A restaurant charges $3.00 for a refillable cup. Tha refills are complementary.

According to national data, 5.1% of burglaries are cleared with arrests. A new detective is assigned to six different burglaries

blagie [28]

Answer:

26.95% probability that at least one of them is cleared with an arrest

Step-by-step explanation:

For each burglary, there are only two possible outcomes. Either it is cleared, or it is not. The probability of a burglary being cleared is independent of other burglaries. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

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

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

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

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

5.1% of burglaries are cleared with arrests.

This means that $p = 0.051$

A new detective is assigned to six different burglaries.

This means that $n = 6$

What is the probability that at least one of them is cleared with an arrest?

Either none are cleared, or at least one is. The sum of the probabilities of these events is 100% = 1. So

$P(X = 0) + P(X \geq 1) = 1$

We want $P(X \geq 1)$

Then

$P(X \geq 1) = 1 - P(X = 0)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{6,0}.(0.051)^{0}.(0.949)^{6} = 0.7305$

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.7305 = 0.2695$

26.95% probability that at least one of them is cleared with an arrest

8 0

3 years ago

The function s(V) = describes the side length, in units, of a cube with a volume of V cubic units. Jason wants to build a cube w

Leni [432]

Answer:

s≤4 cm.

Step-by-step explanation:

Let s be side of cube.

As we know that the volume of cube=side×side×side

Here, it is given that the volume of cube = 64 cubic centimeters.

or we can write

side×side×side=64 cubic centimeters

Taking cube root both sides

side= 4 cm

In order to build a cube with a minimum of 64 cubic centimeters,

we can take the value of s≤4 cm.

Hence, the reasonable range for s, the side length is s≤4 cm.

5 0

3 years ago

Mr. Zhou surveyed his 25 students to find out how much time they spent doing homework each week. The results of his survey are s

Phantasy [73]

Answer:

I think it's 12

Step-by-step explanation: i'm sorry if you got it wrong have the same question to.... sorry

3 0

3 years ago

Read 2 more answers

A student paid at least 51$ for a computer diskette. The total charge includes the price and 2% tax. Find minimum price of the d

BartSMP [9]

52.02 at is the minimum

8 0

3 years ago

1. Five more than a number is eight.

kolezko [41]

Answer

<u>3</u>, the number is 3

Step-by-step explanation:

work backwards, do 8-5 to get three. you can check to see if you're right by adding 5 to 3, which gives you 8.

4 0

3 years ago