The sum of 14 and a number is equali to 17

A single card is drawn from a deck of 52 cards, find the following

aleksandr82 [10.1K]

Answer:

a. 1/13

b. 1/78

c. 1/4

d. 1/12

e. 1/6

f. 1/4

Step-by-step explanation:

First, lets write some basic data

There are total 52 cards.
26 cards are red and 26 cards are black
Out of 26 red cards; 13 cards are of diamond and 13 cards are of heart
Out of 26 black cards; 13 cards are of spade and 13 cards are of clubs
In spade, clubs, heart and diamond there is one card of ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, King, Queen, Jack

a. result is a queen

Each set has one queen; 1 of spade, 1 of clubs, 1 of heart, 1 of heart

There are total 4 queens

Total number of cards is 52

Probability = Number of favourable outcomes/total number of outcomes

Probability = 4/52

Probability = 1/13

b. result is a queen result is a face card

From my understanding, this question is result is a queen given that result is a face card.

Queen: 4 cards

Face card means King, Queen and Jack

Each set has one King, one Queen and one Jack

There are total 4 sets

Therefore, there are 4 Kings, 4 Queens and 4 Jacks

Face cards: 12-4 (because 4 queens have already been taken out) = 8

Total number of cards: 52-4 (because 4 queens have already been taken out) = 48

Probability (A|B) = P(A) * P(A|B)

P(A) = result is a queen = 4/52 = 1/13

P(A|B) = result is a face card = 8/48 = 1/6

Probability (A|B) = P(A) * P(A|B)

Probability (A|B) = 1/13 * 1/6

Probability (A|B) = 1/78 or 0.01282

c. result is a heart

Out of the 52 cards, there are 26 red cards and out of the 26 red cards, there are 13 cards of heart

Heart = 13 cards

Total number of cards = 52 cards

Probability = Number of favourable outcomes/total number of outcomes

Probability = 13/52

Probability = 1/4

d. result is a heart | result is a red card

Result is a heart = P(A) = 13/52 = 1/4

Result is a red card=26/52 Total number of red cards is 26 but 13 cards (heart) are already taken out so 13 will be subtracted from the numerator and denominator

= 13/39 = 1/3

Result is a heart given that result is a red card P(A|B) = 1/3

Probability (A|B) = P(A) * P(A|B)

Probability (A|B) = 1/4 * 1/3

Probability (A|B) = 1/12

e. result is a heart result is a black card

Result is a heart = P(A) = 13/52 = 1/4

Result is a black card=26/52 Total number of cards is 52 but 13 cards (heart) are already taken out so 13 will be subtracted from the denominator

= 26/39 = 2/3

Result is a heart given that result is a black card P(A|B) = 2/3

Probability (A|B) = P(A) * P(A|B)

Probability (A|B) = 1/4 * 2/3 = 1/6

f. result is a heart result is not a diamond

Result is a heart = P(A) = 13/52 = 1/4

Result is not a diamond = there are 13 diamonds in a deck so cards that are not diamond are 52-13 = 39

Total cards = 52 - 13 (because hearts are already taken out) = 39

= 39/39 = 1

Probability (A|B) = P(A) * P(A|B)

Probability (A|B) = 1/4 * 1 = 1/4

!!

4 0

3 years ago

Why is the lcm of two numbers never less than the larger number?

Lady bird [3.3K]

This involves a bit of logic in thinking about what LCM actually means.

LCM is the least common multiple. A common multiple is a multiple shared by two or more numbers. And by multiple, we mean some number multiplied by successive integers; this set contains multiples of 5 {5, 10, 15, 20, 25...}. You can see that the least (or lowest) common multiple is the lowest multiple shared by two numbers. Like for 6 and 9, you have {6, 12, 18, 24...} and {9, 18...}, so LCM(6,9) = 18.

Now, if an LCM must be shared by both numbers, and to get a multiple of the largest number, you have to multiply by an integer greater than or equal to 1, then the LCM of two numbers can never be less than the larger of the twi numbers. Generally, if x and y are positive real numbers, and x is greater than y, $LCM(x,y) \leq x$ .

4 0

3 years ago

Mel works as a delivery person for Amazon. The graph shows a linear model for his delivery times on

lakkis [162]

Answer:

Point slope form: -9 = m(3)

Slope intercept form: y = -3x + 30

At x = 0, his delivery time was 30 minutes. It decreased by 3 minutes per day.

Step-by-step explanation:

We have 2 points to calculate the line.

(3, 21) x1 y1

(6, 12) x2 y2

First, we need to calculate the slope.

m =

m = -3

Point slope form is:

y - y1 = m(x - x1)

So for our case:

-9 = m(3)

And slope intercept form is:

y = mx + b

We need to solve for the y intercept (b)

y = -3x + b --- enter the slope

21 = -3(3) + b --- enter in any point on the line for x and y

21 = -9 + b

b = 30 --- solve for b

Now our slope intercept form of the line is:

y = -3x + 30

At x = 0, his delivery time was 30 minutes. It decreased by 3 minutes per day.

3 0

3 years ago

twice a number plus three times another number equals 4. three times the first number plus four times the other number is 7. wha

Drupady [299]

Answer:

x=5, y=-2. (5, -2).

Step-by-step explanation:

2x+3y=4

3x+4y=7

----------------

3(2x+3y)=3(4)

-2(3x+4y)=-2(7)

----------------------

6x+9y=12

-6x-8y=-14

-----------------

y=-2

2x+3(-2)=4

2x-6=4

2x=4+6

2x=10

x=10/2

x=5

5 0

3 years ago

Write the equation for the line that passes through the points (4, 5) and (6,9). *

N76 [4]

Answer:

y = 2x + 1

Step-by-step explanation:

first find slops

(9-5)/(6-4) = 4/2 = 2 = m

y = mx + b

5 = 2(2) + b

1 = b

y = 2x + 1

5 0

3 years ago

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