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3 years ago

Prove: If a^2-a is even then a is even.

Mathematics

1 answer:

Alla [95]3 years ago

6 0

This is not always true. Consider $a=3$ . Then $3^2-3=9-3=6$ is even, but $a$ is odd.

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The probability that an electronic device produced by a company does not function properly is equal to 0.1. If 10 devices are bo

coldgirl [10]

Answer:

Correct option: A. P=0.057

Step-by-step explanation:

<u>Binomial Distribution</u>

The binomial distribution fits the case of n independent events each one with a probability of success equal to p where k successes have been achieved.

The PMF (Probability Mass Function) of the binomial distribution is

$\displaystyle P(k,n,p)=\binom{n}{k}p^kq^{n-k}$

Where $q = 1-p$

The individual probability that an electronic device does not function properly is p=0.1. We know n=10 devices have been bought and we want to compute the probability that 7 devices function properly. Please notice that this is not the value of k since p is the probability of failure. The correct value of k=10-7=3. The required probability is

$\displaystyle P(3,10,0.1)=\binom{10}{3}0.1^30.9^{10-3}$

$\boxed{P=0.057}$

8 0

3 years ago

The trees at a national park have been increasing in numbers. There were 1,000 trees in the first year that the park started tra

ivanzaharov [21]

The sequence forms a Geometric sequence as the rule to obtain the value for the next term is by ratio

Term 1: 1000
Term 2: 200
Term 3: 40

From term 1 to term 2, there's a decrease by $\frac{1}{5}$
From term 2 to term 3, there's a decrease also by $\frac{1}{5}$

The rule to find the $n^{th}$ term in a sequence is
$n^{th}=a r^{n-1}$ , where $a$ is the first term in the sequence and $r$ is the ratio

So, the formula for the sequence in question is
$n_{th}$ term = $1000( \frac{1}{5} ^{n-1} )$

The sequence is a divergent one. We can always find the value of the next term by dividing the previous term by 5 and if we do that, the value of the next term will get closer to 'zero' but never actually equal to zero.

We can find a partial sum of the sequence using the formula
$S_{∞} = \frac{a}{1-r}$ for -1<r<1
Substituting $a=1000$ and $r= \frac{1}{5}$ we have
$S_{∞}$ = $\frac{1000}{1- \frac{1}{5} }$ = 1250

Hence, the correct option is option number 1

6 0

3 years ago

The student government snack shop sold 32 items this week

Firdavs [7]

Answer:

right the whole question

Step-by-step explanation:

if he sold 32 items this week last week he sold 20

5 0

2 years ago

Eumin pays $3.56 for 4 juice boxes.

Alborosie

Answer:

No, You divide 3.56/4 and you get 0.89 and then after that you multiply it by 7 so you do0.89x7=6.23

Step-by-step explanation:

8 0

2 years ago

Is percent of change less than 100

Ivanshal [37]

You can't change more than 100 percent

6 0

3 years ago