John has $190 in his savings account. He earns 10% in interest per year.

A television network is about to telecast a new television show. Before a show is launched, the network airs a pilot episode and

Basile [38]

Answer:

(E) 0.83

Step-by-step explanation:

We will solve it using conditional probability.

Let A be the event that a TV show is successful.

P(A) = 0.5

A' be event that the show is unsuccessful

P(A') =0.5

Let B be the event that the response was favorable

P(B) = 0.6

Let B' be the event that the response was unfavorable/

P(B') = 0.4

P(A∩B) = 0.5 and P(A∩B') = 0.3

We need to find new show will be successful if it receives a favorable response.

P(A/B) = $\frac{P(A∩B)}{P(B)}$

= 0.5/0.6

= 0.833

7 0

1 year ago

Read 2 more answers

Which of these relations on{0,1,2,3}are partial orderings? Determine the properties of a partial ordering that the others lack.

omeli [17]

Step-by-step explanation:

A = {0,1,2,3}

a): R = {(0,0),(2,2),(3,3)}

R is antisymmetric, because if the (a,b)∈R, than a=b.

R is not reflexive, because (1,1) ∉ R while 1 ∈ A.

R is transitive, because if the (a,b)∈R and (b, c) ∈ R, than a=b=c and (a,c)=(a,a)∈R.

R is not portable ordering because R is not reflexive.

b): R = {(0,0),(1,1),(2,0),(2,2),(2,3),(3,3)}

R is antisymmetric, because if the (a,b)∈R and if the (b, a) ∈ R, than a=b (since (2,0) ∈ R and (0,2) ∉ R; and (2,3) ∈ R and (3,2) ∉ R )

R is reflexive, because (a,a) ∈ R of every element a ∈ A.

R is transitive , because if the (a,b)∈R and if the ( b , c )∈R . then a = b or b = c ( since there are only two element not of the form ( a , a ) and that pair does not satisfy ( a,b ) ∈ R and ( b , a ) ∈ R ), which implies ( a , c ) = ( b , c ) ∈ R or ( a , c ) = ( a , b ) ∈ R.

R is a partial ordering, because R is reflexive, antisymmetric and transitive.

c): R = {(0,0),(1,1),(1,2),(2,2),(3,1),(3,3)}

R is reflexive, because (a,a)∈R of every element a ∈ A.

R is antisymmetric, because if the ( a , b )∈R and if the ( b , a )∈R . then a = b ( since ( 1 , 2 )∈R and ( 2 , 1 ) ∉ R; ( 3 , 1 ) ∈ R and ( 1 , 3 ) ∉ R ).

R is not transitive , because ( 3 , 1 ) ∈ R and ( 1 , 2 )∈R, while ( 3 , 2 ) ∈ R.

R is not a partial ordering. because R is not transitive .

d): R = {(0,0),(1,1),(1,2),(1,3),(2,0),(2,2),(2,3), (3,0),(3,3)}

R is the reflexive, because ( a , a )∈R of every elements∈A.

R is the antisymmetric, because if the ( a , b )∈R and if the ( b , a )∈R, then a = b ( since ( 1 . 2 )∈R and ( 2 . 1 )∉R; similarly, all other elements not of the form (a,a) ).

R is not transitive, because ( 1 , 2 )∈R and ( 2 , 0 )∈R, while ( 1 . 0 )∉R.

R is not a partial ordering, because R is not transitive,

e): R = { ( 0 , 0 ) , ( 0, 1 ) , ( 0 , 2 ) , ( 0 , 3 ) , ( 1 , 0 ) , ( 1 , 1 ) , ( 1 , 2 ) , ( 1 , 3 ) , ( 2 , 0 ) , ( 2 , 2 ) , ( 3 , 3 ) }

R is the reflexive , because ( a , a )∈R of every element a∈A .

R is not antisymmetric, because ( 1 , 0 )∈R and ( 0 , 1 )∈R while 0 is not equal to 1.

R is not transitive, because ( 2 , 0 )∈Rand ( 0 , 3 )∈R, while ( 2 , 3 )∉R .

R is not a partial ordering, because R is not the antisymmetric and not the transitive.

3 0

2 years ago

An open-top rectangular box is being constructed to hold a volume of 150 in3. The base of the box is made from a material costin

Oksanka [162]

Answer:

minimum cost of construction box are x = x = 3.4199 in and y = 10.2598 in and z = 4.2750 in

Step-by-step explanation:

given data

volume = 150 in³

base material costing = 5 cents/in²

front cost = 10 cents/in²

remainder sides cost = 2 cents/in²

to find out

the dimensions that will minimize the cost

solution

we consider here length = x and breadth = y and height = z

and

area of base = xy

area of front = xz

and area of remaining side = xz + 2yz .....................1

so

cost of base will be = 5xy

cost of front = 10xz

cost of remaining side = 2 ( xz+ 2yz)

and

total cost will be

total cost TC = 5xy + 10xz + 2 ( xz+ 2yz)

total cost TC = 5xy + 10xz + 2xz+ 4yz

total cost TC = 5xy + 12xz + 4yz ....................2

and total volume will be = xyz

150 = xyz

z = $\frac{150}{xy}$ .......................3

now put z value in equation 2

total cost TC = 5xy + 12xz + 4yz

total cost TC = 5xy + 12x $\frac{150}{xy}$ + 4y $\frac{150}{xy}$

total cost TC = 5xy + $\frac{1800}{y}$ + $\frac{600}{x}$ ...........4

now differentiate TC w.r.t x and y

TC (x) = 5y - $\frac{600}{x^2}$

TC (x) = 5x - $\frac{1800}{y^2}$

now equating with 0 these

5y - $\frac{600}{x^2}$ = 0

x² = $\frac{120}{y}$

and

5x - $\frac{1800}{y^2}$ = 0

x = $\frac{360}{y^2}$

solve we get

y = 10.2598

x = 3.4199

now put x and y value in equation 3

z = $\frac{150}{xy}$

z = $\frac{150}{3.4199*10.2598}$

z = 4.2750

so minimum cost of construction box are x = x = 3.4199 in and y = 10.2598 in and z = 4.2750 in

4 0

2 years ago

Mick completes a total of 5 assessments for his course. He gets these marks 56,42,47,59,48. Mike needs an average mark of 50 or

Mars2501 [29]

To find the average assessment, add the 5 grades together, then divide by the quantity of grades added together (in this case 5).

=56 + 42 + 47 + 59 + 48
=252

=252 ÷ 5
=50.4 average

ANSWER: Yes, he passes his course with an average grade of 50.4.

Hope this helps! :)

4 0

2 years ago

The diameter of a particle of contamination (in micrometers) is modeled with the probability density function f(x)= 2/x^3 for x

RoseWind [281]

Answer:

a) 0.96

b) 0.016

c) 0.018

d) 0.982

e) x = 2

Step-by-step explanation:

We are given with the Probability density function f(x)= 2/x^3 where x > 1.