On her way to work, a commuter encounters four traffic signals. Assume that the distance between each of the four is sufficiently great that her probability of getting a green light at any intersection is independent of what happened at any previous intersection. The first two lights are green for forty seconds of each minute; the last two, for thirty seconds of each minute.What is the probability that the commuter has to stop at least three times?

Answers

Answer 1
Answer:

The probability that the commuter has to stop at least three times is at least 5.55%.

Since on her way to work, a commuter encounters four traffic signals, assuming that the distance between each of the four is sufficiently great that her probability of getting a green light at any intersection is independent of what happened at any previous intersection, and the first two lights are green for forty seconds of each minute; the last two, for thirty seconds of each minute, to determine what is the probability that the commuter has to stop at least three times the following calculation must be performed:

  • 4/6 = 2/3 = 0.66666  
  • 0.5 x 0.5 x 0.333 = 0.083333
  • 0.5 x 0.333 x 0.333 = 0.055555

Therefore, the probability that the commuter has to stop at least three times is at least 5.55%.

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Answer 2
Answer:

Answer:

7 in 36 or 0.1944

Step-by-step explanation:

The probability of having to stop at least three times is the probability of getting 3 or 4 red lights.

For the first two lights, the probability of getting them red is 20 in 60 (1/3).

For the last two lights, the probability of getting them red is 30 in 60 (1/2).

The probability of all of them being red is:

P(R=4) = (1)/(3)*(1)/(3)*(1)/(2)*(1)/(2)\nP(R=4) =(1)/(36)=(1)/(36)

The probability of three of them being red (3 red + 1 green) is:

P(R=3) = {(1-(1)/(3))*(1)/(3)*(1)/(2)}*(1)/(2)+(1-(1)/(3))*(1)/(3)*(1)/(2)*(1)/(2)+(1)/(3)*(1)/(3)*(1-(1)/(2))*(1)/(2)+(1)/(3)*(1)/(3)*(1-(1)/(2))*(1)/(2)\nP(R=3) =2*((2)/(3)*(1)/(3)*(1)/(2)*(1)/(2))+2*((1)/(3)*(1)/(3)*(1)/(2)*(1)/(2))\n P(R=3) =(4)/(36)+(2)/(36)\n P(R=3) =(6)/(36)

Therefore, the probability of at least three red lights is:

P=(1)/(36)+(6)/(36)=(7)/(36)\n P=0.1944

The probability is 7 in 36 or 0.1944.


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Four runners are training for long races. Noah ran 5.123 miles, Andre ran 6.34 miles, Jada ran 7.1 miles, and Diego ran 8 miles.What is the total running distance of the four runners?

Bryce wrote the linear regression equation y=1.123x-6.443 to predict the armspan, y, of a person who is x inches tall. Riley has an armspan of 67.5 inches. Which is the best prediction of Riley’s height? A. 54.36 inches
B. 65.84 inches
C. 66.55 inches
D. 69.36 inches

Answers

Answer:

B. 65.84

Step-by-step explanation:

You are given the armspan and a relation between that and height. Put the given value in the equation and solve for the unknown.

... 67.5 = 1.123x -6.443

... 73.943 = 1.123x

... 73.943/1.123 = x = 65.84

Riley's height is predicted to be 65.84 inches.

Choose correct way to rewrite 56% as a decimal number.A.
0.056
B.
0.56
C.
5.6

Answers

Answer:

 The correct answer is:  [B]:  " 0.56 " .

Step-by-step explanation:

Note:

 " 56%   = " ((56)/(100)) " ;

              =  (56) ÷ (100)  =  0.56  ;  

  →  which corresponds to:  " Answer choice:  [B]: " 0.56 " .

______________________________________________

You would write 56% as 0.56.

To make orange fizz, Noah mixes 4 scoops of powder with 6 cups of water. Andre mixes 5 scoops of powder with 8 cups of water. How do their two mixtures compare in taste?

Answers

Answer:

Noah's mixture will taste more like orange, than Andre's mixture.  

Step-by-step explanation:

Given:

Noah mixes 4 scoops of powder with 6 cups of water.

Means Noah ratio will be  or 0.67

Andre mixes 5 scoops of powder with 8 cups of water

Means Andre ratio will be  or 0.62

As,

or

0.66 > 0.62

We can say that content of orange powder will be more in Noah mixture than in Andre's Mixture.

Hence, Noah's mixture will taste more like orange, than Andre's mixture.  

The length of a square is 16m, what is the breadth of the square​

Answers

Answer:

The breadth is 16m because a square is a quadrilateral (four sided shape) that has all its side to be of equal measure.

A bank credit card charges interest at the rate of 24% per year, compounded monthly. If a senior in college charges $1,500 to pay for college expenses, and intends to pay it in one yewhat will he have to pay? (Round your answer to the nearest cent.)

$

Answers

Answer: 1902.36

Step-by-step explanation:

When interest is compounded monthly , the formula to find the accumulated amount is

A=P(1+(r)/(12))^(12t) , where P = principal value , r = rate of interest , t = time.

As per given,

r= 24% =  0.24

P= $1500

t= 1 year

Put all value in formula , we get

A= 1500(1+(0.24)/(12))^(12* 1)\n\n=1500(1+0.02)^(12)\n\n=1500(1.02)^(12)\n\n=1500(1.26824179456)\approx1902.36

Hence, he need to pay $1902.36.

A spinner has 3 equal sections that are purple, green, and blue. What is the probability of not landing on blue?

Answers

Answer:

P(not landing on blue section)=2/3

Step-by-step explanation:

Not landing on blue section = landing on one of the other sections

the remaining sections are 2 each one has a P=1/3

2 × 1/3 = 2/3

Answer:

66%

Step-by-step explanation:

2 divided by 3= 0.666666666 which is then converted to percent (66%)