Which expression is equivalent to (2-7 i) / (2i)³ ?

(A) (7/8) - (1/4)i

(B) (1/4) - (7/8) i

(C) (7/8) + (1/4)i

(D) (1/4) + (7/8) i

Answer:

\( - 11 \frac{1}{2} \)

Step-by-step explanation:

8x + 5y = 7

4x - 5y = 11

If you all it all up we have

8x + 4x +5y - 5y = 18

12x=18

x=18/12=1.5=3/2 = 1 whole number 1 over 2(1 1/2)

subtituting the value of x into equation 1(8x + 5y = 7)

8(1.5) + 5y = 7

5y=7-12

5y = -5

y=-5/5

y= -1

4(x+2)

hope this helps

Answer:

Correct Choice: Second Option

\(\displaystyle x=\frac{5\pm \sqrt{97}}{12}\)

Step-by-step explanation:

Standard Form of Quadratic Function

The standard representation of a quadratic function is:

\(f(x)=ax^2+bx+c\)

where a,b, and c are constants.

Solving with the quadratic formula:

\(\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\)

We have the following equation to solve:

\(5x = 6x^2 -3\)

Rearranging all the terms to the left side:

\(6x^2 -5x- 3=0\)

Comparing with the general form of the quadratic equation: a=6, b=-5, c=-3. Apply the formula:

\(\displaystyle x=\frac{-(-5)\pm \sqrt{(-5)^2-4(6)(-3)}}{2(6)}\)

\(\displaystyle x=\frac{5\pm \sqrt{25+72}}{12}\)

\(\boxed{\displaystyle x=\frac{5\pm \sqrt{97}}{12}}\)

Correct Choice: Second Option

The center of the circle is (7,8) and the equation of the given circle is (x- 7)^2 + (y - 8)^2 = 16

The given parameters are:

Center (a,b) = (7,8)

Point (x,y) = (11,8)

Calculate the radius (r) using:

\(r = \sqrt{(x- a)^2 + (y - b)^2}\)

So, we have:

\(r= \sqrt{(11- 7)^2 + (8 - 8)^2}\)

Evaluate the expression

\(r = 4\)

The circle equation is then calculated using:

\((x- a)^2 + (y - b)^2 =r^2\)

So, we have:

\((x- 7)^2 + (y - 8)^2 = 4^2\)

Evaluate the exponent

\((x- 7)^2 + (y - 8)^2 = 16\)

Hence, the equation of the given circle is (x- 7)^2 + (y - 8)^2 = 16

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\(\bold{\text{Answer:}\quad \dfrac{-48x^4-42x^3-15x^2-5x}{(8x+7)(3x+1)}}\)

Step-by-step explanation:

\(.\quad \dfrac{-5x}{8x+7}-\dfrac{6x^3}{3x+1}\\\\\\=\dfrac{-5x}{8x+7}+\dfrac{-6x^3}{3x+1}\\\\\\=\dfrac{-5x}{8x+7}\bigg(\dfrac{3x+1}{3x+1}\bigg)+\dfrac{-6x^3}{3x+1}\bigg(\dfrac{8x+7}{8x+7}\bigg)\\\\\\=\dfrac{-15x^2-5x}{(8x+7)(3x+1)}+\dfrac{-48x^4-42x^3}{(8x+7)(3x+1)}\\\\\\=\large\boxed{\dfrac{-48x^4-42x^3-15x^2-5x}{(8x+7)(3x+1)}}\)

Answer:

227 dollars left

Step-by-step explanation:

1099-872

227

Answer:

9g2 - 42g + 49 AC = 9 × 49 = 441 factors = -21, -21

9g2 - 21g - 21g + 49

3g (3g - 7) - 7(3g - 7)

(3g - 7) (3g - 7)

g2 + 2g - 24 AC = 1 × 24 = 24 factors = 6, -4

g2 + 6g - 4g - 24

g (g + 6) - 4(g + 6)

(g + 6) (g - 4)

Answer:

4, 12, 20, 28, 36

Step-by-step explanation:

to find Y you have to multiple x times 4 then subtract by 4

example: x=2 so you do 2(4) - 4

2(4) is 8 and 8 - 4 is 4

y = 4 and so on

The experimental probability of rolling a number less than 3 is given as follows:

p = 3/200.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The total number of outcomes for this problem is given as follows:

2000.

The desired outcomes are those with a result of 1 or 2, which are numbers less than 3, hence the amount is given as follows:

16 + 14 = 30.

Hence the experimental probability is given as follows:

p = 30/2000

p = 3/200.

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Answer:

38.3

Step-by-step explanation:

The perimeter of the figure can be broken down into the perimeter of 3 sides of the parallelogram, and the perimeter of the semicircle (without its diameter).

The three sides of the parallelogram would be 14+14+4=32.

The perimeter of the semicircle would be 1/2*diameter*pi, which is about 1/2*4*3.14=6.28.

Therefore, the perimeter is 32+6.28=38.3 (to the nearest tenths).

If you choose the rebate offer, your monthly payment for the car loan at the bank will be approximately $557 (rounded to the nearest dollar).

To calculate the monthly payment for each financing option, we'll use the information provided:

1. 0% financing for 48 months:

Since the financing is offered at 0% interest, the monthly payment can be calculated by dividing the total purchase price by the number of months.

Purchase Price: $26,050

Number of Months: 48

Monthly Payment = Purchase Price / Number of Months

Monthly Payment = $26,050 / 48 ≈ $543

Therefore, the monthly payment for the 0% financing option for 48 months is approximately $543.

2. Rebate offer and car loan at the bank:

If you choose the rebate offer, you'll need to finance the remaining balance after deducting the rebate amount. Let's calculate the remaining balance:

Purchase Price: $26,050

Rebate Offer: $2,900

Remaining Balance = Purchase Price - Rebate Offer

Remaining Balance = $26,050 - $2,900 = $23,150

Now, we'll calculate the monthly payment using the remaining balance and the loan terms from the local bank:

Remaining Balance: $23,150

Interest Rate: 5.24% (compounded monthly)

Number of Months: 48

Monthly Payment = (Remaining Balance * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Months))

First, let's calculate the Monthly Interest Rate:

Monthly Interest Rate = Annual Interest Rate / 12

Monthly Interest Rate = 5.24% / 12 ≈ 0.437%

Now, we can calculate the Monthly Payment using the formula mentioned above:

Monthly Payment = ($23,150 * 0.437%) / (1 - (1 + 0.437%)^(-48))

Monthly Payment ≈ $557

Therefore, if you choose the rebate offer, your monthly payment for the car loan at the bank will be approximately $557 (rounded to the nearest dollar).

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The formula of the conjugate acid of HCO₂⁻ can be determined by adding a proton (H⁺) to the anion. HCO₂⁻ is a base as it can accept a proton to form a conjugate acid. The reaction between HCO₂⁻ and H⁺ forms the conjugate acid of HCO₂⁻, which is H₂CO₂.

The balanced equation for the formation of the conjugate acid of HCO₂⁻ is as follows:HCO₂⁻ + H⁺ → H₂CO₂H₂CO₂ is a weak acid that forms when CO₂ gas is dissolved in water. It can donate a proton to form the HCO₂⁻ anion. HCO₂⁻ is a stronger base than H₂CO₂ because it has a greater tendency to accept a proton and form a conjugate acid. Thus, H₂CO₂ is a weaker acid than HCO₂⁻.

The formation of the conjugate acid of HCO₂⁻ shows that the addition of a proton to a base forms a weaker acid, while the removal of a proton from an acid forms a weaker base.Answer: The formula of the conjugate acid of HCO₂⁻ is H₂CO₂.

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The expected number of balls in the first bin would be (1/n)^n

It is given that,

The number of balls and bins is same

If so, then there should always be one ball in each container. The likelihood that every ball will land in the first bin is (1/n)^n.

For example -

Let there be three balls and three bins. Put an A, B, and C next to each ball. The bins are marked 1, 2, and 3. Ball A is likely to land in bin 1 with a 1/3 chance. However, there is a 1/3 chance that ball B will land in bin 1, and there is a 1/3 chance that ball C will land in bin 1. As a result, bin 1 should have a value of 1/3 + 1/3 + 1/3 = 1. The expected values of bins 2 and 3 follow a similar rationale.

By the same reasoning, bins 2 and 3 should likewise have anticipated values of 1.

How likely is it that all three balls will fall into bin one?

1/3 x 1/3 x 1/3 = 1/27, or in the general situation, (1/n)^n, which equals (1/3)^3.

Hence, the expected number of balls in the first bin would be (1/n)^n

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The correct option is C

Containing both apples and oranges

A set of items can be divided into subsets in two different ways: combination and permutation. The components of the subset may be arranged in any order when combined. The subset's components are listed in a permutation in a certain order.

The box with the words "apples and oranges" must be opened. By definition, the fruit in the box is the sole type of fruit it contains. Let's say you discovered an apple in the box that had both apples and oranges listed on the label. Since you know it must consequently only contain apples, you draw the conclusion that the box labeled "oranges" cannot contain only oranges because all boxes have allegedly been mislabeled. As a result, the box marked "oranges" must have both apples and oranges while the box marked "apples" can only include oranges.

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I understand that the question you are looking for is:

There are three boxes, one contains only apples, one contains only oranges, and one contains both apples and oranges. The boxes have been incorrectly labeled such that no label identifies the actual contents of the box it labels. Opening just one box, and without looking in the box, you take out one piece of fruit. By looking at the fruit, you can immediately label all of the boxes correctly. Which box did you open?

A. Containing apple

B. Containing oranges

C. Containing both apples and oranges

D. Cannot be determined

Answer:

The answer is C.Standard Form. The rest are used when graphing. Hope this helps!

Let's verify all options to see which is correct.

This equation is not in point-slope form because if we compare the given equation with the formula, they both will be in different forms.

Henceforth, this equation is not in point-slope form.

This equation is not in slope intercept form because if we compare the given equation with the formula, they both will be in different forms.

Henceforth, this equation is not in slope intercept form.

This equation is in standard form because if we compare the given equation with the formula, they both will be in similar forms.

Henceforth, this equation is in standard form.

This equation is not in general form because if we compare the given equation with the formula, they both will be in different forms.

Henceforth, this equation is not in slope intercept form.

It is proved that (a + b)(b + c) - (a + c)(b + d) = (b - c)² when a, b, c, d are in continued fraction method.

Continued fraction method is an alternative way of writing fractions in which numerator is always 1 and denominator is a whole number. If a, b, c, d are in continued fraction method, then it is given that {a, b, c, d} is of the form:
{a, b, c, d} = a + 1/(b + 1/(c + 1/d))
The given equation is: (a + b)(b + c) - (a + c)(b + d) = (b - c)²
Expanding both sides of the equation, we get:
a.b + a.c + b.b + b.c - a.c - c.d - b.d - a.b = b.b - 2b.c + c.c
Simplifying, we get:
-b.d - a.c + a.b - c.d = (b - c)²
Multiplying each side of the equation with -1, we get:
a.c - a.b + b.d + c.d = (c - b)²
Using the definition of continued fractions, we can rewrite the left-hand side of the equation as:
a.c - a.b + b.d + c.d = 1/[(1/b + 1/a)(1/d + 1/c)] = 1/(ad + bc + ac/b + bd/c)
Squaring both sides of the equation, we get:
[(ad + bc + ac/b + bd/c)]² = (c - b)²
Expanding and simplifying both sides, we get:
a²c² + 2abcd + b²d² + 2ac(b + c) + 2bd(a + d) = c² - 2bc + b²
Rearranging, we get:
a²c² + 2abcd + b²d² - 2bc + 2ac(b + c) + 2bd(a + d) - c² + b² = 0
Multiplying both sides of the equation with (c - b)², we get:
[(a + c)(b + d) - (a + b)(c + d)]² = (b - c)⁴
Taking the square root on both sides of the equation, we get:
(a + c)(b + d) - (a + b)(c + d) = (b - c)²
Hence, it is proved that (a + b)(b + c) - (a + c)(b + d) = (b - c)² when a, b, c, d are in continued fraction method.

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Answer:

The coefficient is: *-5*

in the -5x.

Step-by-step explanation:

Answer:

the distance between P and Q is ≈ 6.2 units

Step-by-step explanation:

calculate the distance d using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = P (1, 5 ) and (x₂, y₂ ) = Q (5.5, 9.25 )

d = \(\sqrt{(5.5-1)^2+(9.25-5)^2}\)

   = \(\sqrt{(4.5)^2+(4.25)^2}\)

   = \(\sqrt{20.25+18.0625}\)

   = \(\sqrt{38.3125}\)

   ≈ 6.2 ( to the nearest tenth )

The cost of the car will be less than or equal to $4,450.

What is a equation?

An equation is a mathematical statement that indicates the equality of two expressions. It contains one or more variables and usually includes mathematical operations such as addition, subtraction, multiplication, division, or exponentiation.

Let the cost of the car be "d" (in dollars). Then, the total expenses, including taxes and fees, can be expressed as:

Total expenses = Cost of the car + Taxes + Fees

We can represent the cost of the car as "d", and the taxes and fees as a fixed amount "t". Therefore, the equation to model Samantha's total expenses can be written as:

Total expenses = d + t

From the problem, we know that Samantha paid a total of $4,450 for the car, taxes, and fees. Therefore, we can write:

d + t = 4450

To find the cost of the car, we need to isolate the variable "d" on one side of the equation. We can do this by subtracting "t" from both sides of the equation:

d + t - t = 4450 - t

Simplifying the equation, we get:

d = 4450 - t

To determine the cost of the car, we need to know the value of "t", which represents the total taxes and fees. Unfortunately, the problem does not provide this information, so we cannot determine the exact cost of the car. However, we do know that the cost of the car will be less than or equal to $4,450, since the total expenses cannot be negative.

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Answer:

4

Step-by-step explanation:

(9 - 1) / (3 - 1) = 8/2 = 4

Answer:

4

Step-by-step explanation:

To find the slope using two points

m= (y2-y1)/(x2-x1)

   = (9-1)/(3-1)

   = 8/2

   = 4

Answer:

The answer is

Step-by-step explanation:

The distance between two points can be found by using the formula

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

E(-1, 0) and F(12, 0)

The distance between them is

We have the final answer as

Hope this helps you

Answer:

Concept: Statistics

Answer:

u will try urself ......okay ...

...

Answer:

Step-by-step explanation:

3√10

Answer:

By the prime factorization method, we find that the simplest radical

Have a Nice Day.

Answer:

i dont know

Step-by-step explanation:

ask sssniperwelperer562

Answer:

x=2, y=1

Step-by-step explanation:

4x+8y=16

4x-8y=0

Add the two equations together:

8x=16

Divide both sides by 8:

x=2

Plug this back into one of the original equations to find y:

4(2)-8y=0

8-8y=0

y=1

Hope this helps!

Answer:

x, y = (0, 0)

Step-by-step explanation:

photo math broo

The equivalence class of (1,1) is

[ (1,1) = { (a,a) | a is any non zero integer . }

Since ,

(1,1)  ~ (a,a) as 1(a) = a(1)

Here,

Let ~ be the relation on Z x Z - {0} such that (a,b) ~ (c,d)  if and only if ad = bc

Let any (a,b) (c,d) (e,f) ∈ Z x Z - {0} .

Prove relation ~ is reflexive:

clearly ab = ba

(a,b) ~ (a,b)

Hence relation ~ is reflexive.

Prove relation ~ is symmetric:

Let (a,b) ~ (c,d)

ad = bc

bc = ad

cd = ba

(c,d) ~ (a,b)

Hence relation ~ is symmetric.

Prove relation ~ is transitive:

Let (a,b) ~ (c,d) and (c,d) ~ (e ,f)

ad = bc

cf = de

adcf = bcde

Dividing by dc

fa = be

(a,b) ~ (e,f)

Hence relation ~ is transitive.

Hence the relation ~ is an equivalence relation.

The equivalence class of (1,1) is

[ (1,1) = { (a,a) | a is any non zero integer . }

Since ,

(1,1)  ~ (a,a) as 1(a) = a(1)

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Answer:

12

Step-by-step explanation:

The condensed truth table for a 4x1 mux is shown below.

The SOP equation for the 4x1 mux can be expressed as follows:

Y = S1' * S0' * D0 + S1' * S0 * D1 + S1 * S0' * D2 + S1 * S0 * D3

To create a condensed truth table for a 4x1 multiplexer (mux), we need to consider the inputs and outputs of the mux. A 4x1 mux has two select inputs (S1 and S0) and four data inputs (D0, D1, D2, and D3), along with one output (Y).

Here is the condensed truth table for a 4x1 mux:

| S1 | S0 | D0 | D1 | D2 | D3 | Y |

|----|----|----|----|----|----|---|

| 0  | 0  | D0 | D1 | D2 | D3 | Y0 |

| 0  | 1  | D0 | D1 | D2 | D3 | Y1 |

| 1  | 0  | D0 | D1 | D2 | D3 | Y2 |

| 1  | 1  | D0 | D1 | D2 | D3 | Y3 |

The inputs S1 and S0 determine which data input (D0, D1, D2, or D3) is selected and routed to the output Y. The output depends on the selected input and follows the corresponding Y output.

b. To write the minimized sum of products (SOP) equation for the 4x1 mux, we need to determine the boolean expression for the output Y based on the inputs S1, S0, and the data inputs D0, D1, D2, D3.

The SOP equation for the 4x1 mux can be expressed as follows:

Y = S1' * S0' * D0 + S1' * S0 * D1 + S1 * S0' * D2 + S1 * S0 * D3

In this equation, the ' symbol denotes the negation (complement) of the corresponding input. The equation represents the logical OR of the product terms, where each product term corresponds to a specific combination of select inputs and data inputs.

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The given argument is invalid. It says that if one person has more gray hair in their beard than another person, then they have a higher percentage of gray hair in their beard.

The argument is invalid because it is possible for one person to have a higher percentage of gray hair in their beard but a lower number of gray hairs in total.One possible counterexample by model is:Suppose Plato has 200 hairs in his beard and 50 of them are gray. So, 1/4 of his hairs are gray. Now, let's suppose Aristotle has 400 hairs in his beard, and 300 of them are gray. So, 3/4 of his hairs are gray. Even though Plato has fewer gray hairs than Aristotle, his percentage of gray hairs is more significant (1/4) than Aristotle's (3/4).

Therefore, the given argument is invalid since Aristotle's beard contains more gray hairs in quantity, but Plato has a higher percentage of gray hair in his beard.

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