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andreev551 [17]

2 years ago

6

Determine whether each of these sets is the power set of aset,wherea and b are distinct elements. a) ∅ c) {∅,{a},{∅,a}} b) {∅,{a

}} d) {∅,{a},{b},{a,b}}

1 answer:

bija089 [108]2 years ago

3 0

Answer:

{∅, {a}, {b}, {a,b}}

Step-by-step explanation:

The value of power of a set is generalized by using the formula,

Power of a set (P) = 2^n where n is the number of element in the set.

Given two distinct elements a and b say;

A = {a,b}

n(A) = 2 i.e the number of elements in the set is 2. Therefore the power of the set will be 2^n which gives 2^2 = 4.

P(A) = 4 means there are 4 subsets of the given set. Subsets are sets of elements that can be found in the set. The subsets of element A will be;

{∅, {a}, {b}, {a,b}} which gives 4 elements in total.

Note that empty set ∅ is always part of the subset of any given set

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How is the graph of y = negative RootIndex 3 StartRoot x minus 4 EndRoot transformed to produce the graph of y = negative RootIn

SVEN [57.7K]

Answer:

Multiply by ∛2 and translate the graph to left by 4 units.

Step-by-step explanation:

The initial function given is:

y = -∛(x - 4)

The transformed function is:

y = -∛(2x - 4)

Consider the initial function.

y = -∛(x - 4)

(Represented by Black line in the graph)

Multiply the function by ∛2. The function becomes:

y = -∛(x - 4) × ∛2

y = -∛(2)(x-4)

y = -∛(2x-8)

(Represented by Red line in the graph represents this function)

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3 0

2 years ago

Read 2 more answers

On average, Betsy read 1 page of her book every 1.5 minutes. Her book has 116 pages. Raymond starts a 94- page book on Saturday

natka813 [3]

Answer:

14 minutes

Step-by-step explanation:

given,

given,

Betsy time taken to read one page = 1.5 minutes

Number of pages in the Betsy book = 116 pages

number of pages in Raymond Book = 94 pages

time taken by the Raymond to read = 11.38 - 8.30

= 3.08 hrs

time taken by Raymond = 188 minutes

time taken by Betsy to read book = 1.5 x 116

= 174 minutes

Raymond take more time than Betsy by = 188 - 174

= 14 minutes

Raymond take 14 minute more than Betsy

4 0

2 years ago

A market analyst is developing a regression model to predict monthly household expenditures on groceries as a function of family

notka56 [123]

Answer:

Monthly household expenditures on groceries

Step-by-step explanation:

The response variable is the one for which measurements are desired and that depends on other variables.

In this case, family size, household income, and household neighborhood are independent variables, while the response variable is the monthly household expenditures on groceries.

8 0

1 year ago

Out of five men and five women, we form a committee consisting of four different people. Assuming that each committee of size fo

masha68 [24]

Answer:

1. 10/21

2. 11/42

3. 41/42

4. 2/15

Step-by-step explanation:

Probability defines the ratio of the number of favorable outcomes to the total number of outcomes.

Combination Operations

$5C2 = \frac{5! }{2! (5-2)!} = \frac{5*4*3! }{2! 3!} =\frac{5*4 }{2*1} =\frac{20}{2}= 10$

$10C4 = \frac{10! }{4! (10-4)!} = \frac{10*9*8*7*6! }{4! 6!} =\frac{10*9*8*7 }{4*3*2*1} =\frac{5040}{24}= 210$

$5C3 = \frac{5! }{3! (5-3)!} = \frac{5*4*3! }{3! 2!} =\frac{5*4 }{2*1} =\frac{20}{2}= 10$

$5C1 = \frac{5! }{1! (5-1)!} = \frac{5*4! }{1! 4!} =\frac{5 }{1} = 5$

$8C2 = \frac{8! }{2! (8-2)!} = \frac{8*7*6! }{2! 6!} =\frac{8*7 }{2*1} = 4*7= 28$

$5C4 = \frac{5! }{4! (5-4)!} = \frac{5*4! }{4! 1!} =\frac{5 }{1} = 5$

$5C0 = \frac{5! }{0! (5-0)!} = \frac{5! }{0! 5!} = 1$

1. Probability of forming a committee consisting of two men and two women

= $\frac{5C2 * 5C2}{10C4} =\frac{10*10}{210} =\frac{10}{21}$

2. Probability of forming a committee that has more women than men

(NOTE: Since the committee desired has only 4 members, forming a committee that has more women than men can only be possible if we have 4 women, 0 men or 3 women 1 man)

= $\frac{5C3 * 5C1 + 5C4*5C0}{10C4} = \frac{10 * 5 + 5*1 }{210} = \frac{50 + 5}{210}=\frac{55}{210} = \frac{11}{42}$

3. Probability of forming a committee that has at least one man

(NOTE: at least one man implies the committee must not have all women members )

= $1 - \frac{5C4}{10C4} = 1 - \frac{5}{210} = 1 - \frac{1}{42} = \frac{41}{42}$

4. Probability of forming a committee with both Alice and Bob are members of the committee (NOTE: If Alice and Bob are compulsory member of the committee, there are only two more people to join the committee from the remaining 8 people)

$=\frac{8C2}{10C4} =\frac{28}{210} =\frac{2}{15}$

it be like a coin toss ut a little more complicated. For every toss we have 4 outcomes from 210 possililities

6 0

2 years ago

A tank initially contains 40 ounces of salt mixed in 100 gallons of water. a solution containing 4 oz of salt per gallon is then

stellarik [79]

Let $A(t)$ be the amount of salt in the tank at time $t$ . We're given that $A(0)=40$ . The rate at which this amount changes is given by

$A'(t)=\dfrac{5\text{ gal}}{1\text{ min}}\cdot\dfrac{4\text{ oz}}{1\text{ gal}}-\dfrac{5\text{ gal}}{1\text{ min}}\cdot\dfrac{A(t)\text{ oz}}{100+(5-5)t\text{ gal}}$

$A'(t)+\dfrac{A(t)}{20}=20$

$e^{t/20}A'(t)+e^{t/20}\dfrac{A(t)}{20}=20e^{t/20}$

$\bigg(e^{t/20}A(t)\bigg)'=20e^{t/20}$

$e^{t/20}A(t)=400e^{t/20}+C$

$A(t)=400+Ce^{-t/20}$

Since $A(0)=40$ , we get

$40=400+C\implies C=-360$

so that the amount of salt at time $t$ is

$A(t)=400-360e^{-t/20}$

After 20 minutes, the tank contains

$A(20)=400-360e^{-20/20}\approx267.56\text{ oz}$

6 0

2 years ago