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3 years ago

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Billy is trying to convince Cynthia that all whole numbers are also natural numbers. To support his argument, Billy points out t

hat 1, 2, 3, 4, 5, and 6 are all whole numbers and are also natural numbers. He goes on to argue that, by continuing the pattern, every integer greater than 6 will also be both a whole number and a natural number, thus making all whole numbers natural numbers.

2 answers:

yaroslaw [1]3 years ago

7 0

Answer: The answer is B have a good one #freedrakeo

Step-by-step explanation:

free ralphie

Temka [501]3 years ago

4 0

<span>He has failed to consider the number 0, which is a whole number but not a natural number.</span>

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Consider the probability that greater than 26 out of 124 software users will call technical support. Assume the probability that

Mekhanik [1.2K]

Answer:

Since $n(1-p) = 3.72 < 10$ , the normal curve cannot be used as an approximation to the binomial probability.

100% probability that greater than 26 out of 124 software users will call technical support.

Step-by-step explanation:

Test if the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.

It is needed that:

$np \geq 10$ and $n(1-p) \geq 10$

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.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

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

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

Out of 124 software users

This means that $n = 124$

Assume the probability that a given software user will call technical support is 97%.

This means that $p = 0.97$

Conditions:

$np = 124*0.97 = 120.28 \geq 10$

$n(1-p) = 124*0.03 = 3.72 < 10$

Since $n(1-p) = 3.72 < 10$ , the normal curve cannot be used as an approximation to the binomial probability.

Consider the probability that greater than 26 out of 124 software users will call technical support.

The lowest possible probability of those is 27, so, if it is 0, since it is considerably below the mean, 100% probability of being greater. We have that:

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

$P(X = 27) = C_{124,27}.(0.97)^{27}.(0.03)^{97} = 0$

1 - 0 = 1

100% probability that greater than 26 out of 124 software users will call technical support.

3 0

3 years ago

The length of a rectangle is 8 inches longer than the width. If the area is 295 square inches, find the

sladkih [1.3K]

Answer:

L=21.6in and w=13.6

Step-by-step explanation:

If the length is 8 inches longer than its width, we can write the width as "w" and the length as the width w+ 8

Area is (width)(Length) = (width)(width+8)

W

----------

| |

| |

| | L = w+8

| |

| |

-----------

A = (w+8)(w)

A = w2 + 8w = 295.

(Problem states that area is 295 sq in)

Need to solve this quadratic equation

w2 +8y - 295 = 0

Factor:

(w - 13.64) (w + 21.64) = 0

So

w - 13.64 = 0. or. w + 21.64= 0

Solve these and get

w = 13.64. or. w = -21.64

Only one that makes sense in real life is the poitive one.

So the dimensions are

Width = 13.64 inches

Length = 21.64 inches

7 0

3 years ago

What integer represents the following situation? ________________. A scuba diver is 43 feet under the ocean conducting research

Softa [21]

an Integer is a while positive or negative number. so your integer would be 43

8 0

3 years ago

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Which fraction represents the decimal 0.12

ryzh [129]

Answer:

$\dfrac 3{25}$

Step-by-step explanation:

$0.12 = \dfrac{12}{100}=\dfrac{3}{25}$

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2 years ago

Can somebody log into my khan and help me with it?

aniked [119]

Answer:

Step-by-step explanation:

Yes

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3 years ago