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1 year ago

Determine whether each of these sets is the power set of a set, where a and b are distinct elements.

1 answer:

4 0

A. $\varnothing$ cannot be the power set of any set. Consult Cantor's theorem, which says that the cardinality of the power set of any set (even the empty set) is strictly greater than the cardinality of the set.

(No part b?)

c. Also not the power set of any set, because any power set must have $2^n$ elements, where $n$ is the cardinality of the original set. The cardinality of this set is 3, but there is no integer $n$ such that $2^n=3$ . This set would be a power set if $\{\varnothing\}$ (that is, the set containing the empty set) were a member of it.

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A group of college DJs surveyed students to find out what music to plan for their upcoming parties. Thirty percent of the studen

Aneli [31]

Answer:

Thus, option “c” 10% is correct.

Step-by-step explanation:

The percentage of students that like dubstep = 30%

The percentage of students that like trance music = 25%

The percentage of student that wants only house music = 20%

The percentage of students that like bot dubstep and trance = 15%

Now we have to find the percentage of students that like trance music but nor dubstep.

The percentage of students that like the trance music but nor dubstep = 100% - 30% – 25 % - 20% - 15%

The percentage of students that like trance music but nor dubstep = 10%

Thus, option “c” 10% is correct.

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1 year ago

At higher altitudes, water boils at lower temperatures. This relationship between altitude and boiling point is linear. At an al

Mashutka [201]

Let's assume

boiling point is y

altitude is x

we are given

This relationship between altitude and boiling point is linear

At an altitude of 1000 feet, water boils at 210°F

so, first point is (1000,210)

so, x1=1000 , y1=210

At an altitude of 3000 feet, water boils at 206°F

so, second point is (3000,206)

so, x2=3000,y2=206

now, we can find slope

$m=\frac{y_2-y_1}{x_2-x_1}$

now, we can plug values

$m=\frac{206-210}{3000-1000}$

$m=-\frac{1}{500}$

now, we can use point slope form of line

$y-y_1=m(x-x_1)$

so, we can plug it

$y-210=-\frac{1}{500}(x-1000)$

so, point slope form of line is

$y-210=-\frac{1}{500}(x-1000)$

now, we can plug x=8000

and then we can solve for y

$y-210=-\frac{1}{500}(8000-1000)$

$y=196$

So,

the boiling point of water at an altitude of 8000 feet is 196°F..........Answer

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1 year ago

Read 2 more answers

There are 1800 gym members in total. 3 4 are aged 25 - 59 years, 1 5 are over 60 years and the remainder are under 25 years. How

fomenos

There are 1751 members under the age of 25.

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1 year ago

A student is deriving the quadratic formula. Her first two steps are shown. Step 1: –c = ax2 + bx Step 2: -c = a[x^2+b/ax] Which

marta [7]

Given choices:

(1) division property of equality

(2) factoring the binomial

(3)completing the square

(4)subtraction property of equality

Answer : (2) factoring the binomial

Step 1: $-c = ax^2 + bx$

Step 2: $-c = a[x^2+\frac{b}{a} x]$

In step 2, 'a' is taken out from $ax^2 + bx$ . when we take out 'a' we divide each term by 'a'. so it becomes $a[x^2+\frac{b}{a} x]$

'a' is factored out in step 2. we call it as factoring a binomial.

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1 year ago

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Willie and his brothers went to TGI Mondays. Their order consisted of 3 cheeseburgers at $8.75 each, a fish sandwich for $6.75,

Sladkaya [172]

<u>Answer:</u>$68.69

<u>Step-by-step explanation:</u>

Calculation of bill value

Cheeseburgers = 26.25

(8.75 x 3)

Fish Sandwich = 6.75

Pizza = 14.99

Sweet Tea

(4 x 2.09) = 8.36

Total of items = 56.35

Sales tax on food = 3.381

(56.35 x 6%)

Total bill value = 59.731

Calculation of tips

Bill value x 15%

=59.731 x 15%

Tips paid=8.95965

Calculation of meals cost

Total meal cost = Bill value + tips

=59.731+8.95965

=$68.69

Total meal cost is $68.69

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1 year ago