What % of the area is shaded

The rate at which customers are served at an airport check-in counter is a Poisson process with a rate of 8.1 per hour. The prob

just olya [345]

Answer:

Value of a is 0.667

Step-by-step explanation:

We are given the following in the question:

The rate of customer at an airport follows a Poisson distribution with

$\lambda = 8.1$

The normal approximation of Poisson distribution can be done in the following manner

$\mu = \lambda = 8.1\\\sigma^2 = \lambda = 8.1\\\sigma = \sqrt{8.1} = 2.85$

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

We have to find the value of a such that

$P(X_p > 50)=P(Z > a)$

More than 50 customers per 5 hours means more than 10 customer per hour.

Thus, we can write

$P( x > 10) = P( z > \displaystyle\frac{10 - 8.1}{2.85}) = P(z > 0.667)$

Therefore, value of a is 0.667

4 0

3 years ago

Write an equation for a circle with a diameter that has endpoints at (7, –4) and (1, –10). Round to the nearest tenth if necessa

Black_prince [1.1K]

The standard form for the equation of a circle is :

(x−h)^2+(y−k)^2=r2 ----------- EQ(1)
where handk are the x and y coordinates of the center of the circle and r is the radius.
The center of the circle is the midpoint of the diameter.

So the midpoint of the diameter with endpoints at (7,-4)and(1,-10) is :

((7+(1))/2,(-4+(-10))/2)=(4,-7)

So the point (4,-7) is the center of the circle.

Now, use the distance formula to find the radius of the circle:

r^2=(7−(4))^2+(-4−(-7))^2=9+9=18

⇒r=√18

Subtituting h=4, k=-7 and r=√18 into EQ(1) gives :

(x-4)^2+(y+7)^2=18

7 0

3 years ago

3x + 1 = y; 2x + 3y = 25

docker41 [41]

Substitute the first y= equation into the y of the second. Distribute as needed and solve for x. x=2 and then plug it in to find y. y=7

4 0

4 years ago

A sprinkler is set to water the backyard flower bed. The stream of water and where it hits the ground at the end of the stream c

pochemuha

The solutions to the quadratic equation of the sprinkler in the exact form are x = 7 + 2√110 and x = 7 - 2√110

<h3>What are quadratic equations?</h3>

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

<h3>How to determine the solution to the quadratic equation?</h3>

A quadratic equations can be split to several equations and it can be solved as a whole

In this case, the quadratic equation is given as

-x^2 + 14x + 61 = 0

Using the form of the quadratic equation y = ax^2 + bx + c, we have

a = -1, b = 14 and c = 61

The quadratic equation can be solved using the following formula

x = (-b ± √(b^2 - 4ac))/2a

Substitute the known values of a, b and c in the above equation

x = (-14 ± √(14^2 - 4*-1*61))/2*-1

Evaluate the exponent

x = (-14 ± √(196 - 4*-1*61))/2*-1

Evaluate the products

x = (-14 ± √(196 + 244))/-2

Evaluate the sum

x = (-14 ± √(440))/-2

Express 440 as 4 * 110

x = (-14 ± √(4 * 110))/-2

Take the square root of 4

x = (-14 ± 2√110)/-2

Evaluate the quotient

x = 7 ± 2√110

Split the equation

x = 7 + 2√110 and x = 7 - 2√110

Hence, the solutions to the quadratic equation of the sprinkler in the exact form are x = 7 + 2√110 and x = 7 - 2√110

Read more about quadratic equations at

brainly.com/question/1214333

#SPJ1

8 0

2 years ago

Plz help!!!!!!!!!!!!!!!!!!!

raketka [301]

Answer:

h(0) = 10

h(4) = 16

Step-by-step explanation:

h(0) = 2(0)² - 3(0) + 10 = 10

h(4) = 2^4 = 16

8 0

3 years ago