\(31.3 \times 9.5\)
​

The values of Z such that e² = 2 + i√3 are Z = ln(2 + i√3) + 2πik, where k is an integer.

To find the values of Z, we can start by expressing 2 + i√3 in polar form. Let's denote it as re^(iθ), where r is the modulus and θ is the argument.

Given: 2 + i√3

To find r, we can use the modulus formula:

r = sqrt(a^2 + b^2)

= sqrt(2^2 + (√3)^2)

= sqrt(4 + 3)

= sqrt(7)

To find θ, we can use the argument formula:

θ = arctan(b/a)

= arctan(√3/2)

= π/3

So, we can express 2 + i√3 as sqrt(7)e^(iπ/3).

Now, we can find the values of Z by taking the natural logarithm (ln) of sqrt(7)e^(iπ/3) and adding 2πik, where k is an integer. This is due to the periodicity of the logarithmic function.

ln(sqrt(7)e^(iπ/3)) = ln(sqrt(7)) + i(π/3) + 2πik

Therefore, the values of Z are:

Z = ln(2 + i√3) + 2πik, where k is an integer.

The values of Z such that e² = 2 + i√3 are Z = ln(2 + i√3) + 2πik, where k is an integer.

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Answer:

6 / 2   or   3

Step-by-step explanation:

y2 - y1

_____      =     (9 - 3) / (6 - 4) = 6 / 2 = 3

x2 - x1

The study conducted by the researcher suffers from several limitations, including the absence of a control group, small sample size, participant bias, and experimenter bias. Furthermore, the sample selection is inadequate, as all the participants are students of one course in a single university.

Moreover, the study fails to account for extraneous variables that might affect the results. Therefore,  that textbooks are not necessary or helpful for learning is premature and cannot be generalized to other courses or universities. T he study is flawed, and more research is needed to assess the effect of textbooks on learning.

The study conducted by the researcher suffers from several limitations. First, there is no control group, which makes it difficult to determine whether the results are due to the absence or presence of the textbook. Second, the sample size is small, which reduces the generalizability of the findings.

Third, there is participant bias, as some students might have bought the textbook even though it was optional, while others might not have bought it even though it was required. Fourth, there is experimenter bias, as the professor who scored the essays knew which section had the textbook and which did not.

Fifth, the sample selection is inadequate, as all the participants are students of one course in a single university. Moreover, the study fails to account for extraneous variables that might affect the results, such as the students' prior knowledge, motivation, and study habits.

Therefore, the  textbooks are not necessary or helpful for learning is premature and cannot be generalized to other courses or universities. The study is flawed, and more research is needed to assess the effect of textbooks on learning.

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(a) Your parents would have to save approximately $7,181.75 each year to reach their goal of $140,000 by your 18th birthday.

(b) Your parents would have to save approximately $9,022.19 each year to reach their new goal of $180,000.

To determine how much your parents would have to save each year to reach their goal of $140,000 by your 18th birthday, we can use the future value of an ordinary annuity formula.

a. The formula to calculate the required annual savings is:

PV = Annual Savings × [(1 + r)ⁿ - 1] / r

Where:

PV = Present Value (goal amount)

r = Interest rate per period

n = Number of periods (number of years)

Given that PV = $140,000, r = 5% (or 0.05), and n = 17 (18 - 1), we can plug these values into the formula:

$140,000 = Annual Savings × [(1 + 0.05)¹⁷ - 1] / 0.05

Solving for Annual Savings:

Annual Savings = $140,000 × 0.05 / [(1 + 0.05)¹⁷ - 1]

= $140,000 × 0.05 / 0.97769

≈ $7,181.75

Therefore, your parents would have to save approximately $7,181.75 each year to reach their goal of $140,000 by your 18th birthday.

b. If your parents decide to have $180,000 saved in case you take five years to graduate, we can use the same formula with a new goal amount of $180,000.

$180,000 = Annual Savings × [(1 + 0.05)¹⁷ - 1] / 0.05

Solving for Annual Savings:

Annual Savings = $180,000 × 0.05 / [(1 + 0.05)¹⁷ - 1]

= $180,000 × 0.05 / 0.97769

≈ $9,022.19

Therefore, your parents would have to save approximately $9,022.19 each year to reach their new goal of $180,000.

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Answer:

A= B= C= D= E= F=

Step-by-step explanation:

Answer:

100°

Step-by-step explanation:

∠A and ∠B are supplementary angles, which means:

∠A° + ∠B° = 180°

\((2x) + (2x + 20) = 180\)

Expand the parenthesis and solve for x:

\(2x + 2x + 20 = 180\)

\(4x + 20 = 180\)

\(4x = 180 - 20\)

\(4x = 160\)

\(x = \frac{160}{40}\)

∴\(x = 40\)

Substitute the value of x to determine the measurement of ∠B:

\(2(40) + 20\)

\(80 + 20\)

= 100°

Answer:

Interes ganado= €59.07

Step-by-step explanation:

Dada la siguiente informacion:

300€ durante 5 años al 0.3% de interés compuesto mensual.

Para calcular el valor final de la inversión y el interés ganado, debemos usar la siguiente formula:

FV= PV*(1 + i)^n

Present Value= 300

i= 0.003

n= 5*12= 60 meses

FV= 300*(1.003^60)

FV= 359.07

Interes ganado= 359.07 - 300

Interes ganado= 59.07

Answer:

1/2 is a rational number.

Step-by-step explanation:

Real numbers are numbers that can represent "distance" along a line. The set of real numbers has subsets that include natural numbers, whole numbers, integers, and rational numbers.

Natural numbers are counting numbers. A.K.A., they are numbers that you would start counting your fingers on (1, 2, 3, ...)

Whole numbers are just natural numbers and 0.

Integers are whole numbers and their opposite. (..., -3, -2, -1, 0, 1, 2, 3, ...)

Rational numbers are integers and numbers that can be put into a fraction of two integers. For example, 3/4 is a fraction of two natural numbers (3 and 4) who are also integers. Therefore, 3/4 is a rational number.

So, what number is 1/2?

It can't be a natural number because no one counts numbers as fractions unless they were made to.

It can't be a whole number because 1/2 is not whole. It is half of 1.

It can't be an integer because integers include whole numbers and their opposites, and 1/2 isn't even a whole number.

1/2 has to be an rational number because it is a fraction of two integers, 1 and 2.

Answer:

(- 1, - 3 )

Step-by-step explanation:

The solution to a system of equations given graphically is at the point of intersection of the 2 lines.

The lines intersect at (- 1, - 3 ) ← solution

Answer:

Step-by-step explanation:

Formula

m =  (y2 - y1)/(x2 - x`1)

Givens

Points M(-5,4) and N(2,-1)

y2 = 4

y1 = -1

x2 = - 5

x1 = 2

Solution

m = (4 - - 1) / (-5 - 2)

m  = (4 + 1) / (- 7)

m = (5) / (- 7)

Answer: m (slope ) = 5/-7

Note

The question is how do you enter it? It depends on how you have been told to enter fractions or mixed numbers. I would answer it as

-5

-----

7

which you will note transfers the minus sign to the top of the fraction. It shouldn't matter as long as the net result is minus.

Use a calculator.

\(\cos \theta=\cos 90^{\circ}=0.00\\\\\sin \theta=\sin 90^{\circ}=1.00\)

The option that proves that line AO ≅ line BO is

According to the hypotenuse-leg (HL) theorem, a right triangle is congruent if each of its hypotenuse and legs are congruent with their corresponding hypotenuse and legs in another right triangle. The HL theorem proves that these triangles are congruent.

Using the theorem to the figure in the question

line AP ⊥ line AB, line BQ ⊥ line AB

this proves that the triangles is a right triangle hence possibility of the Hypotenuse leg theorem

line PQ ≅ line OQ

this is proves that the hypotenuse of the both triangles are equal

line AP ≅ line BQ

this proves that one of the legs are equal hence confirming the use of hypotenuse leg theorem

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Answer:

x = 1

Step-by-step explanation:

The absolute value always gives a positive value. However, the expression inside can be positive or negative , so

4x - 13 = 5x + 4 ( subtract 4x from both sides )

- 13 = x + 4 ( subtract 4 from both sides )

- 17 = x

OR

- (4x - 13) = 5x + 4 , simplify left side

- 4x + 13 = 5x + 4 ( subtract 5x from both sides )

- 9x + 13 = 4 ( subtract 13 from both sides )

- 9x = - 9 ( divide both sides by - 9 )

x = 1

As a check

Substitute these values into the equation and if both sides are equal then they are solutions.

x = - 17

left side = | 4(- 17) - 13 | = | - 68 - 13 | = | - 81 | = 81

right side = 5(- 17) + 4 = - 85 + 4 = - 81 ≠ 81

Then x = - 17 is an extraneous solution

x = 1

left side = | 4(1) - 13 | = | 4 - 13 | = | - 9 | = 9

right side = 5(1) + 4 = 5 + 4 = 9

Then solution is x = 1

Answer:

There is no solution to this equation

Step-by-step explanation:

2x+1=2(x-2)=

2x+1=2x-4

0x = -5

Answer is no solution

this statement is false

2x+1=2(x-2)

2x+1=2x-4

cancel equal terms

1=-4

This expression will give you the probability of drawing exactly two blue marbles.

To find the probability that she draws exactly two blue marbles, we need to consider the probability of drawing two blue marbles and one red marble in any order.

Let's assume the probability of drawing a blue marble is denoted by "P(B)" and the probability of drawing a red marble is denoted by "P(R)". Since she replaces only the blue marbles, the probability of drawing a blue marble remains the same for each draw.

To calculate the probability of drawing exactly two blue marbles, we can use the binomial probability formula:

P(2 blue marbles) = C(3, 2) * (P(B))^2 * (P(R))^1

Where C(3, 2) is the number of ways to choose 2 items out of 3, given by the combination formula:

C(3, 2) = 3! / (2! * (3 - 2)!) = 3

Since the probability of drawing a blue marble remains the same for each draw, we can simplify the formula:

P(2 blue marbles) = 3 * (P(B))^2 * (P(R))^1

Now, substitute the actual values of P(B) and P(R) into the formula. For example, if the probability of drawing a blue marble is 0.4 and the probability of drawing a red marble is 0.6, the calculation would be:

P(2 blue marbles) = 3 * (0.4)^2 * (0.6)^1

Simplifying this expression will give you the probability of drawing exactly two blue marbles.

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Answer:

15x^3y+6x^2y^2+9xy^3

Answer:

8-12=4

4 x 9= 36

that answer

Step-by-step explanation:

Answer:yellow .

Step-by-step explanation: you’re moving over 2 to the right. Right is positive. Down is negative, and since you’re doing 2 to the right, and down 1, we have (2,-1)

The vector z in the component form is z = < 21 , 24 , -27 >

Given data ,

A vector in component form is typically written as an ordered pair or triplet, where each component represents the magnitude of the vector along a specific coordinate axis.

Now , the vector u = < -1 , 3 , 1 >

v = < 4 , -3 , -1 >

w = < 10 , 5 , -10 >

Now , the value of vector z = < 3w - 2v + u >

z = 3w - 2v + u

z = 3w - 2 * < 4 , -3 , -1 > + < -1 , 3 , 1 >

Using scalar multiplication, we get:

z = < 30 , 15 , -30 > - < 8 , -6 , -2 > + < -1 , 3 , 1 >

Adding vectors, we get:

z = < 30 - 8 - 1 , 15 - (-6) + 3 , -30 + 2 + 1 >

z = < 21 , 24 , -27 >

Hence , the vector z in component form is z = < 21 , 24 , -27 >

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Using the Chi-Square distribution table, the confidence interval for the standard deviation of the height of students at uh is (2.20, 5.26)

The following formulas provide the standard deviation's confidence interval:

\((\sqrt{\frac{(n-1)(s)^{2} }{X^{2}_{n-1,\alpha/2 } } } , \sqrt{\frac{(n-1)(s)^{2} }{X^{2}_{n-1, 1-\alpha /2} } }\)

Given parameters:

n= 12 ; s= 3.1

Significance level :

\(\alpha - 1 = 1 - 0.95 = 0.05\)

Using  Chi-square distribution table,

\(X^{2} _{11, 0.025} =21.95\\\\X^{2} _{11, 0.975} = 3.82\)

Currently, the following equations provide the 95% confidence interval for the standard deviation of students' heights at UH:-

\((\sqrt{\frac{(11)(3.1)^{2} }{21.92 } } , \sqrt{\frac{(11)(3.1)^{2} }{3.82 } } =(2.20, 5.26)\)

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Answer:

(-1, -8) (0, -1) (1, 6) Plot these points, connect them, then you have your line.

Step-by-step explanation:

The y intercept is -1 and the slope is 7. Plot a point at (0, -1) then go up 7, then right 1, plot another point, go up 7 more, right one, plot another point and so on.

No, the F-test statistic cannot be less than 1 when it represents the larger of two sample variances.

The F-distribution is always a positive distribution with a range of values greater than zero. The F-test value is always greater than or equal to 0, but it is not always less than or equal to 1.

The numerator, representing the bigger sample variance, is always greater than or equal to the denominator, representing the smaller sample variance. Consequently, the F-ratio, which is the ratio of the larger to the smaller variance, is always greater than or equal to 1. Thus, an F-test statistic that is less than 1 is mathematically incorrect.

Therefore, an F-test statistic is always a positive number that is greater than or equal to zero and greater than or equal to 1. This is because the numerator of an F-distribution is always greater than or equal to the denominator.

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For 2 sec the snowboarder in the air.

We have,

The height (in feet) of a snowboarder above the bottom of the half-pipe can be modeled by h=-16t²+24t + 16.4

So, 3.2 = -16t² + 24t + 16.4

-16t² + 24t + 12.4 = 0

Now, solving the above quadratic equation we get

t = -0.40650, 1.90650

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15 gallons of 30% butterfat cream must be mixed with milk.

How to solve word problems?

It's actually fairly easy to solve word problems using a tried-and-true step-by-step approach.

If m is the gallons of 30% butterfat cream, and c is the gallons of 3% butterfat milk, then:

Let m be the milk and c be the cream:

m + c = 45 ⇒ (i)

0.03m + 0.3c = 0.12 * 45 ⇒ (ii)

Solve the system of equations with substitution or elimination.  Using substitution:

0.30 m + 0.03 (45 − c) = 0.12 * 45

0.30 m + 1.35 − 0.03 c = 5.4

0.27 m = 4.05

m = 15

Hence, 15 gallons of 30% butterfat cream must be mixed with milk.

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Answer: 112.5

Step-by-step explanation: When line AB and CD intersect at point E, angle AEC equals BED so you set them equal to each other and find what x is. 5x -20 = x + 50, solving for x, which gives you 17.5. Finding x will tell you what AEC and BED by plugging it in which is 67.5. Angle BED and BEC are supplementary angles which adds up to 180 degrees. So to find angle CEB, subtract 67.5 from 180 and you get 112.5 degrees.

Answer: Neither

Step-by-step explanation:

For this to be paralell it would need to have the same slope. (They don't  have the same.) For this to perpandicular it would have to reciporcal  ( Ex: -2 reciporcal would -1/2 or 1/4 reciprocal would have to be 4)

Answer:

neither

Step-by-step explanation:

For two lines to be parallel, their slopes must be equal.

For two lines to be perpendicular, their slopes must have a product of -1. (The only exception is a vertical line and a horizontal line which are perpendicular, but the product of their slopes is not -1.)

When the equation of a line is written in the slope-intercept form,

y = mx + b,

m is the slope.

y = -2x + 4 has a slope of -2.

y = (1/4)x -2 has a slope of 1/4.

Clearly, -2 and 1/4 are not equal, so the lines are not parallel.

Now we find the product of the slopes.

(-2) * (1/4) = -2/4 = -1/2

The product of the slopes does not equal -1, so the lines are not perpendicular.

Answer: neither

a) The amount you will repay is approximately $12,000.

b) The annual interest rate charged by the loan company is approximately 18.2715%.

To calculate the amount you will repay and the annual interest rate charged by the loan company, we can follow these steps:

Step 1: Calculate the number of $500 increments for the loan amount:

Number of $500 increments = loan amount / $500

= $1,693 / $500

≈ 3.386

Since we can't have a fraction of an increment, we round up to 4.

Step 2: Calculate the daily payment:

Daily payment = 25 © * Number of $500 increments

= 25 © * 4

= $100

Step 3: Calculate the total repayment amount:

Total repayment amount = Daily payment * number of days

= $100 * 120

= $12,000

Step 4: Calculate the annual interest rate:

Annual interest rate = (Total repayment amount - Loan amount) / Loan amount * (360 / Number of days)

= ($12,000 - $1,693) / $1,693 * (360 / 120)

Now, let's perform the calculations:

Amount you repay ≈ $12,000

Annual interest rate ≈ (($12,000 - $1,693) / $1,693) * (360 / 120)

Calculating the annual interest rate:

Annual interest rate ≈ (($10,307) / $1,693) * 3

Rounding to four decimal places:

Annual interest rate ≈ (6.0905) * 3

≈ 18.2715

Therefore,

a) The amount you will repay is approximately $12,000.

b) The annual interest rate charged by the loan company is approximately 18.2715%.

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According to this property, when both sides of an equation are multiplied by the same real number, both sides of the equation always remain the same. The formula for this property can be expressed in real numbers a, b and c. If a × c = b × c.

Property of Equality:

The equivalence property describes the relationship between two equal quantities. If you apply a math operation to one side of the equation, you must also apply it to the other side of the equation to maintain balance.

That is, a property that does not change the truth value of an equation or does not affect the equivalence of two or more quantities is called an equality property. These equality properties help solve various algebraic equations and define equivalence or equilibrium relationships.

Multiplicative Property of Equality:

According to this property, when both sides of an equation are multiplied by the same real number, both sides of the equation always remain the same.

The formula for this property can be expressed as for the real numbers a, b, and c.

If a × b, then, a × c = b × c.

In algebra, the multiplicative property of an equation helps extract unknown terms from an equation. Because multiplication and division are opposites of each other.

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If the price level in Canada falls and the price level in the United States does not change, Canadian-manufactured sofas are relatively less expensive, so Sherri will likely purchase a Canadian manufactured sofa.

This is because the decrease in price level in Canada would make Canadian goods more affordable, including Canadian manufactured sofas. This makes them a more attractive option for Sherri than U.S. manufactured sofas which would still be relatively more expensive even if their price level did not change. Answer D is correct in this scenario. However, if U.S. manufactured sofas were initially more expensive than Canadian sofas, then answer B could also be correct. Overall, Sherri's decision would depend on the initial price difference between Canadian and U.S. manufactured sofas, as well as her personal preferences and any other relevant factors.

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Answer:

the answer is 5 ^_^

Step-by-step explanation:

hopeee it helpss ^_^