A boat can travel 64 miles on 7 gallons of gasoline. How much gasoline will it need to go 24 miles?

The shuttle bus from your parking lot and your office building operates on a 15 minute schedule. You arrive at the parking lot a

mylen [45]

Answer:

(a) The standard deviation of your waiting time is 4.33 minutes.

(b) The probability that you will have to wait more than 2 standard deviations is 0.4227.

Step-by-step explanation:

Let X = the waiting time for the bus at the parking lot.

The random variable X is uniformly distributed with parameters a = 0 to b = 15.

The probability density function of X is given as follows:

$f_{X}(x)=\frac{1}{b-a};\ a$

(a)

The standard deviation of a Uniformly distributed random variable is given by:

$SD=\sqrt{\frac{(b-a)^{2}}{12}}$

Compute the standard deviation of the random variable X as follows:

$SD=\sqrt{\frac{(b-a)^{2}}{12}}$

$=\sqrt{\frac{(15-0)^{2}}{12}}$

$=\sqrt{\frac{225}{12}}$

$=\sqrt{18.75}\\=4.33$

Thus, the standard deviation of your waiting time is 4.33 minutes.

(b)

The value representing 2 standard deviations is:

$X=2\times SD=2\times4.33=8.66$

Compute the value of P (X > 8.66) as follows:

$P(X>8.66)=\int\limits^{10}_{8.66} {\frac{1}{15-0}}\, dx\\$

$=\frac{1}{15}\times \int\limits^{10}_{8.66} {1}\, dx\\$

$=\frac{1}{15}\times |x|^{15}_{8.66}\\$

$=\frac{15-8.66}{15}\\$

$=0.4227$

Thus, the probability that you will have to wait more than 2 standard deviations is 0.4227.

4 0

1 year ago

Amy is growing basil. On February 1st her plant was 5 inches high. A week later, the plant’s height became 9 inches high. By wha

vladimir1956 [14]

(9-5/5)*100= (4/5)*100 = 80% ( new height- original height /original height ) *100 the plant grew 80%

4 0

1 year ago

Read 2 more answers

Madden and Jenn both worked at the coffee shop today. Madden's total cups of coffee made is represented by f(x); and Jenn's tota

AnnZ [28]

Answer:

The answer is D. 12x - 3.

Step-by-step explanation:

To add these functions, we just add the terms.

f(x) + g(x) = (7x - 4) + (5x + 1)

7x - 4 + 5x + 1 | Simplify

7x + 5x - 3

12x - 3.

5 0

1 year ago

Read 2 more answers

Forty five children attend a preschool. The number of two year olds is one half of the number of three year old's. The number of

Maurinko [17]

To put this into an equation, we can make x the amount of two year old's there are.

x+2x+2x=45

5x=45

x=9

9 two year old's, 18 three year old's, and 18 four year old's.

5 0

1 year ago

Your friend is trying to grow her hair as long as her cousin’s hair. The table shows their hair lengths y (in inches) in differe

Effectus [21]

Given the table that shows the hair lengths y (in inches) of your friend and her cousin in different months x.

Month Friends Hair(in) Cousins Hair(in)
 3 4 7
 8 6.5 9.

To solve for the cousins hair, recall that the equation of a line is given by

y = mx + c

From the table,

7 = 3m + c . . . (1)
9 = 8m + c . . . (2)

(1) - (2) ⇒ -2 = -5m
$\Rightarrow m= \frac{2}{5} =0.4$

Substituting for m into equation (1) gives:

$7=3(0.4)+c \\ \\ \Rightarrow c=7-1.2=5.8$

Therefore, the equation representing the growth of the cousin's hair is given by y = 1.2x + 5.8

7 0

1 year ago