Function g is defined by g(x)=3(x+8) what is the value of g(12)

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

4 years ago

This question is too hard

OLga [1]

Answer:

27 children

Step-by-step explanation:

For every 9 children, there are 4 adults. Those numbers added together equal 13. Now, if we divide the total number of adults and children by 13, we will get the number of how many groups there are of 9 kids and 4 adults.

39 / 13 = 3

There are 3 groups of 9 kids and 4 adults, which means to find the total number of children, we have to multiply 3 by 9.

3 * 9 = 27

Therefore, there are 27 children total. I know this was probably really confusing, but I hope it helped in some way! Have a lovely day!! :)

3 0

2 years ago

> 2 2x < x +5<br>2 s 2x < x + 5 inequality

vodka [1.7K]

answerr:

2 ≤ 2x or 2x ≥ x + 5

x ≤ 1 or x ≥ 2.5

6 0

3 years ago

Describe the two-dimensional cross section that would be created by slicing the cylinder-shaped cheese block as shown.

masha68 [24]

Answer: A RECTANGLE ( It has four sides, its opposite sides are congruent and all its angles measure 90 degrees)

Step-by-step explanation:

For this exercise it is important to remember the definition of a "Cross section".

In Geometry a "Cross section" is defined as that shape obtained when a three-dimensional figure is sliced by a plane.

In this case, according to the information given in the exercise, the cheese block has the shape of a cylinder. This is the three-dimensional figure.

Observe in the picture attached in the exercise that the cylinder-shaped cheese block is cut through perpendicular to its base.

By definition, when this perpendicular cut happens, the shape obtained is a Quadrilateral which has four equal angles that measure 90 degrees and whosepposite sides are parallel have equal length.

Therefore, you can conclude that the two-dimensional cross section that would be created by slicing the cylinder-shaped cheese block perpendicular to its base,is: A RECTANGLE.

3 0

3 years ago

In the figure, find the perimeter of AABC.

erma4kov [3.2K]

Answer:C. 36

Step-by-step explanation: height is 12 base is 9

12^2+9^2= 144+81=225 sq rt of 225 =15

So 12+9+15=36

4 0

3 years ago