Which of the following sets are not well-defined?

A small boat traveled 29.5 miles upstream in 2 hours. The same boat took 3 hours to travel 59.25 miles downstream. If the speed

mel-nik [20]

Answer:

boat speed: 17.25 mph
current: 2.5 mph

Step-by-step explanation:

Upstream, the speed of the current (c) subtracts from the speed of the boat (b) to give the net speed. Downstream, the speed of the current adds. We can make use of the relation ...

speed = distance/time

b-c = 29.5/2 = 14.75 . . . . . miles/hour

b+c = 59.25/3 = 19.75 . . . .miles/hour

Subtracting the first equation from the second, we get ...

(b+c) -(b-c) = 19.75 -14.75

2c = 5

c = 2.5

Then either equation can be used to find b:

b = 14.75 +c = 17.25

The speed of the boat in still water is 17.25 miles per hour; the speed of the current is 2.5 miles per hour.

5 0

3 years ago

If f(x) = x2 and g(x) =1/ 2x+3, find g(f(-1)).

Dvinal [7]

-1=1/2x+3
2=1/2x
(2)2=1/2x(2)
4=x
Answer: x=4

5 0

3 years ago

Find an order pair (x, y) that is a solution to the equation x-3y=3 (x,y) =

aniked [119]

Answer:

(6,1)

Step-by-step explanation:

If you plug these numbers in for x and y, the equation works.

4 0

3 years ago

What is the probability of drawing the compliment of a king or a

inna [77]

Answer:

The probability of drawing the compliment of a king or a queen from a standard deck of playing cards = 0.846

Step-by-step explanation:

Step(i):-

Let 'S' be the sample space associated with the drawing of a card

n (S) = 52C₁ = 52

Let E₁ be the event of the card drawn being a king

$n( E_{1} ) = 4 _{C_{1} } = 4$

Let E₂ be the event of the card drawn being a queen

$n( E_{2} ) = 4 _{C_{1} } = 4$

But E₁ and E₂ are mutually exclusive events

since E₁ U E₂ is the event of drawing a king or a queen

step(ii):-

The probability of drawing of a king or a queen from a standard deck of playing cards

P( E₁ U E₂ ) = P(E₁) +P(E₂)

$= \frac{4}{52} + \frac{4}{52}$

P( E₁ U E₂ ) = $\frac{8}{52}$

step(iii):-

The probability of drawing the compliment of a king or a queen from a standard deck of playing cards

$P(E_{1}UE_{2}) ^{-} = 1- P(E_{1} U E_{2} )$

$P(E_{1}UE_{2}) ^{-} = 1- \frac{8}{52}$

$P(E_{1}UE_{2}) ^{-} = \frac{52-8}{52} = \frac{44}{52} = 0.846$

Conclusion:-

The probability of drawing the compliment of a king or a queen from a standard deck of playing cards = 0.846

5 0

3 years ago

09.04 Continuity at a point Find the indicated limit, if it exists. (2 points)

LenKa [72]

Answer:

6

Step-by-step explanation:

limit is defined when the limit from both side are defined and equal to f

$x-> -10^-$ , limit f(x)=-4-(-10)=6

f(-10)=6

$x-> -10^+$ , limit f(x)=(-10)+16=6

Then

$x->-10$ , limit f(x)=6

6 0

3 years ago