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2 years 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 basket contains 14 white eggs, 15 brown eggs, and 11 lemons. Taylor is in a hurry to make breakfast and picks something from t

guajiro [1.7K]

Okay so probability is just percentage of a whole, right?

So you have 14 White Eggs + 15 Brown Eggs + 11 Lemons.

Add all those numbers together and you get your whole.

14 + 15 = 29 29+11 = 40

40 is your whole.

So because you want to know how likely it is to pick up an egg, you would follow these steps.

100/40 = 2.5 (For each part of the 40, it is worth 2.5 percent.)

2.5 x 29 = 72.5

Your probability of picking an egg out of the bask is 72.5 percent or 72.5 out of 100.

8 0

2 years ago

Read 2 more answers

Each cone of the hourglass has a height of 15 millimeters. The total height of the sand within the top portion of the hourglass

BARSIC [14]

Calculate the volume of sand, the cone will be completely filled and the cylinder will have sand up to the 30 mm level.

Volume of sand will = the volume of the cone:
= 1/3 * pi * (6 mm)^2 * 15
= 1/3 * pi * 36 * 15 =180 pi cubic mm

the cylinder will have a volume of sand equal to:
= pi * (6 mm)^2 * 30 mm
= pi * 36 sq mm * 30 mm
= 1080 pi cubic mm

The total sand is the sum:
= 1080 pi cubic mm +180 pi cubic mm
= 1260 pi cubic mm. <span>
</span>

5 0

2 years ago

Read 2 more answers

Match the following guess solutions ypyp for the method of undetermined coefficients with the second-order nonhomogeneous linear

Sunny_sXe [5.5K]

Answer:

Step-by-step explanation:

1 ) Given that

$(d^2y/dx^2) + 4y = x - x^2 + 20\\\\ (d^2y/dx^2) + 4y = - x^2 + x + 20$

For a non homogeneous part $- x^2 + x + 20$ , we assume the particular solution is

$y_p(x) = Ax^2 + Bx + C$

2 ) Given that

$d^2y/dx^2 + 6dy/dx + 8y = e^{2x}$

For a non homogeneous part $e^{2x}$ , we assume the particular solution is

$y_p(x) = Ae^{2x}$

3 ) Given that

y′′ + 4y′ + 20y = −3sin(2x)

For a non homogeneous part −3sin(2x) , we assume the particular solution is

$y_p(x) = Acos(2x)+Bsin(2x)$

4 ) Given that

y′′ − 2y′ − 15y = 3xcos(2x)

For a non homogeneous part 3xcos(2x) , we assume the particular solution is

$y_p(x) = (Ax+B)cos2x+(Cx+D)sin2x$

4 0

2 years ago

The price of an article is Rs 1200 and a customer pays Rs 1380 with VAT. Find the rate of VAT

garik1379 [7]

Answer:

15%

Step-by-step explanation:

vat amount

= 1380 - 1200

=180

finding the rate of vat

= 1380/1200 *100

= 115%

NB : the 115% shows that 1200 8 115% = 1380 , this give total amount including vat , we only want vat hence we have to deduct the 100% which indicates the amount of article)

hence 115 - 100 = <u>15%</u>

15% * 1200= 180

8 0

2 years ago

The price of the box of 10 markers is $7. The price of the box of 24 markers is $14. All prices without tax, and the price of th

hichkok12 [17]

Answer:

Step-by-step explanation:

let x represent the number of markers.

Let y represent the cost for x boxes of markers.

If we plot y on the vertical axis and x on the horizontal axis, a straight line would be formed. The slope of the straight line would be

Slope, m = (14 - 7)/(24 - 10)

m = 7/14 = 0.5

The equation of the straight line can be represented in the slope-intercept form, y = mx + c

Where

c = intercept

m = slope

To determine the intercept, we would substitute x = 24, y = 14 and m = 0.5 into y = mx + c. It becomes

14 = 0.5 × 24 + c = 12 + c

c = 14 - 12

c = 2

The equation would be

y = 0.5x + 2

7 0

2 years ago