A deck of 52 cards contains 12 picture cards. If the 52 cards are distributed in a random manner among four players in such a way that each player receives 13 cards, what is the probability that each player will receive three picture cards
Answer:
The probability that each player will receive three picture cards = 0.0324
Step-by-step explanation:
As given,
A deck of 52 cards contains 12 picture cards
Remaining card = 52 - 12 = 40
So,
Total number of ways in which 12 picture card is distributed = [tex]\frac{12!}{3! 3! 3! 3!}[/tex]
Now,
The Total number of ways in which Remaining cards are distributed = [tex]\frac{40!}{10! 10! 10! 10!}[/tex]
So,
Total number of ways of getting 3 picture card and remaining card = [tex]\frac{12!}{3! 3! 3! 3!}[/tex]× [tex]\frac{40!}{10! 10! 10! 10!}[/tex]
= [tex]\frac{12! 40!}{(3!)^{4} (10!)^{4} }[/tex]
Now,
Total number of ways to distribute 52 cards so that each people get 13 card = [tex]\frac{52!}{13! 13! 13! 13!} = \frac{52!}{ (13!)^{4} }[/tex]
∴ The probability = [tex]\frac{\frac{12! 40!}{(3!)^{4} (10!)^{4} }}{\frac{52!}{(13!)^{4} }}[/tex]
= [tex]\frac{12! 40!}{(3!)^{4} (10!)^{4} }[/tex]×[tex]\frac{(13!)^{4} }{ 52! }[/tex]
= [tex]\frac{12! 40!}{(3!)^{4} (10!)^{4} }[/tex]×[tex]\frac{(13.12.11.10!)^{4} }{ 52.51.50.49.48.47.46.45.44.43.42.41.40! }[/tex]
= [tex]\frac{12!}{(3!)^{4} }[/tex]×[tex]\frac{(13.12.11)^{4} }{ 52.51.50.49.48.47.46.45.44.43.42.41}[/tex]
= [tex]\frac{479,001,600}{(6)^{4} }[/tex]×[tex]\frac{(1716)^{4} }{ 52.51.50.49.48.47.46.45.44.43.42.41}[/tex]
= 0.0324
∴ we get
The probability that each player will receive three picture cards = 0.0324
Find the slope of the line graphed below.
Answer:
[tex]\displaystyle m=\frac{1}{2}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Reading a Cartesian planeCoordinates (x, y)Slope Formula: [tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Find points from graph.
Point (0, 1)
Point (2, 2)
Step 2: Identify
x₁ = 0, y₁ = 1
x₂ = 2, y₂ = 2
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute in points/variables [Slope Formula]: [tex]\displaystyle m=\frac{2-1}{2-0}[/tex][Slope] [Fraction] Subtract: [tex]\displaystyle m=\frac{1}{2}[/tex]Can someone explain to me better on identifying linear functions? Like how would I know the difference when identifying them? Are they a function or not?
Answer:
A linear function is a straight line and a non-linear function is not a straight line.
Step-by-step explanation:
19.- If P is the circumcenter of ABG, AD = 3x - 11-DB = 5x-29, and PC = 18, find DP
Answer:
DP=5×-29 is your answer right answer
find the length of a rectangle whose area is 144 cm and breadth is 9CM
Answer: 16
Step-by-step explanation:
The area of a rectangle can be found by multiplying its length and its height. You may consider the breadth as just another word for length.
A = L * W
Since we know what are area is, we may substitute it into the equation.
144 = L * W
We also know what our width (our breadth) is, so we will also substitute it in
144 = L * 9
To solve for our length, we divide both sides by 9 to isolate L
[tex]\frac{144}{9} = \frac{L * 9}{9}[/tex]
We see that the two 9's on the right hand side cancel out to give us L
[tex]\frac{144}{9} = 16[/tex]
So our L is equal to 16.
We can check our work by multiplying the length and breadth together again to see if they give 144 as a product, which they do.
Dara:240g
Brüt kütle:760g
Net Kütle:.....g
işlem:
Answer:
Net Mass = 520 g
Step-by-step explanation:
Given:
Waste = 240 g
Gross mass = 760 g
Find:
Net Mass
Computation:
Net Mass = Gross mass - Waste
Net Mass = 760 g - 240 g
Net Mass = 520 g
Elena swan 14 laps in 42 minutes.how many minutes per lap did Elena swim?round your answer to two decimal places must be a decimal answer.
Answer: 4
Step-by-step explanation:
Please help me solve this is due
Answer:
option D is correct answer hope it helps
Find the third term of a proportional if the first, second and fourth terms are 24, 36, 126
Answer:
The third term of a proportional is: 84
Step-by-step explanation:
We know that if a, b, c and d are in proportion, then:
a × d = b × c
In our case, we are given the first, second, and fourth terms are 24, 36, 126.
a = 24
b = 36
d = 126
and we have to determine the third term 'c'.
as we know that if a, b, c, and d are in proportion, then:
a × d = b × c
Thus,
substituting a = 24, b = 36, d = 126 to determine
24 × 126 = 36 × c
c = (24 × 126)/36
c = 3024/36
c = 84
Thus, the third term of a proportional is: 84
The expression sin 57° is equal to
(1) tan 33°
(3) tan 57°
(2) cos 33°
(4) cos 57°
Answer:
[tex]cos(33^{\circ})[/tex]
Step-by-step explanation:
Given
[tex]sin(57^{\circ})[/tex]
Required
Determine an equivalent expression
In trigonometry:
[tex]sin(\theta)= cos(90^{\circ} - \theta)[/tex]
In [tex]sin(57^{\circ})[/tex]
[tex]\theta=57^{\circ}[/tex]
Substitute [tex]57^{\circ}[/tex] for [tex]\theta[/tex]
in [tex]sin(\theta)= cos(90^{\circ} - \theta)[/tex]
[tex]sin(57^{\circ})= cos(90^{\circ} - 57^{\circ})[/tex]
[tex]sin(57^{\circ})= cos(33^{\circ})[/tex]
Hence, the equivalent expression is: [tex]cos(33^{\circ})[/tex]
divide decimal (round off to tenths)6.24÷0.6
Answer:
10.4
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Answer:
Lower quartile = 65
Upper quartile = 95
Median = 80
Step-by-step explanation:
✔️Lower quartile = the value at the beginning of the edge of the rectangular box = 65
✔️Upper quartile = the value at the end of the edge of the rectangular box = 95
✔️Median = the value indicated by the vertical line that divides the box into two = 80
Quadrilateral ABCD is a parallelogram. Determine the measure of Angle A
A) 96°
B) 52°
C) 39°
D) 78°
Answer:
A = 78
Step-by-step explanation:
* since its a Quadrilateral all of angles equal the same
x + 52 = 3x
52 = 2x
26 = x
26 * 3 = 78
-x+5y=8 3x+7y=-3 find the equation
Answer:
The solution to the system of equations be:
[tex]x=-\frac{71}{22},\:y=\frac{21}{22}[/tex]
Step-by-step explanation:
Given the system of equation
[tex]\begin{bmatrix}-x+5y=8\\ 3x+7y=-3\end{bmatrix}[/tex]
Multiply -x+5y=8 by 3: -3x+15y=24
[tex]\begin{bmatrix}-3x+15y=24\\ 3x+7y=-3\end{bmatrix}[/tex]
Add the equations
[tex]3x+7y=-3[/tex]
[tex]+[/tex]
[tex]\underline{-3x+15y=24}[/tex]
[tex]22y=21[/tex]
solving 22y=21 for y
[tex]22y=21[/tex]
Divide both sides by 22
[tex]\frac{22y}{22}=\frac{21}{22}[/tex]
Simplify
[tex]y=\frac{21}{22}[/tex]
For -3x+15y=24 plug in y = 21/22
[tex]-3x+15\cdot \frac{21}{22}=24[/tex]
Subtract 15 · 21/22 from both sides
[tex]-3x+15\cdot \frac{21}{22}-15\cdot \frac{21}{22}=24-15\cdot \frac{21}{22}[/tex]
[tex]-3x=\frac{213}{22}[/tex]
Divide both sides by -3
[tex]\frac{-3x}{-3}=\frac{\frac{213}{22}}{-3}[/tex]
[tex]x=-\frac{71}{22}[/tex]
The solution to the system of equations be:
[tex]x=-\frac{71}{22},\:y=\frac{21}{22}[/tex]
Find the equation of the line that is perpendicular to the x-axis and passes through the point (14,-9). Give the
full equation as your answer.
Answer:
y = -9
Step-by-step explanation:
a line perpendicular to the x-axis is a horizontal line (which means the slope is zero) which pass through the y-axis at -9
PLEASE HELP MATH MIDTERM
Steven bought a cylindrical water tank for his cattle, but he forgot to ask the seller what the diameter of the tank was. He needs to know the diameter of the tank so that he can build a platform for the tank to safely sit on. The seller told him the Volume and the height. Help Steven by calculating the diameter of the tank using the information below.
The volume of the tank is 572π 3 and its height is 9ft
Answer:
Step-by-step explanation:
h and r are the height and radius of the tank, respectively.
volume = πr²h
πr²·9 = 572π
r = √(572π/(9π)) = √(572/9)
diameter = 2r ≅ 15.9 ft
$8.25 for 1 1/2 pounds of coffee beans = $ per
Answer:
$5.50 per pound
Step-by-step explanation:
8.25 / 1 1/2
5.50 per pound
Hope this Helps!!!
Answer: 5.5
Step-by-step explanation:
8.25 divided by 1.5
Ahn had walked 8 blocks. He was 25% of the way to school. How many total blocks was his walk to school?
The price of a technology stock has dropped to $9.74 today. Yesterday's price was $9.87. Find the percentage decrease. Round your answer to the nearest tenth of a percent.
Answer:
Step-by-step explanation:
9.74 - 9.87 = -0.13
0.13/9.87 ≈ 0.013 = 1.3%
Price decreased by 1.3%
1 point
If a ladder 12 feet long leans against a wall and makes an angle of 72° with
the ground. Find, to the nearest tenth of a foot, the distance from the wall
to the base of the ladder. *
Your answer
Answer:
my answer is 6% he can step on
ladder of only two feet if you equate 72% it means you will get 2 points if you jump on the ladder 80% you will stumble and you have 1% like that.
Step-by-step explanation:
I hope I can help you
rewrite the equation y-3=1/2(x+4) in standard form
Answer:
2x−y=5
Step-by-step explanation:
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What is the sum of the zeros of the equation y = 2x2+5x−3
Answer:
2×2+5×-3= -11
Step-by-step explanation:
que te pjefa ayudar
For numbers 7 - 10:
Mr. and Mrs. Banal purchased a house and lot worth P4,000,000. They pa
payment of P800, 000. They plan to amortize the loan of P3. 200,000
monthly for 20 years. The interest rate is 12% convertible monthly.
A. P 5,319.98
C. P 35,234.76
B. P 29,914.78
D. P 5,256,342.40
7. How much is the monthly payment?
8. What is the total interest paid?
9. What is the principal and interest components of the 51st paym
10. What is the interest components of the 51st payment?
Answer:
Lo averiguaste, lo siento, amigos míos, por haberlos ayudado. pero la respuesta es 456 $.
Step-by-step explanation:
Select ALL of the following that would reflect the following triangle onto itself.
Answer:
Over x = 4
Step-by-step explanation:
In its current configuration, our triangle only has vertical symmetry - we can only flip it onto itself if it's over a verticle line. This immediately eliminates our two horizontal lines from the equation: y = 4 and the x axis.
That leaves us chosing between the y axis or the line x = 4. Now that we know the type of symmetry this triangle has (vertical), we need to figure out where to put the line of symmetry. The y axis won't do, since a reflection over that will move the triangle to the far left of the page. So it must be the line x = 4.
need help with this someone send the answer please i don't understand why there are so many boxes.
Answer: See the attached image below. I've filled in the table with the proper values.
Row 2: AFB = 36, BFC = 54, EFA = 144
Row 3: AFB = 40, BCF = 50, DFE = 40
=======================================================
Explanation:
angles AFB and BFC add to 90 degrees since they form a right angle.
In row 1, we see that 48+42 = 90
Angles AFB and DFE are congruent since they are vertical angles. For row 1, we have both of these angles equal to 48 degrees.
Also for row 1, we have angles BFC and CFD add to 42+90 = 132, which is exactly the measure of angle BFD. This angle is congruent to angle EFA because they are vertical angles. So that's how angle EFA is 132.
--------------------------
Now onto row 2
We'll use the ideas of row 1 to work our way backwards to fill in the missing items.
We're given DFE is 36 degrees. This must mean that AFB is also 36 degrees. These angles are vertical angles.
Then we'll use the idea that (angleAFB)+(angleBFC) = 90 to find that
angle BFC = 90 - (angle AFB) = 90 - 36 = 54
Lastly for this row, we can say,
angle BFD = (angle BFC) + (angle CFD) = 54 + 90 = 144
angle EFA = angle BFD = 144
To summarize the missing items of row 2, we have...
angle AFB = 36angle BFC = 54angle EFA = 144---------------------------
Now onto row 3. We use the same tricks (more or less) that were used on row 2.
If angle EFA is 140, then so is angle BFD. These are vertical angles.
(angle BFC) + (angle CFD) = angle BFD
(angle BFC) + 90 = 140
angle BFC = 140-90
angle BFC = 50
This in turn lets us say,
(angle AFB) + (angle BFC) = 90
angle AFB = 90 - (angle BFC)
angle AFB = 90 - 50
angle AFB = 40
angle DFE = angle AFB = 40
To summarize the missing pieces we found:
angle AFB = 40angle BFC = 50angle DFE = 40All of the values are filled in the table shown below.
-2x+3y=15, rearrange to write in slope-intercept form, y=mx+b, by isolating y.
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P is the event Poor weather
D is the event Team draws
G is the event Good weather
poor = 3 draws
good= 5 draws
How do I solve 1/3 = 5n/600
Answer:
n = 40
Step-by-step explanation:
A fraction can be equivlent to another fraction, right? so 1/3 = ?/600 - 3*200 = 600 and 1*200 = 200 so 5n/600 should be equal to 200/600 and since 5n = 200 we divide by 5 on both sides and get n = 40
A wealthy man just died and left his pet dogs the following estate: $20,000 per year for the next 11 years with the first cash flow today. At a discount rate of 4.2%, what is the doggy estate worth in today's dollars?