Angelique says that finding the absolute value of a number is the same as finding the opposite

2.10 Guessing on an exam: In a multiple choice exam, there are 6 questions and 4 choices for each question (a, b, c, d). Nancy h

ololo11 [35]

Answer:

a) $p = (3/4)^5 *(1/4) =0.0593$

b) $P(X=6) = (6C6) (0.25)^6 (1-0.25)^{6-6}= 0.000244$

c) $P(X \geq 1)$

And we can use the complement rule like this:

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

$P(X=0) = (6C0) (0.25)^0 (1-0.25)^{6-0}= 0.17798$

And replacing we have:

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

Step-by-step explanation:

Previous concepts

A Bernoulli trial is "a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted". And this experiment is a particular case of the binomial experiment.

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

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:

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

The complement rule is a theorem that provides a connection between the probability of an event and the probability of the complement of the event. Lat A the event of interest and A' the complement. The rule is defined by: $P(A)+P(A') =1$

We can model the number of correct questions answered with a binomial distribution $X \sim Binom(n = 6, p = 1/4=0.25)$

Solution to the problem

Assuming the following questions:

a) the first question she gets right is the 6th question?

For this case we want the first 5 questions incorrect and the last one correct, assuming independence we have:

$p = (3/4)^5 *(1/4) =0.0593$

(b) she gets all of the questions right?

For this case we want all the questions right so then we want this:

$P(X=6) = (6C6) (0.25)^6 (1-0.25)^{6-6}= 0.000244$

(c) she gets at least one question right?

For this case we want this probability:

$P(X \geq 1)$

And we can use the complement rule like this:

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

$P(X=0) = (6C0) (0.25)^0 (1-0.25)^{6-0}= 0.17798$

And replacing we have:

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

7 0

3 years ago

Match the features of the graph of the rational function.

Sunny_sXe [5.5K]

After applying algebraic analysis we find the right choices for each case, all of which cannot be presented herein due to length restrictions. Please read explanation below.

<h3>How to analyze rational functions</h3>

In this problem we have a rational function, whose features can be inferred by algebraic handling:

Holes - x-values that do not belong to the domain of the rational function:

x³ + 8 · x² - 9 · x = 0

x · (x² + 8 · x - 9) = 0

x · (x + 9) · (x - 1) = 0

x = 0 ∨ x = - 9 ∨ x = 1

But one root is an evitable discontinuity as:

y = (9 · x² + 81 · x)/(x³ + 8 · x² - 9 · x)

y = (9 · x + 81)/(x² + 8 · x - 9)

Thus, there are only two holes. (x = - 9 ∨ x = 1) Besides, there is no hole where the y-intercept should be.

Vertical asymptotes - There is a vertical asymptote where a hole exists. Hence, the function has two vertical asymptotes.

Horizontal asymptotes - Horizontal asymptote exists and represents the end behavior of the function if and only if the grade of the numerator is not greater than the grade of the denominator. If possible, this assymptote is found by this limit:

$y = \lim_{x \to \pm \infty} \frac {9\cdot x + 81}{x^{2}+8\cdot x - 9}$

y = 0

The function has a horizontal asymptote.

x-Intercept - There is an x-intercept for all x-value such that numerator is equal to zero:

9 · x + 81 = 0

x = - 9

There is a x-intercept.

Lastly, we have the following conclusions:

How many holes? 2
One horizontal asymptote along the line where y always equals what number: 0
This function has x-intercepts? True
One vertical asymptote along the line where x always equals what number: 1
There is a hole where the y-intercept should be? False

To learn more on rational functions: brainly.com/question/27914791

#SPJ1

5 0

2 years ago

Lottie buys a pack of 50 cans of lemonade.

malfutka [58]

Answer:

£15.7

Step-by-step explanation:

32 cans x 50P = 1600p

1600p to Pounds = £26.66 (1600 divided by 60)

Remaining cans = 18 (50 - 32)

18 cans x 20p = 360p

360p to Pounds = £6 (360 divided by 60)

£26.66 + £6 = £32.66

£32.66 (Profit) - £17 (Cost of cans) = £15.66

15.66 to 3SF = 15.7

3 0

2 years ago

Read 2 more answers

2/3y + 15 = 9 What are the steps for this question

xenn [34]

Answer:

see below

Step-by-step explanation:

2/3y + 15 = 9

Subtract 15 from each side

2/3y + 15-15 = 9-15

2/3y = -6

Multiply each side by 3/2 to isolate y

3/2 * 2/3y = -6 *3/2

y = -9

4 0

3 years ago

Read 2 more answers

(5 •10^16) • (2.8 • 10^-7)

Gelneren [198K]

That's 7/3 =2.3333333

7 0

3 years ago