together data points that are similar and ignores the outliers.

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Answer:

The distance between the sandbag and the target can be represented by the expression 250 - 75 = 175 meters.

Answer:

2.08 or 2

Step-by-step explanation:

26 = 12.5x

y=mx+b

it will approximately take  2 hours, but to be exact, 2.08

The blanks in each statement about the line segment should be completed as shown below.

Since we know U is the midpoint, we can say TU=8x + 11 substituting in our values for each we get:

8x + 11 = 12x - 1

Solve for x

We now want to solve for x.

−4x+11=−1

−4x = -12

x= 3

Solve for TU, UV, and TV

This is just the first part of our question. Now we need to find TU, UV, and TV. Lets start with TU and UV.

TU=8x+11 We know that x=3 so let’s substitute that in.

TU=8(3)+11

TU= 35

We will do the same for UV. From our knowledge of midpoint, we know that TU should equal UV, however let’s do the math just to confirm.

UV=12x−1 We know that x=3 so let’s substitute that in.

UV=12(3)−1

UV= 35

Based on the segment addition postulate, we have:

TU+UV=TV

35+35=TV

TV= 70

Find the detailed calculations below;

TU = UV

8x + 11 = 12x - 1

8x + 11 - 11 = 12x - 1 - 11

8x = 12x - 12

8x - 12x = 12x - 12 - 12x

-4x = -12

x = 3

By using the substitution method to substitute the value of x into the expression for TU, we have:

TU = 8x + 11

TU = 8(3) + 11

TU = 24 + 11

TU = 35

By applying the transitive property of equality, we have:

UV = TU and TU = 15, then UV = 35

By applying the segment addition postulate, we have:

TV = TU + UV

TV = 35 + 35

TV = 70

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Based on the given information that Caruso, Inc. has an inventory turnover rate of 8 times and a cost of goods sold of $150,000, the company average inventory can be calculated.

To calculate the average inventory, we can use the formula: Average Inventory = Cost of Goods Sold / Inventory Turnover Rate.

Plugging in the values, we have: Average Inventory = $150,000 / 8 = $18,750. Therefore, option c. The company's average inventory is $18,750 is the correct answer.

The inventory turnover rate measures how quickly a company sells its inventory during a specific period. In this case, the turnover rate of 8 times indicates that Caruso, Inc. sells its entire inventory 8 times per year. This suggests that the company has an efficient inventory management system and a relatively high sales volume compared to its inventory level. However, the other options provided (a, b, d) are not supported by the given information and are not accurate in this context.

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Answer: bro just look it up fr fr

Step-by-step explanation:

Answer:

128 in^2

Step-by-step explanation:

L * W

16 * 8 = 128 in^2