cd+(-6c)=150 when d=4

Answers

Answer 1

Answer:

c = -75

Step-by-step explanation:

cd + (-6c) = 150

d = 4

c(4) + (-6c) = 150

4c - 6c = 150

-2c = 150

c = -75


Related Questions

You are offered two jobs selling college textbooks. One company offers an annual salary of $30,000 plus a year-end bonus of 1% of your total sales. The other company offers an annual salary of $25,000 plus a year-end bonus of 2% of your total sales. How much would you need to sell in a year to make the second offer the better offer?

Answers

Answer:

at least $500,000 in sales

Step-by-step explanation:

Solve for x

A. 4
B. 7
C. 1
D. 9

Answers

The value of x when the secants intersect is 4

How to find side when two secant intersect?

A secant of a circle is a line that connects two distinct points on a curve.

The secant touches two sides of the circumference of a circle.

Therefore, using secant rule,

4(x + 2 + 4) = 5(x - 1 + 5)

Hence,

4(x + 6) = 5(x + 4)

Hence, open the brackets

4x + 24 = 5x + 20

Therefore, subtract 4x from both sides

4x - 4x + 24 = 5x - 4x + 20

24 = x + 20

subtract 20 from both sides

24 - 20 = x + 20 - 20

x = 4

Therefore, the value of x is 4.

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1. If A = {a, b, c, d}, B={c, d, e, f}, C={x, y, z} find (A-B)​

Answers

Answer

here

A={a,b,c,d}

B={c,d,e,f}

C={x,y,z}

A-B={e,f}

Simplify each expression. Select the correct answer from the drop-down menu.

−6(3i)(−2i) =


2(3 − i)(−2 + 4i) =

Answers

Answer:

Step-by-step explanation

-6(3i)(-2i)=-6(3i*-2i)=-6*-6i²=36i²

2(3-i)(-2+4i)=(6-2i)(-2+4i)=-12+24i+4i-8i²=-8i²+28i-12

Answer:

1. -36

2. -4+28i

3. 10+8i

Step-by-step explanation:

EDGE2022

suppose you are given the following information and the coordinate plane below

Answers

Answer: 4.9

Step-by-step explanation:

[tex]AB=\sqrt{(-4-3)^2 +(6-4)^2}=\sqrt{53}\\\\A'B'=\frac{2}{3}\sqrt{53} \approx \boxed{4.9}[/tex]

Identify the equation in slope-intercept form for the line containing the points (−4,1) and (2,3).
y=1/3x+7/3


y=1/4x+2

y=1/2x−4

y=1/3x−5/3

Answers

The slope-intercept form for the line is y = 1/3 x -5/3. and the option D is correct option.

According to the statement

we have given that the points (−4,1) and (2,3) and we have to find the slope-intercept form.

And we have to find the equation of line.

So, For this purpose,

The given points are:

(−4,1) and (2,3)

And the slope m become

[tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]

So, put the values in it

then m= 3-1 / 2+4

m = 1/3

And and b point becomes (2+3) / (−4+1)

Then B = -5/3

Then the general equation of slope intercept form is y = mx +b

Then

y = 1/3 x -5/3.

So, The option D is correct and the slope-intercept form for the line is y = 1/3 x -5/3.

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X is 30% of Y and Y is 45% of 600. What is the value of X?

Answers

Answer:

X = 81

Step-by-step explanation:

600 × 0.45 = 270

270 × 0.3 = 81

X = 81

I need help with the problem

Answers

Answer:

you better give me brainliest

Step-by-step explanation:

The answer is the first two

Name a pair of opposite rays on plane L.

Answers

Answer:

  GD and GC

Step-by-step explanation:

Opposite rays lie on the same line and extend in opposite directions from the same end point. Rays are named by naming the end point first, then another point on the ray.

Opposite rays

Points D, G, C lie on the same line with point G between the other two. That means rays GD and GC are opposite rays.

Decimals from greatest to least
.750
.475
-0.123
.675
.253

Answers

Answer:

0.75, 0.675, 0.475, 0.253, -0.123

Step-by-step explanation:

Positive Numbers will always be greater than negative numbers, so you know -0.123 comes at the end.

Example

0.ABC

The tenth's place (A in the number above) holds the most weight. 0The hundreth's place (B in the number above) holds the second most weight. The thousandth's place (C in the number above) holds the third most weight.

Comparing 0.75 and 0.675 is the same as comparing 75 and 67.5. When in doubt, you can multiply the decimals by 100 to determine their order of value.

Consider the equation
x/x − 1 = 6x + 1/x − 1
What is the LCD?
Multiply both sides of the equation by the LCD and rewrite the resulting quadratic equation in general form. _____=0
Solve the equation and check the solutions in the original equation. (Enter your answers as a comma-separated list.) x=________

Answers

The solution to the original equation is 1, 1/6

Solving equation

Equations are expressions separated by mathematical operations.

Given the equation below

x/x − 1 = 6x + 1/x − 1

From the given expression, the least common denominator is x -1

Multiply both sides by x-1 to have;

x = 6x(x-1) +1

Expand

x = 6x^2-6x + 1

Equate to zero

6x^2-6x-x + 1 = 0

6x^2-7x +1= 0

The resulting quadratic equation in general form is 6x^2-7x +1 = 0

Factorize

6x^2 -6x-x + 1 = 0

Group the result

6x(x-1)-1(x-1) = 0

(6x-1)(x-1) = 0

6x - 1 = 0 and x -1 = 0

x = 1 and 1/6

Hence the solution to the original equation is 1, 1/6

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m= -1/4, b=4
give the equation of the line with the given slope and y intercept.
I am still very confused by this..... i cant seem to make it stick in my brain.

Answers

Answer: y = -1/4x + 4

Step-by-step explanation:

slope intercept form = y = mx + b

since you are given m and b, plug in the points into the formula

-1/4 goes in for m and 4 goes in for b

leaving us with:

[tex]y=-\frac{1}{4} x+4[/tex]

Answer:

[tex]y=-\frac{1}{4}x+4[/tex]

Step-by-step explanation:

Ok, so the slope-intercept form is generally expressed as: [tex]y=mx+b[/tex]

y-intercept:

Let's start by explaining why the "b" value represents the y-intercept. So I attached a graph to make this a bit more understandable, but the gist is that anywhere on the y-axis, is going to have x=0, any point on the y-axis can generally be expressed as (0, y).

This means, if we want to find the y-intercept, using the slope intercept form, we simply plug in 0 as x, since that's what x will always be equal to at the y-intercept.

We get the following equation: [tex]y=m(0) + b[/tex], and since anything times zero is just zero, we can simplify this to: [tex]y=b[/tex], meaning the y-intercept will be the "b" value in any slope-intercept form equation.

The slope:

By definition the slope is just how much the y-value changes as x increase by one. Whenever we increase the x-value by one, in the equation y=mx+b, we have one more "m", or the value is increasing by m.

Let's look at an example:

[tex]y=m(1) +b\implies m+b[/tex]

[tex]y=m(2) + b \implies m + m + b[/tex]

[tex]y = m(3) + b \implies m + m + m +b[/tex]

See how each time we increase the value "x" by one, the value of "y" increases by m. So by definition "m" is the value of the slope.

So putting this all together with your example, we get the following equation:

[tex]y=-\frac{1}{4}x+4[/tex]

T=235+980d

The torque, TTT, in newton-meters, on a diving board with a 100 kilogram weight placed "d" meters from the diving board's fulcrum is given by the equation above. How much torque in newton-meters is on the diving board when the weight is placed at the fulcrum?

Questions:
1. what does 980 in the equation represent?
2. Why is the answer 235?

Answers

The answer is 235 because the weight is placed at the fulcrum

What are linear equations?

Linear equations are equations that have constant average rates of change, slope or gradient

1. What does 980 in the equation represent?

The linear equation is given as:

T = 235 + 980d

A linear equation is represented as:

T = b + md

Where m represents the slope

So, we have

m = 980

This means that 980 represents the amount of Torque per meter

2. Why is the answer 235?

When the weight is placed at the fulcrum, the value of d is 0

So, we have

T = 235 + 980d

Evaluate

T = 235 + 980 * 0

This gives

T = 235

Hence, the answer is 235 because the weight is placed at the fulcrum

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Describe all x-values within a distance of 9 from the number 9

Answers

The value |x−9|≤9 is equivalent to [18,0] in interval notation.

According to the statement

We have given that the distance of 9 from the number 9. and we have to find the all value of x between it.

So, For find all x value we use absolute value inequalities.

distance of 9 from number 9.

So, when we draw the number line

we see that the number will become

The distance from x to 9 can be represented using an absolute value symbol, |x−9|.

Write the values of x that satisfy the condition as an absolute value inequality.

So, it become

|x−9|≤9

Now write two inequalities then it become

x−9≤9 and x−9≥−9

x≤18  and x≥0

So, The solution set is x≤18 and x≥0,

then the solution set is an interval including all real numbers between and including 18 and 0.

So |x−9|≤9 is equivalent to [18,0] in interval notation.

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A group of people were asked which of three ice cream flavors they prefer. The results are shown in the table.


Ages Vanilla Strawberry Chocolate
20 years and younger 8 10 6
Over 20 years 8 6 12
What is the probability of a person being over 20 years old and preferring vanilla ice cream?
8%
13%
16%
26%

Answers

Answer: 8/50 = 16%

Step-by-step explanation:

the sum of three numbers is 3068.Two of the numbers are 1266 and 1755,find the third number

Answers

Answer:

47

Step-by-step explanation:

3068 - 1266 - 1755 = 47

Answer:

The third number is 47.

Step-by-step explanation:

The sum of three numbers is 3068 - this can be expressed mathematically as:

[tex]\displaystyle{x + y + z = 3068}[/tex]

Given that two of the numbers are 1266 and 1755 (in order) then substitute x = 1266 and y = 1755:

[tex]\displaystyle{1266 + 1755 + z = 3068}[/tex]

Find the third number - solve for z-variable:

[tex]\displaystyle{3021 + z = 3068}\\\\\displaystyle{z = 3068-3021}\\\\\displaystyle{z = 47}[/tex]

Therefore, the third number is 47.

⦁ Mr. A likes playing a game and the probability that he wins this game is p. He enters the casino and he promises himself that he plays the game until he wins one time and then he stops. Let X be the number of plays in order to win one time. ⦁ What are the values of X? ⦁ What is the probability that X=n?. Prove that it satisfies the PMF conditions. ⦁ Calculate E(X) ⦁ Calculate V(X) ⦁ Study the memoryless property of X.

Answers

The possible values of X for this game are 0, 1, 2, 3, 4.......n, where n ≥ 1

How to determine the values of X?

From the complete question, we understand that Mr. A wants to plays the game until he wins

This means that

He might win at the first game and he might win after n attempts

So, the values of X are

X = 0, 1, 2, 3, 4.......n

Hence, the possible values of X for this game are 0, 1, 2, 3, 4.......n, where n ≥ 1

The probability that X = n

The probability of x is represented as:

P(x) = nCx * p^x * (1 - p)^(n-x)

So, the probability that X = n is:

P(n) = nCn * p^n * (1 - p)^(n - n)

Evaluate the exponent

P(n) = nCn * p^n * 1

Evaluate the combination expression

P(n) = 1 * p^n * 1

This gives

P(n) = p^n

Hence, the probability that X = n is p^n

Prove that it satisfies the PMF conditions.

The distribution satisfies PMF conditions because

The sum of the probabilities is 1 No probability is negativeEach probability value is between 0 and 1 (inclusive)

Calculate E(X)

The expected value E(x) is calculated using

E(x) = n * p

So, we have:

E(x) = np

Hence, the value of E(x) is np

Calculate V(X)

The variance V(x) is calculated using

V(x) = √n * p * (1 - p)

So, we have:

V(x) = √np(1 - p)

Hence, the value of V(x) is √np(1 - p)

Study the memoryless property of X.

The memoryless property of X is that each probability of X is independent

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What is the solution to the system of equations graft below​

Answers

Answer:

( 2,-3)

Step-by-step explanation:

The solution to the system of equations is where the two graphs intersect

The two graphs intersect at x = 2 and y = -3

( 2,-3)

What is the length of S?

Answers

Answer:

c

Step-by-step explanation:

By the Pythagorean theorem,

[tex]28^2 + 15^2 = s^2 \\ \\ s^2 = 1009 \\ \\ s = \sqrt{1009}[/tex]

The amount of detergent dispensed into bottles of liquid laundry detergent bottles for a particular brand is normally distributed with a mean of 84.5 ounces with a standard deviation of 1.1 ounces. If seventeen bottles are randomly chosen from the factory, what is the probability that the mean fill is more than 84.8 ounces

Answers

The probability that the mean fill is more than 84.8 ounces is 0.39358

How to determine the probability that the mean fill is more than 84.8 ounces?

From the question, the given parameters about the distribution are

Mean value of the set of data = 84.5Standard deviation value of the set of data = 1.1The actual data value = 84.8

The z-score of the data value is calculated using the following formula

z = (x - mean value)/standard deviation

Substitute the given parameters in the above equation

z = (84.8 - 84.5)/1.1

Evaluate the difference of 84.8 and 84.5

z = 0.3/1.1

Evaluate the quotient of 0.3 and 1.1

z = 0.27

The probability that the mean fill is more than 84.8 ounces is then calculated as:

P(x > 84.8) = P(z > 0.27)

From the z table of probabilities, we have;

P(x > 84.8) = 0.39358

Hence, the probability that the mean fill is more than 84.8 ounces is 0.39358

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NEED HELP QUICKLY! 75 POINTS!!!!
Only 2 questions

1. Given the functions f(x) = log2(5x) and g(x) = [tex]5^{x}[/tex] – 2, which of the following statements is true?


a. Both f(x) and g(x) decrease on the interval of (–∞, 1).

b. Both f(x) and g(x) have the same domain of (0, ∞).

c. Both f(x) and g(x) have a common range on the interval (–2, ∞).

d. Both f(x) and g(x) have the same x-intercept of (1, 0).


2. What is the solution to 3y2 + 5y > –2?


a. x < –1 or x is greater than negative two thirds

b. x is greater than or equal to negative two thirds or x < 1

c. negative two thirds is less than or equal to x is less than or equal to 1

d. negative two thirds is greater than x is greater than negative 1

Answers

1. Given the functions f(x) = log₂(5x)  and g(x) = 5ˣ - 2 only statement c is true

2. The solution of 3y² + 5y > -2 is a. x < –1 or x is greater than negative two thirds

1. How to find which statements are true.

Statement a

Since f(x) = log₂(5x) which is a logarithm function is undefined for (-∞, 0) and defined for (0, +∞) and g(x) = 5ˣ - 2 which is an exponential function is defined for (-∞, +∞).

Also, since f(x) is decreasing on the interval (0, 1/5) while g(x) decreases on the interval (-∞, 0). So, they have do not have a common interval on (0, 1).

So, statement a. Both f(x) and g(x) decrease on the interval of (–∞, 1).

is false

Statement b

Since f(x) = log₂(5x) which is a logarithm function is defined for (0, +∞)  and g(x) = 5ˣ - 2 which is an exponential function is defined for (-∞, +∞).

So, the statement b Both f(x) and g(x) have the same domain of (0, ∞) is false

Statement c

Since f(x) = log₂(5x) which is a logarithm function has a range of (0, +∞).  and g(x) = 5ˣ - 2 which is an exponential function is has a range of (-2, +∞).

So, they have a common interval of (0, +∞).

So, the statement c. Both f(x) and g(x) have a common range on the interval (–2, ∞) is true

Statement d

To find the x-intercept of f(x), we equate f(x) to zero.

So, f(x) = log₂(5x)

0 = log₂(5x)

2⁰ = 5x

1 = 5x

x = 1/5

To find the x-intercept of g(x), we equate g(x) to zero.

g(x) = 5ˣ - 2

0 = 5ˣ - 2

2 = 5ˣ

x = ㏒₅2

Since the x-intercept of f(x) = 1/5 and the x- intercept of g(x) = ㏒₅2. So, they do not have a common x - intercept.

So, the statement d. Both f(x) and g(x) have the same x-intercept of (1, 0) is false.

So, only statement c is true

2. How to find the solution of 3y² + 5y > -2?

3y² + 5y > -2

3y² + 5y + 2 > 0

3y² + 3y + 2y + 2 > 0

3y(y + 1) + 2(y + 1) > 0

(3y + 2)(y + 1) > 0

So, the boundary values are at

(3y + 2)(y + 1) = 0

(3y + 2) = 0 or (y + 1) = 0

y = -2/3 or y = -1

So, we require (3y + 2)(y + 1) > 0

For y < -1 say -2, (3y + 2)(y + 1) = (3(-2) + 2)((-2) + 1)

= (-6 + 2)(-2 + 1)

= -4(-1)

= 4 > 0

For -1 < y < -2/3 say -1/3, (3y + 2)(y + 1) = (3(-1/3) + 2)((-1/3) + 1)

= (-1 + 2)(-1 +3)/2

= 1(-2/2)

= -1 < 0

For y > -2/3 say 0, (3y + 2)(y + 1) = (3(0) + 2)((0) + 1)

= (0 + 2)(0 + 1)

= 2(1)

= 2 > 0

So, for (3y + 2)(y + 1) > 0, y < -1 or y > -2/3

So, the solution of 3y² + 5y > -2 is a. x < –1 or x is greater than negative two thirds

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Answer:

1. D. Both f(x) and g(x) have the same x-intercept of (1, 0).

2. A. x < –1 or x is greater than negative two thirds

Step-by-step explanation:

I took the exam

i need help pls.............

Answers

Answer:

P = 6750n +7800rn ≤ 19r ≤ 31160n +620r ≤ 8110n = 19r = 8190,650 people

Step-by-step explanation:

This linear programming problem is described by an objective function and constraints on the variables. A graphical solution works well.

Objective function

The goal is to maximize the number of people exposed to the company's ad(s). The number of people reached is the sum of the products of the number of ads and the number reached per ad.

For n newspaper ads, we are told that 6750n people are reached.

For r radio ads, we are told that 7800r people are reached.

The total number of people reached is ...

  P = 6750n +7800r . . . . . . . the function we wish to maximize

Newspaper ads

We can run at most 19 newpaper ads:

  n ≤ 19

Radio ads

We can run at most 31 radio ads:

  r ≤ 31

Budget

The cost of n newspaper ads will be $160n.

The cost of r radio ads will be $620r.

We must stay within a budget for the ads, $8100:

  160n +620r ≤ 8110

Solution

The white area in the first quadrant of the attached graph represents the feasible solution space. (We reversed the inequality symbol in each inequality so the solution space would be white, not triple-shaded.) The corners of the solution space represent possible (n, r) pairs where the objective function might be maximized.

The solid red line on the graph shows the maximum value the objective function might have, and the (n, r) pairs that would give that maximum value. The value of the objective function increases the farther the line is from the origin. Drawing the line on the graph lets us readily identify the (n, r) coordinate pair that will place this line as far as possible from the origin, maximizing P. We find that to be (n, r) = (19, 8).

the number of newspaper ads to run is 19the number of radio ads to run is 8the group exposure is (6750)(19) +(7800)(8) = 190,650

Determine whether the function is linear or quadratic. Identify the quadratic, linear, and constant terms.

f(x)= (3x-4)(-6x-5)

quadratic function
quadratic term: −18x2
linear term: 39x
constant term: –20

quadratic function
quadratic term: −12x2
linear term: −42x
constant term: –20

linear function
linear term: 39x
constant term: –20

linear function
linear term: −18x2
constant term: –20

Answers

The given function is quadratic. The quadratic term is -18x², the linear term is 39x, and the constant term is -20. So, first option is correct.

What is a quadratic function?

A function in which the highest degree of the variable is 2, then that function is said to be a quadratic function.

The general form of a quadratic function is ax² + bx + c. Where the terms are:

ax² - quadratic term;

bx - linear term;

c - constant term;

What is a linear function?

A function in which the highest degree of the variable is 1, then that function is said to be a linear function.

The general form of a linear function is ax + c. Where the terms are:

ax - linear term;

c - constant term;

Expanding the given function:

The given function is f(x) = (3x - 4)(-6x + 5)

Expanding the given function,

f(x) = (3x)(-6x) + (3x)(5) + (-4)(-6x) + (-4)(5)

     = -18x² + 15x + 24x - 20

     = -18x² + 39x - 20

Since the highest degree of the variable x in the obtained function is 2, it is a quadratic function.

The terms in the obtained quadratic function are:

quadratic term: -18x²

linear term: 39x

constant term: -20

Therefore, the first option is correct.

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Disclaimer: The question has a mistake in the function. The corrected question is here.

Question: Determine whether the function is linear or quadratic. Identify the quadratic, linear, and constant terms.

f(x)= (3x - 4)(-6x + 5)

4. Find the value of x & y from the following equation 4x+5y=90, x+y=20 a. 10, 15 b. 10, 5 c. 10, 8 d. 10, 10​

Answers

Answer:

d. 10, 10

Step-by-step explanation:

4(10)+5(10) = 40 + 50 = 90

10 + 10 = 20

Hope this helps

An equation is formed of two equal expressions. In the two of the given equations, the value of x and y are 10 and 10, respectively. The correct option is D.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given the two of the equation, which can be named as,

4x+5y=90   ...... equation 1

x+y=20   ............ equation 2

Solve the second equation for x,

x + y = 20

x = 20 - y ................ equation 3

In the first equation substitute the value of x from the third equation,

4x + 5y = 90

4(20 - y) + 5y = 90

Solving the equation for y,

80 - 4y + 5y = 90

y = 90 - 80

y = 10

Substitute the value of y in the second equation, to get the value of x,

x + y = 20

x + 10 = 20

x = 20 - 10

x = 10

Hence, In the two of the given equations, the value of x and y are 10 and 10, respectively.

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find the domain of the function expressed by the formula:
y=1/x-7

Answers

The domain of the function is x  ≠ 7

How to determine the domain?

The function is given as:

y = 1/x - 7

Set the denominator not equal to 0

x - 7 ≠ 0

Add 7 to both sides

x  ≠ 7

Hence, the domain of the function is x  ≠ 7

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y+6=5(x-4)
wtirte the formula for f(x) in terms of x

Answers

The formula for f(x) in y + 6 = 5(x - 4) in terms of x is f(x) = 5(x - 4)- 6

What is a linear equation?

A linear equation is a equation that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

How to rewrite the formula?

A system of linear equations is a collection of at least two linear equations.

In this case, the linear function in the question is given as:

y + 6 = 5(x - 4)

Subtract 6 from both sides of the equation

y + 6 - 6 = 5(x - 4) - 6

Evaluate the difference in the above equation

y = 5(x - 4) - 6

Express the above equation as a function f(x)  i.e. we express y as a function of x

f(x) = 5(x - 4) - 6

Hence, the formula for f(x) in y + 6 = 5(x - 4) in terms of x is f(x) = 5(x - 4) - 6

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The average speed of a car on a stretch of interstate is 70 miles per hour. Convert this rate to feet per second.

Answers

Answer:

102. 66 feet / Second

Step-by-step explanation:

To do conversion change miles into feet and hour into second.

One foot is 5280 feet

And an hour is 3600sec

70 miles / Hour

70 * 5280feet / 3600 second

369600 feet / 3600seconds

Then simplify

102. 66 feet / Second

Speed given

70mph

1 mi=5280ft

1h=3600s

So convert

70×5280ft/3600s7×528ft/36s102.67ft/s

What is the following quotient?
√120 divided by √30
02
4
O 2√10
O 3√10

Answers

Step-by-step explanation:

sqrt(120) / sqrt(30) = sqrt(120/30) = sqrt(4) = 2

The quotient of √120 divided by √30 is 2.

What is Square Root?

Square root of a number is the value such that the value when multiplied to itself two times gives the original number.

It is denoted by the symbol √.

For example, square root of 16 is 4 since 4 × 4 = 16

The given numbers are √120 and √30.

We have to find the quotient when √120 is divided by √30.

Try to write each of the number as a product of perfect squares if possible.

√120 = √(4 × 30)

We know that √(ab) = √a √b

So, √120 = √4 × √30 = 2√30      (∵√4 =2)

√120 /√30 = 2√30 / √30 = 2    

Hence the required quotient is 2.

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Do the 1. In a class of 60 students, a survey was conducted, 30 students had applied for Addis Ababa University, 25 students applied for Bahir Dar University and 24 students applied for Wachemo University. 11 students applied for both Addis Ababa and Bahir Dar Universities, 6 applied for both Addis Ababa and Wachemo Universities, 9 applied for both Wachemo and Bahir Dar Universities while 4 applied neither of the aforementioned universities. Find i. 11. 111. iv. number of students that applied for all the universities. number of students that applied for at least two of the universities. number of students that applied at most two universities. number of students that applied for Addis Ababa but not Bahir Dar University. 13Z 2. Solve the equation: = 11-3i, Z E C, where Z = x + iy, x&y E R. Z+1 3. Given that Z & W are complex numbers. 2 Prove that IZ + W1²-|Z - W² = 4Re(Z)Re(W). 4. Solve the equation: 2² + 4z +20 + iz(A + 1) = 0 where A is a constant, has complex conjugate root. If one of the roots of this quadratic is Z = B + 2i, where B is a real constant, find the possible values of A.​

Answers

The number of students that applied for all universities is 3, the number of students that applied for at least two of the universities is 20, the number of students that applied for at most two of the universities is 53, and the number of students that applied for Addis Ababa but not Bahir Dar University is 5.

Given that there are 60 students out of which 30 students had applied for Addis Ababa University, 25 students applied for Bahir Dar University and 24 students applied for Wachemo University. 11 students applied for both Addis Ababa and Bahir Dar Universities, 6 applied for both Addis Ababa and Wachemo Universities, 9 applied for both Wachemo and Bahir Dar Universities while 4 applied neither of the aforementioned universities.

Let A, B, and W denote the sets of students apply to Addis Ababa Uni (A), Bahir Dar Uni (B), or Wachemo Uni (W). Let U denote the universal set of all students in the class.

We're given the cardinalities of several sets:

total number of students n(U)=60, A applicants is n(A)=30, B applicants n(B)=25, W applicants n(W)=24, A and B applicants n(A∩B)=11, A and W applicants n(A∩W)=6, B and W applicants n(B∩W)=9 non-applicants n(U\(A∪B∪W))=4

The last cardinality tells us n(A∪B∪W),60-4=56 students applied anywhere at all.

We want to find n(A∩B∩W), the number of students that applied to each of the three universities.

By the inclusion/exclusion principle,

n(A∪B∪W)=n(A)+n(B)+n(W)-n(A∩B)-n(A∩W)-n(B∩W)+n(A∩B∩W)

56=30+25+24-11-6-9+n(A∩B∩W)

n(A∩B∩W)=3

Now, we will find the number of students that applied for at least two of the universities.

n(A∩B)=n(A∩B∩W)+n(A∩B∩W')

11=3+n(A∩B∩W')

8=n(A∩B∩W')

Similarly, we will find

n(A∩B'∩W)=3

n(A'∩B∩W)=6

n(A∩B'∩W')=16

n(A'∩B∩W')=8

n(A'∩B'∩W)=12

then the total number of students applied for at least two students is

n(A∩B∩W')+n(A∩B'∩W)+n(A'∩B∩W)+n(A∩B∩W)=20

Now, we will find the number of students that applied for atmost two universities, we get

n(A∩B∩W')+n(A∩B'∩W)+n(A'∩B∩W)+n(A∩B'∩W')+n(A'∩B∩W')+n(A'∩B'∩W)=53

now, we will find the number of students that applied for Addis Ababa but not Bahir Dar University is

n(A∩B')=n(A)-n(B)

n(A∩B')=30-25

n(A∩B')=5

hence, the total students is 60 and the number of students that applied for all universities is 3, the number of students that applied for at least two of the universities is 20, the number of students that applied for at most two of the universities is 53, and the number of students that applied for Addis Ababa but not Bahir Dar University is 5.

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The three circles in the diagram have the same centre and have radii 3cm, 4cm and 5cm.
What percentage of the area of the largest circle is shaded?

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Answer:

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Bahr Ltd flu not ld6wlw

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