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2 years ago

How many ways can 12 swimmers finish in first, second, and third place

1 answer:

7 0

1320 ways
This can be solved using something called permutation. There are 12 possible swimmers that can be in first place. After that, 11 swimmers left to be in second place. Finally there are 10 swimmers left for third place. Multiply these together you get 12•11•10=1320. Hope this helps!!

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Suppose a random variable, x, arises from a binomial experiment. If n = 6, and p = 0.30, find the following probabilities using

AlladinOne [14]

Answer:

a) P(X=1) = 0.302526

b) P(X=5) = 0.010206

c) P(X=3) = 0.18522

d) P(X≤3) = 0.92953

e) P(X≥5) = 0.010935

f) P(X≤4) = 0.989065

Explanation:

Binomial experiments are modeled by the formula:

$P(X=x)=C(n,x)\cdot p^x\cdot (1-p)^{(n-x)}$

Where

P(X=x) is the probability of exactly x successes

$C(n,x)=\dfrac{n!}{x!\cdot (n-x)!}$

p is the probability of one success, which must be the same for every trial, and every trial must be independent of other trial.

n is the number of trials

1 - p is the probability of fail

there are only two possible outcomes for each trial: success or fail.

a.) P (x=1)

$P(X=1)=\dfrac{6!}{1!\cdot (6-1)!}\times (0.3)^1\times(1-0.3)^{(6-1)}=0.302526$

b.) P (x=5)

$P(X=5)=\dfrac{5!}{5!\cdot (6-5)!}\times (0.3)^5\times (1-0.3)^{(6-5)}=0.010206$

c.) P (x=3)

Using the same formula:

$P(X=3)=0.18522$

d.) P (x less than or equal to 3)

P(X≤3)= P(X=3) + P(X=2) + P(X=1) + P(X=0)

Also,

P(X≤3) = 1 - P(X≥4) = 1 - P(X=4) - P(X=5) - P(X=6)

You can use either of those approaches. The result is the same.

Using the second one:

P(X=4) = 0.059335
P(X=5) = 0.010206
P(X=6) = 0.000729

P(X≤3) = 1 - 0.05935 - 0.010206 - 0.000729 = 0.92953

e.) P(x greather than or equal to 5)

P(X≥5) = P(X=5) + P(X=6)

P(X≥5) = 0.010206 + 0.000729 = 0.010935

f.) P(x less than or equal 4)

P(X≤4) = 1 - P(X≥5) = 1 - P(X=5) - P(X=6)

P(X≤4) = 1 - 0.010206 - 0.000729 = 0.989065

5 0

3 years ago

PLEasE i need help brainlist if u get right

Juli2301 [7.4K]

Answer:

c or a i just did the test

Step-by-step explanation:

3 0

3 years ago

Which graph represents the function f(x)=0.25x+5

ozzi

Answer:

Its the graph at the top left.

Step-by-step explanation:

Take the graph of f(x) = 0.25^x:

when x = 0 , f(x) = 1 so it will pass through the point (0,1). Also as x increases f(x) will decrease because the base 0.25 is < 1. So the graph will decrease to the right.

The + 5 in the function moves the whole graph up 5 units so the graph will pass through the point (0, 6).

6 0

2 years ago

a rectangle has a length of 12 units and an unknown width, x. using p to represent the perimeter and a to represent the area, wr

Amanda [17]

$\begin{gathered} L\text{ = 12} \\ \text{Breadth / width = x} \\ \text{Area, a = L }\times\text{ B} \\ \text{ = 12 }\times\text{ a } \\ \text{ = 12a} \\ \text{Perimeter, P: = 2(L + B)} \\ \text{ = 2(12 + x)} \\ \text{ = 24 + 2x} \\ \end{gathered}$

4 0

1 year ago

Use a transformation to solve the equation.

olchik [2.2K]

D-(-17)=-14
d+17=-14
d=-14-17
d=-31
answer is A

8 0

3 years ago