Mathematics College

Subtract the complex numbers.

(5 + 4i) - (7 + 8i)

Answers

Answer 1

Answer:

Step-by-step explanation:

5 + 4i - 7 - 8i

-2 - 4i

Related Questions

What is the value of x in the equation below?
4(x + 1) = 3x +7

Answers

Answer:

89

Step-by-step explanation:

4(x+1) = 3x + 7
4x + 4 = 3x + 7
4x + 4 - 3x = 7
x + 4 = 7
x = 7 - 4
x= 3

A production facility employs 20 workers on the day shift, 15 workers on the swing shift, and 10 workers on the graveyard shift. A quality control consultant is to select 6 of these workers for in-depth interviews. Suppose the selection is made in such a way that any particular group of 6 workers has the same chance of being selected as does any other group (drawing 6 slips without replacement from among 45). (Enter your answers to four decimal places.)

Required:
a. How many selections result in all 7 workers coming from the day shift?
b. What is the probability that all 7 selected workers will be from the day shift?
c. What is the probability that all 7 selected workers will be from the same shift?
d. What is the probability that at least two different shifts will be represented among the selected workers?
e. What is the probability that at least one of the shifts will be unrepresented in that sample of workers?

Answers

Answer:

Step-by-step explanation:

Total number of workers = 20+ 15 + 10 = 45

Suppose 6 workers are selected from 45 workers, the number of ways they can be selected is [tex](^{45}_6)[/tex] ways

If 7 workers are selected from 20 workers on a day shift;

Then, the number of ways to select 7 members from a group of 20 is [tex](^{20}_7)[/tex] ways;

∴

P( all 7 selected workers will be from the day shift) is:

[tex]= \dfrac{(^{20}_7)}{(^{45}_6)}[/tex]

[tex]=\dfrac{ \dfrac{20!}{7!(20-7)!} } { \dfrac{45!}{6!(45-6)!}}[/tex]

= 0.0095

The possible number of ways to select all day shift workers is:

[tex]=(^{20}_{7})[/tex]

The  possible number of ways to select all swing shift workers is:

[tex]=(^{15}_{7})[/tex]

The possible number of ways to select all graveyard shift workers is:

[tex]= ( ^{10}_{7})[/tex]

∴

The probability that all selected workers are from the same shift is:

[tex]= \Bigg [ \dfrac{ (^{20}_7) }{(^{45}_6) } + \dfrac{ (^{15}_7) }{(^{45}_6) } + \dfrac{ (^{10}_7) }{(^{45}_6) } \Bigg][/tex]

[tex]= \begin {bmatrix} \dfrac{ \dfrac{20!} {7!(20-7)!}}{ \dfrac{ 45! }{6!(45-6)!} } + \dfrac{ \dfrac{15!} {7!(15-7)!}}{ \dfrac{ 45! }{6!(45-6)!} } + \dfrac{ \dfrac{10!} {7!(10-7)!}}{ \dfrac{ 45! }{6!(45-6)!} } \end {bmatrix}[/tex]

= 0.0095 + 0.00079 + 0.000015

= 0.010305

P(selected workers are from at least two different shifts)

= 1 - P(selected workers are from 1 shift from any of the 3 shifts)

= 1 - 0.010305

= 0.989695

≅ 0.9897

We can determine the probability that at least one shift is unrepresented through the following ways:

Let assume that:

[tex]X_1 =[/tex] event that day shift is unrepresented

[tex]X_2 =[/tex] event that swing shift is unrepresented

[tex]X_3 =[/tex] event that graveyard shift is unrepresented

Thus; [tex](X_1 \cap X_2)[/tex] = event that all of them are drawn from graveyard shift.

[tex](X_1 \cap X_3) =[/tex] event that all are drawn from swing shift

[tex](X_2 \cap X_3) =[/tex] event that they are all drawn from day shift.

So;

[tex]P(X_1) = \dfrac{(^{25}_{7})} { (^{45}_{6}) } = 0.0590[/tex]

[tex]P(X_2) = \dfrac{(^{30}_{7})} { (^{45}_{6}) } = 0.2499[/tex]

[tex]P(X_3) = \dfrac{(^{35}_{7})} { (^{45}_{6}) } = 0.8256[/tex]

[tex]P(X_1 \cap X_2) = \dfrac{(^{10}_{7})} { (^{45}_{6}) } = 0.000015[/tex]

[tex]P(X_1 \cap X_3) = \dfrac{(^{15}_{7})} { (^{45}_{6}) } = 0.00079[/tex]

[tex]P(X_2 \cap X_3) = \dfrac{(^{20}_{7})} { (^{45}_{6}) } = 0.0095[/tex]

[tex]P(X_1 \cap X_2 \cap X_3) =0[/tex]

Probability (that at least one shift is unrepresented) is:

[tex]= P(X_1) + P(X_2) +P(X_3) - P(X_1 \cap X_2) - P(X_1 \cap X_3) - P(X_2 \cap X_3) + P(X_1 \cap X_2 \cap X_3)[/tex]

= 0.0590 + 0.2499 + 0.8256 - 0.000015 - 0.00079 - 0.0095 + 0

≅ 1.124

The number of boys at CMS is 56% of the total number of students. If there are 1050 students, how many are boys?

Answers

Answer:

558

Step-by-step explanation:

Discussion Prompt: A fair coin is tossed twice and the number of heads is recorded. Jose says the P(1 head) = 1/2, while Jeff students says P(1 head) = 1/3. Explain in detail why Jose is correct.

Answers

Let H represent heads and T represent tails.

Writing HH means we get two heads and HT means we get heads first, then tails second, and so on.

We have these four possible outcomes when flipping two coins

HHHTTHTT

Of those four outcomes, two of them have exactly one head show up (HT and TH). The probability of getting exactly one head is 2/4 = 1/2, so this is why Jose is correct.


2. Using the ruler below, construct a triangle that has side lengths of 3 cm, 4 cm, and 5 cm.
triangle does this appear to be? Verify by using your protractor to measure angles.
What type of

Answers

Step-by-step explanation:

if to apply the Piphagorean theoreme, then one of the angles is 90° (opposite to the side with the length 5):

3²+4²=5²; ⇔ 9+16=25.

What is the ratio of the calories Robyn

burned on Wednesday le the celories she

burned on Monday?

Answers

Question isn't complete but we make assumptions in order to complete the question and explain

Answer and explanation:

If we are given a table on calories burned by Robyn on weekdays from Monday to Friday and on this table Robyn burnt 500 calories on Monday and burnt 400 calories on Wednesday, then we are required to determine the ratio of calories burnt on Wednesday to calories burnt on Monday:

Calories burnt on Wednesday = 400

Calories burnt on Monday =500

Ratio of calories burnt on Wednesday to calories burnt on Monday =400/500=4/5

Ratio =4:5

There were 10 bunches of roses and tulips. Each bunch had 5 of the same flowers. There were 2 more bunches of tulips than roses. How many tulips were there?

Answers

Answer:

I think the answer is 12 (sorry if i misunderstood the question)

Step-by-step explanation:

Because if there are 10 things of roses and tulips and then 2 more tulips are added in the question in total thats 12.... 10+2=12

The table shows values for functions f(x) and g(x) .

What is the solution to f(x)=g(x) ?
Select each correct answer.

A. −3

B. −2

C. −1

D. 0

E. 1

F. 2

G. 3

Answers

G. 3 but I’m not sure you should double check

solve for x -2x + 2 = x -13

Answers

Answer:

x = 5

Step-by-step explanation:

Add 2x to both sides: 2 = 3x - 13

Add 13 to each side: 15 = 3x

Divide both sides by 3: 5 = x

Isolate with the variable by dividing each side by factors that don't contain the variable. So, x= 15

HELP PLZZZ EASY AREA MATH

Answers

Answer:

4,400

Step-by-step explanation:

geometric mean of 384 and 6

Answers

Answer:

48 is the geometric mean of 384 and 6

48 is the meaning of geometric

The Gomez’s deck is shown below. The deck is a regular hexagon. It has a perimeter of 45 units. What is the are of the deck

Answers

Answer:

The area of the deck is of 146.14 squared units.

Step-by-step explanation:

Regular hexagon:

A regular hexagon has 6 sides, all with the same measure.

Perimeter of a regular hexagon:

The perimeter of a regular hexagon with side x is given by:

[tex]P_h = 6x[/tex]

Area of a regular hexagon:

The area of a regular hexagon with side x is given by:

[tex]A_h = \frac{3\sqrt{3}x^{2}}{2}[/tex]

It has a perimeter of 45 units.

This means that:

[tex]6x = 45[/tex]

[tex]x = \frac{45}{6}[/tex]

[tex]x = 7.5[/tex]

What is the are of the deck

[tex]A_h = \frac{3\sqrt{3}x^{2}}{2} = \frac{3\sqrt{3}*(7.5)^{2}}{2} = 146.14[/tex]

The area of the deck is of 146.14 squared units.

Someone help me on question 10 please!

Answers

Answer:

Step-by-step explanation:

500÷9=55.56miles/h (correct to 3 decimal places)

Please. help me guys. ​

Answers

Answer:

40

Step-by-step explanation:

there are 4 quarters so if one quarter is 10 then 4 quarters are 40

10 x 4 = 40

Simplify using Synthetic Division

Answers

Step 1
Write down the first coefficient without changes:
−3223−10−3
−3
2
3 −10 −3
2

Step 2
Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
−3223(−3)⋅2=−63+(−6)=−3−10−3
−
3
2
3
−10 −3
(
−
3
)
⋅
2
=
−
6
2
3
+
(
−
6
)
=
−
3

Step 3
Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
−3223−6−3−10(−3)⋅(−3)=9(−10)+9=−1−3
−
3
2 3
−
10
−3 −6
(
−
3
)
⋅
(
−
3
)
=
9
2
−
3
(
−
10
)
+
9
=
−
1

Step 4
Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
−3223−6−3−109−1−3(−3)⋅(−1)=3(−3)+3=0
−
3
2 3 −10
−
3
−6 9
(
−
3
)
⋅
(
−
1
)
=
3
2 −3
−
1
(
−
3
)
+
3
=
0

We have completed the table and have obtained the following resulting coefficients: 2,−3,−1,0
2
,
−
3
,
−
1
,
0
.
All the coefficients except the last one are the coefficients of the quotient, the last coefficient is the remainder.
Thus, the quotient is 2x2−3x−1
2
x
2
−
3
x
−
1
, and the remainder is 0
0
.
Therefore, 2x3+3x2−10x−3x+3=2x2−3x−1+0x+3=2x2−3x−1
2
x
3
+
3
x
2
−
10
x
−
3
x
+
3
=
2
x
2
−
3
x
−
1
+
0
x
+
3
=
2
x
2
−
3
x
−
1
Answer: 2x3+3x2−10x−3x+3=2x2−3x−1+0x+3=2x2−3x−1

Given that P=x+y. Find P when: x=−5 and y=−3

Answers

Answer:

P = - 8

Step-by-step explanation:

Given

P = x + y ← substitute x = - 5 and y = - 3

P = - 5 + (- 3) = - 5 - 3 = - 8

-4x-y=24 complete the missing value in the solution to the equation

Answers

Answer:

point

Step-by-step explanation:

wei kiat is 4 times as old as hafiz. Find the ratio of Wei kiat's age to hafiz's age. pls help​

Answers

1:4
Example:
There are 4 squares and 1 triangle
There are 4 more times as many squares than triangles

Complete the following statements.

A soda bottle contains 2 liters of liquid. Therefore:

The soda bottle contains  fluid ounces of liquid.

The soda bottle contains  gallons of liquid.

A milk jug contains 2 gallons of milk. Therefore:

The milk jug contains  quarts of milk.

The milk jug contains  liters of milk.

​

Answers

Answer:

A soda bottle contains 2 liters of liquid. Therefore:

The soda bottle contains  67.62 fluid ounces of liquid.

The soda bottle contains 0.525  gallons of liquid.

2) A milk jug contains 2 gallons of milk. Therefore:

The milk jug contains 8  quarts of milk.

The milk jug contains 7.6 liters of milk.

Step-by-step explanation:

We need to complete the statements.

1)

A soda bottle contains 2 liters of liquid. Therefore:

The soda bottle contains -------  fluid ounces of liquid.

Converting Liters to fluid ounces

We know that 1 liter = 33.81 fluid ounces

So,  2 liter = 2 x 33.81 = 67.62 fluid ounces

The soda bottle contains 67.62  fluid ounces of liquid.

The soda bottle contains  gallons of liquid.

Converting liters to gallons

As, we are not given direct conversion from liters to gallons, first we convert liter to quarts and then convert quarts to gallons

We know that

1 liter = 1.05 quarts

2 liters = 2 x 1.05 = 2.1 quarts

4 quarts = 1 gallon

1 quarts = 1/4 gallon

2.1 quarts = 1/4 * 2.1 = 0.525 gallon

The soda bottle contains 0.525  gallons of liquid.

2)

A milk jug contains 2 gallons of milk. Therefore:

The milk jug contains -------- quarts of milk.

Converting gallons to quarts

We know:

1 gallon = 4 quarts

2 gallons = 2 x 4 = 8 quarts

The milk jug contains 8 quarts of milk.

The milk jug contains ------  liters of milk.

Converting gallons to liters

We know:

1 gallon = 4 quarts

2 gallon = 8 quarts

1.05 quarts = 1 liter

1 quarts = 1/1.05 liter

8 quarts = 1/1.05 * 8 = 7.6 liter

The milk jug contains 7.6 liters of milk.

Which type of transformation is described by (x, y)
->
+ (x + 3, y — 2)?

Answers

Answer:

(x, y) → (x+3, y-2) means Translation 3 units left and 2 units down.

Step-by-step explanation:

Given the rule of transformation:

(x, y) → (x+3, y-2)

If we move horizontally 3 units to the right, 3 is added to the x-coordinate of any given point, and then 2 units down.

In other words,

(x, y) → (x+3, y-2) means Translation 3 units left and 2 units down.

For example,

Let say if we have the point A(4, 5)

Using the translation rule:

(x, y) → (x+3, y-2)

A(4, 5) → A'(4 + 3, 5 - 2) → A'(7, 3)

Therefore, the new position of A(4, 5) after translating 3 units left and 2 units down would be: A'(7, 3)

What is the slope-intercept form of this equation?
3x + 9 y = 18

Answers

y = -1/3x + 2

Explain: subtract 3x from 18, which will get you -3x + 18.
Next, get 9y and divide it by everything so it’ll look like 9y = -3x + 18
-——-————
9y
and you’ll get y = -1/3x + 2
Hope this helped

A bakery did a survey among 100 customers to find their food preference . The customers were asked about their preferences for cupcakes or brownies. Out of the total 72 people who liked cupcakes, 37 also liked brownies. There were 59 people who liked brownies.


Part A. Summarize the data by writing the values that the letters A to I in the table below represents

PART B. What percentage of the survey respondents did not like cupcakes or brownies ?


PART C . Do the survey results reveal a greater dislike for brownies or cupcakes? Justify your answer.






PLZZZ HELP

Answers

Have you found the answer yet?

Answer:

put 37, 22,59,35,6,41,72,28,100 in chart < That is for the ppl who cant click on the brainly site but it still shows alitttle

For the ppl who can click on brainly:

Part A:

Like Cupcakes

Do Not Like Cupcakes

Total

Like Brownies

37

22

59

Do Not Like Brownies

35

6

41

Total

72

28

100

Part b: 6

Part c: You really have to figure out how to word this 37- 72=35 35-41=6

hope it helps

PLEASE HELP WITH THESE QUESTIONS I HAVE 5 MINUTES LEFT

What is 4 superscript 5 written in expanded form?
O 4 + 4 + 4 + 4 + 4
O 4 times 4 times 4 times 4 times 4
O 5 + 5 + 5 + 5
O 5 times 5 times 5 times 5

Answers

Answer:

4+4+4+4+5

Step-by-step explanation:

is 5 times the number only expanded

Answer:

4+4+4+4+5

Step-by-step explanation:

Please help! I'm writing a test and don't have much time. Step by step please! (20 point)

Answers

Answer:

-3+6x

x+3

Step-by-step explanation:

Answer:

23x^3+9x^2-5x+1/x^2

Step-by-step explanation:

I hope you don't mind me putting my explanation as a screenshot of this lol

(THIS IS 30 POINTS!!) In Ms. Hollbrook's class, 62% of the class enjoys watching anime. If there are 32 students in Ms. Hollbrooks class, about how many students enjoy watching anime?

A) 12 students

B) 14 students

C) 16 students

D) 20 students​

Answers

Answer:

D)

Step-by-step explanation:

32*0.62=19.84≈20.

Does ≥ 5 have an open circle or closed circle?

Answers

Answer:

Closed circle

Step-by-step explanation:

When it's ≤ or ≥ it's a closed circle, when it's < or > it's an open circle.

I may be wrong, but I think it’s a closed circle.

I really need help on this question.!

Answers

Answer:

[tex]60 + 55 + x + 20 = 180 \\ x + 135 = 180 \\ x = 180 - 135 \\ x = 45[/tex]

The ratio of 15 and a number.

Answers

Answer:

15 to 20

Step-by-step explanation: hope this helps! have a supercalifragilisticexpialidocious day ◑﹏◐

Answer:

15:x or 15 to x

Step-by-step explanation:

it depends on what the question is asking, so if they want you to fill in a number, you could replace x with any number you'd like. but its probably a word problem they want you to put as numbers, so bc you dont know what 'a number' is, you can pick a variable such as x to replace it with.

hope this helps :)

A man spend 10% of his salary on rent, 25% on food, 18% on transportation and the balance he saves. If his salary is $1500 per month, how much does he save each month?

Answers

Answer:

He saved $705 pls mark brainliest

Step-by-step explanation:

So 10% is $150 and 25% is 375 and 18% is 270 so you would add all those togeather to get 795 and 1500-795 is 705 so he saved $705!

Evaluate the expression when b=9 .

24/9 + 8 =

Answer:

Answers

Answer:

Exact Form:

32 /3

Decimal Form:

10. 6

Mixed Number Form:

10

2 /3

Step-by-step explanation:

Other Questions
Ugh these are hard questions On a test, 4 students receive an 84%, 3 students receive a 72%, and 2 students receive an 89%. What is the average test score for the group of students? 100 points"Ay, marry, will I join with you all," quoth the Tinker, "for I love a merry life, and I love thee, good master, though thou didst thwack my ribs and cheat me into the bargain. Fain am I to own thou art both a stouter and a slyer man than I; so I will obey thee and be thine own true servant."So all turned their steps to the forest depths, where the Tinker was to live henceforth.What universal theme does this excerpt represent?A. Money is everything. B. Rebels inspire loyalty.C. Obedience is better than rebellion.D. Cheating will get you everywhere. What is the slope-intercept form of the equation y-7 = 3(x-11) ?A. y--3x-36B.y-3x - 40C. y - 3x-26O D. y=-3x - 40 Which of these resulted from the modification of the environment shown in the illustration ? A. Community parks were established to preserve wildlife B. Crop irrigation declined because of water pollution C. Property was damaged by increased flooding D. Surrounding are became more industrialized Which list shows the fractions in order from greatest to least? will mark brainliest !! pleas help . travel through matter or empty space where matter is not present ? What is the latitudinal extent of India? Write its implications in context to India Do you think government should be more active, providing assistance to achieve a common good for all citizens; or, should government be more limited, involved only to the extent that it protects individual rights and liberties Why did the British parliament send even more troops to Boston? Solve the simultaneous equationsx + 5y = 20x + 3y = 14 X= ?Y= ? 14. That food was so hot my ears were smoking! *O A. SimileO B. HyperboleO C. MetaphorO D. Personification What is the area of this figure?Enter your answer in the box. mmComposite figure composed of a a right triangle with a base of 3 mm and a height of 4 mm, and two rectangles, one with side lengths of 3mm and 4mm, the other with side lengths of 1 mm and 6 mm. *EXTRA POINTS*Answer the boxes subtract 637.42 - 29.71 whatd the area pls im gonna die The Washington monument in our nations capital is 169 m high. What would be the speed of the penny as it hit the ground? QUESTION 5DOK 23 ALIGNED STANDARDSWhat does Two-Bit mean when he says, "I forgot"?SELECT AN ANSWERTwo-Bit forgot Johnny and Ponyboy don'tlike to be scared around girls.Two-Bit forgot about the movie, and he'ssorry for being late.Two-Bit forgot Dally had just walked awaymad, and it made Johnny jumpy.Two-Bit forgot that Johnny had beenjumped by Socs and was still nervous andscared because of it.SUBMIT The variety of organisms within an ecosystem is characteristic of which type of diversity?Genetic diversityb. Ecosystem diversityc. Species diversityd. Regional diversityPlease select the best answer fron] the choices providedB Many small firms seek to establish a particular niche in the market, realizing that they cannot afford to operate on a larger scale without exposing themselves to considerable risk of retaliation from larger companies. When a number of small businesses are operating in this manner, they are forcing the larger businesses to recognize and account for their influence on the market. In this way, small businesses are primarily Question 49 options: