Learn with an example






The art club had an election to select a president. 46 out of the 92 members of the art club voted in the election. What percentage of the members voted?

Solution :

We have to prove that [tex]$\overline{A \cup B} = \overline{A} \cap \overline{B}$[/tex]   (De-Morgan's law)

Let  [tex]$x \in \bar{A} \cap \bar{B}, $[/tex] then [tex]$x \in \bar{A}$[/tex] and [tex]$x \in \bar{B} $[/tex]

and so [tex]$x \notin \bar{A}$[/tex] and [tex]$x \notin \bar{B} $[/tex].

Thus, [tex]$x \notin A \cup B$[/tex] and so [tex]$x \in \overline{A \cup B}$[/tex]

Hence, [tex]$\bar{A} \cap \bar{B} \subset \overline{A \cup B}$[/tex]   .........(1)

Now we will show that [tex]$\overline{A \cup B} \subset \overline{A} \cap \overline{B}$[/tex]

Let [tex]$x \in \overline{A \cup B}$[/tex] ⇒ [tex]$x \notin A \cup B$[/tex]

Thus x is present neither in the set A nor in the set B, so by definition of the union of the sets, by definition of the complement.

[tex]$x \in \overline{A}$[/tex] and  [tex]$x \in \overline{B}$[/tex]

Therefore, [tex]$x \in \overline{A} \cap \overline{B}$[/tex] and we have [tex]$\overline{A \cup B} \subset \overline{A} \cap \overline{B}$[/tex]  .............(2)

From (1) and (2),

[tex]$\overline{A \cup B} = \overline{A} \cap \overline{B}$[/tex]

Hence proved.

{2l+2w=62}

1-2w=1

I don't know the answer its not in my syllabus nor I was thought this one

Answer:

X=200

First your going to add all sides together. Once you finish you should get

50+55+90=195

after you got your answer your going to round to the tenths if it's higher than 5 your going to make it 200 but if it's lower than 5 than your going to make it 180.

So in our case because it's 195 we're going to turn it into a 200.

I hope this helps

Answer:

the exact form is 22/5

decimal form is 4.4

mixed number form is 4 2/5

Step-by-step explanation

isolate the variable by dividing each side by factors that don't contain the variable

Answer: 16cm

Step-by-step explanation:

The radius is half of the diameter so you would have to double the radius.

Answer:

16cm

Step-by-step explanation:

The diameter of a circle is double the radius, so if a circle has a radius of 8cm, it has a diameter of 16cm because that's double 8cm.

Answer:

8

Step-by-step explanation:

Answer: 8

Step-by-step explanation: 10 / 1.25 = 8

Answer:

96

Step-by-step explanation:

Answer:

products - -3x and 6x^2

factors - 8 and 2x

Step-by-step explanation:

Answer:

-8x would go in the box above -16x and -8 would go in the other box

Answer:

6[tex]x^{3}[/tex]- 19[tex]x^{2}[/tex]+[tex]x[/tex]+6

Step-by-step explanation:

Answer:

6x³ - 19x² + x + 6

Step-by-step explanation:

Answer:

Bueno, sí y no. Si está multiplicando dos términos como (x - 2) y (x - 2), usaría el método FOIL: primero, adentro, afuera, último. Vea el diagrama adjunto. Los dos signos negativos se cancelarían entre sí solo al multiplicar los últimos valores. Avísame si necesitas más explicaciones.

-cjhunter.26

Answer: Look below =3

The greatest common factor of numerator and denominator is (x-4).

Answer:

The answer is 40 degrees

Answer:

y=-5x+9

Step-by-step explanation:

y=-5x+b

y=4 x=1

4=-5(1)+b

9=b

Answer:

[tex] \frac{73}{48} [/tex]

Step-by-step explanation:

.......

Answer:

Answer :

8/-11

y=8 x=-11

Answer:

16 - 8 / 9 - 20

Step-by-step explanation:

y2 = 16 y1 = 8

x2 = 9 x1 = 20

your answer is going to be 8/-11

king jon un

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Step-by-step explanation:

[tex] 200 = \pi{r}^{2} \\ {r}^{2} = \frac{200}{\pi} = 63.66 \\ r = 7.97 = 8[/tex]

Answer:

21.47

Step-by-step explanation:

I just used the Pythagorean theorem

Hey there!

The answer to your question is, yes, it is

Given:

[tex]\frac{8}{5}[/tex] [tex]and[/tex] [tex]\frac{24}{15}[/tex]

To see if they are equal, we can use cross products (see below for information about this, if you don't know what it is). Let us assume they are equal. This would mean that:

[tex]8*15=24*5[/tex]

Let's solve it and see if it is true:

[tex]8*15=24*5[/tex]

[tex]120=120[/tex]

Therefore, they are proportional.

Cross products

WORD DEFINITION:

Given two fractions, you can take the numerator of the first fraction multiplied by the denominator of the second fraction and it should equal the denominator of the first fraction multiplied by the numerator of the second fraction.

ALGEBRAIC DEFINITION:

Given two fractions, [tex]\frac{a}{b}[/tex] [tex]and[/tex] [tex]\frac{c}{d}[/tex], [tex]a*d[/tex] should equal to [tex]b*c[/tex]

Hope it helps, and have a terrificly amazing day!

Answer:

$3

Step-by-step explanation:

Because you have to also think about tax of the item. Plus add them both up and it costs $2.24 without tax. Which means it's already above $2.

Answer:

Angle BOC is 80 degrees

Angle COD is 60 degrees

Answer:

∠ BOC = 80°, ∠ COD = 60°

Step-by-step explanation:

∠ AOC = ∠ DOF = 120° ( vertical angles ), then

∠ BOC = ∠ AOC - ∠ AOB = 120° - 40° = 80°

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

∠ COD = 180° - ∠ AOC = 180° - 120° = 60°

Answer:

9x^2 - 10x -4

Step-by-step explanation:

It is set up like this

     9x^2 - 8x

-              (x-2)2

First solve (x-2)2

the answer is (2x-4)

so now you can do this instead

    9x^2 - 8x

-              2x - 4

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

9x^2 - 10x +4

9x^2 minus zero is 9x^2

-8x-2x is -10x

0- -4 is 4 because that is like saying 0 + 4 because double negatives equal a positive

A simpler way is to change all the numbers to the opposite sign and then change the minus to a plus

like this

    9x^2 - 8x

+              -2x + 4

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

9x^2 - 10x +4

Answer:

8x^2-4x-4

Step-by-step explanation:

On delta math

Answer:

14-2x=4*2x-38

Step-by-step explanation:

Answer:

The answer is below

Step-by-step explanation:

The sprinklers have a radius of 5 ft each. Since the larger semicircle (entire lawn) has a diameter that is formed from the 2 semicircles, therefore the radius of the larger semicircle is 10 ft.

Area that wont be watered can be gotten by subtracting the area of the two smaller circles from the area of larger semicircle.

Area that wont be watered = 1/2(π * 10²) - 2[1/2(π * 5²)] = 50π - 25π = 25π ft²

Answer:

$1500

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 20%/100 = 0.2 per year,

then, solving our equation

I = 500 × 0.2 × 10 = 1000

I = $ 1,000.00

The simple interest accumulated

on a principal of $ 500.00

at a rate of 20% per year

for 10 years is $ 1,000.00.

Answer:

It will take 3.65 seconds at the rate it's being poured.

Step-by-step explanation:

Answer:

Step-by-step explanation:

g(x) is vertical translation of f(x) by -12 units

Answer:

24 = x

Step-by-step explanation:

You use Pythagorean theorem. Since the normal equation is [tex]a^{2} + b^{2} =c^{2}[/tex], you already have the [tex]c^{2}[/tex] and another side which can be [tex]a^{2}[/tex] or [tex]b^{2}[/tex].

Because you have the hypotenuse and a side , your equation looks like this now: [tex]7^{2} +b^{2} = 25^{2}[/tex]

and when you solve for be you just subtract [tex]25^{2} -7^{2}[/tex] to get 24.

Answer:

182

Step-by-step explanation:

Add them all which is 178 and subtract that number from 360.

370-178=182