1. What value is equivalent to 3 x 12 - (4 + 2)?

A complex number is a part of a number system that includes a real unit and an imaginary unit. All the statements are true except C and E.

A complex number is a part of a number system that includes the real numbers as well as a particular element labelled i, sometimes known as the imaginary unit, and which obeys the equation i² = 1.

As it is given that x=(a+bi), y=(c+di), and z=(f+gi), therefore, we need to plug in the values to check which all are true.

A.) x+y=y+x

\(x+y=y+x\\a+bi+c+di=c+di+a+bi\)

As the two sides of the equation are equal, the equation is true.

B.) (x × y) × z = x × (y × z)

\((x \times y) \times z = x \times (y \times z)\\\\\ [ (a+bi) \times (c+di) ]\times (f+gi) = (a+bi) \times [(c+di) \times (f+gi)]\\\\(ac+adi+bci-bd) \times (f+gi)= (a+bi) \times (cf+cgi+fdi-dg)\)

\((ac+adi+bci-bd) \times (f+gi)= (a+bi) \times (cf+cgi+fdi-dg)\\\\\\acf+adfi+bcfi-bdf+acgi-adg-bcg-bdgi = acf+acgi+afdi-adg + bcfi-bcg-bfd-bdgi\)

As the two sides of the equation are equal, the equation is true.

C.) x−y=y−x

\(x-y=y-x\\\\(a+bi)-(c+di)=(c+di)-(a+bi)\\\\a+bi-c-di=c+di-a-bi\)

As the two sides of the equation are not equal, the equation is not true.

D.) (x+y)+z=x+(y+z)

\((x+y)+z=x+(y+z)\\\\(a+bi+c+di)+f+gi = a+bi+(c+di+f+gi)\\\\a+bi+c+di+f+gi = a+bi+c+di+f+gi\)

As the two sides of the equation are equal, the equation is true.

E.) (x−y)−z=x−(y−z)

\((x-y)-z=x-(y-z)\\\\(a+bi-c-di)-f-gi = a+bi-(c+di-f-gi)\\\\a+bi-c-di-f-gi =a+bi-c-di+f+gi)\)

As the two sides of the equation are not equal, the equation is not true.

Hence, all the statements are true except C and E.

Learn more about Complex Number:

https://brainly.com/question/12464608

Answer:

9.7264

Step-by-step explanation:

I hope this helps!

The rate at which the distance is changing is calculated to be 14.42 miles per hour.

Consider the east direction to be denoted by x and the north direction to be denoted by y, therefore;

dx / dt = 12 mph

dy / dt = 8 mph
x is equal to 4 miles

Consider the distance between them to be s

Time taken by you to travel 4 miles = distance / speed

Time taken by you to travel 4 miles = 4/12 hour

Distance traveled by the friend in that time = speed × time

Distance traveled by the friend in that time = 8 × (4/12) = 2.67 miles

Now we use the Pythagorean theorem,

x^2 + y^2 + s^2 ...... (1)

Substitute, x = 4 miles and y = 2.67 miles

s^2 = 16 + 7.1289 = 23.1289

s = 4.81

Now differentiate equation 1 with respect to t as follows;

2x (dx/dt) + 2y (dy/dt) = 2s (ds/dt)

2(4) (12) + 2(2.67) (8) = 2 (4.81) (ds/dt)

96 + 42.72 = 9.62 (ds/dt)

138.72 = 9.62 (ds/dt)

ds/dt = 138.72/9.62 = 14.42 miles per hour

Thus the distance is changing at the rate of 14.42 miles per hour.

To learn more about distance; click here:

https://brainly.com/question/13049940

#SPJ4

Answer:

The linear equation is y = 450 - 30 x, where y is the number of pages

Lourdes has left to read after x days

Step-by-step explanation:

Each day, Lourdes reads 30 pages of a 450-page book

- We need to write a linear equation to represent the number of pages

 Lourdes has left to read after x days

∵ Lourdes reads 30 pages each day

∵ Lourdes will read for x days

∴ The number of pages Lourdes will read in x day = 30 x

- The left pages will be the difference between the total pages of the

 book and the pages Lourdes read

∵ The book has 450 pages

∵ Loured will read 30 x in x days

∴ The number of pages left = 450 - 30 x

- Assume that y represents the number of pages Lourdes has left

 to read after x days

∴ y = 450 - 30 x

The linear equation is y = 450 - 30 x, where y is the number of

pages Lourdes has left to read after x days

The minimum possible probability that chip A is defective can be calculated using conditional probability. Given that chips (A, B) and (A, C) are tested defective, the minimum possible probability that chip A is defective is 1/3.

Let's consider the different possibilities for the status of chips A, B, and C.

Case 1: Chip A is defective.

In this case, both (A, B) and (A, C) are tested defective as stated in the problem.

Case 2: Chip B is defective.

In this case, (A, B) is tested defective, but (A, C) is not tested defective.

Case 3: Chip C is defective.

In this case, (A, C) is tested defective, but (A, B) is not tested defective.

Case 4: Neither chip A, B, nor C is defective.

In this case, neither (A, B) nor (A, C) are tested defective.

From the given information, we know that at least one of the pairs (A, B) and (A, C) is tested defective. Therefore, we can eliminate Case 4, as it contradicts the given data.

Among the remaining cases (Case 1, Case 2, and Case 3), only Case 1 satisfies the condition where both (A, B) and (A, C) are tested defective.

Hence, the minimum possible probability that chip A is defective is the probability of Case 1 occurring, which is 1/3.

To know more about Probability visit-

brainly.com/question/31828911

#SPJ11

Answer:

29/24π

Step-by-step explanation:

To get coterminal angles, you simply have to add or subtract 2π

In this problem, we are looking for a coterminal angle that is between

0 and 2π, so we will add 2π to −19/24π.

−19/24π+2π

=

−19/24π+48/24π

=

29/24π

29/24π

is the answer to the question.

\(\frac{11\pi }{4}\) is the coterminal between of \(\frac{19\pi }{4}\) between (0, 2\(\pi\)).

Coterminal angles are the angles that have the same initial side and share the terminal sides.

To find the coterminal angle of an angle, we just add or subtract multiples of 360 degrees from the given angles.

According to the given question.

We have

Angle = \(\frac{19\pi }{4}\)

Since, the coterminal angle is to be between 0 and 2π.

Therefore, we subtract 2π from \(\frac{19\pi }{4}\)to get coterminal angle.

⇒ \(\frac{19\pi }{4} -2\pi\) \(= \frac{19\pi -8\pi }{4} =\frac{11\pi }{4}\)

Hence, \(\frac{11\pi }{4}\) is the coterminal between of \(\frac{19\pi }{4}\) between (0, 2\(\pi\)).

Find out more information about coterminal angle here:

https://brainly.com/question/23093580

#SPJ2

Answer:

0.98 ≤ x ≤ 2.9

Step-by-step explanation:

use graphing calculator

Answer:

Dance class and soccer

Step-by-step explanation:

because in those two fractions the numerators are more than half of the denominators

Stephen's average speed for the round trip was 48 mph.

To find Stephen's average speed, we can use the formula:

Average Speed = Total Distance / Total Time

Let's assume the distance from Stephen's house to his aunt's house is 'd' miles.

On the way to his aunt's house, Stephen traveled at a speed of 60 mph. So the time taken for this leg of the trip is given by:

Time = Distance / Speed = d / 60

On the return trip, Stephen traveled at a speed of 40 mph. So the time taken for this leg of the trip is:

Time = Distance / Speed = d / 40

The total time for the round trip is the sum of the times for the outward and return trips:

Total Time = d / 60 + d / 40

To find the average speed, we divide the total distance by the total time:

Average Speed = Total Distance / Total Time

The total distance for the round trip is 2d (since it's the same roadway for both trips).

Average Speed = 2d / (d / 60 + d / 40)

Simplifying this expression, we get:

Average Speed = 2d / ((3d + 2d) / 120) = 2d / (5d / 120) = 2d * 120 / 5d = 240 / 5 = 48 mph

Therefore, Stephen's average speed for the round trip was 48 mph.

For more questions like Speed  click the link below:

https://brainly.com/question/17661499

#SPJ11

Answer:

C. 48°

Step-by-step explanation:

Answer:

4 – 5x = 59, x = -11

Step-by-step explanation:

The given equations is :

4 – 5x = 59

Subtracting 4 both sides,

4 – 5x -4 = 59-4

-5x = 55

Dividing both sides by -5.

x = -11

So, the answer of the given equation is -11.

Answer:

? lol I will edit this and answer if you actually have a question

Step-by-step explanation:

Answer:

what

Step-by-step explanation:

The most appropriate choice for perimeter of rectangle will be given by

It costs $76.16 to buy enough of the border to go around the room.

What is perimeter of a rectangle?

The total length of the outline of a rectangle is called perimeter of rectangle.

If the length of a rectangle is l units and breadth of a rectangle is b units, then perimeter of rectangle will be given by

                                      \(2 \times (l+b)\) units

Here,

Length of room = 20 feet

Width of room = 12 feet

Perimeter of room = \(2 \times (20 + 12)\)

                               = \(2 \times 32\)

                               = \(64\) feet

cost of 1 foot of border = $1.19

cost of 64 foot of border = $\(1.19 \times 64\)

                                         = $\(76.16\)

To learn more about perimeter of rectangle, refer to the link:

https://brainly.com/question/24571594

#SPJ9

The t-score of 2.779 is used to find the 99% confidence interval for the population mean.

Given,

Assume that orangutans' heights, measured in inches, are regularly distributed with an unidentified mean and standard deviation. The population means are calculated using the orangutan heights of 27 orangutans that were randomly selected.

What t-score should be applied to determine the population mean's 99% confidence interval?

n = 27

confidence level = 0.99

We have to find a critical value for the confidence level of 0.99.

To find the critical value we need degrees of freedom and significance level.

df = n-1 = 27 - 1 = 26

α = 1 - 0.99 = 0.01

α/2 = 0.01/2 = 0.005

For α/2 = 0.005 and df = 26, the critical value using the above table is,

t-critical value = 2.779

To learn more about confidence interval click here:

brainly.com/question/24131141

#SPJ4

Answer:

t is the number of years since 1980

1,500 + 250t = 400(1.18^t)

t = 15.77 years (sometime in 1995)

Answer:

2x+3y

Step-by-step explanation:

you add up the known sides: (x-y)+(x+y) = 2x

Then you subtract the answer from the perimiter: 4x+3y-2x=2x+3y

Answer:

i think the answer is 96

Step-by-step explanation:

The magnitude of the x-component of this vector is 9.05m.

The angle of inclination of the vector is calculated as;

θ = 90 ⁰ - 48.4 ⁰

θ = 41.6 ⁰

The magnitude of the x-component of the vector is calculated as;

Vx = 12.1 m x cos ( 41.6 )

Vx = 9.05 m

A vector can be represented by an ordered set of numbers, called components, that indicate the magnitude and direction of the vector in a particular coordinate system. The components of a vector can be added or subtracted using vector addition and subtraction, and multiplied by a scalar (a real number) using scalar multiplication.

Vectors can be visualized as arrows in a two- or three-dimensional space, where the length of the arrow represents the magnitude of the vector, and the direction of the arrow represents the direction of the vector. Vectors can also be represented as matrices, which can be used to perform various operations on vectors, such as dot product and cross product.

To learn more about Vector visit here:

brainly.com/question/29740341

#SPJ4

Complete Question:-

Answer:

1. )0.35

2. )1.15

3.)0.5 (5 repeating's)

4.)2.72

Step-by-step explanation:

7 divide  20=0.35

-23 divide 20=1.15

-60 divide 22 = 2.727272 but it is 2.72

The exiting humidity is 45% and the amount of water passing is 0.0025 kg/h.

Calculating the required rate of heat transfer

The required rate of heat transfer can be calculated using the following equation:

Q = m * cp * (\(T_2\) - \(T_1\))

where:

Q is the rate of heat transfer (kW)

m is the mass flow rate of air (kg/s)

cp is the specific heat of air (kJ/kgK)

\(T_2\) is the final temperature of the air (K)

\(T_1\) is the initial temperature of the air (K)

In this case, we have:

m = 2.5 kg/s

cp = 1.005 kJ/kgK

\(T_2\) = 50°C + 273.15 = 323.15 K

\(T_1\) = 25°C + 273.15 = 298.15 K

Therefore, the required rate of heat transfer is:

Q = 2.5 * 1.005 * (323.15 - 298.15) = 6.31 kW

Calculating the amount of water added in an hour

The amount of water added in an hour can be calculated using the following equation:

\(m_w\) = m * (\(w_2\) - \(w_1\))

where:

\(m_w\) is the mass of water added (kg/h)

m is the mass flow rate of air (kg/s)

\(w_2\) is the final humidity ratio of the air (kg/kg)

\(w_1\) is the initial humidity ratio of the air (kg/kg)

In this case, we have:

m = 2.5 kg/s

\(w_2\) = 0.05 (50% humidity)

\(w_1\) = 0.035 (35% humidity)

Therefore, the amount of water added in an hour is:

\(m_w\) = 2.5 * (0.05 - 0.035) = 0.035 kg/h

Calculating the exiting humidity and the amount of water passing though the wicks per hour

The exiting humidity can be calculated using the following equation:

\(w_e\) = \(w_1\) * (\(T_2\) / \(T_1\))

where:

\(w_e\) is the exiting humidity ratio of the air (kg/kg)

\(w_1\) is the initial humidity ratio of the air (kg/kg)

\(T_2\) is the final temperature of the air (K)

\(T_1\) is the initial temperature of the air (K)

In this case, we have:

\(w_e\) = 0.035 * (50°C + 273.15) / (25°C + 273.15) = 0.045

The amount of water passing though the wicks per hour can be calculated using the following equation:

\(m_w\) = \(m_w\) * (\(w_e\) - \(w_2\))

where:

\(m_w\) is the amount of water added (kg/h)

\(w_e\) is the exiting humidity ratio of the air (kg/kg)

\(w_2\) is the final humidity ratio of the air (kg/kg)

In this case, we have:

\(m_w\) = 0.035 * (0.045 - 0.05) = 0.0025 kg/h

Therefore, the exiting humidity is 45% and the amount of water passing though the wicks per hour is 0.0025 kg/h.

To learn more about humidity here:

https://brainly.com/question/30672810

#SPJ4

well im guessing it the average highway speed 60 mph so it is $7

The toroid formed by rotating the rectangular figure gives;

a. A toroid

b. 374•π

c. 400•π

d. The surface area will be 4 times the initial surface area

The volume will be 8 times the initial volume

Taking the distance from the y-axis as 8

Width of the rectangle; 2.5

Length; 6

We have;

a. The solid of revolution is a toroid, having sharp corner edges

b. The surface area is found using the surface area of a hollow cylinder as follows;

Outer radius = 8 + 6 = 14

Inside radius = 8

Width = 2.5

Outer area = 2• π × 14 × 2.5 = 70•π

Inner area = 2• π × 8 × 2.5 = 40•π

\({\pi \cdot 14 }^{2} - {\pi \cdot 8 }^{2} = 132 \cdot\pi\)

The surface area of the figure is therefore;

c. The volume of the solid of revolution is found as follows;

\({\pi \cdot 14 }^{2} \times 2.5 - {\pi \cdot 8 }^{2} \times 2.5= 400 \cdot \pi\)

e. When the dimensions are doubled, we have;

The linear scale factor = 2

The area scale factor = 2^2 = 4

Therefore;

The volume scale factor = 2^3 = 8

The volume of the solid following the enlargement, is therefore;

Learn more about scale factor s here:

https://brainly.com/question/9658411

#SPJ1

The population of squirrels in the Louisiana forest growing monthly at a rate of 5% currently from 100, will be 182 after a year.

The final value of any quantity growing constantly at a particular rate is given as \(V = V_{0}e^{rt}\) ,

where V is the final value, V₀ is the initial value, r is the rate of growth per time period, and t is the number of time periods.

The current population of squirrels (V₀) = 100.

The growth rate (r) = 5% per month.

The time period (t) = 1 year = 12 months.

Hence, the final population of squirrels (V), is given as:

\(V = V_{0}e^{rt}\) ,

or, \(V = 100e^{(0.05*12)}\) ,

or, \(V = 100e^{0.60}\) ,

or, V = 100*1.822119,

or, V = 182.2119 ≈ 182.

Therefore, the population of squirrels in the Louisiana forest growing monthly at a rate of 5% currently from 100, will be 182 after a year.

Learn more about growth at

https://brainly.com/question/15241333

#SPJ4

Answer:

14a+22b

Step-by-step explanation:

4(2a+4b) + 3(2a+2b)

Distribute the 4

8a+16b + 3(2a+2b)

Distribute the 3

8a+16b+6a+6b

Combine like terms

14a+22b

Answer:

14a + 22b

Step-by-step explanation:

First, we need to expand:

4(2a) + 4(4b) + 3(2a) + 3(2b)

Now, we can continue and solve

8a + 16b + 6a + 6b

We can simplify

8a + 6a + 16b + 6b

14a + 22b

The answer is 14a + 22b because we don't know the values of a or b, so we cannot solve anymore.

Happy learning!

A race car driver is 3.79 km away from where she started.

Assume that a race car driver turns southwest, at an angle of  45 degrees.

Also she turns East making another 45 degree angle.

So, we get a right triangle.

Let ABC be right triangle with A = 90°, B = 45° and C = 45°

For right triangle ABC, a = 2.75km, b = y km and c = x km (the distance she has traveled east before crossing her northern path)

Consider the sine of angle B

sin(B) = Opposite side of angle B / Hypotenuse

sin(45) = x / 2.75

x = 1.94

sin(C) = Opposite side of angle C / Hypotenuse

sin(45) = y/2.75

y = 1.94

So, the distance to north before paths crossed would be,

N = 4.69 - y

N = 3.31

And the distance after she passed her northern path.

E = 3.89 - x

E = 1.85

Let m be the distance from Starting Point to End Point.

Using Pythagoras theorem,

m² = N² + E²

m² = (3.31)² + (1.85)²

m = 3.79 km

Learn more about the Pythagoras theorem here:

https://brainly.com/question/343682

#SPJ4

Answer:

5. Obtuse

6. Right

7. Acute

Step-by-step explanation:

5. 5,12,15

The square of the longest side is 15^2 = 225. The sum of the squares of the two shorter sides is 5^2 + 12^2 = 169. Since 169 < 225, the triangle is obtuse.

6. 6,8,10

The square of the longest side is 10^2 = 100. The sum of the squares of the two shorter sides is 6^2 + 8^2 = 100. Since 100 = 100, the triangle is right.

7. 12,10,13

The square of the longest side is 13^2 = 169. The sum of the squares of the two shorter sides is 12^2 + 10^2 = 244. Since 244 > 169, the triangle is acute.

Double-check the input and review the solution provided by the matrix calculator to ensure accuracy.

The matrix calculator is a useful tool for solving equations involving matrices. To find the values of the variables in the matrix calculator, follow these steps:

1. Enter the coefficients of the variables and the constant terms into the calculator. For example, if you have the equation 2x + 3y = 10, enter the coefficients 2 and 3, and the constant term 10.

2. Select the appropriate operations for solving the equation. The calculator will provide options such as Gaussian elimination, inverse matrix, or Cramer's rule. Choose the method that suits your equation.

3. Perform the selected operation to solve the equation. The calculator will display the values of the variables based on the solution method. For instance, Gaussian elimination will show the values of x and y.

4. Check the solution for consistency. Substitute the obtained values back into the original equation to ensure they satisfy the equation. If they do, you have found the correct values of the variables.Remember to double-check the input and review the solution provided by the matrix calculator to ensure accuracy.

Learn more about Matrix here,https://brainly.com/question/27929071

#SPJ11

Answer:

-8.8x + 5

Step-by-step explanation:

Equation:

-0.8x + 40 - 8x - 35

-0.8x -8x + 5

-8.8x + 5

*This answer might be from a misunderstanding*

Answer:

-8.8x + 5

Step-by-step explanation:

See attached picture!!

Hope this helps!!