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3 years ago

The product of two consecutive positive even integers is 168. What are the two integers?

Mathematics

1 answer:

Aneli [31]3 years ago

7 0

Answer:

Step-by-step explanation:

$n,\ n+2-\text{two consecutive positive even integers}\\\\(n)(n+2)-\text{their product}\\\\168-\text{their product}\\\\\text{The equation:}\\\\n(n+2)=168\qquad\text{use the distributive property}:\ a(b+c)=ab+ac\\\\(n)(n)+(n)(2)=168\\\\n^2+2n=168\qquad\text{add 1 to both sides}\\\\n^2+2n+1=168+1\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\n^2+2(n)(1)+1^2=169\\\\(n+1)^2=169\iff n+1=\pm\sqrt{169}\\\\n+1=\pm13\qquad\text{subtract 1 from both sides}\\\\n+1-1=-13-1\ \vee\ n+1-1=13-1\\\\n=-14$

$n+2=12+2=14$

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P(B)=1320,P(A∩B)=1325,P(A|B)=?

Dafna1 [17]

Formula for the Conditional Probability is:
P ( A \ B ) = P ( A ∩ B ) / P ( B )
But it is not possible to have the probability greater than 1.
0 ≤ P ( n ) ≤ 1
So let`s assume that: P ( A ∩ B ) = 1320 and P ( B ) = 1325
P ( A \ B ) = 1320 / 1325 = 0.9962

3 0

2 years ago

Suppose a continuous probability distribution has an average of μ=35 and a standard deviation of σ=16. Draw 100 times at random

yulyashka [42]

Answer:

To use a Normal distribution to approximate the chance the sum total will be between 3000 and 4000 (inclusive), we use the area from a lower bound of 3000 to an upper bound of 4000 under a Normal curve with its center (average) at 3500 and a spread (standard deviation) of 160 . The estimated probability is 99.82%.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For sums, we have that the mean is $\mu*n$ and the standard deviation is $s = \sigma \sqrt{n}$

In this problem, we have that:

$\mu = 100*35 = 3500, \sigma = \sqrt{100}*16 = 160$

This probability is the pvalue of Z when X = 4000 subtracted by the pvalue of Z when X = 3000.

X = 4000

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

By the Central Limit Theorem

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

$Z = \frac{4000 - 3500}{160}$

$Z = 3.13$

$Z = 3.13$ has a pvalue of 0.9991

X = 3000

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

$Z = \frac{3000 - 3500}{160}$

$Z = -3.13$

$Z = -3.13$ has a pvalue of 0.0009

0.9991 - 0.0009 = 0.9982

So the correct answer is:

5 0

3 years ago

Could you please explain it?

Troyanec [42]

Hello,
there are some words that I could not read. But:
I support evements are independants.
p(s)=0.2
p(l)=1-0.2=0.8 l=lose

1)0.8*0.2=0.16

2) 0.8²*0.2=0.128

3) 0.8^3*0.2=0.1024

4) 0.2*0.8^(n-1)

6 0

3 years ago

Please help I’ll give you brainiest :)

juin [17]

Answer:

i think its b

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

Does anyone have a answer to this?

jolli1 [7]