Anurak has nickels, dimes, and pennies in his pocket. The coins in Anurak's pocket have a total value of 75 cents. He has three more nickels than dimes and five times as many pennies as dimes. How many coins of each type does Anurak have?

Answer:

a) 0.135 = 13.5% probability that during a given 1 min period, the first operator receives no requests.

b) 0.03185 = 3.185% probability that during a given 1 min period, exactly three of the six operators receive no requests

Step-by-step explanation:

To solve this question, we need to understand the Poisson distribution and the binomial distribution.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

In which

x is the number of sucesses

e = 2.71828 is the Euler number

is the mean in the given time interval.

Binomial distribution:

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

Poisson process with rate 2 per minute

This means that

a. What is the probability that during a given 1 min period, the first operator receives no requests?

Single operator, so we use the Poisson distribution.

This is P(X = 0).

0.135 = 13.5% probability that during a given 1 min period, the first operator receives no requests.

b. What is the probability that during a given 1 min period, exactly three of the six operators receive no requests?

6 operators, so we use the binomial distribution with

Each operator has a 13.5% probability of receiving no requests during a minute, so

This is P(X = 3).

0.03185 = 3.185% probability that during a given 1 min period, exactly three of the six operators receive no requests

Answer:

m=1

Step-by-step explanation:

The plots (-4,3) and (2,1) have a slope of -1. Perpendicular lines would mirror that, making it a positive 1

Answer is provided in the image attached.

3x+3x-5= 1

6x-5=1

Whenever moving a number, the sign always changes.

6x-5+5= 1+5

6x= 1+5

6x= 6

divide both sides by 6

6x/6= 6/6

x= 1

Check solution by using the substitution method

3(1)+3(1)-5=1

3+3-5=1

6-5= 1

1=1

Answer: x=1

Answer:

• the hypotenuse side, c = 23.1 cm

• angle A = 41.26 ⁰

• angle B = 48.74 ⁰

Step-by-step explanation:

Given;

first leg of the right triangle, a = 15.21 cm

second leg of the right triangle, b = 17.34 cm

Angle C = 90 ⁰

The missing parameters;

• the hypotenuse side = c

• angle A

• angle B

Use Pythagoras theorem to calculate the missing side "c", which is the hypotenuse

c² = a² + b²

c² = (15.21)²  +  (17.34)²

c² = 532.02

c = √532.02

c = 23.1 cm

The missing angle A is calculated as;

The missing angle is calculated as;

B = 90⁰ - A

B = 90⁰ - 41.26⁰

B = 48.74⁰

Answer:

3.15

Step-by-step explanation:

15.75 divided by 5 gets you 3.15