In a given permutation of 52 cards, if the 3 of spades is to follow all of the hearts, that means the 3 of spades must be at least the 14th card in the deck.
Consider some possible orderings of the deck:
• If the 3 of spades is the 14th card, then the deck looks like
[all 13 ♥] … 3 ♠ … [all other 38 cards]
There are 13! ways to arrange the 13 hearts at the beginning and 38! ways to arrange the tail of 38 cards. Hence there are 13! × 38! possible rearrangements of the deck where 3 ♠ is the 14th card.
• If 3 ♠ is the 15th card, then the deck looks like
[13 ♥ and 1 other] … 3 ♠ … [all other 37 cards]
and there would be 14! × 37! ways of arranging the cards in this order.
There are 39 possible positions for 3 ♠. Extrapolating, it follows that the total number of permutations of the deck in which all hearts occur before 3 ♠ is
[tex]\displaystyle \sum_{k=0}^{38} (13+k)! \times (38-k)![/tex]
There are 52! total possible ways of rearranging the deck. Then the probability of rearranging the deck so that all hearts are drawn before 3 ♠ is
[tex]\displaystyle \frac1{52!} \sum_{k=0}^{38} (13+k)! \times (38-k)! = \frac{87,031,512,096,420,449}{221,360,321,731,856,907,600} \approx \boxed{0.000393}[/tex]
4. Teanna drove 366 miles in 6 hours. How many miles did she drive in one hour?
Answer:
61 miles
does this help??
Step-by-step explanation:
\sf 45-2x=75-3x
Free
[tex]\sf \longmapsto45 - 2x = 75 - 3x[/tex]
[tex]\sf \longmapsto45+−2x=75+−3x[/tex]
[tex]\sf \longmapsto−2x+45=−3x+75[/tex]
[tex]\sf \longmapsto \: −2x+45+3x=−3x+75+3x[/tex]
[tex]\sf \longmapsto \: x+45=75[/tex]
[tex]\sf \longmapsto \: x+45−45=75−45[/tex]
[tex]\sf \longmapsto \: x=30[/tex]
[tex] \boxed{\sf 30}[/tex]
what is the y- intercept of this quadratic funtions f(x)=-x2+10x-22
Blake's bank statement shows a
balance of $2000.00. Since the
statement date, Blake had
deposits of $1000.00 and $450.00.
He has visited the ATM for
withdrawals of $275,00 and
$40.00 when he took Christie to
the movies. He has written checks
for $47.00, $92.00, $101.00, and
$209,00. What is his account
balance?
His balance is $2,686.00
$2,000.00 + $1,000.00 = $3,000.00 + $450.00 = $3,450.00
$3,450.00 - (($275.00 + $40.00) + (($47.00 + $92.00) + ($101.00 + $209.00)) = $2,686.00
At time t = 0, water begins to drip out of a pipe into an empty bucket. After 77 minutes, there are 11 inches of water in the bucket. Write a linear function rule to model how many inches of water w are in the bucket after any number of minutes t.
The linear function rule is W =
Answer:
w = 1/7t
Step-by-step explanation:
Assuming the rate is constant, the function will be ...
w = kt
We can find k using the given values:
11 = k·77
k = 11/77 = 1/7
The linear function rule is w = 1/7·t.
What is 2 hundredths in standard form in fifth grade
0.02
0._ is tenths and
0.0_ is hundredths
Answer:
Step-by-step explanation:
5th Grade Math 1.2, Place Value of Whole Numbers, Standard Form ... this is the name of the video. I hope it helps.
Roxana makes bracelets and necklaces and sells them at the farmers’ market. She sells the bracelets for $12 each and the necklaces for $18 each. At the market next weekend she will have room to display no more than 40 pieces, and she needs to sell at least $500 worth in order to earn a profit. (Thank you so much for anyone who answers it
Answer:
She could out 20 necklaces and 20 bracelets on display and she would make $600.
Step-by-step explanation:
$18 necklaces x 20= $360
$12 bracelets x 20 = $240
totalling $600
Simplify: 7.2 x10^4/3.0 x 10^2
Answer:
240
Step-by-step explanation:
Jason has sixteen books and fifteen magazines in his library. He bought several books at a yard sale over the
weekend. He now has ninety-four books in his library. How many books did he buy at the yard sale?
Answer:
48 books
Step-by-step explanation:
you would take away the 15 magazines because that doesn't matter.you would put 94 books on top first and then subtract 16 books to thatthen putting that problem together you should get 48pls give all numbers
PLEASE HELP ME FOR 25 POINTS NO LINKS!
Answer:
The answer is C. Yes, Abc= Adc
Answer:
Yes, ABC is congruent to CDA by SSS
Your answer is correct; and here's why:
side AB corresponds to side CD.
and side BC corresponds to DA
So ABC = CDA.. and of course they also share AC which makes it congruent by side side side congruency.
Step-by-step explanation:
help ? lol..
i’m stuck on this
Answer:
24 ?
Step-by-step explanation:
I may be wrong but I believe the answer is 24 since she lost half of her CDs a week later. The number 6 is not important to the word problem as the only information we need in the amount she has left and the amount she lost. I may be wrong so please check the work again?
Answer:
18 CDs
Step-by-step explanation:
To find how many she started with, It says she lost half, meaning she had must have had 24. Because 12 is half of 12. If she lost half of 24, she would have 12 left. Before she bought 24, she had 6 less, because she bought meaning plus, 6. But to get the beggining, you do the oppisite, which is minus 6. So, 24-6 to get 18.
To make sure we are correct plug in 18. She starts out with 18. She buys, 6. So plus 6. 18+6 to get 24. But she then a week later lost half, leaving her with 12 CDs. By seeing this, we can tell, she did in fact, have 18 CDs to start out.
P.S wow she must really be dum b to lose an entire an entire 12 CDs in a couple hours.
Which expressions are equivalent to 2^5 2^4? CHECK ALL THAT APPLY!!!
2^20
2.2^9
2^10 • 2²
2^-2 2^11
(2.2.2.2.2).(2.2.2.2)
Answer:
last option is correct
...................................
Given the function f(x)=-x^2+6x+17 determine the average rate of change of the function over the interval −3≤x≤7.
Answer:
2
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Here [ a, b ] = [ - 3, 7 ] , then
f(b) = f(7 ) = - 7² + 6(7) + 17 = - 49 + 42 + 17 = 10
f(a) = f(- 3) = - (- 3)² + 6(- 3) + 17 = - 9 - 18 + 17 = - 10
average rate of change = [tex]\frac{10-(-10)}{7-(-3)}[/tex] = [tex]\frac{10+10}{7+3}[/tex] = [tex]\frac{20}{10}[/tex] = 2
a
8) A bridge builder plans to construct a cable suspension bridge in your town. The cable being used will form
a curve modeled by the equation h(x) = 3x2 - 6x + 200, where x represents the length of cable used (in feet)
and h(x) represents the height of the cable (in feet). At what height will the cable hang closest to the bridge
deck?
Answer:
197
Step-by-step explanation:
https://www.cusd80.com/cms/lib/AZ01001175/Centricity/Domain/8294/HA2%20Chapter%202%20Review%20Key.pdf
4.
Graph the equation 3x – 2y = -4.
If m∠2=6x+8 and m∠6=8x-6, find the value of x so that l||m.
Answer:
x = 7
Step-by-step explanation:
∠2 and ∠6 are known as alternate interior angles. These angles equal one another. Set up the following equation and solve for x.
[tex]m\angle2=m\angle6\\\\6x+8=8x-6\\\\8=2x-6\\\\14=2x\\\\7=x[/tex]
What is the value of x in the triangle?
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
The value of x is ~
[tex] \boxed{5 \sqrt{3} }[/tex]
[tex] \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}[/tex]
The Triangle stated in the diagram is a right angled Triangle, so
[tex] \tan(30) = \dfrac{x}{15} [/tex][tex] \dfrac{1}{ \sqrt{3} } = \dfrac{x}{15} [/tex][tex]x = \dfrac{15}{ \sqrt{3} } [/tex][tex]x = 5 \sqrt{3} [/tex]what is the answer too 2y-3=-5
2 − 3 = −5
First we need to Add 3 to both sides of the equation:
2 − 3 + 3 = −5 + 3
Then we simplify:
2 = −5 + 3
2 = −2
Now we divide both sides of the equation by the same term:
2 / 2 = −2 / 2
Final answer: = −1
I hope this helps!
Answer:
Y= - 1
Step-by-step explanation:
2y-3= - 5
+3 +3
2y= -2
/2 /2
Y= -1
Step 1: Add 3 to both sides because you want to cancel out the 3 so you do the opposite of what is say's. For example, if it says 2y-3 add 3 or 2y+3 subtract 3 from both sides.
Step 2: Add 3 to -5 which would be -2
Step 3: Since you're "multiplying" Y to 2 you're going to divide 2 to get Y by itself. So 2/2 cancels out and now you're left with y
Step 4: Divide 2 form -2 and you get -1
Let me know if you have any questions and I hope this helps
Mika is making a beaded necklace. Each bead is a14inch cube.If the necklace is 18 inches long, how many beads will Mika need?
Answer: The answer is 4
Step-by-step explanation: 2 ( g + 5 ) − 2 ( g + 3 ) = 2 ( g + 5 ) − 2 ( g + 3 )
= 2g + 10 - 2g - 6
= 2g -2g + 10 - 6
= 0 + 4
= 4
Hope this helps!
???????????????????plz
Answer:
right right
Step-by-step explanation:
5(6a +1) = 7(4x + 3) w/steps
Answer:
[tex]\frac{15a- 8}{14} = x[/tex]
Step-by-step explanation:
Step 1 - Divide both sides of the equation by 7:
[tex]5(6a + 1) = 7(4x + 3)\\[/tex]
[tex]\frac{5(6a + 1)}{7} = \frac{7(4x + 3)}{7} \\\\\frac{5(6a + 1)}{7} = 4x + 3[/tex]
Step 2 - Subtract 3 from both sides to isolate the 4x:
[tex]\frac{5(6a + 1)}{7} - 3 = 4x + 3 - 3\\\frac{5(6a + 1)}{7} - 3 = 4x[/tex]
Step 3 - Expand equation:
[tex]\frac{5(6a + 1)}{7} - 3 = 4x \\\\\frac{30a + 5}{7} - 3 = 4x[/tex]
Step 4 - Translate -3 into a fraction and add it:
[tex]\frac{30a + 5)}{7} - 3 = 4x\\\frac{30a + 5 + (7 * -3)}{7} = 4x\\\frac{30a + 5 + (-21)}{7} = 4x\\[/tex]
[tex]\frac{30a - 16}{7} = 4x[/tex]
Step 5 - Divide both sides of the equation by 4:
[tex]\frac{\frac{30a - 16}{7}}{4} = \frac{4x}{4}[/tex]
Multiply the two fractions together to simplify:
[tex]\frac{30a - 16}{4 * 7} = \frac{4x}{4}[/tex]
[tex]\frac{30a - 16}{28} = x[/tex]
Step 6 - Simplify by dividing the fraction by 2:
[tex]\frac{(30a \div 2)- ( 16 \div 2)}{28 \div 2} = x[/tex]
[tex]\frac{15a- 8}{14} = x[/tex]
Hope this helps!
A rectangle has an area of 888 square centimeters.
Which of the following could be the rectangle's length and width?
Answer:
i think 222 for eatch side
Step-by-step explanation:
A train travels with a constant speed
of 32 km/h. How long will it take to
travel a distance of 80 kilometers?
Answer:
2.5 hours
Step-by-step explanation:
time = distance / speed
t = 80 / 32
t = 2.5 hours
y=[3/2] x+3.
Pls help me .
Its a graph sum
Answer:
I'm not sure what the question is. Graph?
Step-by-step explanation:
See graph.
Answer:
352
what r u do
789
why nt coming
why r u nt talking
plss hurry For a brainlist Please help:)
Determine the graph of the function f(x)=3^x−4
Answer:
It is D
Step-by-step explanation:
The equation of the horizontal asymptote is y = − 4 .Horizontal Asymptote: y = - 4
u=xk , for x
please help me
Answer:
x=u/k
Step-by-step explanation:
To get x, you would divide by k. Because its x times k. The oppisite is division. This gets you u/k=x
x is equal to u divided by k.
x=u/k
3g + 4y - 8 + 2t + 5
Answer: 3g + 4y - 13 + 2t
Step-by-step explanation:
[tex]3g + 4y - 8 + 2t + 5 \\ 3g + 4y + 2t - 8 - 5 \\ = 3g + 4y + 2t - 3[/tex]
make v the subject of the formula t=4v+3
Step-by-step explanation:
t=4v+3
t-3=4v
(t-3)/4=v
hope this helps you.
spilled $40 into the ratio of 3:7
Answer:
$12/$28
Step-by-step explanation:
Let x and y represent the two amounts of money adding up to $40.
Assume that x is the smaller amount. Then:
x 3
----- = ----- Remembering that x + y = $40, we get x = $40 - y
y 7
amd sp we have
$40 - y 3
-------------- = ------ which, after cross-multiplication, is $280 - $7y = 3y
y 7
Simplifying this, we get $280 = 10 y, so that y must be $28. If y = $28, x must be $40 - $28, or $12.
$12
Then $40, split in the ratio 3/7, is the ratio ----------------
$28
Check: Note that $12 + $28 = $40, as required, and that $12/$28 = 3/7.