Find the measure of the arc. C D A 1469 E B MAB = [ ? ]°

The annual rainfall (in inches) in a certain region is normally distributed with = 40 and = 4. What is the probability that star

sdas [7]

Answer:

0.93970

Step-by-step explanation:

Solution:-

- Denote a random variable "X" The annual rainfall (in inches) in a certain region . The random variable follows a normal distribution with parameters mean ( μ ) and standard deviation ( σ ) as follows:

X ~ Norm ( μ , σ^2 )

X ~ Norm ( 40 , 4^2 ).

- The probability that it rains more than 50 inches in that certain region is defined by:

P ( X > 50 )

- We will standardize our test value and compute the Z-score:

P ( Z > ( x - μ ) / σ )

Where, x : The test value

P ( Z > ( 50 - 40 ) / 4 )

P ( Z > 2.5 )

- Then use the Z-standardize tables for the following probability:

P ( Z < 2.5 ) = 0.0062

Therefore, P ( X > 50 ) = 0.0062

- The probability that it rains in a certain region above 50 inches annually. is defined by:

q = 0.0062 ,

- The probability that it rains in a certain region rains below 50 inches annually. is defined by:

1 - q = 0.9938

n = 10 years ..... Sample of n years taken

- The random variable "Y" follows binomial distribution for the number of years t it takes to rain over 50 inches.

Y ~ Bin ( 0.9938 , 0.0062 )

- The probability that it takes t = 10 years for it to rain:

= 10C10* ( 0.9938 )^10 * ( 0.0062 )^0

= ( 0.9938 )^10

= 0.93970

3 0

3 years ago

dion flips a coin 20 times and records if it comes up heads. if getting heads is a success, what is the probability of a success

kolbaska11 [484]

Answer:

$\frac{1}{2}$

Step-by-step explanation:

The probability of success (getting heads) on one roll DOESNT affect other rolls, so we need to find probability of getting a head in a roll.

Probability is defined as the number of favorable outcomes divided by the total number of outcomes.

Here, favorable outcome is getting a head. So, on one roll, getting a head is 1. Also, the total number of outcomes is either a head or a tail. So total number of outcomes is 2.

Thus,

P(Heads) = 1/2

3 0

3 years ago

Rachelle has $6.30 in nickels and quarters in her coin purse. The number of nickels is twice the number of quarters. How many co

timurjin [86]

Each group of 2 nickels and 1 quarter has a value of $0.35. Rachelle has $6.30/$0.35 = 18 such groups.

Rachelle has 18 quarters and 36 nickels.

5 0

3 years ago

Veronica has been saving dimes and quarters she has 110 coins in all and the total value is 18.50 how many dimes and quarters do

Lady_Fox [76]

This problem can be solved by the chicken rabbits method or you can just do simple algebra.

I.) Chicken and rabbits method

First assume all 110 coins are dimes and none are quarters.

We will have a total value of 11 dollars

Now for each dime we switch out for a quarter, we adds 15 cents to the total value.

18.50-11=7.50 dollars

There are 750/15=50 group of 15 cents in the 7 dollars and 50 cents.

This also meant that we need to switch out 50 dimes for 50 quarters.

So we have 50 quarters.

That first method is very good and very quick once you get the hang of it, now I'm going to show you the algebraic way to solve this.

Let's say there are x dimes and y quarters.

Set up equation

x+y=110

10x+25y=1850

Now solve multiply first equation by 10

10x+10y=1100

subtract

15y=750

y=50

Now we set the numbers of quarters to y so the answer is 50 quarters.

I personally recommend using algebra whenever you can because the practice is very important and you will eventually get really fast at setting up and solving equations. The first method is faster in this case but the second is more generalize, hope it helps.

6 0

3 years ago

5. (9) Letf- ((-2, 3), (-1, 1), (0, 0), (1,-1), (2,-3)) and let g- ((-3, 1), (-1, -2), (0, 2), (2, 2), (3, 1)j. Find: a. (g f (0

pashok25 [27]

Answer: g(f(0)) = 2 and (f ° g)(2) = -3.

Step-by-step explanation: We are given the following two functions in the form of ordered pairs :

f = {(-2, 3), (-1, 1), (0, 0), (1,-1), (2,-3)}

g = {(-3, 1), (-1, -2), (0, 2), (2, 2), (3, 1)} .

We are to find g(f(0)) and (f ° g)(2).

We know that, for any two functions p(x) and q(x), the composition of functions is defined as

$(p\circ q)(x)=p(q(x)).$

From the given information, we note that

f(0) = 0, g(0) = 2, g(2) = 2 and f(2) = -3.

So, we get

$g(f(0))=g(0)=2,\\\\(f\circ g)(2)=f(g(2))=f(2)=-3.$

Thus, g(f(0)) = 2 and (f ° g)(2) = -3.

8 0

3 years ago