In a room there are a mixture of people and dogs. there are 72 heads, and 200 legs. how many dogs are in the room?

rusak2 [61]

Minus 3y both sides
2y-6=-20
add 6 to both sids
2y=-14
divide 2
y=-7

7 0

2 years ago

Ralph is paid twice per month. His work offers a flexible-spending account to be used for medical expenses. This plan allows Ral

slava [35]

In this question, we're assuming Ralph had 0 in his saving funds to start with.

The glasses cost 1200 dollars.

There are 12 months in a year.

Each month, Ralph is given his check two times, that means that Ralph receives his check 2(12), or 24, times per year.

Divide 1200 (the cost of the glasses) by 24 (the amount of times Ralph is given his check)

1200 / 24
Divide both numerator and denominator by 12
100 / 2
Simplify
50

Ralph should have put 50 dollars per pay check to pay for the glasses.

A is your answer.

Have an awesome day! :)

6 0

2 years ago

n 2019, approximately 97.4% of all the runners who started the Boston Marathon (in Boston, Massachusetts, USA) were able to comp

Zarrin [17]

Answer:

0.1199 = 11.99% probability that at least 5 of them did not finish the marathon

Step-by-step explanation:

For each runner, there are only two possible outcomes. Either they finished the marathon, or they did not. The probability of a runner completing the marathon is independent of any other runner. This means that the binomial probability distribution is used 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.

97.4% finished:

This means that 100 - 97.4 = 2.6% = 0.026 did not finish, which means that $p = 0.026$

100 runners are chosen at random

This means that $n = 100$

Find the probability that at least 5 of them did not finish the marathon

This is:

$P(X \geq 5) = 1 - P(X < 5)$

In which

$P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)$

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

$P(X = 0) = C_{100,0}.(0.026)^{0}.(0.974)^{100} = 0.0718$

$P(X = 1) = C_{100,1}.(0.026)^{1}.(0.974)^{99} = 0.1916$

$P(X = 2) = C_{100,2}.(0.026)^{2}.(0.974)^{98} = 0.2531$

$P(X = 3) = C_{100,3}.(0.026)^{3}.(0.974)^{97} = 0.2207$

$P(X = 4) = C_{100,4}.(0.026)^{4}.(0.974)^{96} = 0.1429$

$P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0718 + 0.1916 + 0.2531 + 0.2207 + 0.1429 = 0.8801$

$P(X \geq 5) = 1 - P(X < 5) = 1 - 0.8801 = 0.1199$

0.1199 = 11.99% probability that at least 5 of them did not finish the marathon

4 0

2 years ago

A television network is about to telecast a new television show. Before a show is launched, the network airs a pilot episode and

Basile [38]

Answer:

(E) 0.83

Step-by-step explanation:

We will solve it using conditional probability.

Let A be the event that a TV show is successful.

P(A) = 0.5

A' be event that the show is unsuccessful

P(A') =0.5

Let B be the event that the response was favorable

P(B) = 0.6

Let B' be the event that the response was unfavorable/

P(B') = 0.4

P(A∩B) = 0.5 and P(A∩B') = 0.3

We need to find new show will be successful if it receives a favorable response.

P(A/B) = $\frac{P(A∩B)}{P(B)}$

= 0.5/0.6

= 0.833

7 0

2 years ago

Read 2 more answers

kadeem and quinn both drive 25 miles. Kadeem drives at a constant speed of 50 miles an hour. Quinn drives at a constant speed of

Phantasy [73]

Answer:

Kadeem will take 0.166 h more to complete the course.

Step-by-step explanation:

The speed is the rate at which the distance changes, when the speed goes up the distance changes more quickly, therefore if the distance is the same and the speed is higher the one who will take longer is the one that has less speed. In this case the one who will take longer to drive the 25 miles is Kadeem, since he's driving at 50 mph. In order to calculate how much longer we need to calculate the time at which each of them complete the course, this is shown below:

time = distance/speed

For Kadeem:

time = 25/50 = 0.5 h

For Quinn:

time = 25/75 = 0.334 h

The difference between the is 0.5 - 0.334 = 0.166 h.

8 0

2 years ago