A study found that the mean amount of time cars spent in drive-through of a certain fast-food restaurant was 136.6400 seconds. Assuming drive-through times are normally distributed with a standard deviation of 33.4000 seconds. a) What is the probability that a randomly selected car will spend more than 179 seconds in the restaurant's drive-through?
b) What proportion of cars spend between 2 and 3 minutes in the restaurant's drive-through?

a) What is the probability that a randomly selected car will spend more than 179 seconds in the restaurant's drive-through?

0.10235

b) What proportion of cars spend between 2 and 3 minutes in the restaurant's drive-through?

= 30.917% to 90.289%

= 0.30917 to 0.90289

= 0.30917 : 090289

Step-by-step explanation:

We solve for this questions using z score formula

z-score is z = (x-μ)/σ,

where

x is the raw score,

μ is the population mean

σ is the population standard deviation.

a) What is the probability that a randomly selected car will spend more than 179 seconds in the restaurant's drive-through?

x = 179 seconds μ =136.64 seconds, σ = 33.4 seconds

z = (x - μ)/σ

= (179 - 136.64)/33.4

= 1.26826

Determining the probability value from Z-Table:

P(x≤ 179) = 0.89765

P(x< 179) = P(z = 1.26826) = 0.89765

P(x>179) = 1 - P(x<179)

= 1 - 0.89765

= 0.10235

Therefore, the probability that a randomly selected car will spend more than 179 seconds in the restaurant's drive-through is 0.10235

b) What proportion of cars spend between 2 and 3 minutes in the restaurant's drive-through?

Converting the time in minutes to seconds

1 minute = 60 seconds

2 minutes = 60 seconds × 2

= 120 seconds

3 minutes = 60 seconds × 3

= 180 seconds

For 2 minutes = 120 seconds

x = 120 seconds μ =136.64 seconds, σ = 33.4 seconds

Since we are asked to find proportion, n =

z = (x - μ)/σ

= (120 - 136.64)/33.4

= -0.4982

Determining the probability value from Z-Table:

P(x≤ 120) = 0.30917

P(x = 120) = P(z = -0.4982) = 0.30917

Converting to percentage

0.30917 × 100 = 30.917 %

This means 30.917% spend 2 minutes in the restaurant drive through

For 3 minutes

x = 180 seconds μ =136.64 seconds, σ = 33.4 seconds

z = (x - μ)/σ

= (180 - 136.64)/33.4

=1.2982

Determining the probability value from Z-Table:

P(x≤ 180) = 1.2982

P(x = 180) = P(z =1.2982) = 0.90289

Converting to percentage

0.90.289 × 100 = 90.289%

This means 90.289% spend 3 minutes in the restaurant drive through

The proportion of cars that spend between 2 and 3 minutes in the restaurant's drive-through is:

= 30.917% to 90.289%

= 0.30917 to 0.90289

= 0.30917 : 090289

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1

c.

step-by-step explanation:

substitution for (0,1)

y=x^2+4x+1

1=0^2+4(x)0+1

1=0+4(x)0+1

1=4(x)0+1

1=0+1

1=1

substitution for (-3,-2)

y=x+1

-2=-3+1

-2=-2