can someone please help me with number one asap!!

Rounding to 3 decimal places, the primary root of (4-3i)^(1/5) is approximately:

(4-3i)^(1/5) = 1.380(cos(-0.129) + i sin(-0.129))

To find the primary root of the complex number (4-3i)^(1/5), we can use the polar form of complex numbers.

First, we need to find the modulus (or absolute value) and the argument (or angle) of the complex number (4-3i):

|4-3i| = sqrt(4^2 + (-3)^2) = 5

Arg(4-3i) = arctan(-3/4) = -0.6435 (rounded to 4 decimal places)

Next, we can write the complex number (4-3i) in polar form as:

4-3i = 5(cos(-0.6435) + i sin(-0.6435))

To find the primary root, we need to take the fifth root of the modulus and divide the argument by 5:

|4-3i|^(1/5) = 5^(1/5) = 1.3797 (rounded to 4 decimal places)

Arg(4-3i) / 5 = -0.1287 (rounded to 4 decimal places)

Finally, we can write the primary root in rectangular form by multiplying the modulus by the cosine of the argument divided by 5 for the real part and multiplying the modulus by the sine of the argument divided by 5 for the imaginary part:

(4-3i)^(1/5) = 1.3797(cos(-0.1287) + i sin(-0.1287))

Rounding to 3 decimal places, the primary root of (4-3i)^(1/5) is approximately:

(4-3i)^(1/5) = 1.380(cos(-0.129) + i sin(-0.129))

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Answer

KK

Step-by-step explanation:

1/3+2/3 so first u do 1+2=3 and u dont add 3+3 so there for it would be 3/3 or 1.

Answer:

The four cats ate 1 cup of food all together.

Step-by-step explanation:

1/3 + 2/3 = 3/3

3/3 as a simplified fraction is 1.

Answer:

2 x 3.14 = 6.28

6.28 divided by 3 = 2.093 around 2.1

Answer: The probability that a millet seed will fall next can be found by dividing the number of millet seeds by the total number of remaining seeds.

Total number of remaining seeds = 40 + 65 + 60 + 35 = 200

Probability that a millet seed will fall next = Number of millet seeds / Total number of remaining seeds

= 65 / 200

= 0.325 or 32.5% (rounded to one decimal place)

Therefore, the probability that a millet seed will fall next is 0.325 or 32.5%.

Step-by-step explanation:

Microeconomics is a branch of economics that focuses on the behavior of individuals and firms in making decisions regarding the allocation of limited resources

Microeconomics is a branch of economics that studies the behavior of individuals and firms in making decisions about the allocation of limited resources, specifically focusing on the interaction of supply and demand in specific markets and how different factors influence the behavior of individuals and firms. It is concerned with the study of how people and firms make decisions about production, consumption, and distribution of goods and services.

Microeconomics analyzes how supply and demand in specific markets interact to determine the prices of goods and services. It also examines how different factors, such as taxes, government regulations, and technological changes, affect the behavior of individuals and firms.

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The standard matrix is:

| 0      -1 |
| -1      0 |

The standard matrix of the linear transformation T: R2 to R2 that reflects each vector through the line x1=-x2 can be found by following these steps:

1. Start with the standard basis vectors for R2, which are (1,0) and (0,1).

2. Apply the transformation T to each of these vectors to find the new vectors. For the first vector, (1,0), we have x1=1 and x2=0. The reflection through the line x1=-x2 gives us a new vector with x1=-x2=-0=0 and x2=-x1=-1. So the new vector is (0,-1).

3. For the second vector, (0,1), we have x1=0 and x2=1. The reflection through the line x1=-x2 gives us a new vector with x1=-x2=-1 and x2=-x1=-0=0. So the new vector is (-1,0).

4. The standard matrix of the transformation T is the matrix whose columns are the new vectors we found. So the standard matrix is:
```
| 0 -1 |
| -1  0 |
```
This is the standard matrix of the linear transformation T: R2 to R2 that reflects each vector through the line x1=-x2.

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The provided polygon is a quadrilateral, and by solving it, we discovered that x is, \(x = 23.5^\circ\)

Used the concept of angle as a quadrilateral,

The total of the angles on two adjacent sides equals 180° when there are two additional angles on the same side.

Given that,

A polygon is shown in the image.

Now from the property of the quadrilateral, the equation is,

\((6x+3)^\circ + (x + 12.5)^\circ = 180^\circ\)

\(7x + 15.5 = 180\)

Subtract 15.5 on both sides,

\(7x= 164.5\)

Divide 7 on both sides,

\(x= 23.5^ \circ\)

Therefore, the value of x is 23.5°.

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The method that can be used to prove that the triangles are congruent is B. AAS.

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.

Angle-Angle-Side is abbreviated as AAS. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.

There are two angles in the two triangles that are shown to be equal and there is also a side of one triangle that is equal to anther side. These triangles are therefore congruent.

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Solution

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given combination expression

STEP 2:Write the formula for combination

STEP 3: Substitute the values

Rewrite n!

We stop at (n-4)! so that it can be used to cancel out the (n-4)! which is the denominator of the combination expression. Therefore, we have:

Hence, the reason for having the expression in the image question.

Answer:

25 x

Step-by-step explanation:

7

We can solve it by using a fractional part of a component of your body known as brain... which you might not have considering you asked such an high end mathematical question... This can be solved using the concept of Addition...

Answer:

it’s years

Step-by-step explanation:

\(in \: pounds \\ 12 \times 288 = 3456 \: pounds\)

\(1 \: kilo = 2.2046 \: pounds\)

\(x \: kilos = 3456 \: pounds\)

\(x = \frac{3456}{2.2046} = 1567.61 \: kilos\)

The name of every month ends in the letter y is the given statement. February is a counterexample to this statement. This is because February does not end with the letter 'y'. So the right  option is (c) February.

What is a counterexample?

In mathematics, a counterexample is an example that opposes or disproves a statement, proposition, or theorem. It is a scenario, an instance, or an example that goes against the given statement.

Therefore, a counterexample demonstrates that the given statement is false or invalid.In this case, the statement is: "The name of every month ends in the letter y." We have to find which of the months listed does not end in "y."February is the only month in the options listed that does not end in the letter "y."

Thus, it is a counterexample to the given statement. Therefore, the correct option is C, February.

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Answer:

if your adding all the sides together the asnwere is: 36

Step-by-step explanation:

Answer:

-4y-12+4b

Step-by-step explanation:

Use the Distributive Property:

\( - 4(y + 3 - b)\)

\( - 4y - 12 + 4b\)

\(-4y-12+4b\) is an equivalent expression.

Answer:

8/19

Step-by-step explanation:

Use this rule: a b/c=ac+b/c

2x8+3/8

the possible dimensions of the rectangular prism are:

1 unit by 12 units by 10 units

2 units by 6 units by 10 units

3 units by 4 units by 10 units

Let the length and width of the rectangular prism be represented by l and w, respectively. Since the height of the prism is 10 unit cubes, we know that the volume of the prism is:

V = l × w × 10

We are also given that the prism requires 120 unit cubes to fill completely, which means:

V = l × w × 10 = 120

Dividing both sides by 10, we get:

l × w = 12

Now we need to find pairs of positive integers l and w that multiply to 12. These are:

1 × 12

2 × 6

3 × 4

Therefore, the possible dimensions of the rectangular prism are:

1 unit by 12 units by 10 units

2 units by 6 units by 10 units

3 units by 4 units by 10 units

Note that these dimensions are not unique, as we can also obtain different dimensions by exchanging the length and width, or by rotating the prism.

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Answer:

15 inches

Step-by-step explanation:

18/90= price for 18 inches.

To get to 75 cents, we have to make the top equal to 1. We can do this by dividing the numerator and denominator by 18. That leaves us with 1/5.

Now, we can multiply the top and bottom by 15. This is because 5 x 15= 75.

What you do to the bottom of the fraction you also do to the top. This leaves us with the answer: 15/75. That means you can buy 15 inches of wire for 75 cents.

Answer:

£0.34

£0.43

€3.04

£3.40

£4.03

Step-by-step explanation:

One pound (€) is less than one Pound Sterling (£), so 3.04 pounds is worth less than 3.40 Pound Sterlings.

The inflection point of f(t) is approximately t = 3.73.

(a) To determine if the function f(t) = -0.425t^3 + 4.758t^2 + 6.741t + 43.7 is increasing or decreasing, we need to find its derivative and examine its sign.

Taking the derivative of f(t), we have:

f'(t) = -1.275t^2 + 9.516t + 6.741

To determine the sign of f'(t), we need to find the critical points. Setting f'(t) = 0 and solving for t, we have:

-1.275t^2 + 9.516t + 6.741 = 0

Using the quadratic formula, we find two possible values for t:

t ≈ 0.94 and t ≈ 6.02

Next, we can test the intervals between these critical points to determine the sign of f'(t) and thus the increasing or decreasing behavior of f(t).

For t < 0.94, choose t = 0:

f'(0) = 6.741 > 0

For 0.94 < t < 6.02, choose t = 1:

f'(1) ≈ 14.982 > 0

For t > 6.02, choose t = 7:

f'(7) ≈ -5.325 < 0

From this analysis, we see that f(t) is increasing on the intervals (0, 0.94) and (6.02, ∞), and decreasing on the interval (0.94, 6.02).

(b) To find the inflection point of f(t), we need to find the points where the concavity changes. This occurs when the second derivative, f''(t), changes sign.

Taking the second derivative of f(t), we have:

f''(t) = -2.55t + 9.516

Setting f''(t) = 0 and solving for t, we find:

-2.55t + 9.516 = 0

t ≈ 3.73

Therefore, The inflection point of f(t) is approximately t = 3.73.

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The equation that can be used to find the length of the hypotenuse of a right triangle is the Pythagorean theorem, which states that the sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse.

In the given triangle with side lengths 63, 16, and x, the length of the hypotenuse is represented by x. Thus, we can apply the Pythagorean theorem to find the value of x.

Using the Pythagorean theorem, we get:

x^2 = 63^2 + 16^2

Simplifying the equation, we get:

x^2 = 3969 + 256

x^2 = 4225

Taking the square root of both sides, we get:

x = 65

Therefore, the length of the hypotenuse of the right triangle is 65.

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The probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.

The number of possible subcommittees that contain only undergraduate students can be calculated by choosing 3 members from the 4 undergraduate students. This can be done in

(4 choose 3) = 4 ways.

The total number of possible subcommittees of three students that can be formed from the 6 members of the committee can be calculated by choosing 3 members from the 6 students. This can be done in

(6 choose 3) = 20 ways.

Therefore, the probability that there will be no graduate students on the subcommittee is:

Number of subcommittees with only undergraduate students / Total number of possible subcommittees

= 4 / 20

= 1/5

= 0.2

So, the probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.

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Answer:

The Domain is X and Range is Y

Step-by-step explanation:

Top values are domain and bottom values are Range

The researcher is BEST served by creating a frequency distribution table with a cumulative frequency column and a histogram with the class boundaries marked

When a researcher examines quantitative data and wants to know the number of observations that fall below the upper limit of a particular class, the researcher is BEST served by creating a frequency distribution table with a cumulative frequency column and a histogram with the class boundaries marked. The frequency distribution table would allow the researcher to see how many observations fall into each class, while the cumulative frequency column would show how many observations fall below the upper limit of each class. The histogram would provide a visual representation of the distribution of the data, and the class boundaries marked on it would allow the researcher to easily identify the upper limit of each class. By examining the cumulative frequency column, the researcher would be able to determine the number of observations that fall below the upper limit of a particular class.

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The APR, or stated rate, is calculated as the annualized interest rate expressed as a percentage.

The APR, or stated rate, represents the annualized interest rate on a loan or investment, expressed as a percentage.

To calculate the APR, we need to consider the nominal interest rate and the compounding frequency. The formula to calculate the APR is:

APR = (1 + nominal interest rate/compounding periods)^(compounding periods) - 1

The nominal interest rate is the stated rate without taking compounding into account.

The compounding periods refer to the number of times interest is compounded in a year, typically based on daily, monthly, or quarterly periods.

By applying the formula and considering the appropriate compounding periods, we can determine the APR.

The APR is an important metric as it allows for easy comparison of interest rates across different financial products.

It helps consumers and investors understand the true cost or yield associated with a loan or investment and enables them to make informed decisions.

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The probability of choosing the winning numbers in the Maryland Lotto game is 1 in 13,983,816.

To win the grand prize in the Maryland Lotto game, the contestant must correctly match all six distinct numbers randomly drawn from a pool of 49 numbers.

The probability of choosing the first winning number correctly is 1/49, the second number is 1/48, the third number is 1/47, the fourth number is 1/46, the fifth number is 1/45, and the sixth number is 1/44.

To calculate the probability of choosing all six numbers correctly, we multiply the probabilities of each individual event:

1/49 * 1/48 * 1/47 * 1/46 * 1/45 * 1/44 = 1/13,983,816

Therefore, the probability of choosing the winning numbers in the Maryland Lotto game is 1 in 13,983,816, which is a very low probability. It means that on average, a person would have to buy millions of tickets to have a chance of winning the grand prize.

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If billion dollars in taxes were collected in 2005, then 30 billion was collected in 2017.

In 2005 the population was 2 million and it had increased to 3 million by 2017.

If 20 billion dollars in taxes were collected in 2005 then we have to determine how much tax was collected in 2017.

The amount of taxes of the city is proportion to the population of that city.

Tax(T) = kP(Population)

where k is a constant.

In 2005 Population = 2 millions and T = 20 billion. So

20 = 2k

Divide by 2 on both side, we get

k = 10

In 2017 Population = 3 millions and k = 10. So the tax collection in 2017 is:

t = 10 × 3

t = 30 billion

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The complete question is:

The amount of taxes a city collects is proportional to the population of the city. In 2005 the population was 2 million and it had increased to 3 million by 2017. If 20 billion dollars in taxes were collected in 2005 how much was collected in 2017? billion dollars help?

Answer:

Does this answer your question

Step-by-step explanation: