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2 years ago

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During the summer months one ice cream truck visit Janice neighborhood every four days and another ice cream truck visit her nei

ghborhood every seven days if both trucks visited today when is the next time both trucks for a visit on the same day

1 answer:

alisha [4.7K]2 years ago

5 0

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A poll found that 5% of teenagers (ages 13 to 17) suffer from arachnophobia and are extremely afraid of spiders. At a summer cam

brilliants [131]

Answer:

a) Calculate the probability that at least one of them suffers from arachnophobia.

x = number of students suffering from arachnophobia

= P(x ≥ 1)

= 1 - P(x = 0)

= 1 - [0.05⁰ x (1 - 0.05)¹¹⁻⁰ ]

= 1 - (0.95)¹¹

= 0.4311999 = 0.4312

b) Calculate the probability that exactly 2 of them suffer from arachnophobia? 0.08666

= P(x = 2)

= (¹¹₂) x (0.05)² x (0.95)⁹

where ¹¹₂ = 11! / (2!9!) = (11 x 10) / (2 x 1) = 55

= 55 x 0.0025 x 0.630249409 = 0.086659293 = 0.0867

c) Calculate the probability that at most 1 of them suffers from arachnophobia?

P(x ≤ 1)

= P(x = 0) + P(x = 1)

= [(¹¹₀) x 0.05⁰ x 0.95¹¹] + [(¹¹₁) x 0.05¹ x 0.95¹⁰]

= (1 x 1 x 0.5688) + (11 x 0.05 x 0.598736939) = 0.5688 + 0.3293 = 0.8981

4 0

2 years ago

a woman is looking for a bigger square office. she finds an office twice the area of her square office. if the perimeter is 88ft

UNO [17]

Answer:

Option C is the correct answer.

Step-by-step explanation:

Perimeter of current office = 88 ft

We have perimeter = 4a , where a is the side of square.

Equating

4a = 88

a = 22 sqft

Area of current office = a x a = 22 x 22 = 484 square feet.

Area of new office is twice the area of current office.

Area of new office = 2 x 484 = 968 square feet.

Option C is the correct answer.

6 0

2 years ago

Read 2 more answers

Jayden starts with $1575 in a college savings account. His account earns interest at a rate of 2.7% compounded annually. How muc

Korolek [52]

Step-by-step explanation:

2.7/100*1575=42.525

then for 9years

9*42.525=$382.725

8 0

2 years ago

A hand of 5-card draw poker is a simple random sample from the standard deck of 52 cards. How many 5 draw poker hands are there?

kupik [55]

Answer:

There are 2,598,960 5 draw poker hands are there.

There are 311,875,200 5-stud poker hands.

Step-by-step explanation:

When the order is not important, we use the combinations formula:

For example, eating an apple and an orange is the same as eating an orange and an apple.

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

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

When the order is important, we use the permutations formula:

For example, a 3 digit credit card password, 123 is different than 213.

The number of possible permutations of x elements from a set of n elements is given by the following formula:

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

A hand of 5-card draw poker is a simple random sample from the standard deck of 52 cards. How many 5 draw poker hands are there?

Here, the ordering is not important, so we use the combinations formula.

$C_{52,5} = \frac{52!}{5!47!} = 2598960$

There are 2,598,960 5 draw poker hands are there.

In 5-card stud poker, the cards are dealt sequentially and the order of appearance is important. How many 5-stud poker hands are there?

The ordering is important, so we use the combinations formula.

$P_{(52,5} = \frac{52!}{47!)} = 311875200$

There are 311,875,200 5-stud poker hands.

7 0

2 years ago

Suppose the time interval between two consecutive defective light bulbs from a production line has a uniform distribution over a

ioda

Answer:

a) The mean of the time interval is 45 minutes.

b) 27.78% probability that the time interval between two consecutive defective light bulbs will be between 10 and 35 minutes

c) The standard deviation of the time interval is 25.98 minutes.

d) 11.11% probability that the time interval between two consecutive defective light bulbs will be less than 10 minutes

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X lower than x is given by the following formula.

$P(X < x) = \frac{x - a}{b-a}$

The probability of finding a value X between c and d is:

$P(c \leq X \leq d) = \frac{d-c}{b-a}$

The mean of the uniform distribution is:

$M = \frac{a+b}{2}$

The standard deviation of the uniform distribution is:

$S = \sqrt{\frac{(b-a)^{2}}{12}}$

Uniform distribution over an interval from 0 to 90 minutes.

This means that $a = 0, b = 90$

a) What is the mean of the time interval?

$M = \frac{a+b}{2} = \frac{0 + 90}{2} = 45$

The mean of the time interval is 45 minutes.

b) What is the probability that the time interval between two consecutive defective light bulbs will be between 10 and 35 minutes?

$P(10 \leq X \leq 35) = \frac{35-10}{90-0} = 0.2778$

27.78% probability that the time interval between two consecutive defective light bulbs will be between 10 and 35 minutes.

c) What is the standard deviation of the time interval?

$S = \sqrt{\frac{(90-0)^{2}}{12}} = 25.98$

The standard deviation of the time interval is 25.98 minutes.

d) What is the probability that the time interval between two consecutive defective light bulbs will be less than 10 minutes?

$P(X < 10) = \frac{10 - 0}{90 - 0} = 0.1111$

11.11% probability that the time interval between two consecutive defective light bulbs will be less than 10 minutes

8 0

2 years ago