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3 years ago

Solve and graph 81<9x

Mathematics

1 answer:

spayn [35]3 years ago

3 0

Answer:

x=9

Step-by-step explanation:

9*9=81

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Approximate the sum of the convergent infinite series the least usingnumber of terms so that the error is less than .0001. What

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Solution :

$\sum_{n=1 }^{\infty } \frac{(-1)^n}{n ! 2^n}$ $a_n= \frac{(-1)^n}{n ! 2^n} \ \ \ \ \ a_{n+1}= \frac{(-1)^{n+1}}{(n+1) ! 2^{n+1}}$

Error = $|a_{n+1}|$

Error ≤ 0.0001

$|\frac{(-1)^{n+1}}{(n+1)!2^{n+1}}| \leq 0.0001$

$|\frac{1}{(n+1)!2^{n+1}}| \leq 10^{-4}$

$(n+1)! 2^{n+1} \geq 10000$

Now try, n ≥ 5

$\sum_{n=1 }^{\infty } \frac{(-1)^n}{n ! 2^n}$ = $\sum_{n=1 }^{5 } \frac{(-1)^n}{n ! 2^n}$ (with error 0.0001)

$\sum_{n=1 }^{\infty } \frac{(-1)^n}{n ! 2^n}$ = $\frac{-1}{1!2}+\frac{1}{2!2^2}-\frac{1}{3! 2^3}+\frac{1}{4! 2^4}-\frac{1}{5! 2^5}$

$\sum_{n=1 }^{\infty } \frac{(-1)^n}{n ! 2^n}$ = 0.6065104

3 0

3 years ago

Simplify this math problem 2x +3 -x=

8090 [49]

Combine like terms:

2x - x + 3

x + 3

Once there is no more simplification to be done, your final answer remains which is the above equation.

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4 years ago

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Convert 3 over 8 to a decimal and tell whether it terminates or repeats.

Rasek [7]

the answer is c) 0.375, a number that terminates.

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3 years ago

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It was found that the mean length of 100 diodes (LED) produced by a company

Lelechka [254]

Using the normal distribution, it is found that there is a 0.0228 = 2.28% probability that a diode selected at random would have a length less than 20.01mm.

<h3>Normal Probability Distribution</h3>

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

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

It 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, which is the percentile of X.

In this problem, we have that:

The mean is of $\mu = 20.05$ .

The standard deviation is of $\sigma = 0.02$ .

The probability that a diode selected at random would have a length less than 20.01mm is the <u>p-value of Z when X = 20.01</u>, hence:

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

$Z = \frac{20.01 - 20.05}{0.02}$

$Z = -2$

$Z = -2$ has a p-value of 0.0228.

0.0228 = 2.28% probability that a diode selected at random would have a length less than 20.01mm.

More can be learned about the normal distribution at brainly.com/question/24663213

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2 years ago

Fifteen percent of the persons taking a driving test fail to pass first time. What percentage passes first time?

Ber [7]

85 % of drivers pass the first time.

Calculations:

100%-15%=85%

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4 years ago

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