When are x2+2x/5x and it's simplified form equal

Suppose you toss a fair coin 10 times, let X denote the number of heads. (a) What is the probability that X=5? (b) What is the p

zubka84 [21]

Answer: The required answers are

(a) 0.25, (b) 0.62, (c) 6.

Step-by-step explanation: Given that we toss a fair coin 10 times and X denote the number of heads.

We are to find

(a) the probability that X=5

(b) the probability that X greater or equal than 5

(c) the minimum value of a such that P(X ≤ a) > 0.8.

We know that the probability of getting r heads out of n tosses in a toss of coin is given by the formula of binomial distribution as follows :

$P(X=r)=^nC_r\left(\dfrac{1}{2}\right)^r\left(\dfrac{1}{2}\right)^{n-r}.$

(a) The probability of getting 5 heads is given by

$P(X=5)\\\\\\=^{10}C_5\left(\dfrac{1}{2}\right)^5\left(\dfrac{1}{2}\right)^{10-5}\\\\\\=\dfrac{10!}{5!(10-5)!}\dfrac{1}{2^{10}}\\\\\\=0.24609\\\\\sim0.25.$

(b) The probability of getting 5 or more than 5 heads is

$P(X\geq 5)\\\\=P(X=5)+P(X=6)+P(X=7)+P(X=8)+P(X=9)+P(X=10)\\\\=^{10}C_5\left(\dfrac{1}{2}\right)^5\left(\dfrac{1}{2}\right)^{10-5}+^{10}C_6\left(\dfrac{1}{2}\right)^6\left(\dfrac{1}{2}\right)^{10-6}+^{10}C_7\left(\dfrac{1}{2}\right)^7\left(\dfrac{1}{2}\right)^{10-7}+^{10}C_8\left(\dfrac{1}{2}\right)^8\left(\dfrac{1}{2}\right)^{10-8}+^{10}C_9\left(\dfrac{1}{2}\right)^9\left(\dfrac{1}{2}\right)^{10-9}+^{10}C_{10}\left(\dfrac{1}{2}\right)^{10}\left(\dfrac{1}{2}\right)^{10-10}\\\\\\=0.24609+0.20507+0.11718+0.04394+0.0097+0.00097\\\\=0.62295\\\\\sim 0.62.$

(c) Proceeding as in parts (a) and (b), we see that

if a = 10, then

$P(X\leq 0)=0.00097,\\\\P(X\leq 1)=0.01067,\\\\P(X\leq 2)=0.05461,\\\\P(X\leq 3)=0.17179,\\\\P(X\leq 4)=0.37686,\\\\P(X\leq 5)=0.62295,\\\\P(X\leq 6)=0.82802.$

Therefore, the minimum value of a is 6.

Hence, all the questions are answered.

3 0

3 years ago

13 divided by 1209 please help

loris [4]

The answer is 93 It’s 1209 divided by 13 not 13 divide by 1209 ;) hope this helps ! Because when we’re dividing the number get smaller and when we multiplying the number gets bigger , have a nice day !

5 0

2 years ago

Using the side lengths

In-s [12.5K]

Given

The three sides are given 24, 30 and 18.

Explanation

To find the triangle is acute, obtuse or right triangle.

To determine whether the triangle is acute, right, or obtuse.add the squares of the two smaller sides, and compare the sum to the square of the largest side. Since this sum is greater, the triangle is acute.

A

If the sum of the squares of the two smaller sides is equal to the square of the largest side , then it is right triangle.

Now c.

$\begin{gathered} 30^2=24^2+18^2 \\ 900=576+324 \\ 900=900 \end{gathered}$

Answer

Hence the sum of the squares of the two smaller sides is equal to the square of the largest side , then it is right triangle.

The correct option is A.

3 0

1 year ago

A babysitter earns $24 for 2 hours and $42 for 4 hours. Determine the rate of change

dedylja [7]

Answer:

im not 100% sure but this is the answer i got you need to add a number to that to get the next payment for 6 hours

Step-by-step explanation:

8 0

3 years ago

Use standard notation to write this number. 4.045x10^-3

Inessa05 [86]

<span>4.045 x10^-3 in standard notation = 4,045</span>

5 0

3 years ago

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