9-3 divided by 1<br> _ plus 1 =?<br> 3

A line intersects the points

Hoochie [10]

Answer:

m=-11

point-slope form _y-y1=m(x-x1)

so 5 , 2 is x1,y1

so y-2=-11(x-5)

4 0

3 years ago

Read 2 more answers

In a study of the progeny of rabbits, Fibonacci (ca. 1170-ca. 1240) encountered the sequence now bearing his name. The sequence

snow_lady [41]

Answer:

The correct answer is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89.

Step-by-step explanation:

In a study of the progeny of rabbits, Fibonacci encountered the sequence now bearing his name.

The sequence is defined recursively as:

$a_{n+2}$ = $a_{n}$ + $a_{n+1}$ , where a1 = 1 and a2 = 1 where n is a natural number.

For n = 0 ; a2 = a0 + a1

⇒ a0 = 0.

For n = 1 ; a3 = a1 + a2 = 1+1

⇒ a3 = 2.

For n = 2 ; a4 = a2 + a3 = 1+2

⇒ a4 = 3.

For n = 3 ; a5 = a3 + a4 = 2+3

⇒ a3 = 5.

For n = 4 ; a6 = a4 + a5 = 3+5

⇒ a6 = 8.

For n = 5 ; a7 = a5 + a6 = 5+8

⇒ a7 = 13.

For n = 6 ; a8 = a6 + a7 = 8+13

⇒ a8 = 21.

For n = 7 ; a9 = a7 + a8 = 21+13

⇒ a9 = 34.

For n = 8 ; a10 = a8 + a9 = 21+34

⇒ a10 = 55.

For n = 9 ; a11 = a9 + a10 = 55+34

⇒ a11 = 89.

Thus the first 12 terms of fibonacci sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89.

6 0

3 years ago

The circular opening of an ice cream cone has a diameter of 7 centimeters. The height of the cone is 10 centimeters. What is the

marin [14]

We have been given that the circular opening of an ice cream cone has a diameter of 7 centimeters. The height of the cone is 10 centimeters. We are asked to find the volume of the ice-cream cone.

We will use volume of cone formula to solve our given problem.

$V=\frac{1}{3}\pi r^2 h$ , where

r = Radius of cone,

h = Height of cone.

We know that diameter is two times the radius, so radius will be half of diameter that is $r=\frac{7}{2}$ .

$V=\frac{1}{3}\pi\cdot (\frac{7}{2})^2\cdot 10$

$V=\frac{1}{3}\pi\cdot (\frac{49}{4})\cdot 10$

$V=128.2817$

$V\approx 128.3$

Therefore, the volume of the cone would be approximately 128.3 cubic cm.

6 0

3 years ago

According to the National Institute of Allergy and Infectious Diseases, 6% of American adults have a food allergy. A large compa

Vinil7 [7]

Answer:

a) The requirements is that each trial can only have two outcomes(success/failure), and each trial has the same probability of a success, that is, they are independent of each other.

In this problem, for each person, either they are allergic to some kind of food, or they are not. The probability of a person being allergic is independent of any other people. So this situations meets all these requirements.

b) The expected value is 30 and the standard deviation is 5.31.

c) Close to 0% probability that none of the 500 employees has a food allergy

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they have food allergy, or they do not. The probability of an adult having allergy is independent of other adults. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

6% of American adults have a food allergy

This means that $p = 0.06$

500 employees.

This means that $n = 500$

(a) What are the assumptions/requirements of a Binomial distribution? Does this situation meet all these requirements?

The requirements is that each trial can only have two outcomes(success/failure), and each trial has the same probability of a success, that is, they are independent of each other.

In this problem, for each person, either they are allergic to some kind of food, or they are not. The probability of a person being allergic is independent of any other people. So this situations meets all these requirements.

(b) What are the expected value and standard deviation of X (i.e., of the population)?

$E(X) = np = 500*0.06 = 30$