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kirill [66]
3 years ago
7

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:

<h2>12, 14</h2>

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:

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%.

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]
It would be 224 , the base is 64 and every triangle is 80 but if you follow the rule for area to a triangle you get 40
So 64+40+40+40+40= 224
4 0
2 years ago
Read 2 more answers
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