Which expression is equal to (1+6i)−(7+3i) ?

Answers

Answer 1

Answer:

- 6+3i

Step-by-step explanation:

[tex](1+6i)-(7+3i) ?\\Group\:the\:real\:part\:and\:the\:imaginary\\\:part\:of\:the\:complex\:number\\\left(a+bi\right)\pm \left(c+di\right)=\left(a\:\pm \:c\right)+\left(b\:\pm \:d\right)i\\=\left(1-7\right)+\left(6-3\right)i\\1-7=-6\\6-3=3\\=-6+3i[/tex]


Related Questions


Factor.
x2 + 11x

x2 + 11x
x(x + 11)
11(x + 11)
0(x2 + 11x)

Answers

Answer:

x(x + 11)

Step-by-step explanation:

x^2 + 11x when factored gives a result of x(x + 11)

Answer:

x(x+11)

Step-by-step explanation:

We are given the expression:

[tex]x^2+11x[/tex]

This can be factored using the Greatest Common Factor (GCF).

The GCF of x^2 and 11x is x.

Factor out an x.

[tex]x(x+11)[/tex]

x^2+11x factored is: x(x+11).

On an exam, the average score is 76 with a standard deviation of 6 points What is the probability that an individual chosen at random will have a score below 67 on this exam

Answers

Answer:

P [ X < 67 ] =  0,66,81      or    66,81 %

Step-by-step explanation:

We assume Normal Distribution  N ( μ ; σ )    N ( 76 ; 6 )

z score for 67 is :

z(s) =  (  X - μ  ) /σ

z(s) =  (  67 - 76 ) / 6

z(s) =  - 9 / 6

z(s) = - 1,5

with 1,5 we fnd n z-table area undr the curve  α = 0,6681

Then  P [ X < 67 ] =  0,66,81      or    66,81 %

A professor at a local community college noted that the grades of his students were normally distributed with a mean of 74 and standard deviation of 10. The professor has informed us that 6.3 percent of his students received A's while only 2.5 percent of his students failed the course and received F's.
a. What is the minimum score needed to make an A?
b. What is the maximum score among those who received an F?
c. If there were 5 students who did not pass the course, how many students took the course?

Answers

Answer:

a)  z (score) 1,53

b)  z ( score) - 1,96

c) 200 students

Step-by-step explanation:

Normal Distribution N ( 74;10)

a) From z-table, and for 6,3 %  ( 0,063 ) we find the z (score) 1,53

Note : 6,3 % or 0,063 is the area under the curve, the minimum score neded to get A

b) To fail   2,5 %  ( 0,025 ) from z-table  get - 1,96

c) If the group of  student who did not pass the course (5) correspond to 2,5 % then by simple rule of three

5                 2,5

x ?               100

x = 500/2,5

x = 200

The graph shown below expresses a radical function that can be written in the form f(x)=a(x+k)^1/n + c. What does the graph tell you about the value of n in this function?

Answers

Answer: n is a positive odd number.

Step-by-step explanation:

Ok, we know that the function is something like:

f(x)=a(x+k)^1/n + c

In the graph we can see two thigns:

All the values of the graph are positive values (even for the negative values of x), but in the left side we can see that the function decreases and is different than the right side.

So this is not an even function, then n must be an odd number (n odd allows us to have negative values for y = f(x) that happen when x + k is negative).

Also, we can see that the function increases, if n was a negative number, like: n = -N

we would have:

[tex]f(x) = \frac{a}{(x+k)^{1/N}} + c[/tex]

So in this case x is in the denominator, so as x increases, we would see that the value of y decreases, but that does not happen, so we can conclude that the value of n must be positive.

Then n is a positive odd number.

Answer:

D) Positive Even Integer

Step-by-step explanation:

just did it

what is the least common denominator of 1/8, 2/9, and 3/12

A. 864

B. 108

C. 72

D. 48

Answers

Answer:

c. 72

Step-by-step explanation:

you just have to see what is the lowest number the three denominators: 8, 9, 12, all go into

8 times 9=72 and 12 times 6=72, which makes answer choice C. &2 the least common denominator for the fractions 1/8, 2/9, and 3/12.

Answer:

c.72 he's right love you guys byeee you all welcome

Step-by-step explanation:

will rate you brainliest

Answers

Answer:

third option is the first step

Answer:

C

Step-by-step explanation:

It is c bro

7.19 We are given the following probability distribution. x P(x) b. c. d. 0 1 2 3 .1 .4 .3 .2 a. Calculate the mean, variance, and standard deviation.

Answers

Answer:

Mean = 1.6

Variance = 0.84

Standard deviation = 0.916

Step-by-step explanation:

We are given the following probability distribution below;

            X                         P(X)              [tex]X \times P(X)[/tex]         [tex]X^{2} \times P(X)[/tex]

            0                          0.1                     0                        0

            1                           0.4                   0.4                     0.4

            2                          0.3                   0.6                     1.2

            3                          0.2                  0.6                    1.8      

         Total                                               1.6                    3.4    

Now, the mean of the probability distribution is given by;

         Mean, E(X) =  [tex]\sum X \times P(X)[/tex]  = 1.6

Also, the variance of the probability distribution is given by;

        Variance, V(X) =  [tex]\sum X^{2} \times P(X) - (\sum X \times P(X))^{2}[/tex]

                                 =  [tex]3.4 - (1.6)^{2}[/tex]

                                 =  3.4 - 2.56 = 0.84

And the standard deviation of the probability distribution is given by;

          Standard deviation, S.D. (X) =  [tex]\sqrt{Variance}[/tex]

                                                         =  [tex]\sqrt{0.84}[/tex]  = 0.916.

4(x/2-2) > 2y-11 which of the following inequalities is equivalent to the inequality above?
1) 4x+2y-3 > 0
2) 4x-2y+3 > 0
3) 2x+2y-3 > 0
4) 2x-26+3 > 0

Answers

4) 2x-2y+3 > 0

although it is spelt "26" on the choices

1+3^2⋅2−5 order of operations

Answers

The order for operations:

()
^
* /
+ -

So,
1+3^2*2-5 =
1+((3^2)*2)-5 =
1+(9*2)-5 =
1+18-5 =
14

Answer:

Below

Step-by-step explanation:

● 1 + 3^2 × 2 -5

Start by calculating 3^2 wich is 9

● 1 + 9 × 2 -5

Multiply 2 by 9 (9×2=18)

● 1 + 18 -5

Add 1 to 18 (1+18 = 19)

● 19 -5

Substract 5 from 19 (19-5 = 14 )

● 14

Twice one number added to another number is 18. if the 2nd number is equaled to 12 less than 4 times the 1st number, find the two numbers

2x + y= ? ; y= ?x - ?​

Answers

Answer:

8

Step-by-step explanation:

Math Word Problem: Twice one number added to another number is 18. Four times the first number minus the other number is 12. Find the number.?

Let the two numbers be x and y

As per statement twice one number added to another number is 18.

2x + y = 18

y = 18 - 2x…Eq..1

Four times the first number minus the other number is 12.

4x - y = 12…Eq..2

Now substituting the value of y from Eq..1 to Eq..2

4x - y = 12

4x - (18 - 2x) = 12

4x - 18 + 2x = 12

4x + 2x = 12 + 18

6x = 30

x = 30 / 6

x = 5

Thus one number is 5. Now calculating the other number by putting the value of x in Eq. 1

y = 18 - 2x

y = 18 - 2×5

y = 18 - 10

y = 8

Other number is 8

Answer the two numbers are 5 and 8

Let us check the correctness of answer by putting the value of x and y in Eq. 1

y = 18 - 2x

8 = 18 - 2 × 5

8 = 18 - 10

8 = 8

Means answer is correct

2x + y = 18
y = 4x - 12

2x + y = 18
2x + (4x - 12) = 18
6x - 12 = 18
6x = 30
x = 5

y = 4x - 12
y = 4(5) - 12
y = 20 - 12
y = 8

Therefore the first number is 5 and the second number is 8.

Dan weighs 205 pounds but is only 5 feet 8 inches tall. Evan is 6 feet tall. How much would you expect Evan to weigh if they have the same height/weight ratio? WILL MARK BRAINLIST

Answers

Answer:

217.0588235294118

Step-by-step explanation:

Convert all height to inches.

5' 8" = 68 inches

6' = 72

205/68 = 3.014705882352941

Height/Weight Ratio * Evan's Height = 217.0588235294118


Paula drives 130 miles in 2.5 hours. How far would she drive in 4.5 at the same speed?
*Please answer
I will award the Brainliest answer

Answers

Answer:

Paula will travel 234 miles in 4.5 hours

Step-by-step explanation:

Step 1: We first find the speed Paula is going in hours, we divide 130 mile by 2.5 hours to get 52 miles per hour

Step 2: We multiple 52 miles per hour with 4.5 hours to get 234 miles

Therefore Paula will travel 234 miles in 4.5 hours

If In (x) = 3.53, what is the value of x ?

Answers

I need more information please ?

A string passing over a smooth pulley carries a stone at one end. While its other end is attached to a vibrating tuning fork and the string vibrates forming 8 loops. When the stone is immersed in water 10 loops are formed. The specific gravity of the stone is close to
 
A)  1.8
B)  4.2
C)  2.8
D)  3.2​

Answers

Answer:

correct option is C)  2.8

Step-by-step explanation:

given data

string vibrates form =  8 loops

in water loop formed =  10 loops

solution

we consider  mass of stone = m

string length = l

frequency of tuning = f

volume = v

density of stone = [tex]\rho[/tex]

case (1)  

when 8 loop form with 2 adjacent node is [tex]\frac{\lambda }{2}[/tex]

so here

[tex]l = \frac{8 \lambda _1}{2}[/tex]      ..............1

[tex]l = 4 \lambda_1\\\\\lambda_1 = \frac{l}{4}[/tex]

and we know velocity is express as

velocity = frequency × wavelength   .....................2

[tex]\sqrt{\frac{Tension}{mass\ per\ unit \length }}[/tex]   =   f × [tex]\lambda_1[/tex]

here tension = mg

so

[tex]\sqrt{\frac{mg}{\mu}}[/tex]   =   f × [tex]\lambda_1[/tex]     ..........................3

and

case (2)  

when 8 loop form with 2 adjacent node is [tex]\frac{\lambda }{2}[/tex]

[tex]l = \frac{10 \lambda _1}{2}[/tex]      ..............4

[tex]l = 5 \lambda_1\\\\\lambda_1 = \frac{l}{5}[/tex]

when block is immersed

equilibrium  eq will be

Tenion + force of buoyancy = mg

T + v × [tex]\rho[/tex] × g = mg

and

T = v × [tex]\rho[/tex] - v × [tex]\rho[/tex] × g    

from equation 2

f × [tex]\lambda_2[/tex] = f  × [tex]\frac{1}{5}[/tex]  

[tex]\sqrt{\frac{v\rho _{stone} g - v\rho _{water} g}{\mu}} = f \times \frac{1}{5}[/tex]     .......................5

now we divide eq 5 by the eq 3

[tex]\sqrt{\frac{vg (\rho _{stone} - \rho _{water})}{\mu vg \times \rho _{stone}}} = \frac{fl}{5} \times \frac{4}{fl}[/tex]

solve irt we get

[tex]1 - \frac{\rho _{stone}}{\rho _{water}} = \frac{16}{25}[/tex]

so

relative density [tex]\frac{\rho _{stone}}{\rho _{water}} = \frac{25}{9}[/tex]

relative density = 2.78 ≈ 2.8

so correct option is C)  2.8

I need help on this question :(​

Answers

Answer: 40 degree

Explanation:

FT bisect angle EFD dividing it into 2 equal angles (EFT and DFT)

And EFD = 80

We get :
EFT = 80/2
EFT = 40

And EFT + DFT = EFD = 80 degree

Therefore EFT = 40 degrees

PLEASE HELP!!!!!!! FIRST CORRECT ANSWER WILL BE THE BRAINLIEST....PLEASE HELP
Lunch Choices of Students
The bar graph shows the percent of students that chose each food in the school
cafeteria. Which statement about the graph is true?

Answers

Answer:

(2) If 300 lunches were sold, then 120 chose tacos.

Step-by-step explanation:

We can evaluate each option and see if it makes it true.

For 1: If 200 lunches were served, 10 more students chose pizza over hotdogs.

We can find how many pizzas/hotdogs were given if 200 lunches were served by relating it to 100.

20% chose hotdog, which is [tex]\frac{20}{100}[/tex]. Multiply both the numerator and denominator by two: [tex]\frac{40}{200}[/tex] - so 40 students chose hotdogs.

Same logic for pizza: 30% chose pizza - [tex]\frac{30}{100} = \frac{60}{200}[/tex] so 60.

60 - 40 = 20, not 10, so 1 doesn't work.

2: If 300 lunches were sold, then 120 chose tacos.

Let's set up a proportion again. 40% of 100 is 40.

[tex]\frac{40}{100} = \frac{40\cdot3}{300} = \frac{120}{300}[/tex]

So 120 tacos were chosen - yes this works!

Hope this helped!

How do I solve? Show with steps.

Answers

Step-by-step explanation:

or,[(√-x-1)+(√x+9)]^2=4^2

or,(√-x-1)^2+2√(-x-1)(x+9)+(√x+9)^2=16

or,-x-1+2√-x^2-10x-9 +x+9=16

or,2√-x^2-10x-9=8

or,√-x^2-10x-9=4

squaring on both sides

or,-x^2-10x-9=16

or,-x^2-10x=25

or,-x(x+10)=25

Either,

x=-25 or, x=15.

Plaz guys help me on this question additional mathematics ​

Answers

Answer:

Step-by-step explanation:

vector OA=a

vector OB=b

vector OX= λ vector OA=λa

vector OY=μ vector OB=μb

a.

1.vector BX=(vector OX-vector OB)=λa-b

ii. vector AY=(vector OY-vector OA)=μb-a

b.

5 vector BP=2 vector BX

5(vector OP-vector OB)=2 (vector OX-vector OB)

5(vector OP-b)=2(λa-b)

5 vector OP-5b=2λa-2b

5 vector OP=2λa-2b+5b

vector OP=1/5(2λa+3b)

ii

complete it.

A wheel with radius 1 m is rolled in a straight line through one complete revolution on a flat horizontal surface. How many metres did the centre of the wheel travel horizontally from its starting location?

Answers

Answer:

6.28 m

Step-by-step explanation:

If a wheel travels with one full revolution, it would have travelled the circumference's distance from it's starting point.

The circumference of a circle is [tex]2\pi r[/tex]

Let's assume [tex]\pi[/tex] is 3.14 and solve for the equation.

[tex]2\cdot3.14\cdot1\\6.28[/tex]

Hope this helped!

Line l has a slope of −6/13. The line through which of the following pair of points is perpendicular to l? A. (13,−4),(−7,2) B. (6,−4),(−7,2) C. (2,6),(−4,−7) D. (6,9),(−4,−4)

Answers

Answer: Choice C.  (2,6) and (-4,-7)

=========================================================

Explanation:

The original line has a given slope of -6/13. The opposite reciprocal is 13/6. We flip the fraction and the sign from negative to positive.

With any two perpendicular slopes, they always multiply to -1

(-6/13)*(13/6) = (-6*13)/(13*6) = -78/78 = -1

--------------------

Since the perpendicular slope is 13/6, we need to see which of the four answer choices produces a slope of 13/6. Use the slope formula.

This is something you do through trial and error. You could start with A and work your way to D, or just pick at random. I'll go through each one by one starting at choice A.

---------------------

Let's try choice A

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

m = (2 - (-4))/(-7 - 13)

m = (2 + 4)/(-7 - 13)

m = 6/(-20)

m = -3/10, we can see that choice A is not the answer, since we want m = 13/6 instead.

-----------------------

Let's try choice B

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

m = (2 - (-4))/(-7 - 6)

m = (2 + 4)/(-7 - 6)

m = 6/(-13)

m = -6/13, that doesn't work either

------------------------

Let's try choice C

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

m = (-7 - 6)/(-4 - 2)

m = -13/(-6)

m = 13/6, we found the answer

------------------------

For the sake of completeness, here is what choice D would look like

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

m = (-4 - 9)/(-4 - 6)

m = -13/(-10)

m = 13/10, which isn't the slope we want

the dot plot above identifies the number of pets living with each of 20 families in an apartment building .what fraction of families have more than two pets

Answers

Answer:

B. ⅕

Step-by-step explanation:

Fraction of families having more than 2 pets = families with pets of 3 and above ÷ total number of families in the apartment

From the dot plot above, 3 families have 3 pets, and 1 family has 4 pets.

Number of families with more than 2 pets = 3 + 1 = 4

Fraction of families with more than 3 pets = [tex] \frac{4}{20} = \frac{1}{5} [/tex]

The fraction of families that have more than two pets is B. [tex]\frac{1}{5}[/tex]

Calculations and Parameters

Given that:

Fraction of families having more than 2 pets = families with pets of 3 and above/total number of families in the apartment

From the dot plot above:

3 families have 3 pets,  1 family has 4 pets.

Number of families with more than 2 pets

= 3 + 1

= 4

Fraction of families with more than 3 pets = [tex]\frac{4}{20} = \frac{1}{5}[/tex]

Read more about dot plots here:

https://brainly.com/question/25957672

#SPJ5

PLEASE I NEED HELP 30 POINTS AND BRAINLYEST Order from least greatest 3.5, -2.1, square root of 9, -7/2, and square root of 5

Answers

Answer:

-7/1, -2.1, square root of 5, square root of 9, and last 3.5

Step-by-step explanation:

Square root of 9 is 3.

Square root of 5 is 2.24

-7/2 as a decimal is -3.5

So, from least to greatest order is:

-7/2 > -2.1 > Square root of 5 > Square root of 9 > 3.5

Which of these functions could have been the graph shown below?

Answers

Answer:

B

Step-by-step explanation:

we take the only point we know

(0,20)

in A when x =0

[tex]f(x)=e^{20x} =e^{20*0}=1[/tex]

in B when x=0

[tex]f(x)=20e^x=20e^0=20*1=20[/tex]

fits

in C

[tex]f(x)=20^x=20^0=1[/tex]

in D

[tex]f(x)=20^{20x}=20^{20*0}=20^0=1[/tex]

so the only choice is B

Nicole ordered a volleyball for $9.75

Answers

That’s Nice!!

I don’t think you copied the WHOLE ENTIRE question. I would suggest resubmitting the question so we can help you with it!!

Have a great day and stay safe and positive!!

Answer:

the other person is right

you should try putting the WHOLE question

Step-by-step explanation:

Find the length of segment YZ in the diagram below.

Answers

Answer:

2√2

Step-by-step explanation:

hope you understand.

Ben is tiling the floor in his bathroom the area he is tiling is 4m times 2m each tiles measures 400mm times 400mm he has 45 tiles is that enough

Answers

Answer:

No, it's not enough

Step-by-step explanation:

Given

Tilling Dimension = 4m by 2m

Tile Dimension = 400mm by 400mm

Required

Determine the 45 tiles is enough

First;

The area of the tiling has to be calculated

[tex]Area = Length * Breadth[/tex]

[tex]Area = 4m * 2m[/tex]

[tex]Area = 8m^2[/tex]

Next, determine the area of the tile

[tex]Area = Length * Breadth[/tex]

[tex]Area = 400mm * 400mm[/tex]

Convert measurements to metres

[tex]Area = 0.4m* 04m[/tex]

[tex]Area = 0.16\ m^2[/tex]

Next, multiply the above area result by the number of files

[tex]Total = 0.16m^2 * 45[/tex]

[tex]Total = 7.2m^2[/tex]

Compare 7.2 to 8

Hence, we conclude that the 45 tiles of 400mm by 400 mm dimension is not enough to floor his bathroom

150,75,50 what number comes next

Answers

Answer:

35 or 25

Step-by-step explanation:

1. Find the conditional probability of the indicated event when two fair dice (one red and one green) are rolled. The sum is 6, given that the green one is either 4 or 1.
2. Find the conditional probability of the indicated event when two fair dice (one red and one green) are rolled. The red one is 6, given that the sum is 11.

Answers

Answer:

1. 1/6

2. 1/6

Step-by-step explanation:

Let A be the event that the sum of the two die is 6 and B be an event that the green die is either 4 or 1.

The conditional probability will be given by P (A/B) = P (A∩B)/ P (B).

Now the total sample space consists of 36 outcomes .

And to find (A∩B) we need to find the outcomes in which green die is either 4 or 1 and the sum of the two die is 6.

So when green is 1 red must be 5

So when green is 4 red must be 2

So there are two ways in which green die is either 4 or 1 and the sum of the two die is 6.

Therefore the probability of (A∩B)= P (A∩B)= 2/36= 1/18

Now we find the probability of green die having 4 or 1

So when green is 4 red can have all the numbers from 1- 6

And when green is 1 red can have all the numbers from 1- 6

The total number would be 12 .

So probability of green die having 1 or 4 is given by = P (B)= 12/36

Now the conditional probability = P (A/B) = P (A∩B)/ P (B)=1/18/ 1/3

= 3/18= 1/6

2. Similarly we find the conditional probability of the two die when the red one is 6, given that the sum is 11.

When red is 6 the green must be 5 to get 11. So the probability

=P (A∩B)=  1/36

Now we find the probability of red die having 6 =P(B)= 6/36

Now the conditional probability = P (A∩B)/P(B) =  1/36/ 6/36= 1/6

Answer 1:

Let A be the event that the sum of the two die is 6 Let B be an event that the green die is either 4 or 1.

Conditional probability Formula :

P (A/B) = P (A∩B)/ P (B).

Total sample space=36 outcomes

Conditions are :

So when green is 1 red must be 5 So when green is 4 red must be 2 So there are two ways in which green die is either 4 or 1 and the sum of the two die is 6.

The probability of (A∩B)= P (A∩B)= 2/36= 1/18

Now we find the probability of green die having 4 or 1

When green is 4 red can have all the numbers from 1- 6

And when green is 1 red can have all the numbers from 1- 6

Total number = 12

 P (B)= 12/36

Therefore, conditional probability = P (A/B)

P (A/B) = P (A∩B)/ P (B) P (A/B)=1/18/ 1/3  P (A/B)= 3/18 P (A/B)= 1/6

The conditional probability of the indicated event when two fair dice  are rolled will be 1/6.

Answer 2:

Let A be the event that the sum of the two die is 6 Let B be an event that the green die is either 4 or 1. The sum is 11.

Condition :

When red is 6 the green must be 5 to get 11.

P (A∩B)=  1/36

The probability of red die having 6 =P(B)= 6/36

The conditional probability= P (A∩B)/P(B)

P (A∩B)/P(B) =  1/36/ 6/36P (A∩B)/P(B)= 1/6

The conditional probability of the indicated event when two fair dice are 1/6.

Learn more :

https://brainly.com/question/14660973?referrer=searchResults

A portion of the quadratic formula proof is shown. Fill in the missing reason.

Answers

Answer:

Find a common denominator on the right side of the equation

Step-by-step explanation:

The equation before the problem is

X² + b/a(x) + (b/2a)²= -c/a + b²/4a²

The next step in solving the above equation is to fibd tge common denominator on the right side of the equation.

X² + b/a(x) + (b/2a)²= -c/a + b²/4a²

X² + b/a(x) + (b/2a)²= -4ac/4a² + b²/4a²

X² + b/a(x) + (b/2a)²=( b²-4ac)/4a²

The right side of the equation now has a common denominator

The next step is to factorize the left side of the equation.

(X+b/2a)²= ( b²-4ac)/4a²

Squaring both sides

X+b/2a= √(b²-4ac)/√4a²

Final equation

X=( -b+√(b²-4ac))/2a

Or

X=( -b-√(b²-4ac))/2a

120 meals to 52 meals what is the percentage change?

Answers

Answer: The percentage change is 56.67%.

Step-by-step explanation:

From 120 meals to 52 meals, change in meals = ( 120- 52) meals

= 68 meals

The percentage change = [tex]\dfrac{\text{change in meals}}{\text{Original quantity of meals}}\times100[/tex]

[tex]=\dfrac{68}{120}\times100\\\\=56.67\%[/tex]

Hence, the percentage change is 56.67%.

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