How does multiplying both the dividend and the divisor by a factor of 10 sometimes make a problem easier to solve?

Let X = the time between two successive arrivals at the drive-up window of a local bank. If X has an exponential distribution wi

LuckyWell [14K]

Answer:

a) E(X)=1

b) σ=1

c) P(X>1)=0.368

d) P(2<X<5)=0.128

Step-by-step explanation:

We have X: "the time between two successive arrivals at the drive-up window of a local bank", exponentially distributed with λ = 1.

a) We have to compute the expected time between two successive arrivals.

The expected value for X as it is exponentially distributed is:

$E(X)=\dfrac{1}{\lambda}=\dfrac{1}{1}=1$

b) We have to compute the standard deviation of X.

The standard deviation is calculated as:

$\sigma=\dfrac{1}{\lambda}=\dfrac{1}{1}=1$

c) The probability that X is larger than 1 (P(X>1))

We can express the probability as:

$P(X>t)=e^{-\lambda t}\\\\P(X>1)=e^{-\lambda\cdot 1}=e^{-1}=0.368$

d) The probability that X is between 2 and 5 (P(2<X<5))

$P(X>t)=e^{-\lambda t}\\\\\\P(25)\\\\P(2$

4 0

3 years ago

Beth left school driving toward the lake one hour before tim. tim drove in the opposite direction going 6 mph slower than beth f

m_a_m_a [10]

Beth's speed was 60 mph.

<h3>What is speed?</h3>

The speed (commonly referred to as v) of an object in everyday use and kinematics is the magnitude of the change in its position over time or the magnitude of the change in its position per unit of time; it is thus a scalar quantity.
The distance traveled by an object in a time interval is divided by the duration of the interval; the instantaneous speed is the limit of the average speed as the duration of the time interval approaches zero.
Velocity is not the same as speed.

To find what was Beth's speed:

Beth's data:

time = 2 hrs; rate = r mph; distance = r×t = 2r miles

Tim's data:

time = 1 hr; rate = r-6 mph; distance = r-6 miles

Equation:

distance + distance = 174 miles

So,

2r + r - 6 = 174
3r - 6 = 174
3r = 180
r = 60 mph (Beth's rate)
r-6 = 54 mph (Tims's rate)

Therefore, Beth's speed was 60 mph.

Know more about speed here:

brainly.com/question/4931057

#SPJ4

3 0

1 year ago

Volume of a cube is 1728 cm3.Find its surface area

Leno4ka [110]

Answer:

Step-by-step explanation:

<h2>Using the formula</h2><h2>V=a3</h2>

<h2>it is right answer </h2><h3>hope it will help you </h3>

8 0

3 years ago

Write an equation for the statement: A kilogram is equal to approximately 2.2 pounds. A cinder block weighs x pounds. A brick ha

navik [9.2K]

the total mass in kilograms y of the cinder block and brick is $y=0.45x + 0.6$ .

<u>Step-by-step explanation:</u>

Here we have , A kilogram is equal to approximately 2.2 pounds. A cinder block weighs x pounds. A brick has a mass of 0.6 kilogram. We need to find What is the total mass in kilograms y of the cinder block and brick . Let's find out :

According to given data in question ,

⇒ $1kg = 2.2pounds$

⇒ $1(pounds) = \frac{1}{2.2}kg$

A cinder block weighs x pounds and a brick has a mass of 0.6 kilogram . Let total mass in kg of the cinder block and brick is y , i.e.

⇒ $y (kg)= x (pounds) + 0.6 kg$

⇒ $y (kg)= x (\frac{1}{2.2}kg) + 0.6 kg$

⇒ $y=0.45x + 0.6$

Therefore , the total mass in kilograms y of the cinder block and brick is $y=0.45x + 0.6$ .

7 0

3 years ago

Find the perimeter of △ABC with vertices A(−4, 3), B(1, −5), and C(−4, −5). Round your answer to the nearest hundredth.

miss Akunina [59]

Let's use the distance formula: $\sqrt{ (x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}$

So it is:

AB : $\sqrt{(-5)^2 + 8^2} = 9.43$
BC: $\sqrt{5^2 + 0^2 } = 5$
CA: $\sqrt{0^2 + 8^2} = 8$

So 9.43 + 5 + 8 =22.43

8 0

3 years ago