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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A trapezoid has an area of 60 square inches. The height of the trapezoid is 5 inches. What is the length of the longer base if the longer base is three times the length of the shorter base?

Answers

Answer:

Step-by-step explanation:

Remark

Let the shorter base = x

Let the longer base = 3x

h = 5

Area = 60

Formula

Area = (b1 + b2)*h /2

Solution

60 = (x + 3x)*5 / 2 Multiply both sides by 2

2*60 = (x + 3x)*5 Combine like terms

120 = 4x *5

120 = 20x Divide by 20

120/20 = x

x = 6

Therefore the two bases are

x = 6

3x = 18

Answer:

Step-by-step explanation:

I NEED AN EXPLANATION PLEASE!! I need a fast answer

Answers

Answer:

B) 74 degrees

Step-by-step explanation:

three angles = 180

2x+32=180

2x=148

x=74

Hope this helps plz hit the crown :D

Answer:

i think B which is 74

Step-by-step explanation:

Liam is a rewards member at a local restaurant. He can buy four tacos at regular price and get 5.50 off of his purchase. Zachary found a coupon to buy three tacos at regular price and get 6.50 off his total. What would the taco price x need to be in order for Liam and Zachary to spend the same amount?

Answers

Liam can buy 4 tacos at regular price and get 5.50 off of his purchase while Zachary can buy 3 tacos at regular price and get 6.50 off his total.

There is no price of the taco that makes that both of them spend the same.

Liam and Zachary buy tacos at the same place. Let "x" be the price of each taco and "y" be the total amount spent.

Liam can buy 4 tacos at regular price and get 5.50 off of his purchase.

We can represent the situation through the following linear equation.

y = 4x - 5.50 [1]

Zachary found a coupon to buy three tacos at regular price and get 6.50 off his total.

We can represent the situation through the following linear equation.

y = 3x - 6.50 [2]

We want to know the prices of the taco so that both of them spend the same amount.

We calculate it making [1] equal to [2].

4x - 5.50 = 3x - 6.50

4x - 3x = -6.50 + 5.50

x = -1.00

The taco would have cost -1.00 for both of them to spend the same. Since in reality, this is unlikely, we can say that there is no price of the taco that makes that both of them spend the same.

Liam can buy 4 tacos at regular price and get 5.50 off of his purchase while Zachary can buy 3 tacos at regular price and get 6.50 off his total.

There is no price of the taco that makes that both of them spend the same.

Learn more about linear equations here: brainly.com/question/2263981

What is the probability that the average of four babies' weights will be within .6 pounds of the mean; will be between 8.4 and 9.6 pounds

Answers

The probability will be "0.7497".

Given:

Mean,

Standard deviation,

Number of babies,

The standard error of sample will be:

→ $S.E. = (sd)/(√(n) )$

$= (0.6)/(√(4) )$

$= (0.6)/(2)$

$= 0.3$

hence,

→ P(4 babies will be between 8.4 - 9.6 pounds)

$P(8.4 \leq X \leq 9.6) = (((8.4-9))/(0.3) \leq X \leq ((9.6-9))/(0.3) )$

$= P(-2 \leq X \leq 2)$

$= P(Z \leq 2) - P(Z \leq -2)$

$= 0.9772-0.2275$

$= 0.7497$

Thus the above response is right.

Learn more:

brainly.com/question/14008215

Complete question:

Some sources report that the weights of full-term newborn babies in a certain town have a mean of 9 pounds and a standard deviation of 0.6 pounds and are normally distributed.

Answer: 0.7497

Step-by-step explanation:

Mean = 9

sd = 0.6

n = 4

P(4 babies will be between 8.4 and 9.6 pounds)

P(8.4 ≤ X ≤ 9.6)

Standard error of the sample (S. E) :

S. E = sd/√n

= 0.6 /√4

= 0.6/2

= 0.3

P(8.4 ≤ X ≤ 9.6)= ((P(8.4 - 9) / 0.3) ≤ X ≤ (9.6 - 9)/0.3)

P(8.4 ≤ X ≤ 9.6) = P(-2 ≤ X ≤ 2)

P(Z ≤ 2) - P(Z < - 2)

0.9772 - 0.2275 = 0.7497

Can somebody pleaase answer for me

Answers

Just read carefully the directions and ask google for help because other is don’t know it and it’s too hard to solve it
-Just sayi’n

Yes look on google have a good day

Solve the equation for n

y=nx+m

N=?

Answers

n= (y-m)/x

y minus m over x

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