Is f(x)=40-1.25x a function

What is the surface area?

Semenov [28]

Answer:

of what?

Step-by-step explanation:

3 0

3 years ago

A home security system is designed to have a 99% reliability rate. Suppose that nine homes equipped with this system experience

bulgar [2K]

Answer:

a) $P(X \geq 1) = 1-P(X$

$P(X=0)=(9C0)(0.99)^0 (1-0.99)^{9-0}=1x10^{-18}$

And replacing we got:

$P(X \geq 1) =1 -1x10^{-18} \approx 1$

b) $P(X=7)=(9C7)(0.99)^7 (1-0.99)^{9-7}=0.003355$

$P(X=8)=(9C8)(0.99)^8 (1-0.99)^{9-8}=0.083047$

$P(X=9)=(9C9)(0.99)^9 (1-0.99)^{9-9}=0.913517$

And adding we got:

$P(X \geq 7) = 0.003355+0.083047+0.913517 =0.99992$

c) $P(X \leq 8) =1 -P(X>8) = 1-P(X=9)$

$P(X=9)=(9C9)(0.99)^9 (1-0.99)^{9-9}=0.913517$

And replacing we got:

$P(X \leq 8)= 1-0.913517=0.086483$

Step-by-step explanation:

Let X the random variable of interest "numebr of times that an alarm is triggered", on this case we now that:

$X \sim Binom(n=9, p=0.99)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

Part a

We want to find this probability:

$P(X \geq 1) = 1-P(X$

$P(X=0)=(9C0)(0.99)^0 (1-0.99)^{9-0}=1x10^{-18}$

And replacing we got:

$P(X \geq 1) =1 -1x10^{-18} \approx 1$

Part b

$P(X \geq 7)= P(X=7) +P(X=8)+ P(X=9)$

$P(X=7)=(9C7)(0.99)^7 (1-0.99)^{9-7}=0.003355$

$P(X=8)=(9C8)(0.99)^8 (1-0.99)^{9-8}=0.083047$

$P(X=9)=(9C9)(0.99)^9 (1-0.99)^{9-9}=0.913517$

And adding we got:

$P(X \geq 7) = 0.003355+0.083047+0.913517 =0.99992$

Part c

$P(X \leq 8) =1 -P(X>8) = 1-P(X=9)$

$P(X=9)=(9C9)(0.99)^9 (1-0.99)^{9-9}=0.913517$

And replacing we got:

$P(X \leq 8)= 1-0.913517=0.086483$

4 0

3 years ago

The average temperature for freezing foods is less than -17°C. Which of the following best describes this situation?

frutty [35]

D..............!! Idkkkkkkkkkkk

6 0

3 years ago

Find the length of the diameter of circle 0

r-ruslan [8.4K]

Answer:

Diameter = 19.33

Step-by-step explanation:

Imaging a radius line from O to the endpoints of the 7. call this line R.

Label the part of the vertical line from O to the 90 degree intersection y.

Now you have a right triangle.

Using the Pythagorean theorem:

R² = 7² + y²

also

y = R - 3

substitute for y:

R² = 49 + (R-3)²

R² = 49 + R² - 6R + 9

simplify:

0 = 58 - 6R

6R = 58

R = 9.6667

Diameter = 2(9.6667) = 19.33

5 0

2 years ago

an airplane flies in the path shown by the vector line UV on the graph below. what is the magnitude and direction of line UV? (1

GaryK [48]

The magnitude and direction of line UV is 19.7° South of West for 8.1 miles

<h3>How to find the magnitude of the vector line UV?</h3>

The magnitude of the vector line UV is given by the length of the line UV,

d = √[(x₂ - x₁)² + (y₂ - y₁)²] where

(x₁, y₁) = (2, 3) and
(x₂, y₂) = (-2, -4)

Substituting the values of the variables intot he equation, we have

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

d = √[(-2 - 2)² + (-4 - 3)²]

d = √[(-4)² + (-7)²]

d = √[4² + 7²]

d = √[16 + 49]

d = √65

d = 8.06 miles

d ≅ 8.1 miles

So, the magnitude of vector line UV is 8.1 miles

<h3>How to find the direction of the vector line UV</h3>

The direction of the vector line UV is given by Ф = tan⁻¹[(y₂ - y₁)/(x₂ - x₁)] where

(x₁, y₁) = (2, 3) and
(x₂, y₂) = (-2, -4)

Substituting the values of the variables into the equation, we have

Ф = tan⁻¹[(y₂ - y₁)/(x₂ - x₁)]

Ф = tan⁻¹[(-4 - 3)/(-2 - 2)]

Ф = tan⁻¹[(-7)/(-4)]

Ф = tan⁻¹[7/4]

Ф = tan⁻¹[1.75]

Ф = 60.26°

Ф ≅ 60.3°

Its bearing from the north-south line is α = 90° - Ф

= 90° - 60.3°

= 19.7°

So, its direction is 19.7° South of West

So, the magnitude and direction of line UV is 19.7° South of West for 8.1 miles

Learn more about vectors here:

brainly.com/question/26700114

#SPJ1

4 0

2 years ago