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3 years ago

11

Suppose a submarine has a crew of 135 sailors, and 6 of them are women. If 2 sailors are selected at random, find the probabilit

y that they are both women. Express your answer in simplified rational form.

1 answer:

Tasya [4]3 years ago

4 0

The answer is the picture

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Two cards are drawn with replacement, one after the other, and the outcomes recorded. What is the probability that at least one

babymother [125]

Answer:

The probability is 0.231

Step-by-step explanation:

In this question, we are tasked with calculating the probability that out of two cards drawn with replacement from a pack of cards , at least one of the two is a face card.

In a standard pack of cards, there are 52 cards.

Now let’s calculate the number of face cards we have.

There are 12 face cards in a pack of cards. There are 4 of each of Jack, Queen or King

The probability of drawing a face card is 12/52 = 3/13

Now, we want to calculate the probability of at least one of the cards drawn are face cards.

Mathematically, what we are needing to calculate is

Probability of drawing a single face card or probability of the two being a face card

Now let’s calculate.

The probability of the first card drawn being a face card is 3/13. The probability of the second card not being a face card will be 1-3/13 = 10/13

The joint probability under this first set of condition will be 3/13 * 10/13 = 30/169

Now, for the second condition, here we are considering that both cards drawn are face cards. What we have is 3/13 * 3/13 = 9/169

Now in probabilities, whenever we are having the statement or, we add the probabilities together

Thus, the probability here would be 30/169 + 9/169 = 39/169 = 3/13

In decimal this will be 0.231

8 0

2 years ago

Solve the following system of inequalities graphically on the set of axes below. State

Serhud [2]

Answer:

$(x,y) = (-1,1)$

Step-by-step explanation:

Given

$y>-2x - 1$

$y>x + 2$

Required

Solve graphically

See attachment for graph;

The black shade represents $y>-2x - 1$

While the green, represents $y>x + 2$

Next, determine the intersection points between the two lines

From the attached graph, we have:

$(x,y) = (-1,1)$

<em>Hence, the solution is:</em> $(-1,1)$

8 0

2 years ago

Two planes are driving toward each other with the speeds 250 mph and 420 mph respectively. If the distance between them are 1250

lakkis [162]

Answer:

They will meet in 1.866 hours.

Step-by-step explanation:

This is actually quite a simple question once we think about it in a different way.

Instead of thinking of two different planes that are going at two different speeds, think of it like this: the distance between the two planes is decreasing by 670mph (250mph + 420 mph).

Note: miles per hour is equivalent to miles/hour (<em>miles divided by hours</em> or <em>miles over hours</em>)

670m/h becomes our new rate. The rate the distance between the planes is decreasing.

Now, if the distance between them is 1250 miles, how long until they meet?

If we have miles and multiply it by hours/miles, the miles cancel out and you are left with hours.

We have miles (1250) and miles/hours (670). If we multiply these we get units of miles^2 / hours which is not what we want.

we need to multiply 1250 miles by something with the units of hours/miles.

It turns out that the reciprocal of miles/hours is hours/miles

That means we need to multiply 1250 miles by the reciprocal of 670 miles/hours

Note: the reciprocal of a fraction is the fraction flipped around. 1/2 becomes 2/1, reciprocal of 3/5 is 5/3, etc...

the reciprocal of 670 miles/hours = 1/670 miles/hours

Multiplying 1250 miles by 1/670 miles/hours is the SAME as

dividing the number of miles(1250m) by the rate(670m/h)

1250m / 670m/h = 1250m x 1/670 x h/m = 1.866 h = 1.866 hours (the miles cancel out)

<h2>Note: I explained it so you know why dividing 1250miles by 670mph gives you hours. Once you understand why, all you need to do in the future is divide the distance by the rate and you get time. </h2><h2>Distance / rate = time</h2><h2 />

8 0

3 years ago

HELP DUE IN 5 MInUTes ASAp

musickatia [10]

Answer:

The expression that calculates the speed in meters per second of an object that travels a distance of 100 m every 20 s is $\mathbf{Speed=\frac{100}{20} }$

Step-by-step explanation:

We are given:

Distance = 100 m

Time = 20 s

We need to find:

Speed

The formula used is: $Speed=\frac{Distance}{Time}$

Putting values and finding the expression

$Speed=\frac{Distance}{Time}\\Speed=\frac{100}{20}$

So, the expression that calculates the speed in meters per second of an object that travels a distance of 100 m every 20 s is $\mathbf{Speed=\frac{100}{20} }$

<em>Note: Kindly recheck your options, As option B is not written correctly.</em>

5 0

2 years ago

One speed skater starts across a frozen lake at an average speed of 8 m/s. Ten seconds later, a second speed skater starts from

Galina-37 [17]

Answer: Hello mate!

Let's define the variable t as the time, and define t = 0 as the moment when the first skater starts to move:

We know that the speed of the first skater is 8 m/s, and we need to find the position as a function of time, then we need to integrate the velocity over time

if v1(t) = 8m/s

then p1(t) = (8m/s)*t

now we also know that the second skater has a velocity of 9m/s and enters in the frozen lake at t= 10s.

then the velocity of the second skater is: v2(t) = 9m/s, and the position is:

p2(t) = (9m/s)*(t - 10s)

now we want to know how many seconds after the second skater starts are needed for the second skater to overtake the first one.

this is equivalent to see when his positions will be equal.

so p1(t) = p2(t):

(8m/s)*t = (9m/s)(t - 10s) = (9m/s)*t - 90m

(8m/s)*t - (9m/s)*t = -90m

(-1m/s)*t = 90m

t = 90m/(1m/s) = 90s

Then in t = 90 seconds, the second skater will overtake the first one, and knowing that the second skater started at t = 10 seconds; there are 80 seconds after the second skater started needed to overtake the first skater.

7 0

2 years ago