Answer:
a.) 0.7063
b.) 23
Step-by-step explanation:
a.)
Let X be an event in which at least 2 students have same birthday
Y be an event in which no student have same birthday.
Now,
P(X) + P(Y) = 1
⇒P(X) = 1 - P(Y)
as we know that,
Probability of no one has birthday on same day = P(Y)
⇒P(Y) = [tex]\frac{365!}{(365)^{n} (365-n)! }[/tex] where there are n people in a group
As given,
n = 30
⇒P(Y) = [tex]\frac{365!}{(365)^{30} (365-30)! } = \frac{365!}{(365)^{30} (335)! }[/tex] = 0.2937
∴ we get
P(X) = 1 - 0.2937 = 0.7063
So,
The probability that at least two of them have their birthdays on the same day = 0.7063
b.)
Given, P(X) > 0.5
As
P(X) + P(Y) = 1
⇒P(Y) ≤ 0.5
As
P(Y) = [tex]\frac{365!}{(365)^{n} (365-n)! }[/tex]
We use hit and trial method
If n = 1 , then
P(Y) = [tex]\frac{365!}{(365)^{1} (365-1)! } = \frac{365!}{(365)^{1} (364)! }[/tex] = 1 [tex]\nleq[/tex] 0.5
If n = 5 , then
P(Y) = [tex]\frac{365!}{(365)^{5} (365-5)! } = \frac{365!}{(365)^{5} (360)! }[/tex] = 0.97 [tex]\nleq[/tex] 0.5
If n = 10 , then
P(Y) = [tex]\frac{365!}{(365)^{10} (365-10)! } = \frac{365!}{(365)^{10} (354)! }[/tex] = 0.88 [tex]\nleq[/tex] 0.5
If n = 15 , then
P(Y) = [tex]\frac{365!}{(365)^{15} (365-15)! } = \frac{365!}{(365)^{15} (350)! }[/tex] = 0.75 [tex]\nleq[/tex] 0.5
If n = 20 , then
P(Y) = [tex]\frac{365!}{(365)^{20} (365-20)! } = \frac{365!}{(365)^{20} (345)! }[/tex] = 0.588 [tex]\nleq[/tex] 0.5
If n = 22 , then
P(Y) = [tex]\frac{365!}{(365)^{22} (365-22)! } = \frac{365!}{(365)^{22} (343)! }[/tex] = 0.52 [tex]\nleq[/tex] 0.5
If n = 23 , then
P(Y) = [tex]\frac{365!}{(365)^{23} (365-23)! } = \frac{365!}{(365)^{23} (342)! }[/tex] = 0.49 [tex]\nleq[/tex] 0.5
∴ we get
Number of students should be in class in order to have this probability above 0.5 = 23
Maya took a taxi from her house to the airport. The taxi company charged a pick-up
fee of $1.90 plus $4.50 per mile. The total fare was $24.40, not including the tip.
Write and solve an equation which can be used to determine m, the number of miles
in the taxi ride.
Solve the equation -10(d+1)=-14 I ready, please help ASAP!!
Answer:
d = 0.4
Step-by-step explanation:
-10 (d + 1) = - 14
=> -10d - 10 = -14
=> -10d = -14 + 10
=> -10d = -4
=> 10d = 4
=> d = 4 / 10
=> d = 0.4
Hope it helps :)
Please mark my answer as the brainliest
A math student has a plan to solve the following system by the elimination method. To eliminate the x-terms, he wants to multiply the top equation by 7. What
should he multiply the second equation by so that when he adds the equations, the x-terms are eliminated?
-3x-7--56
-7x+10y - 1
Answer:
-3
Step-by-step explanation:
7(-3x-7y-56)
-21x-49y-392
-3(-7x+10y-1)
21x-30y+3
because the eq. multiplied by 7 is negative, the second eq mus be positive in order to eliminate the x variable. this is why we multiply by a (-). by multiplying the second eq by 3, both eq. will result in a coefficient of 21. one positive one negative allowing the x variable to be eliminated from the problem.
how do you simplify 4 ^2 × 4^5
Answer:
4^7
Step-by-step explanation:
4^2 + 4^5
=> 4^ 2+5
=> 4^7
Answer:
Step-by-step explanation:
find the value 4/25 1/2
Answer:
2/5
Step-by-step explanation:
we know any number raised to power 1/2 means that we need to find the square root of that number.
(4/25)^1/2= =√(4/25)√4/√25
√4=2
√25=5
√(4/25=2/5
(hope this helps can i plz have brainlist :D hehe)
answer and show work and ill give brainliest, Steven has one bag that contains three table-tennis balls numbered 1, 2, and 3. He also has a second bag that contains four table-tennis balls lettered A, B, C, and D.
Answer:
B
Step-by-step explanation:
Assuming Part A is the situation where the bags aren't merged, the probability of drawing a "1" followed by a "B" is (1/3)(1/4) or 1/12. This is because you have a 1/3 chance of getting a "1" and a 1/4 chance of getting a "B".
Now if we merge the bags, we have a 1/7 chance of getting a "1". We then have a 1/6 chance of getting a "B". This is because after we complete the first draw, the bag only has 6 remaining not 7. This gives us a probability of (1/7)(1/6) or 1/42.
So we know the probability will change so C is wrong. In both scenarios, we draw two balls anyways so A is wrong.
This leaves B, which is supported by the reasoning presented above.
Can someone help? Please I need it quickly
Answer:
Step-by-step explanation:
ok so the answer for the one after 12x is 8x I think but it would only make sens i dunno the answer to the fraction
Answer and Step-by-step explanation:
Let's solve your equation step-by-step.
−2(x+5)=4
Step 1: Simplify both sides of the equation.
−2(x+5)=4
(−2)(x)+(−2)(5)=4(Distribute)
−2x+−10=4
−2x−10=4
Step 2: Add 10 to both sides.
−2x−10+10=4+10
−2x=14
Step 3: Divide both sides by -2.
-2x/2 = 14/-2
x equals...
x=-7
How do you turn 4(m+3+5m) into 12(2m+1)
Plz help
Answer:
4(m+3+5m)=
4(6m+3)
factor out the three
4x3(2m+1)
12(2m+1)
Step-by-step explanation:
4(m+3+5m)=
4(6m+3)
factor out the three
4x3(2m+1)
12(2m+1)
This is midpoints geometry I need help soon.
Answer:
x=4.5
Step-by-step explanation:
PR=28
PQ= 2x+5
Require
Find X
One number is five less than another. Their sum is fifteen. Find the numbers.
Answer:
THE NUMBERS ARE 10 AND 5
Step-by-step explanation:
LET THE ANOTHER NUMBER BE X THEN
ONE NUMBER = X - 5
BY THE QUESTION
X - 5 + X = 15
2X = 15 + 5
2X = 20
X = 10
X - 5 = 10 - 5 = 5
Answer:
hi 5 and 10 is required no.
let no. be x
another no.be x+5
Step-by-step explanation:
sum=15
x+x+5=15
2x=15-5
2x=10
x=10/2=5
x+5=5+5=10
Write an expression to show k less than 10
Step-by-step explanation:
"Write an expression to show k less than 10"
"less than" means that the number is being subtracted from a different number.
This means that "10" is being subtracted from "k"
Thus,
k - 10 is the appropriate expression for the statement, "k less than 10"
ANSWER: k - 10
The coordinate grid shows the plot of four equations:
A coordinate grid is shown from negative 12 to positive 12 on the x axis and also on the y axis. Line A passes through the ordered pairs negative 3, 4 and 9, negative 2. Line B passes through the ordered pairs 2, 8 and 8, negative 8. Line C passes through the ordered pairs negative 3, negative 4 and 4, 6. Line D passes through the points 2, negative 2 and 5 and 6.
Which set of equations has (3, 5) as its solution? (1 point)
A. A and D
B. C and D
C. A and C
D. B and C
Answer:
D. B and C
Step-by-step explanation:
The set of equations that has the (3, 5) as a solution would be the two lines that intercepts at the point where when x = 3, y = 5.
From the graph shown, line B and line C intercepts at the point where x = 3, and y = 5.
Therefore, B and C has (3, 5) has its solution.
Answer:
B and C.
Step-by-step explanation:
Find the value of y
95
15
19
85
Answer:
im only doing this bc im forced to
Answer:
19
Step-by-step explanation:
180-85 = 5y
5y = 95
y = 19
Which customary unit would you use to measure the amount of flour in
a cake recipe?
1. cups
2. feet
3. fluid ounces
4. inches
5. ounces
Answer:
cups !!
Step-by-step explanation:
What is BD? please help bru i keep getting trollers
Answer:
BD=13
(This must not be drawn to scale)
Step-by-step explanation:
You have to use the Angle Bisector Theorem to get a ratio.
12/x=27/(x+5)
cross multiply
12(x+5)=27x
12x+60=27x
60=27x-12x
60=15x
60÷15=x
x=4
BD=x+x+5=4+4+5=13
Help me with number 8 plz
Answer:
c
Step-by-step explanation:
u welcome my dude
pls solve these i beg u!!!!
Answer:
1) A 4
2) B 96
3) C 7
4) C -22
5) B 16p²+24p+9
Step-by-step explanation:
1) 96÷6=16. √16=4 (A)
2) 2x6(5+3)=96 (B) (assuming 6 is the height)
3) 175÷25=7 (C)
4) 2(-1-3-7)=2(-11)=-22 (C)
5) (4p+3)(4p+3)=16p²+12p+12p+9=16p²+24p+9(B)
X^3+9X^2–25X–33=0
Find The root of X??
Answer:
x=-11, -1, and 3
Step-by-step explanation:
x^3+9x^2-25x-33=0
There are formulas to solve cubics, but that probably is not the way you are expected to go. Here is a trial and error approach that works in this case.
Assume that the cubic can be factored and that the roots are r1, r2, and r3. Then the factored form is
(x-r1)(x-r2)(x-r3)=0
This shows that the constant must equal the product of the roots.
(r1)(r2)(r3)=-33
One possibility is that the roots are integers. In this case, a factor of 33 might work. Prime factorization of 33 gives 3 and 11. Try 3. Then (x-3) is a factor.
Divide the cubic by (x-3). It works. the result is
x^2+12x+11
This has factors of (x+11) and (x+1). Therefore, the roots are 3, -1, and -11
What is the image of the point (5, -9) after a rotation of 180° counterclockwise
about the origin?
Answer:
(-5, 9)
Step-by-step explanation:
for a 180 degree rotation the points move from (x, y) to (-x, -y)
Hello, happy Friday, I am just here with some geometry questions.
Please only answer this if you know the answer. If you have a comment, please add it to the comment box. Only answer the question if you can explain your answer and why you think it is accurate. Thanks, good luck!
Show your work!
Answer:
[tex]x=12[/tex]
Step-by-step explanation:
Notice that the segment bisects the obtuse angle.
Then by the Angle Bisector Theorem:
[tex]\displaystyle \frac{x-4}{6}=\frac{x}{9}[/tex]
Cross-multiply:
[tex]6(x)=9(x-4)[/tex]
Distribute:
[tex]6x=9x-36[/tex]
So:
[tex]-3x=-36[/tex]
Therefore:
[tex]x=12[/tex]
HELP...The volume of a rectangular prism is 36x^6y^8. The length of the prism is 4x^3y^5, and the width of the prism is 3xy^2. What is the height of the prism? Write a justification of your result. v=lwh
Answer:
[tex]H = 3x^2y[/tex]
Step-by-step explanation:
Given
[tex]V = 36x&^6y^8[/tex]
[tex]L = 4x^3y^5[/tex]
[tex]W = 3xy^2[/tex]
Required
Find the height of the prism
Volume (V) is calculated as:
[tex]V =LWH[/tex]
Substitute values for V, L and W
[tex]36x^6y^8 =4x^3y^5 * 3xy^2 * H[/tex]
Make H the subject
[tex]H = \frac{36x^6y^8}{4x^3y^5 * 3xy^2}[/tex]
[tex]H = \frac{36x^6y^8}{4*3x^3*x*y^5y^2}[/tex]
[tex]H = \frac{36x^6y^8}{12x^4*y^7}[/tex]
Divide:
[tex]H = 3x^{6-4}y^{8-7}[/tex]
[tex]H = 3x^2y[/tex]
The height of the prism is: [tex]3x^2y[/tex]
A gas station sells 1600 gallons of gasoline per hour if it charges $ 2.70 per gallon but only 900 gallons per hour if it charges $ 2.95
per gallon. Assuming a linear model
(a) How many gallons would be sold per hour of the price is $ 2.90 per gallon?
Answer:
(b) What must the gasoline price be in order to sell 1300 gallons per hour?
Answer:
Answer:
Look just at finding the linear model. Two points. Use price per gallon for x and gallons per hour sold for y. Your two points (x,y) are (2.15,1600) and (2.55,800).
Slope m=%281600-800%29%2F%280.15-0.55%29
m=800%2F0.40
m=2000
Using point-slope form for a line, and the lower-y point,
y-800=2000%28x-2.55%29
highlight%28y=2000%28x-2.55%29%2B800%29
Can someone please answer and EXPLAIN ILL MARK BRAINLIEST
Answer:
adjust city gallons to 3 gallons and freeway to 7 gallons
make your line in the chart:
3 | 10-3 = 7 | 3(25) = 75 | 7(40) = 280 | 75 =280 =355 | 355 | yes
Step-by-step explanation:
x = city gallons
y = freeway gallons
x+y = 10 then y = 10-x
25x+40y = 355
substitute for y
25x+40(10-x) = 355
25x+400-40x = 355
-15x+400 = 355
subtract 400 from each side
-15x = -45
divide both sides by -15
-15x/-15 = -45/-15
x = 3 gallons
y = 7 gallons
Answer:
hshjs
Step-by-step explanation:
kzkksk
Can you put this in order least to greatest?
Answer:
7.6,7.45,7.48,7.431,7.504,7.536
this us your answer
Answer:
Least to greatest order:
7.431 < 7.45 < 7.48 < 7.504 < 7.536 < 7.6
Greatest to least order:
7.6 > 7.536 > 7.504 > 7.48 > 7.45 > 7.431
Please help and quick
4 and 2 because she is the acrooss line
Victor saved $90 to buy a bicycle. He has saved 60% of the cost of the bicycle. What is the total cost of the bicycle?
Answer:
$150
Step-by-step explanation:
90/60=1.5 tthat means 1% of the bike costs $1.50. You ar trying to find 100% so multiply by 100. 1.5x100=150
Answer:
$150
Step-by-step explanation:
You can divide the 90 by 0.60 to get 150. You can check again by multiplying 150 by 0.6 to get 90, which Victor has 60% of the total (being 150)
Hope this helps!
Could someone please explain how to get the answer?
the missing side of the right triangle is 10.568
Pythagorean theorem formulaa² + b² = c²
Which c is the hypotenuse part of triangle.
Known thata = 5.2
b = 9.2
c = ...?
so the missing part is c.
Way to calculatea² + b² = c²
5.2² + 9.2² = c²
111.8 = c²
c = √111.8
c = 10.568
#Moderators please don't be mean, dont delete my answers just to get approval from your senior or just to get the biggest moderation daily rank.
A convex octagon has interior angles with measures (x + 55). (3x + 20), 4x°. (4x - 10). (6x - 55) (3x + 52). 3.xº, and (2x + 30). Find
the value of x.
Answer:
mmmmmmmmkkkkkkkkkkkkkkkkkk
What is the GCF for the following terms?
48p^4q^2 and 6p^2n^4
Please help, thank you!
Answer:
6p^2
Step-by-step explanation:
48p^4q^2=2×2×2×2×3×p×p×p×p×q×q
6p^2n^4=2×3×p×p×n×n×n×n
GCF=2×3×p×p
=6p^2
Help
===============
Answer:
x=140°
Step-by-step explanation:
to get the exterior angle add the 2 given sides 72 and 68 to find the last interior angle
72°+68°=140°
all sums of interior angles should equal 180° so
180°-140=40°
take 40° and subtract is by 180°
180°-40°=140°
(A flat line is 180°)
so x=140°
Answer:
x = 140°
Step-by-step explanation:
All angles in a trinagle add up to 180 so to find out the missing angle, subtract 72 and 68 from 180.
180 - 72 - 68 = 40
Straight angles are equal to 180, so subtract 40 from 180.
180 - 40 = 140
x = 140°