Use the following probabilities to answer the question. It may be helpful to sketch a Venn diagram.

P(A)=0.5 ,P(B)=0.3 and P(A and B)=0.20.
P(B∣ not A)=

Answer:

\((\frac{1}{2}+\frac{\sqrt{3}}{2}i)^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Step-by-step explanation:

Convert 1/2 + i√3/2 to rectangular form

\(\displaystyle z=a+bi=\frac{1}{2}+\frac{\sqrt{3}}{2}i\\\\r=\sqrt{a^2+b^2}=\sqrt{\biggr(\frac{1}{2}\biggr)^2+\biggr(\frac{\sqrt{3}}{2}\biggr)^2}=\sqrt{\frac{1}{4}+\frac{3}{4}}=\sqrt{1}=1\\\\\theta=\tan^{-1}\biggr(\frac{b}{a}\biggr)=\tan^{-1}\biggr(\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\biggr)=\tan^{-1}(\sqrt{3})=\frac{\pi}{3}\\\\z=\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\)

Use DeMoivre's Theorem

\(\displaystyle z^n=r^n(\cos(n\theta)+i\sin(n\theta))\\\\z^5=1^5\biggr(\cos\biggr(\frac{5\pi}{3}\biggr)+i\sin\biggr(\frac{5\pi}{3}\biggr)\biggr)\\\\z^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

{ 0, -2 , 3 , -5 } Domain of the function .

What is domain math example?

What does range in math mean?

The gap between the greatest and lowest numbers is known as the range. The average of the largest and smallest number is the midpoint.

Domain - { 0, -2 , 3 , -5 }

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Answer:

3

Step-by-step explanation:

13-4=9

9/3=3

Answer:

n=3

Step-by-step explanation:

Four more than three times a number is thirteen

3n + 4 = 13 subtract 4 on both sides

3n + 4 - 4 = 13 - 4 Simplify

3n = 9 divide both sides by 3

3n/3 = 9/3 Simplify

n=3 Answer

I hope this helps

Answer:

Step-by-step explanation:

the selections that are equivalent to 4 + w + 12:

1st and 3rd

Answer:

round answer is : 10 ft

Step-by-step explanation:

The explanation is in the picture!

If you are an apprentice plumber earning an annual salary of $21,060, and you lay claim to 3 allowances, the amount that will be withheld from your weekly pay for federal income tax is: $7.

To obtain the correct amount to be paid, we need to use the table provided by the IRS. First note that there are 52 weeks in a year, so we need to divide your annual earnings by the total number of weeks in a year.

So, 21060/52 = $405

When we look at the table to see the chart for a person who has a weekly wage of 400 - 410, and lays claim to three allowances, we will see that the right amount that such an individual is meant to pay is $7.

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Answer:

64 tea bags for 9.28

Step-by-step explanation:

The area bounded by the Curves y=4-x² and y = 2x + 1 is 10 1/3 units.

Area is the amount of space occupied by a two dimensional shape or object.

y = 4 - x² and y = 2x + 1

4 - x² = 2x + 1

x² + 2x - 3 = 0

(x + 3)(x - 1) = 0

x = -3; or x = 1

The area (A) is given by:

\(A=\int\limits^1_{-3} {x^2+2x-3} \, dx \\\\A=10\frac{1}{3}\)

The area bounded by the Curves y=4-x² and y = 2x + 1 is 10 1/3 units.

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Answer:
If the slopes of two lines are the same then the line is parallel.

If the slope of one line is the negative inverse of the other line then it is perpendicular.

If the two lines intersect and they are not perpendicular they are neither (so if they do not follow the rules above then they are neither).

Step-by-step explanation:

If you have y=2x+3 and y=2x-3 then they are parallel because they have the same slope and they are not the same line.

If you have y=2x+3 and y= (-1/2)x - 3 then they are perpendicular because the slope of line two is the negative inverse of the first line.

If you don't get negative inverse:
If you have 2x then the inverse is 1/2x. Then the negative of (1/2)x is (-1/2)x

Answer:

2x + 3x

3x + 10x

Step-by-step explanation:

like Terms are individual terms that have the same variable in them

Answer:

Check out the graph below the explanation.

Step-by-step explanation:

1. x ≥ 9 means that x is more than or equal to 9.

Here's the graph!

Answer:

50 pictures.

Step-by-step explanation:

It's lit just 35+15=50 pictures

Answer:50

Step-by-step explanation:

Meg took 35 pictures

Kim took 15 pictures

Total pictures =35+15

Total pictures =50

The slope of the line passing through the points (5, 3) and (8, 2) is -1/3.

To find the slope of the line passing through the points (5, 3) and (8, 2), we can use the formula for slope:

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

Let's substitute the coordinates of the given points into the formula:

x1 = 5, y1 = 3

x2 = 8, y2 = 2

slope = (2 - 3) / (8 - 5)

Calculating the numerator and denominator:

slope = -1 / 3

Therefore, the slope of the line passing through the points (5, 3) and (8, 2) is -1/3.

Note: The slope represents the rate of change between the y-coordinates and x-coordinates of two points on a line. In this case, for every 3 units increase in the x-coordinate, the y-coordinate decreases by 1 unit.

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Answer:

➜ Four units upwards

➜ Eight units to the right

Step-by-step explanation:

   The parent function of g(x) = (x - 8)² + 4 is f(x) = x². This function is transformed by f(x) = a(x − h)² + k where a is the amplitude, h is the shift left and right, and k is the shift up and down.

   We will look at the function and list the transformations.

g(x) = (x - 8)² + 4

➜ Four units upwards (+ 4)

➜ Eight units to the right (-(-8) = +8)

An expression for the area of △KNM is = 1/2 x 2b x a

Given,

In the question:

In triangle KNM ;

The length of the base (MK) = 2b

and, height of the triangle is= a

To write an expression  for the area of △KNM .

Now, According to the question:

We know that :

Area of triangle is = 1/2 x base x height

The length of the base (MK) = 2b

and, height of the triangle is= a

Plug all the values in the area of triangle :

Here, Area of triangle is = 1/2 x 2b x a

Hence, An expression for the area of △KNM is = 1/2 x 2b x a.

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The  equation of the parabola with the following properties y = (-1/4)(x+3)^2 -1

To find the equation of a parabola, we can use the formula f(x) = ax^2 + bx + c, where a, b and c are congruent vertices.

Alternatively, we can use PF = PM to find the equation of the parabola.

vertex is half way between the focus and directrix

It's a downward opening parabola, general form

y= a(x-h)^2 + k

where (h,k) = vertex= (-3,-1)

plug in another point on the parabola to solve for a which gives

am answer with either x coefficient = -1'/4 or =4 Check the math.

one or the other is right another point is the y intercept = 9a-1

Another point is directly to the right of the focus  (-1, -2)  It's 2 down from the directrix and 2 to the right of the focus, equidistant.   plug that point into y= a(x+3)^2 -1 and solve for "a"  

-2 = a((-1+3)^2 -1

-2 = 4a -1

4a = -

a = -1/4

The parabola is y = (-1/4)(x+3)^2 -1

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Answer:

B. the weight of a dog and the amount of food it eats per day.

This is because dogs only eat around 1/3 of their body weight a day, hence the dogs weight having a positive comparison value to the weight of the food that it eats.

Hope this helps!

Answer: B

Answer:

-132/5

Step-by-step explanation:

-4(2x+13) + 3x = 80

-8x - 52 + 3x = 80

-5x = 80+52

5x = -132

x = -132/5

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The correct answers are A) 7cm, C) 9cm and D) 12cm

The process of changing a given quantity that is expressed in one unit of measurement to another unit of measurement that is equivalent in value is referred to as conversion of units.

If every 2 cm on a scale drawing is equal to 7 feet in real life, then we can use proportions to find out which lines on the drawing would be greater than 21 feet in real life.

Let x be the length of a line on the scale drawing in centimeters. Then, we can set up the following proportion:

⇒  \(\frac{2cm}{7 feet} = \frac{x cm }{yfeet}\)

where y is the length of the line in real life. Solving for y, we get:

⇒  \(y = \frac{7 feet} {2cm} *x\)  

⇒  \(y = 3.5 x feet\)

If we put x = 2cm (given) then, y = 7 feet

For y = 21 feet, the value of x = 6cm.

Therefore, any line on the scale drawing that is greater than 6cm in length corresponds to a length greater than 21 feet in real life.

So, the lines on the drawing that are greater than 21 feet in real life are:

A) 7cm, C) 9cm, D) 12cm

Therefore, the correct answers are A) 7cm, C) 9cm and D) 12cm

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The true equations for the given value of x are C, D and E

3x = 5

x = 5/3

x = 1.667

Substituting x=1.667 in the equations given in the option

The equations C, D and E are true for the value of x in the equation given.

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Answer:

the 20th animal

Step-by-step explanation:

we need to find the least number dividable by 4 and 10

20 is the lowest number divided by both

20 divided by 4 = 5

20 divided by 10 = 2

Answer:

\(\frac{3x+7}{x+2}\)

Step-by-step explanation:

Given the following question:

\(\frac{(x+4)(3x+7)}{(x+4)(x+2) }\)

In order to simplify the expression given we can only cancel the common factor which is four.

\(\frac{(x+4)(3x+7)}{(x+4)(x+2) }\)
\(cf=(x+4)\)
\(\frac{x+4}{x+4}\)
\(=\frac{3x+7}{x+2}\)

Cannot be simplified further due to it not having any more common factors. Your answer is "3x + 7 / x + 2."

Hope this helps.

Answer:

( 3x+7 ) / ( x+2 )

Step-by-step explanation:

\frac{(x+4)(3x+7)}{(x+4)(x+2)}

When you set up the equation like a fraction, you can now cancel out like terms. (x+4) is in the denominator- as well as the numerator. They are the same in parentheses. So you can cancel. Once that's done, you'll be left with

\frac{3x+7}{x+2}

You cant simplify any further because there are no more (like groups) aka (common factors)

( 3x+7 ) / ( x+2 )

Answer:

15

Step-by-step explanation:

1 turns in to 3 and you multiply that by 5

We have the following equation:

since we need P, we must move k and V to the left hand side as

By substituting the given values, we get

that is, P is equal to 2.

Answer:

0.12

Step-by-step explanation:

Answer:

0.12

Step-by-step explanation:

first divide 3/5 and than divide the number with the 5.

3/5=0.6

0.6/5=12

=0.12

Answer:

please follow me and take thanks

All 3 angles add up to 180 degrees.

so 40 + 2x + 3x = 180

40 + 5x = 180

5x = 140

x = 28

So angle A = 2x = 2(28) = 56 degrees.

Answer: 56°

Step-by-step explanation:

We know that a triangle's angles add up to 180 degrees. We will create an equation to help us solve for x using this information.

     Given:

           2x + 3x + 40 = 180

     Combine like terms:

           5x + 40 = 180

     Subtract 40 from both sides of the equation:

           5x = 140

     Divide both sides of the equation by 5:

           x = 28

Next, we will substitute this value of x into the expression for ∠A.

     ∠A = 2x = 2(28) = 56°

Answer:

7 hours

Step-by-step explanation:

take the original distance traveled to find the speed traveled and take the new distance to travel devided by the speed 325÷5=65 455÷65=7

The fee is 50$

Step-by-step explanation: The way I got this is by checking the differences between each month and finding out that each one is 30 and then I subtracted it from 80 and got 50$