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marysya [2.9K]
3 years ago
13

A card is drawn at random out of a​ well-shuffled deck of 52 cards. Find the probability of drawing a six comma seven comma or e

ight.
A card is drawn at random out of a​ well-shuffled deck of 52 cards. Find the probability of drawing a six comma seven comma or eight.
Mathematics
1 answer:
Rina8888 [55]3 years ago
8 0

Answer: \frac{3}{13}, or ~23.07%

Step-by-step explanation:

There are 52 cards in your average deck.

For this question, you need the numbers of the cards in the deck. There are four of each number from 2 through 10, and four aces, jacks, queens, and kings.

Considering there are four 6s, four 7s, and four 8s, there are 12 cards that fit the description.

Divide 12 by the total number of cards in the deck, 52, to get your answer.

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Find the degree measure of each angle.
DanielleElmas [232]

Step-by-step explanation:

The angle between EF = 90 - 39 = 51°

Th angle between ED = 90 - 73 = 17°

3 0
2 years ago
Damon is shooting 2 free throws. The probability that Damon will make a free throw is 80%.
kati45 [8]
If he makes it 80% of the time that means he makes it .80 of the time (I just made it a decimal)
After 1 shot his probability is .80
After 2 shots his probability is .80X.80 = .64 or 64%

5 0
3 years ago
HELP ASAP!!!!!!!!!!!!!!!
vekshin1

Answer:

-1 and 5

-2 and 6

-4 and 8

<u><em>They all give the same total i.e. 4</em></u>

3 0
3 years ago
Solve the given linear Diophantine equation. Show all necessary work. A) 4x + 5y=17 B)6x+9y=12 C) 4x+10y=9
aliina [53]

Answer:

A) (-17+5k,17-4k)

B)  (-4+3k,4-2k)

C) No integer pairs.

Step-by-step explanation:

To do this, I'm going to use Euclidean's Algorithm.

4x+5y=17

5=4(1)+1

4=1(4)

So going backwards through those equations:

5-4(1)=1

-4(1)+5(1)=1

Multiply both sides by 17:

4(-17)+5(17)=17

So one integer pair satisfying 4x+5y=17 is (-17,17).

What is the slope for this equation?

Let's put it in slope-intercept form:

4x+5y=17

Subtract 4x on both sides:

     5y=-4x+17

Divide both sides by 5:

      y=(-4/5)x+(17/5)

The slope is down 4 and right 5.

So let's show more solutions other than (-17,17) by using the slope.

All integer pairs satisfying this equation is (-17+5k,17-4k).

Let's check:

4(-17+5k)+5(17-4k)

-68+20k+85-20k

-68+85

17

That was exactly what we wanted since we were looking for integer pairs that satisfy 4x+5y=17.

Onward to the next problem.

6x+9y=12

9=6(1)+3

6=3(2)

Now backwards through the equations:

9-6(1)=3

9(1)-6(1)=3

Multiply both sides by 4:

9(4)-6(4)=12

-6(4)+9(4)=12

6(-4)+9(4)=12

So one integer pair satisfying 6x+9y=12 is (-4,4).

Let's find the slope of 6x+9y=12.

6x+9y=12

Subtract 6x on both sides:

      9y=-6x+12

Divide both sides by 9:

       y=(-6/9)x+(12/9)

Reduce:

       y=(-2/3)x+(4/3)

The slope is down 2 right 3.

So all the integer pairs are (-4+3k,4-2k).

Let's check:

6(-4+3k)+9(4-2k)

-24+18k+36-18k

-24+36

12

That checks out since we wanted integer pairs that made 6x+9y=12.

Onward to the last problem.

4x+10y=9

10=4(2)+2

4=2(2)

So the gcd(4,10)=2 which means this one doesn't have any solutions because there is no integer k such that 2k=9.

6 0
3 years ago
<img src="https://tex.z-dn.net/?f=%20-%2032%20%2B%204%20x%20%3D%205%28%20-%207%20%2B%20x%29" id="TexFormula1" title=" - 32 + 4 x
harkovskaia [24]

\bf -32+4x=5(-7+x)\implies -32+4x=\stackrel{\textit{distributing}}{-35+5x} \\\\\\ \stackrel{\textit{subtracting 4x to both sides}}{-32=-35+x}\implies \stackrel{\textit{adding 35 to both sides}}{3=x}

7 0
3 years ago
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