All categories

2 years ago

A 5-card hand is dealt from a deck of 52 cards. what is the probability that 4 are hearts

1 answer:

5 0

Hii mate__ ^_^
.
.
.
.
.
.______
here's your answer____⤵

You're essentially dealing a three-card hand from a deck of 50 (missing the spade and heart kings), wanting to know the probability of getting the remaining two kings among those three. The number of ways of dealing three cards is 50C3=1960050C3=19600; the number of hands with two kings is 4848 (one for each of the remaining cards in the hand); so the probability is 48/19600=3/122548/19600=3/1225.

You might be interested in

What are some Examples of similar triangles or polygons that you may see in the real world?

Fofino [41]

Answer:

You can see objects, nd buildings that have those shapes, and roof tops.

Step-by-step explanation:

8 0

2 years ago

What is the area of triangle HGF? Round your answer to the nearest tenth of a square centimeter. Recall that you need to round u

denpristay [2]

Answer:

9.8

Step-by-step explanation:

The formula for the area of a triangle is a=bh/2, where a is area, b, is the base, and h is the height. If we substitute the values in the question in the equation, we get:

a=(6.5*3)/2

a=19.5/2

a=9.75

a≈9.8

7 0

2 years ago

Prove the divisibility of the following numbers:

Brut [27]

Answer:

Step-by-step explanation:

To prove divisibility, we need to factor the divident such that one of its factors matches the divisor.

(I use the notation x|y to denote that x divides y)

(A)

$75^{30}|45^{45}\cdot15^{15}\\45^{45}\cdot15^{15}=3^{45}\cdot 15^{45}\cdot 15^{15}=\\=3^{45}\cdot 15^{60}=3^{45}\cdot 15^{30}\cdot 15^{30}=3^{45}\cdot (3\cdot5)^{30}\cdot 15^{30}=\\=3^{45}\cdot 3^{30}\cdot(5\cdot 15)^{30}=3^{45}\cdot 3^{30}\cdot(75)^{30}\\\implies\\75^{30}|3^{45}\cdot 3^{30}\cdot75^{30}$

(B)

$72^{63}|24^{54}\cdot 54^{24}\cdot2^{10}\\24^{54}\cdot 54^{24}\cdot2^{10}=(2^{162}\cdot 3^{54})\cdot(2^{24}\cdot 3^{72}) \cdot 2^{10}\\=2^{196}\cdot 3^{126}$

In this case, it is easier to also factor the divisor to primes:

$72^{63}=2^{189}\cdot 3^{126}$

Both of these factor must be matched in the dividend in order to prove divisibility, and that indeed turns out to be true:

$2^{189}\cdot 3^{126}|2^{196}\cdot 3^{126}\implies\\2^{189}|2^{196}\,\,\mbox{and}\,\,3^{126}|3^{126}$

6 0

2 years ago

The ratio of girls to boys at a movie is 5 : 4. If there are 12 boys, how many girls are at the movie?

dalvyx [7]

Answer:

12/5 is 2.4 so

9 girls I think.

Step-by-step explanation:

8 0

2 years ago

Two chemicals A and B are combined to form a chemical C. The rate, or velocity, of the reaction is proportional to the product o

Keith_Richards [23]

Answer:

32.1 g

Step-by-step explanation:

In each 3 grams of C, there are 2 grams of A and 1 gram of B. So, for some amount C, the amount remaining of A is 40 -(2C/3), and the amount remaining of B is (50 -C/3). Since the reaction rate is proportional to the product of these amounts, we have ...

C' = k(40 -2C/3)(50 -C/3) = (2k/9)(60 -C)(150 -C) . . . for some constant k

This is separable differential equation with a solution of the form ...

ln((150 -C)/(60 -C)) = at + b

We know that C(0) = 0, so b=ln(150/60) = ln(2.5). And we know that C(10) = 20, so ln(130/40) = 10a +ln(2.5) ⇒ a = ln(1.3)/10

Then our equation for C is ...

ln((150 -C)/(60 -C)) = t·ln(1.3)/10 +ln(2.5)

For t=20, this is ...

ln((150 -C)/(60 -C)) = 2ln(1.3) +ln(2.5) = ln(2.5·1.3²) = ln(4.225)

Taking antilogs, we have ...

(150 -C)/(60 -C) = 4.225

1 +90/(60 -C) = 4.225

C = 60 -90/3.225 ≈ 32.093 . . . . . grams of product in 20 minutes

In 20 minutes, about 32.1 grams of C are formed.

7 0

2 years ago