How far up a wall will an 11-meter ladder reach, if the foot of the ladder is 4 meters away from the base of the wall?

P and Q are sunsets of the universal set U={n:1<n<10} and n is an integer. P consists of even numbers less than 7 and Q co

Sauron [17]

Part A

<h3>Answer: P' u Q' = {3,4,5,6,7,8,9}</h3>

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

Work Shown:

The universal set here is U = {2,3,4,5,6,7,8,9} so we're listing all the integers between 2 and 9. We don't include 1 or 10 since n is larger than 1, and smaller than 10.

P = even numbers less than 7, subset of U

P = {2,4,6,8}

P ' = {3,5,7,9}

Note how the set P' is the set of everything in U that is not in set P. It's the opposite of set P. We call this the complement of set P.

Q = prime numbers less than 10, subset of U

Q = {2,3,5,7}

Q ' = {4,6,8,9}

Applying the union set operation on the sets P' and Q' leads to

P' u Q' = {3,5,7,9, 4,6,8,9}

All I did was combine the two sets of numbers under one umbrella. From here we toss out the duplicate entry of 9. This next step is optional, but sorting the values is standard convention.

Doing all this leads to

P' u Q' = {3,4,5,6,7,8,9}

This set represents all the values that are in set P' or in set Q' or both.

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

Part B

<h3>Answer: P' n Q' = {9}</h3>

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

Work Shown:

Now we're looking at the intersection of sets P' and Q'

List out those sets

P ' = {3,5,7,9}

Q ' = {4,6,8,9}

We see that only the value 9 is in common

Therefore,

P' n Q' = {9}

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

Part C

Answer:

(P' n Q')' = {2,3,4,5,6,7,8}

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

Work Shown:

You start with the result from part B. Then you erase that item (9) from the universal set. Everything in this answer set is not found in the set {9}

Put another way: we're finding the complement or opposite of P' n Q'

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

Part D

<h3>Answer: (P u Q)' = {9}</h3>

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

Work Shown:

P = {2,4,6,8}

Q = {2,3,5,7}

P u Q = {2,3,4,5,6,7,8}

Everything in set P u Q is either found in P, Q, or both. Any duplicates are tossed out.

Take the opposite of this to get

(P u Q)' = {9}

It is not a coincidence we get the same result as part B. It turns out that the two equations are true for any two sets P and Q

(P u Q)' = P' n Q'
(P n Q)' = P' u Q'

For more information, check out De Morgan's Laws. Use of a Venn Diagram may help visualize what is going on, so you can organize the values.

5 0

3 years ago

If our visible universe is 144 billion light years in diameter, how many kilometres is this?

balu736 [363]

1.362345188052e+24 Kilometers. Using advanced ladder method.

5 0

4 years ago

if venus is 30.9 mi farther from the sun than mercury, the the earth is 23.6 mi farther from the sun than venus. when the total

luda_lava [24]

Answer: The mercury is 38 mi far from sun.

Step-by-step explanation:

Let x denotes the distance ( in mi )between the Sun and Mercury .

Distance from Venus to Sun = x+30.9

Distance from Earth = x+30.9+ 23.6 =x+30.9+ 23.6 =x+54.5

When the total of the distances for these plants from the sun is 199.4 mi.

According to the given statements , we have

$x+x+30.9+x+54.5=199.4$

$3x+85.4=199.4$

$3x=199.4-85.4=114$

$x=38$ [Divide both sides by 3]

Hence, the mercury is 38 mi far from sun.

6 0

3 years ago

Which of the following is a rational number?

icang [17]

$\sqrt{1} = 1$

Only sqrt(1) is a rational number.

7 0

3 years ago

Mr. Sanchez’s class sold fruit pies for $1.55 each and Mr. Kelly’s class sold bottles of fruit juice for $1.40 each. Together, t

hoa [83]

Answer:

Mr. Sanchez's class sold 28 fruit pies and Mr. Kelly's class sold 32 bottles of fruit juice.

Step-by-step explanation:

Let x be the number of fruit pies sold and y be the number of bottles of fruit juice sold.

Together, the classes sold 60 items, so

x + y = 60

Mr. Sanchez’s class sold fruit pies for $1.55 each, so x fruit pies cost $1.55x.

Mr. Kelly’s class sold bottles of fruit juice for $1.40 each, so y bottles of fruit juice cost $1.40y.

Together, the classes earned $88.20 for their school, so

1.55x + 1.40y = 88.20.

You get the system of two equations:

$\left\{\begin{array}{l}x+y=60\\ \\1.55x+1.40y=88.20\end{array}\right.$

From the first equation:

$x=60-y$

Substitute it into the second equation:

$1.55(60-y)+1.40y=88.20\\ \\93-1.55y+1.4y=88.2\\ \\-0.15y=88.2-93\\ \\-0.15y=-4.8\\ \\0.15y=4.8\\ \\15y=480\\ \\y=32\\ \\x=60-32=28$

Mr. Sanchez's class sold 28 fruit pies and Mr. Kelly's class sold 32 bottles of fruit juice.

8 0

3 years ago