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3 years ago

How to solve for 40! / 10!30!

1 answer:

3 0

40! / 30! = 40*39*38*37*36*35*34*33*32*31

dividing this by 10! 10*9*8*7*6*5*4*3*2*1

= 4*13*19*37*17*11*4*31

= 847,660,528

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A yoga club had 54 members and the ratio of men to women is 4:5. This year, 18 new members joined the club and the ratio of men

castortr0y [4]

Answer:

Step-by-step explanation:

5 0

3 years ago

1 3/4 x 1 1/3 give your answer as a mixed number

WARRIOR [948]

Answer:

2 1/3

Step-by-step explanation:

1 3/4 is equivalent to 7/4

1 1/3 is equivalent to 4/3

7/ 4 x 4/3

reduce with greatest common factor so the two 4 are out (show a line crossing out the top and bottom 4 )

now you're left with 7 x 1/3 = 7/3

7/3 = 2 1/3

4 0

2 years ago

Read 2 more answers

What is the z-score of a newborn who weighs 4,000 g?.

vagabundo [1.1K]

The z-score of the considered newborn having 4,000 g weight is $\dfrac{4000 - \mu}{\sigma}$

<h3>How to get the z scores?</h3>

If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.

If we have

$X \sim N(\mu, \sigma)$

(X is following normal distribution with mean $\mu$ and standard deviation $\sigma$ )

then it can be converted to standard normal distribution as

$Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)$

(Know the fact that in continuous distribution, probability of a single point is 0, so we can write

$P(Z \leq z) = P(Z < z) )$

Also, know that if we look for Z = z in z tables, the p value we get is

$P(Z \leq z) = \rm p \: value$

For the considered case, the statement in the problem is missing the mean weight of the newborn and standard deviation of the data set of weights of newborn.

Thus, for them, we can consider variables in place of their actual values.

Let we have:

X = weights of newborns for some considered system (in grams)
$\mu$ = mean weight of newborns (in grams)
$\sigma$ = standard deviation of the data set of weights of newborns

Then, the z-score for X = 4000 is

$z = \dfrac{x - \mu}{\sigma} = \dfrac{4000 - \mu}{\sigma}$

Thus, the z-score of the considered newborn having 4,000 g weight is $\dfrac{4000 - \mu}{\sigma}$

Learn more about z-scores here:

brainly.com/question/13299273

3 0

2 years ago

2) 9 lbs. of mixed nuts containing 55% peanuts were

Sonbull [250]

Answer:

<em>The new mixture is 49% peanuts.</em>

Step-by-step explanation:

The first batch of 9 lb of mixed nuts contains 55% peanuts. This means the quantity of peanut is:

9*55/100=4.95 lb

The second batch of 6 lb of mixed nuts contains 40% peanuts. This means the quantity of peanut is:

6*40/100=2.4 lb

The total quantity of peanut in the mix is

4.95 lb + 2.4 lb =7.35 lb

There are 9 lb + 6 lb = 15 lb of mix. Thus, the percent of peanut in the mix is:

7.35 / 15 * 100 = 49%

The new mixture is 49% peanuts.

6 0

3 years ago

The sum of 30 times (1/3)^(n-1) from 1 to infinity

sergeinik [125]

Let

$S_n=\displaystyle1+\frac13+\frac1{3^2}+\cdots+\frac1{3^n}$

Then

$\dfrac13S_n=\displaystyle\frac13+\frac1{3^2}+\frac1{3^3}+\cdots+\frac1{3^{n+1}}$

and

$S_n-\dfrac13S_n=\dfrac23S_n=1-\dfrac1{3^{n+1}}\implies S_n=\dfrac32-\dfrac1{2\cdot3^n}$

and as $n\to\infty$ , we end up with

$\displaystyle\lim_{n\to\infty}S_n=\lim_{n\to\infty}\sum_{i=1}^{n+1}\frac1{3^{i-1}}=\lim_{n\to\infty}\left(\frac32-\frac1{2\cdot3^n}\right)=\frac32$

So we have

$\displaystyle\sum_{n=1}^\infty30\left(\frac13\right)^{n-1}=30\cdot\frac32=45$

8 0

3 years ago