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3 years ago

What is the area of the square?

Mathematics

1 answer:

Vsevolod [243]3 years ago

4 0

C. 84
12 x 8 is the area of the whole thing but you subtract 12 because of the missing 6x2 part of the square

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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

Please answer this correctly.

Ganezh [65]

Answer:

The given function is a nonlinear function because the degree of the function is 2 and we get same value of y for more than one values of x.

Step-by-step explanation:

The given function is

$y=2x^2-5$

To find the points which lie on the function, put difference values of x in the given function and find the values of y.

Put x= -2

$y=2(-2)^2-5=2(4)-5=8-5=3$

Put x= -1

$y=2(-1)^2-5=2(1)-5=2-5=-3$

Put x= 0

$y=2(0)^2-5=2(0)-5=-5=-5$

Put x=1

$y=2(1)^2-5=2(1)-5=2-5=-3$

Put x= 2

$y=2(2)^2-5=2(4)-5=8-5=3$

The table of values is shown below.

Plot these points on a coordinate plane and connect them by a free hand curve.

The given function is a nonlinear function because the degree of the function is 2 and we get same value of y for more than one values of x.

The graph of function is shown below.

5 0

3 years ago

Suppose Austin, Texas, is hit by a tornado that destroys 25 percent of the housing in the area. Would you expect the total expen

notsponge [240]

Answer:

greater than what it was before

Step-by-step explanation:

Remember, a tornado usually causes significant structural damages to houses within its area of impact., and this requires running expenses to repair the damage.

Hence, since the term expenditure, also implies expenses; we can expect the total expenditure on housing after the tornado to be greater than what it was before the tornado since families would be paying for repairs.

4 0

2 years ago

Use the algebraic procedure explained in section 8.9 in your book to find the derivative of f(x)=1/x. Use h for the small number

Triss [41]

Answer:

By definition, the derivative of f(x) is

$lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}$

Let's use the definition for $f(x)=\frac{1}{x}$

$lim_{h\rightarrow 0} \frac{\frac{1}{x+h}-\frac{1}{x}}{h}=\\lim_{h\rightarrow 0} \frac{\frac{x-(x+h)}{x(x+h)}}{h}=\\lim_{h\rightarrow 0} \frac{\frac{(-1)h}{x^2+xh}}{h}=\\lim_{h\rightarrow 0} \frac{(-1)h}{h(x^2+xh)}=\\lim_{h\rightarrow 0} \frac{-1}{x^2+xh)}=\frac{-1}{x^2+x*0}=\frac{-1}{x^2}$

Then, $f'(x)=\frac{-1}{x^2}$

7 0

3 years ago

ten people put there name into two different drawings. The first drawing is a trip to hawaii and the second is a new car. what i

kondor19780726 [428]

Answer:

unlikely

Step-by-step explanation:

thats alot of people

3 0

3 years ago