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Ulleksa [173]
3 years ago
5

The daily high temperature on October 31 in a certain city is normally distributed with µ = 50 and σ = 8 . What is the probabili

ty that the high temperature on October 31 in a randomly chosen year will be between 46 degrees and 58 degrees? (Give your answer as a decimal rounded to 4 decimal places.)
Mathematics
1 answer:
tatyana61 [14]3 years ago
8 0

Answer:

0.5328

Step-by-step explanation:

µ = 50

σ = 8

We are supposed to find the probability that the high temperature on October 31 in a randomly chosen year will be between 46 degrees and 58 degrees

P(46 < x< 58)

Formula : Z=\frac{x-\mu}{\sigma}

at x = 46

Z=\frac{46-50}{8}

Z=-0.5

Refer the z table for p value

p value = 0.3085

at x = 58

Z=\frac{58-50}{8}

Z=1

Refer the z table for p value

p value = 0.8413

P(46 < x< 58)=P(x

Hence the probability that the high temperature on October 31 in a randomly chosen year will be between 46 degrees and 58 degrees is 0.5328

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Solve for x. Round your answer to the nearest tenth.<br> 42<br> 37<br> X=<br> units
natita [175]

Answer:

10

Step-by-step explanation:

That little square gives you a hint that it's an 90 degree angle/ acute angle First add 42 and 37 and you will get 79. Next subtract 79 from 90 and you will get 11. (5 or more, raise the score, for or less, let it rest.) 11 equals 10.

Numarical form:

47 + 37 = 79

90 - 79 = 11

1<u>1</u> = 1<u>0</u>

6 0
3 years ago
Let log P/N=8 and log M/N=5<br><br> What is the relationship between P and M?
Radda [10]
Want to use some of the algebra rules of log's:

log(a)-log(b)= log(a/b),

so log(P/N) - log(M/N) = log( P/N:M/N) = log(P/M),

Then: 8-5 = log(P/M), log(P/M)=3.

If log here means natural logarithm (base e), then P/M = e^3,

If log here means basis 10, decimal logarithm, then P/M = 10^3 = 1000.
8 0
3 years ago
Consider the series ∑n=1[infinity]2nn!nn. Evaluate the the following limit. If it is infinite, type "infinity" or "inf". If it d
Vikki [24]

I guess the series is

\displaystyle\sum_{n=1}^\infty\frac{2^nn!}{n^n}

We have

\displaystyle\lim_{n\to\infty}\left|\frac{\frac{2^{n+1}(n+1)!}{(n+1)^{n+1}}}{\frac{2^nn!}{n^n}}\right|=2\lim_{n\to\infty}\left(\frac n{n+1}\right)^n

Recall that

e=\displaystyle\lim_{n\to\infty}\left(1+\frac1n\right)^n

In our limit, we have

\dfrac n{n+1}=\dfrac{n+1-1}{n+1}=1-\dfrac1{n+1}

\left(\dfrac n{n+1}\right)^n=\dfrac{\left(1-\frac1{n+1}\right)^{n+1}}{1-\frac1{n+1}}

\implies\displaystyle2\lim_{n\to\infty}\left(\frac n{n+1}\right)^n=2\frac{\lim\limits_{n\to\infty}\left(1-\frac1{n+1}\right)^{n+1}}{\lim\limits_{n\to\infty}\left(1-\frac1{n+1}\right)}=\frac{2e}1=2e

which is greater than 1, which means the series is divergent by the ratio test.

On the chance that you meant to write

\displaystyle\sum_{n=1}^\infty\frac{2^n}{n!n^n}

we have

\displaystyle\lim_{n\to\infty}\left|\frac{\frac{2^{n+1}}{(n+1)!(n+1)^{n+1}}}{\frac{2^n}{n!n^n}}\right|=2\lim_{n\to\infty}\frac1{(n+1)^2}\left(\frac n{n+1}\right)^2

=\displaystyle2\left(\lim_{n\to\infty}\frac1{(n+1)^2}\right)\left(\lim_{n\to\infty}\left(\frac n{n+1}\right)^n\right)=2\cdot0\cdot e=0

which is less than 1, so this series is absolutely convergent.

6 0
3 years ago
Simplify each expression. <br> -10 (n+6)
sertanlavr [38]

Answer:

-10n - 60

Step-by-step explanation:

Use the distributive property to simplify [ a(b + c) = ab + ac ]

-10(n + 6)

(-10 * n) + (-10 * 6)

-10n + -60

-10n - 60

Best of Luck!

4 0
3 years ago
Read 2 more answers
5. On the fifth day of my winter break, I got five golden rings. BUT—— the golden rings were five separate water rings around my
kvv77 [185]

Answer:

Step-by-step explanation:

1 ring has a radius of 3 feet

1 ring has a circumfrence of 2*pi*r = 2 * 3.14 * 5 = 10*Pi

5 rings would have a length of 50 * pi length = 50*3.14 = 157 feet

That's a lot of Brillo pads.

4 0
3 years ago
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