F(x)=x^3+6x^2+9x+2, k=-2

A teacher teaches two classes with 8 students each. Each student has a 95% chance of passing their class independent of the othe

dsp73

Answer:

0.4466 = 44.66% probability that, in exactly one of the two classes, all 8 students pass.

Step-by-step explanation:

For each student, there are only two possible outcomes. Either they pass, or they do not. The probability of an student passing is independent of other students, which means that the binomial probability distribution is used 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.

Probability that all students pass in a class:

Class of 8 students, which means that $n = 8$

Each student has a 95% chance of passing their class independent of the other students, which means that $p = 0.95$

This probability is P(X = 8). So

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

$P(X = 8) = C_{8,8}.(0.95)^{8}.(0.05)^{0} = 0.6634$

Find the probability that, in exactly one of the two classes, all 8 students pass.

Two classes means that $n = 2$

0.6634 probability all students pass in a class, which means that $p = 0.6634$ .

This probability is P(X = 1). So

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

$P(X = 2) = C_{2,1}.(0.6634)^{1}.(0.3366)^{1} = 0.4466$

0.4466 = 44.66% probability that, in exactly one of the two classes, all 8 students pass.

3 0

2 years ago

Find the height of a square pyramid that has a volume of 75 cubic feet and a base length of 5 feet.

kodGreya [7K]

Volume of the pyramid = (1/3) x Area of the base x Height ---------- (1)

As the base length = 5 feet

So Area of the base = 5 x 5 = 25 square feet

While volume of the pyramid = 75 cubic feet

Putting values in equation (1);

75 = (1/3) x 25 x Height

Height = (75 x 3) / 25

Height = 9feet

<span>So 2nd option is correct.</span>

4 0

2 years ago

At 5:00 pm Antonio turned off the oven

jasenka [17]

Answer:

Or did he?

Step-by-step explanation:

6 0

2 years ago

What is the sum of the infinite geometric series? Sigma-Summation Underscript n = 1 Overscript 4 EndScripts (negative 144) (one-

Irina18 [472]

The sum of the infinite geometric series is -288.

<h2>Given that</h2>

A finite geometric series with n = 4, a₁ = -144, and r = ½.

<h3>We have to determine</h3>

What is the sum of the infinite geometric series?

<h3>According to the question</h3>

The sum of the infinite is determined by the following formula;

$\rm S\infty = \dfrac{a_1(1-r^n)}{1-r}\\\\$

A finite geometric series with n = 4, a₁ = -144, and r = ½.

Substitute all the values in the formula;

$\rm S\infty = \dfrac{a_1(1-r^n)}{1-r}\\\\S\infty = \dfrac{-144 (1- \dfrac{1}{2}^4)}{1-\dfrac{1}{2}}\\\\S \infty = \dfrac{-144 \times \dfrac{15}{16}}{\dfrac{1}{2}}\\\\S \infty = -270$