A pack or cinnamon-scented pencils sells for $4.00. What is the sales tax rate if the total cost of the pencils is $4.32?

Jake tossed a paper cup 50 times and recorded how it landed. The table shows the results:

JulsSmile [24]

Answer:

0.06 = 6% probability of landing open side up.

0.14 = 14% probability of landing closed side up.

0.8 = 80% probability of landing on its side.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes. For an experimental probability, these numbers are taken from previous trials.

Landing open side up:

3 out of 50, so:

$p = \frac{3}{50} = 0.06$

0.06 = 6% probability of landing open side up.

Landing closed side up:

7 out of 50, so:

$p = \frac{7}{50} = 0.14$

0.14 = 14% probability of landing closed side up.

Landing on its side:

40 out of 50, so:

$p = \frac{40}{50} = 0.8$

0.8 = 80% probability of landing on its side.

5 0

3 years ago

What is the formula for the expected number of successes in a binomial experiment with n trials and probability of success p? C

charle [14.2K]

Answer:

$(D)E[ X ] =np.$

Step-by-step explanation:

Given a binomial experiment with n trials and probability of success p,

$f(x)=\left(\begin{array}{c}n\\k\end{array}\right)p^x(1-p)^{n-x}, 0\leq x\leq n$

$E(X)=\sum_{x=0}^{n}xf(x)= \sum_{x=0}^{n}x\left(\begin{array}{c}n\\k\end{array}\right)p^x(1-p)^{n-x}$

Since each term of the summation is multiplied by x, the value of the term corresponding to x = 0 will be 0. Therefore the expected value becomes:

$E(X)=\sum_{x=1}^{n}x\left(\begin{array}{c}n\\x\end{array}\right)p^x(1-p)^{n-x}$

Now,

$x\left(\begin{array}{c}n\\x\end{array}\right)= \frac{xn!}{x!(n-x)!}=\frac{n!}{(x-)!(n-x)!}=\frac{n(n-1)!}{(x-1)!((n-1)-(x-1))!}=n\left(\begin{array}{c}n-1\\x-1\end{array}\right)$