Solve the equation w+ 2 = for c.

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>

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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>

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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}

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Part C

Answer:

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

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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

In the casino game of roulette, a $1 bet on red pays $2 with probability 18/38 and $0 with probability 20/38. So if X denotes th

Flauer [41]

Answer:

$P_X(1) = 9/19$

$P_X(-1) = 10/19$

Step-by-step explanation:

You need to take the payment and substract $1 from them, corresponding to the bet cost. With this in mind, you will win $1 with probability 18/38 = 9/19 and you will lose $1 with probability 20/38 = 10/19. With this in mind, the distribution of X is given by the following probability mass function, with range {-1,1}

$P_X(1) = 9/19$

$P_X(-1) = 10/19$

4 0

3 years ago

Juan and Lizzy are in the final week of their training for a marathon. Juan's goal is to run one mile on the first day of the we

miss Akunina [59]

Answer:

1. Juan's marathon training schedule is an example of a geometric sequence

2. Lizzy's marathon training schedule is an example of an arithmetic sequence

3. Lizzy will be better prepared for the marathon

Step-by-step explanation:

In the arithmetic sequence there is a common difference between each two consecutive terms

In the geometric sequence there is a common ratio between each two consecutive terms

Juan's Schedule

∵ Juan's will run one mile on the first day of the week

∴ $a_{1}$ = 1

∵ He will double the amount he runs each day for the next

6 days

- That means he multiplies each day by 2 to find how many miles

he will run next day

∴ $a_{2}$ = 1 × 2 = 2 miles

∴ $a_{3}$ = 2 × 2 = 4 miles

∴ $a_{4}$ = 4 × 2 = 8 miles

∴ $a_{5}$ = 8 × 2 = 16 miles

∴ $a_{6}$ = 16 × 2 = 32 miles

∴ $a_{7}$ = 32 × 2 = 64 miles

That means there is a common ratio 2 between each two consecutive days

1. Juan's marathon training schedule is an example of a geometric sequence

Lizzy's Schedule

∵ Lizzy's will run 10 miles on the first day of the week

∴ $a_{1}$ = 10

∵ She will increase the amount she runs by 3 miles each day for

the next six days

- That means she adds each day by 3 to find how many miles

she will run next day

∴ $a_{2}$ = 10 + 3 = 13 miles

∴ $a_{3}$ = 13 + 3 = 16 miles

∴ $a_{4}$ = 16 + 3 = 19 miles

∴ $a_{5}$ = 19 + 3 = 22 miles

∴ $a_{6}$ = 22 + 3 = 25 miles

∴ $a_{7}$ = 25 × 3 = 28 miles

That means there is a common difference 3 between each two consecutive days

2. Lizzy's marathon training schedule is an example of an arithmetic sequence

The rule of the sum of nth term in the geometric sequence is $S_{n}=\frac{a_{1}(1-r^{n})}{1-r}$

∵ $a_{1}$ = 1 , r = 2 and n = 7

∴ $S_{7}=\frac{1(1-2^{7})}{1-2}$

∴ $S_{7}$ = 127

∴ Juan will run 127 miles in the final week

The rule of the sum of nth term in the arithmetic sequence is $S_{n}=\frac{n}{2}[a_{1}+a_{n}]$

∵ n = 7, $a_{1}$ = 10 and $a_{7}$ = 28

∴ $S_{7}=\frac{7}{2}(10+28)$

∴ $S_{7}$ = 133

∴ Lizzy will run 133 miles in the final week

∵ 133 miles > 127 miles

∴ Lizzy will run more miles than Juan

3. Lizzy will be better prepared for the marathon

7 0

3 years ago

Which describes the cross section of the rectangular prism that passes through vertices A, B, C, and D?

erma4kov [3.2K]

Answer:

A, C, D B, or A D B C

Step-by-step explanation:

7 0

4 years ago

Read 2 more answers

J&J Manufacturing issued a bond with a $1,000 par value. The bond has a coupon rate of 7% and makes payments semiannually. I

Andreyy89

Answer:

The correct option is d. $ 785

Step-by-step explanation:

Since,

$\text{Bond price}=\frac{C}{YTM}(1-\frac{1}{(1+\frac{YTM}{2})^{2M}})+\frac{FV}{(1+\frac{YTM}{2})^{2M}}$

Where,

C = Annual coupon payment,

FV = Face value,

M = Maturity in years,

YTM = yield to maturity,

Here,

FV = $ 1,000,

C = 7% of 1000 = $\frac{7\times 1000}{100}$ = 70,

M = 20 years,

YTM = 9.4% = 0.094,

By substituting the values,

$\text{Bond price}=\frac{70}{0.094}(1-\frac{1}{(1+\frac{0.094}{2})^{40}})+\frac{1000}{(1+\frac{0.094}{2})^{40}}$

= $ 785.3454 ( Using calculator )

≈ $ 785

Hence, OPTION d. is correct.

8 0

3 years ago