For # 7-10, find the number of possible 4-card hands that contain the cards specified
Answers:
Problem 7) 105,625Problem 8) 8800Problem 9) 715Problem 10) 2860Note: The answer to problem 7 is a single value. The comma is there to make the number more readable.
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Explanation for problem 7)
There are 26 red cards (13 diamonds + 13 hearts).
We have 26 ways to pick the first red card, and then 25 ways to pick the second red card. If order mattered, then we'd have 26*25 = 650 ways to do this. However, order doesn't matter. All that matters is the hand itself rather than the individual cards. By "hand" I mean the collection of cards, and not the literal physical hand holding them.
Since the count 650 is a double count, this means 650/2 = 325 is the correct count where order doesn't matter. The black cards will follow identical logic to get the same value. There are 325 ways to pick the two black cards. This is because there are an equal number of red and black cards, and we're selecting an equal number of both colors.
So we have 325*325 = 105,625 different hands possible.
To help show some context, there are 52C4 = 270,725 different ways to pick four cards without any restrictions. I'm using the nCr combination formula.
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Explanation for problem 8)
The face cards are Jack, Queen, King. There are 3 face cards per suit and 4 suits total, so 3*4 = 12 face cards in all.
We have 12*11*10 = 1320 permutations and 1320/(3!) = 1320/6 = 220 combinations. We side with combinations because like before, order doesn't matter. There are 220 different ways to pick the three face cards. Then we have 52-12 = 40 ways to pick the fourth non-face card.
Overall, we have 220*40 = 8800 different ways to pick exactly three face cards.
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Explanation for problem 9)
There are 13 diamond cards, so n = 13. We're filling r = 4 slots.
Use the nCr combination formula to find that 13C4 = 715
See the attached image below for more detailed steps.
We have 715 ways to pick all diamonds.
----------------------
Explanation for problem 10)
We'll build from problem 9. We found there are 715 ways to pick four diamonds. This is the same number of ways to pick four hearts, or four clubs, or four spades. The actual suit doesn't matter. So we have 4*715 = 2860 different ways to pick 4 cards of the same suit
In poker, having all cards of the same suit is known as a flush. Though with poker, it involves 5 cards instead of 4.
Find QR.
Write your answer as an integer or as a decimal rounded to the nearest tenth.
QR = ___
Answer:
Step-by-step explanation:
take 64 degree as reference angle
using cos rule
cos 64=adjacent/hypotemuse
0.43=QR/10
10*0.43=QR
4.3=QR
PLEASE HELP IM BEING TIMED
Answer:
missing angle=36 degree
Find the
vertex of this
quadratic.
([?], [ ]
2
1
X
-4 -3 -2 -1 0 1 2 3 4
-1
-2
-3
-4
Answer:
The vertex of the parabola is [tex]V(x,y) = (0, 3)[/tex].
Step-by-step explanation:
In this case, the vertex of the parabola is the absolute maximum of the graph, that is, the point [tex]V(x,y) = (0, 3)[/tex]. Mathematically speaking, the vertex of the parabola is represents the only point of the range ([tex]y[/tex]) which is related to an only value of the domain ([tex]x[/tex]).
at a movie theater, the adult ticket price is $8 and the child ticket price is $6. For a certain movie, 200 tickets were sold and $1440 was collected. the equations a+c=200 and 8a+6c=1440 represent the situation. how many adult tickets were sold.
help with no link
NO LINK PLEASE
THANK YOU SO MUCH
Answer:
how much are they selling them for
Verify the identity:
sin(AB)
sin(A B
tan(A) | tan(B)
tan(A) =tan(B)
Answer:
Step-by-step explanation:
Right side =
sin A / cos A + sinB/ cosB (sinAcosB + sinB cos A ) * cosA cosB
------------------------------------- = cosA cosB (sinAcosB - snBcosA ) sinA/cosA - sinB/cos B
= Left side.
The trigonometry identity [tex]\frac{sin(A+B)}{sin(A-B)}[/tex] is equals to [tex]\frac{tan(A)+tan(B)}{tan(A)-tan(B)}[/tex].
What is trigonometric identity?Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation.
According to the given question.
We have a trigonometric identity.
[tex]\frac{sin(A+B)}{sin(A-B)} =\frac{tan(A)+tan(B)}{tan(A)-tan(B)}[/tex]
To prove the above trigonometric identity we will show L.H.S = R.H.S
[tex]L.H.S=\frac{sin(A+B)}{sin(A-B)}[/tex]
⇒ [tex]L.H.S = \frac{cosBsinA-sinBcosA}{sinAcosB-cosAsinB}[/tex]
⇒ [tex]L.H.S = \frac{\frac{sinAcosB}{cosAcosB} + \frac{sinBsinA}{cosBcosA} }{\frac{sinAcosB}{cosAcosB}-\frac{cosAsinB}{cosAcosB} }[/tex] (dividing the numerator and denominator by [tex]cosAcosB[/tex] )
⇒ [tex]L.H.S = \frac{\frac{sinA}{cosA} +\frac{sinB}{cosB} }{\frac{sinA}{cosA}-\frac{sinB}{cosB} }[/tex]
⇒ [tex]L.H.S = \frac{tanA+tanB}{tanA- tanB}= R.H.S[/tex]
Hence, L.H.S = R.H.S
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An urn contains 9 black and 8 pink balls. Five balls are randomly drawn from the urn in succession, with replacement. That is, after each draw, the selected ball is returned to the urn. What is the probability that all 5 balls drawn from the urn are black
Answer:
0.0416
Step-by-step explanation:
Given :
Number of balls :
Pink = 8 ; black = 9
Total number of balls = 8+9 = 17
Choosing with replacement :
Probability = required outcome / Total possible outcomes
Required outcome = number of black balls
Total possible outcomes = total number of balls
P(black) = 9/17
Number of picks = 5
Hence, Probability that all 5 picks are black :
P(all black) = 9/17 * 9/17 * 9/17 * 9/17 * 9/17 = 0.0415879
= 0.0416
Jenny bought gallons of lemonade and milk for a banquet. A gallon of lemonade costs $5, and a gallon of milk costs $3. Jenny spent $120 and bought 32 total gallons. How many gallons of milk did Jenny buy?
Answer:
She Bought 40 Gallons of Milk
Step-by-step explanation:
Jill bought 3 boxes of ice pops. Each box contains 4 orange ice pops and some cherry ice pops. The number of cherry ice pops in each box was the same. Jill bought 36 ice pops in all. What are the 2 steps of this equation and how many cherry ice pops are in each box?
Answer: 9 cherry ice pops
Step-by-step explanation:
if you bought 3 boxes and there is four orange one in each pack the that is
12 and 36 divided by 4 is 9 so there is 9 cherry ice pops
Convert the following repeating decimal into a fraction in the simplest format .61
Answer: 61/100 would be the answer
A gymnasium floor is being covered by square shock-absorbing tiles. The new tiles are 2 inches larger in length and width than the old tiles. The new flooring will require only 600 tiles. What is the length of a side of one of the new shock-absorbing tiles
This question is incomplete, the complete question is;
A gymnasium floor is being covered by square shock-absorbing tiles.
The old gym floor required 864 square tiles. The new tiles are 2 inches larger in length and width than the old tiles. The new flooring will require only 600 tiles. What is the length of a side of one of the new shock-absorbing tiles
Answer:
Length of the side of one of the new shock-absorbing tiles is 12 inches
Step-by-step explanation:
Given the data in the question;
Since both the area for old tiles and new tiles are the same;
so Area of old tiles = Area of new tiles,
given that; The old gym floor required 864 square tiles and new flooring will require only 600 tiles as new tiles are 2 inches larger in length and width than the old tiles.
Now let the length of the sides of the square tiles be x
Area of a square = length × length = x × x = x²
So, Area of Old tiles = 864 × x² = 864x²
Area of New tiles = 600( x + 2 )²
= 600( x² + 4x + 4 )
= 600x² + 2400x + 2400
Now, Area of old tiles = Area of new tiles
864x² - 600x² - 2400x - 2400 = 0
264x² - 2400x - 2400 = 0
we find x
Using; x = [-b ±√( b² - 4ac )] / 2a
x = [-( -2400) ±√( (-2400)² - (4 × 264 × -2400 )] / 2( 264 )
x = [ 2400 ±√( 5760000 + 2534400) ] / 528
x = [ 2400 ±√8294400 ] / 528
x = [ 2400 ±2880 ] / 528
x = [ 2400 - 2880 ] / 528 or [ 2400 + 2880 ] / 528
x = [ -480 / 528 ] or [ 5280 / 528 ]
x = [ -0.909 ] or [ 10 ]
the length of the sides of the square tiles cannot be Negative
Hence, x = 10
Therefore, the length of a side of one of the new shock-absorbing tiles will be;
⇒ x + 2 = 10 + 2 = 12 inches
Length of the side of one of the new shock-absorbing tiles is 12 inches
Divide the following complex numbers:
(4-i)/(3+4i)
A.-8/7 + 19/7i
B. 16/25 - 19/25i
C. 8/25 - 19/25i
D. -16/7 + 19/7i
Answer:
C. 8/25 - 19/25i
Step-by-step explanation:
Given that:
[tex]\dfrac{4-i}{3+4i}[/tex]
[tex]= \dfrac{(4-i) (3-4i)}{(3+4i)(3-4i)}[/tex]
[tex]= \dfrac{(4-i) (3-4i)}{(3+4i)(3-4i)} \\ \\ =\dfrac{12 -16i -3i+4i^2}{9 - 12i +12i -16i^2} \\ \\ = \dfrac{12-19i+4i^2}{9-16i^2} \\ \\ = \dfrac{8-19i}{25}[/tex]
[tex]=\dfrac{8}{25}- \dfrac{19i}{25}[/tex]
Is 5+2y=13 a linear relationship
Answer:
Yes 5+2y=13 is a linear relationship
Two straight lines that intersect at a right angle are __?__ to each other.
Answer: perpendicular lines
Step-by-step explanation:
look up "Two straight lines that intersect at a right angle"
Answer:
Perpendicular! hope this helps :)
FOR 100 POINTS!!!! BRAINLIEST TOO PLEASE HELP!!!!
Estimate an equation for the line of best fit for the following scatter plot. Pic below. Open ended.
Answer:
y = 8.667x + 8Step-by-step explanation:
Use two points on the graph to get an equation:
(0, 8), (6, 60)The slope: m = (60 - 8)/6 = 8.667
The y- intercept is 8
The equation of the line of best fit:
y = 8.667x + 8The answer to your question is y = 8.667x + 8. Hope this helps; have a great day!
16. (24.6L) The time t (in minutes) that it takes Danielle
to drive to work varies inversely with the average
speed S (in miles per hour). It takes Danielle 24
minutes to get to work when he drives at an
average speed of 30 mph. What is Danielle's
average speed if he gets to work in 36 minutes.
Answer:
20 mph
Step-by-step explanation:
Varies inversely
ts = k
------------------------------
It takes Danielle 24 minutes to get to work when he drives at an average speed of 30 mph
24(30) = 720
------------------------
What is Danielle's average speed if he gets to work in 36 minutes.
36s = 720
s = 720/36
s = 20
20 mph
A = 7x2 - 3x + 10
B = -4x2 + 6x - 4
A - B =
Your answer should be a polynomial in standard form.
Answer:
A - B = 11x² -9x + 14
A - B = 11x² -9x + 14
Kyle typed 574 words in 14 minutes. How many
Answer:
Kyle typed 574 words in 14 minutes. How many...........?????????
il.l just divide 574 divided by 14= 41
Step-by-step explanation:
:)
Answer:
41 like I said in the comments.
Step-by-step explanation:
WILL GIVE U BRAINLIEST
ABCD is a rectangle. AB = x + 7, BC = 2x + 19. What is the CD?
A. 2x + 133
B. X + 7
C. 5x + 38
D. 2x + 14
Answer:
A rectangle has its Opposite sides Equal.
Draw one so you'd grab it better.
AB=CD
BC= AD
Since CD=AB and We're given AB=x+7...
CD = x + 7
OPTION B IS LEGIT!!
Find the circumference of a circle with a radius of 6 cm.
Hi besties i need. help ASAP please and. ty
Answer:
37.7
Step-by-step explanation:
Circumference = [tex]2\pi r[/tex]
Circumference = [tex](2)(\pi )(6)[/tex]
Circumference = 37.69911184 / 37.7
Therefore, circumference of the circle with the radius 6 cm is 37.7.
Answer:
37.7
Step-by-step explanation:
formula for circumference of a circle=2πr
2×π×6=37.7cm
What is 2/5 in three equivalent forms
Answer:
4/10 8/20 16/40
Step-by-step explanation:
find a value of (2power-1*4power-1)
2^( - 1 ) × 4^( -1 ) =
2^( -1 ) × 2^( 2 × ( - 1) ) =
2^( - 1 ) × 2^( - 2 ) =
2^( - 1 - 2 ) =
2^( - 3 ) =
1/ 2^( 3 ) =
1/8
An archeologist is digging at a former lake and finds items at the following elevations.
Place the items in order from highest elevation to lowest
________________________________________________
Write the elevation where each item was found as a positive or negative integer:
Arrowhead = _______ feet
Fishbone = ______ feet
Fish Hook = _______ feet
Fossil = _______ feet
Pottery = _______ feet
Shell = ________ feet
Answer:
Fossil > Arrow Head > Pottery > Shell > Fishbone > Fish Hook
Step-by-step explanation:
Arrowhead = ___20___ feet
Fishbone = __-10___ feet
Fish Hook = ___-40__ feet
Fossil = __30___ feet
Pottery = ___10___ feet
Shell = ____0___ feet
If something is above sea level, it would have a positive elevation, and if below sea level, a negative elevation. And at sea level, you have 0 elevation.
After this, just put them in order of decreasing elevation. So, the highest elevation is 30ft with the fossil, then 20 with the arrow head, pottery at 10, shell at 0, fishbone at -10, fish hook at -40.
The following diagram shows part of the graph off with x-intercept (5,0) and y-intercept (0,8).
Find the y-intercept of the graph of f(x) + 3.
Step-by-step explanation:
By question , it's given that the X intercept is (5,0) and the y intercept is (0,8) . And we need to find the y-intercept of the graph of f(x) + 3 . For that , firstly let's find out the equation of the line.
We can use here two point form of the line .So that , the equation would be ,[tex]\sf\implies y- y_1 = \bigg(\dfrac{y_2-y_1}{x_2-x_1}\bigg) ( x - x_1) \\\\\sf\implies y - 0 = \bigg(\dfrac{0-8}{5-0}\bigg)( x - 5 ) \\\\\sf\implies y = \dfrac{-8}{5}( x - 5 ) \\\\\sf\implies 5y = -8x +40 \\\\\sf\implies 8x + 5y - 40 = 0 [/tex]
Let us say that this is f(x) :-
[tex]\\\\\sf\implies f(x) = 8x + 5y - 40 \\\\\sf\implies \boxed{\sf\red{ f(x)+3 = 8x +5y -37 }}[/tex]
Plot its graph :-
We can either convert it into intercept form but plotting a graph can also be done to find y intercept .
[tex]\implies \boxed{\pink{\sf y - intercept = 7.4}}[/tex]
Refer to attachment for graph .
Hence the y Intercept is 7.4 .
Wat is the Ans?
Got the question
Answer:
C
Step-by-step explanation:
C= 2* pi*r = 2* pi* 5 ≈ 31.4 cm
300 ml of an IV fluid contains 50 mcg of Drug A. If a patient is receiving 1000 ml of this IV fluid, how much of Drug A is this patient getting?
Answer: 166.666 mcgs
Step-by-step explanation:
If a patient is receiving 1000 ml of this IV fluid, then the amount of Drug A the patient will be getting is 166.667 mcg.
What is a Ratio?A ratio shows us the number of times a number contains another number.
Given that 300 ml of an IV fluid contains 50 mcg of Drug A. Therefore, the ratio of IV fluid to drugs A can be written as,
IV fluid / Drug A = 300ml / 50 mcg
IV fluid / Drug A = 6 ml/ mcg
Now, If a patient is receiving 1000 ml of this IV fluid, then the amount of Drug A the patient will be getting,
IV fluid / Drug A = 6 ml/ mcg
1000 ml / Drug A = 6 ml/ mcg
Drug A = 1000 ml / 6 ml/ mcg
Drug A = 166.667 mcg
Hence, If a patient is receiving 1000 ml of this IV fluid, then the amount of Drug A the patient will be getting is 166.667 mcg.
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In a class of 6 there are 4 students who are secretly robots
Answer:
then 2 are human
Step-by-step explanation:
because 4 are robots
Answer:
The rest are normal students.
6-4= 2 so that's how many normal students there are.
Please add a little bit more detail to the question please :)
For a sample size of n = 26 and a population parameter of p = 0.6, a normal
curve can be used to approximate the sampling distribution.
O A. True
O B. False
Answer:true
Step-by-step explanation:
just took the test < 3
The statement : "for a sample size of n = 26 and a population parameter of p = 0.6, a normal curve can be used to approximate the sampling distribution" is true.
What is normal curve?Normal curve is used to represent the class shapes in the statistical probability. Mathematically, we can describe the normal curve as -
[tex]$f(x)= {\frac{1}{\sigma\sqrt{2\pi}}}e^{- {\frac {1}{2}} (\frac {x-\mu}{\sigma})^2}[/tex]
where -
f(x) = probability density function
σ = standard deviation
μ = mean
Given is that for a sample size of n = 26 and a population parameter of
p = 0.6, a normal curve can be used to approximate the sampling
distribution.
It is asked to identify whether the given statement regarding the normal curve is true or false. The given statement is - "for a sample size of n = 26 and a population parameter of p = 0.6, a normal curve can be used to approximate the sampling distribution". The given statement is true.
Therefore, the statement : "for a sample size of n = 26 and a population parameter of p = 0.6, a normal curve can be used to approximate the sampling distribution" is true.
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How many different five digit members can be formed from the digits 5, 6, 7, 8 and 9 if digits can be repeated? If digits cannot be repeated? NO LINKS!!!
Answer:
Solution given:
5,6,7,8,9,
When repeated:
it has
5 ways for each
different five digit members can be formed from the digits:5*5*5*5*5=3125
When not repeated:
it has
5 ways for 1st
4 ways for 2nd
3 ways for 3rd
2 ways for 4th
1 ways for 5th
different five digit members can be formed from the digits:5*4*3*2*1=120