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Marina CMI [18]
2 years ago
10

Find the probability of drawing two diamonds in a row from a standard deck of 52 cards. After the first card is drawn it is set

aside and not returned to the deck.
Mathematics
1 answer:
Rina8888 [55]2 years ago
5 0

Answer: 1/17

Step-by-step explanation:

First and foremost, we should note that there are 13 diamonds in a standard deck of 52 cards.

If the first card is drawn, the probability of picking a diamond is 13/52. Since it's not replaced, when another one is picked, the probability that it will be diamond will be 12/51.

We then multiply both together. This will be:

= 13/52 × 12/51

= 1/4 × 4/17

= 1/17

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A truck is 300 miles east of a car and is traveling west at the constant speed of 30 miles/hr meanwhile the car is going north a
Lerok [7]

Answer:

d(t)=\sqrt{(300+30t)^2+(60t)^2}

Step-by-step explanation:

Let t represents the time in hours,

We know that,

Speed =\frac{Distance}{Time}

\implies Distance = Speed\times time

Since, the speed of truck = 30 miles per hour,

So, the distance covered by the truck in t hours = 30t miles,

Similarly,

Speed of car = 60 miles per hour,

So, the distance covered by car in t hours = 60t miles,

∵ Truck is 300 miles east of the car initially,

Thus, the distance of the truck from the starting point = 30t + 300,

While the distance of the car from the starting point = 60 t,

Now, these two vehicles are going in the directions which are at right angled ( car is going north and truck is going west )

Using the Pythagoras theorem,

Distance between them after t hours,

d(t)=\sqrt{(300+30t)^2+(60t)^2}

Which is the required function.

3 0
3 years ago
Which problem situation can be represented by the equation below? 150 – 3x = 60
Leni [432]
X is 30 because we can minus 60on both sides and add 3x on both sides to find the answer
7 0
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Step-by-step explanation:

5 0
3 years ago
A study of college business majors included 150 sophomores and 200 juniors. The study showed that 80 sophomores and 150 juniors
vlabodo [156]

Answer:

0.3478

Step-by-step explanation:

Given:-

- The number of sophomore, S = 150

- The sophomore and had summer internship, x = 80

- The number of juniors, J = 200

- The junior and had summer internship, y = 150

Find:-

What is the probability that the person is a sophomore given that the person had a summer internship?

Solution:-

- The total sum of sophomore and junior students is N:

                         N = S + J

                         N = 150 + 200

                         N = 350 students.

- We will denote event A as random selection of sophomore from total.

- We will denote event B as random selection of student who had summer internship.

- We are to determine the conditional probability that a person selected is sophomore given that the person had a summer internship. That is the probability of event A given that event B has already occured.

- The conditional probability can be written as:

                        P ( A / B ) = P ( A & B ) / P ( B )

Where,

        P ( A & B ) : The probability the person is a sophomore and had a summer internship.

        P ( B ): The probability that the person selected had a summer internship.

                      P ( A & B ) = x / N

                                        = 80 / 350

                                        = 0.22857143

                     P ( B ) = ( x + y ) / N

                               = ( 80 + 150 ) / 350 = 230/350

                               = 0.65714286

Therefore the required probability is:

           

                     P ( A / B ) = 0.22857143 / 0.65714286

                                      = 0.3478  ... Answer

                                       

                         

6 0
3 years ago
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