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3 years ago

Find the number of permutations of the first eight letters of the alphabet taking four letters at a time.

1 answer:

3 0

The number of permutations of 8 different things taken 4 at a time is given by:
$8C4=\frac{8!}{(8-4)!}=8\times7\times6\times5=1680$

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a coin will be tossed 10 times. Find the chance that there will be exactly 2 heads among the first five tosses and exactly 4 hea

777dan777 [17]

Answer:

The chance that there will be exactly 2 heads among the first five tosses and exactly 4 heads among the last 5 tosses is P=0.0488.

Step-by-step explanation:

To solve this problem we divide the tossing in two: the first 5 tosses and the last 5 tosses.

Both heads and tails have an individual probability p=0.5.

Then, both group of five tosses have the same binomial distribution: n=5, p=0.5.

The probability that k heads are in the sample is:

$P(x=k)=\dbinom{n}{k}p^k(1-p)^{n-k}=\dbinom{5}{k}\cdot0.5^k\cdot0.5^{5-k}$

Then, the probability that exactly 2 heads are among the first five tosses can be calculated as:

$P(x=2)=\dbinom{5}{2}\cdot0.5^{2}\cdot0.5^{3}=10\cdot0.25\cdot0.125=0.3125\\\\\\$

For the last five tosses, the probability that are exactly 4 heads is:

$P(x=4)=\dbinom{5}{4}\cdot0.5^{4}\cdot0.5^{1}=5\cdot0.0625\cdot0.5=0.1563\\\\\\$

Then, the probability that there will be exactly 2 heads among the first five tosses and exactly 4 heads among the last 5 tosses can be calculated multypling the probabilities of these two independent events:

$P(H_1=2;H_2=4)=P(H_1=2)\cdot P(H_2=4)=0.3125\cdot0.1563=0.0488$

7 0

3 years ago

Imagine that you take a road trip from A to D, but you have to do it in segments. Let’s say the distance from A to B is 145 mile

Rzqust [24]

Answer: The average is 70.

Step-by-step explanation:

145+160+115=420

420 divided by 6 =70

So the average is 70.

4 0

3 years ago

Read 2 more answers

Taylor bought a watch on sale for 60% off of the original price, and another 10% off of the discounted price. If the watch origi

Lorico [155]

Answer:

I think the answer is $4.92.

Step-by-step explanation:

Although the answer seems a little unreasonable, I think this is the answer:

$82 * 60% = $49.2

49.2 * 10% = $4.92

Please mark brainliest if correct!!!!!!!!!!!!!!! have a nice day!!

8 0

3 years ago

F(x) =x2+2x-3 g(x)=3x-14

Leviafan [203]

The solution to the composite function f(g(x)) is 9x² - 78x + 165.

<h3>What is composite function?</h3>

A composite function is generally a function that is written inside another function.

Function composition is an operation that takes two functions f and g, and produces a function h = g ∘ f such that h(x) = g.

From the given composite function, the solution is determined as follows;

to solve for f(g(x)), we use the following methods.

f(x) = x² + 2x - 3, g(x) = 3x - 14

f(g(x)) = (3x - 14)² + 2(3x - 14) - 3

= 9x² - 84x + 196 + 6x - 28 - 3

= 9x² - 78x + 165

Thus, the solution to the composite function f(g(x)) is 9x² - 78x + 165.

Learn more about composite function here: brainly.com/question/10687170

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The complete question is below:

F(x) =x2+2x-3 g(x)=3x-14, find f(g(x))

8 0

1 year ago

A rectangle has a height of 5 and a width of 4x2– 2x - 6.

joja [24]

Answer:

area = 20x^2 - 10x - 30

Step-by-step explanation:

5(4x2 - 2x - 6)

area = 20x^2 - 10x - 30

5 0

3 years ago