Here are seven tiles Tom takes a tile at random. He does not replace the tile. Tom then takes at random a second tile. a) Calculate the probability that both tiles Tom takes have the number 1 on them. b) Calculate the probability that the number on the second tile Tom takes is greater than the number on the first tile he takes.
Answer:
a) 1/21
b) 8/21
Complete question:
There are seven tiles:
1,1,3,3,3,5,5
Tom takes a tile at random. He does NOT replace the tile.
Tom then takes another tile at random.
a) Calculate the probability that both tiles Tom takes have the number 1 on them. b) Calculate the probability that the number on the second tile Tom takes is greater than the number on the first tile he takes.
Step-by-step explanation:
Total number of tiles = 7
Let Probability of having number 1 on the tiles = Pr (having 1)
Pr (having 1) = (number of times 1 appears on tiles)/(total number of tiles)
Number of times 1 appears on tiles = 2
Pr (having 1) = 2/7
Two tiles are drawn without replacement:
Probability of both tiles having number 1 on them = Pr (having 1 for both 1st and 2nd time)
= Pr (having 1) × Pr (having 1)
Since it is without replacement, the numbers in the second pick would reduce by 1 in both the numerator and denominator since we are picking same number. That is from 7 to 6 and from 2 to 1 to reflect that it was replaced.
= 2/7 × 1/6
= 2/42
Probability of both tiles having number 1 on them = 1/21
b) If 1st tile = 1, the second tile could be = 3 or 5
The pairs = Pr(1 and 3) and Pr(1 and 5)
Where Pr = probability
The probability is still without replacement. For both probability, the numbers in the second pick would reduce by 1 in the denominator since we are picking different numbers. That is from 7 to 6
Number of times 3 appears on tiles = 3
Number of times 5 appears on tiles = 2
Pr(1 and 3) = (2/7 × 3/6) = 1/7
Pr(1 and 5) = (2/7 × 2/6) = 2/21
If 1st tile = 3, the second tile = 5
Pr(3 and 5) = (3/7 × 2/6) = 1/7
If 1st tile = 5, the second tile = 0 (no number is greater than 5
Pr(5 and 0) = 0
Probability that the number on the second tile Tom takes is greater than the number on the first tile he takes = Pr(1 and 3) + Pr(1 and 5) + Pr(3 and 5) + Pr(5 and 0)
= 1/7 + 2/21 + 1/7 + 0
= (3+2+3)/21 = 8/21
Probability that the number on the second tile Tom takes is greater than the number on the first tile he takes = 8/21
What is the solution to the following equation? 4(3x − 11) + 23 = 5x − 14 a 0 b 1 c 10 d 14
Answer:
b 1
Step-by-step explanation:
Let $z$ and $w$ be complex numbers satisfying $|z| = 4$ and $|w| = 2$. Then enter in the numbers\[|z+w|^2, |zw|^2, |z-w|^2, \left| \dfrac{z}{w} \right|^2 \]below, in the order listed above. If any of these cannot be uniquely determined from the information given, enter in a question mark.
Answer:
a) |z+w|² cannot be uniquely determined from the information provided.
b) |zw|² = [|z| × |w|]² = (4×2)² = 64.
c) |z+w|² cannot be uniquely determined from the information provided.
d) |z/w|² = [|z|/|w|]² = (4/2)² = 4
Step-by-step explanation:
z & w are complex numbers with magnitudes
|z| = 4
|w| = 2
We are the told to find
|z + w|²
|zw|²
|z - w|²
|z/w|²
Let the complex numbers be
z = x + iy
w = a + ib
|z| = √(x² + y²) = 4
|w| = √(a² + b²) = 2
|z|² = x² + y² = 16
|w|² = a² + b² = 4
z+w = (x + iy) + (a + ib) = (x + a) + i(y + b)
|z+w|² = (x + a)² + (y + b)² = x² + 2ax + a² + y² + 2by + b²
= (a² + b²) + (x² + y²) + 2ax + 2by
= |w|² + |z|² + 2ax + 2by
= 4 + 16 + 2ax + 2by
= 20 + 2(ax + by)
This cannot be determined from the information provided.
zw = (x + iy)(a + ib) = ax + i(bx + ay) - by
= (ax - by) + i(bx + ay)
|zw|² = a²x² + b²y² - 2abxy + b²x² + a²y² + 2abxy
= a²x² + b²y² + b²x² + a²y²
= a²(x² + y²) + b²(x² + y²)
= (a² + b²)(x² + y²)
= |w|² × |z|²
= 4×16
= 64
c) z-w = (x + iy) - (a + ib) = (x - a) + i(y - b)
|z-w|² = (x - a)² + (y - b)²
= x² - 2ax + a² + y² - 2by + b²
= (a² + b²) + (x² + y²) - 2ax - 2by
= |w|² + |z|² - 2ax - 2by
= 4 + 16 - 2ax - 2by
= 20 + 2(ax + by)
This cannot be determined from the information provided.
d) z/w = (x + iy)/(a + ib)
Rationalizing by multiplying numerator and denominator by (a - ib)
(z/w)= [(x + iy)(a - ib)/(a + ib)/(a - ib)]
= [ax - by + i(ay - bx)]/(a² + b²)
|z/w|² = [(ax + by)² + (ay - bx)²]/(a² + b²)²
= [a²x² + b²y² + 2abxy + b²x² + a²y² - 2abxy]/(a⁴ + b⁴ + 2a²b²)
= [a²x² + b²y² + b²x² + a²y²]/[(a² + b²)² - 2a²b² + 2a²b²]
= [(a² + b²)(x² + y²)]/[(a² + b²)²]
= [(x² + y²)/(a² + b²)]
= |z|²/|w|²
= (4/2)²
= 4
Hope this Helps!!!
if f(x) = 2x+1/x-4 what is the value of f^-1(3)
Answer:
f^-1(3) = 1.719 or f^-1(3) = 0.149
Step-by-step explanation:
for inverse function x and y coordinates are flipping so graph the function and find for what x - coordinate y- coordinate = 3
in case that f(x) = [tex]2x + \frac{1}{x-4}[/tex] than f^-1(3) = 1.719
in case that f(x) = [tex]2x + \frac{1}{x} -4[/tex] than f^-1(3) = 0.149
Answer: B
B (19/11) when divided = 1.72 repeat
of all the options given, this is the closest to the above answer.
Find the perimeter of a rectangle whose length is (4a+b)cm and width (a+6)cm
Answer:
P = 10a +2b+12
Step-by-step explanation:
P = 2 (l+w) for a rectangle
P = 2 ( 4a+b + a+6)
Combine like terms
P = 2(5a+b+6)
Distribute
P = 10a +2b+12
Answer:
Given below
Hope it helps
Step-by-step explanation:
Perimeter= 2(l+b)
= 2(4a+b+a+6)
= 2(5a+b+6)
= 10a+2b+12 cm^2
b2 - 7b + 12 = 0
Factored equation: ( ) ( ) = 0
ANSWERS: b = ____, and b = ____
Answer: (b - 4)(b - 3); b = 4 and 3
Step-by-step explanation:
ima assume these are exponents since you didnt care to correctly write the equation.
What two numbers multiply to equal 12, but add to equal -7? That's -4 and -3
So the factored form of this trinomial is (b - 4)(b - 3) = 0. Make each of these expressions equal to 0 in order to get your answer.
What is a real life example for an integer
Answer:
Some examples of integers are -1, 0, and 1.
Which is the value of this expression when p=-2 and q=-1?
A. -4
B. -1/16
C. 1/16
D. 4
Answer:
D. 4
Step-by-step explanation:
[tex] [(p^2) (q^{-3}) ]^{-2}.[(p)^{-3}(q)^5] ^{-2}\\\\
=[(p^2) (q^{-3}) \times(p)^{-3}(q)^5 ]^{-2}\\\\
=[(p^{2}) \times(p)^{-3} \times (q^{-3}) \times(q)^5 ]^{-2}\\\\
=[(p^{2-3}) \times (q^{5-3}) ]^{-2}\\\\
=[(p^{-1}) \times (q^{2}) ]^{-2}\\\\
=(p^{-1\times (-2)}) \times (q^{2\times (-2) }) \\\\
=p^{2}\times q^{-4} \\\\
= \frac{p^2}{q^4}\\\\
= \frac{(-2)^2}{(-1)^4}\\\\
= \frac{4}{1}\\\\
= 4[/tex]
In how many ways can you
select a group of 6 friends to
invite over from a group of
22 friends?
Answer:74613
Step-by-step explanation:
n!/r!(n-r)!
22!/6!(22-6)!
=74613
Can you please help me
Answer:
complementary angle: 63
supplementary angle: 153
Step-by-step explanation:
Complementary angles mean angles that add up to 90. Therefore 90-27=63
Supplementary angles are angles that add up to 180. Therefore 180-27=153
The lengths of a lawn mower part are approximately normally distributed with a given mean Mu = 4 in. and standard deviation Sigma = 0.2 in. What percentage of the parts will have lengths between 3.8 in. and 4.2 in.? 34% 68% 95% 99.7%
Answer:
b) 68%
The percentage of the parts will have lengths between 3.8 in. and 4.2 in
P( 3.8 ≤ x ≤ 4.2) = 0.6826 = 68 %
Step-by-step explanation:
Let 'X' be the normally distributed
mean 'μ'= 4 inches
standard deviation 'σ' = 0.2 inches
Case(i):-
when x₁ = 3.8 inches
[tex]Z_{1} = \frac{x_{1}-mean }{S.D} = \frac{3.8-4}{0.2} = -1[/tex]
Case(ii):-
when x₂= 3.8 inches
[tex]Z_{2} = \frac{x_{2}-mean }{S.D} = \frac{4.2-4}{0.2} = 1[/tex]
The probability of the parts will have lengths between 3.8 in and 4.2 in
[tex]P( 3.8\leq x\leq 4.2) = P(-1\leq z\leq 1)[/tex]
= P(Z≤1) - P(Z≤-1)
= 0.5 +A(1) -(0.5-A(1)
= 2 A(1)
= 2×0.3413
= 0.6826
Conclusion:-
The percentage of the parts will have lengths between 3.8 in. and 4.2 in
P( 3.8 ≤ x ≤ 4.2) = 0.6826 = 68 %
Answer:
B
Step-by-step explanation:
E2020
let f be defined as follows f(x)=4x find f^-1(x)
Answer:
So this is the inverse function
Please say ---- solve for the inverse f(x)
instead of ---- solve for f^-1(x)
x/4 division is the opposite of multiplication
so instead of multiplying by 4 we divide by 4
:)
Thanks for the question, Im working up to get a brainly answer and Master Answerer.
:)
Step-by-step explanation:
Solve for x 3x - 5 = 2x + 6.
01
O-1
O 11
0-11
Answer:
X= 11
Step-by-step explanation:
Move constant to the right side and change its sign
Mitchell's family is slow cooking 2 3/4 pounds of meat. The recipe says to cook the meat 1 1/2 nours per pound,
How long should Mitchell's family cook the meat?
A 1 5/6
B. 2 3/8
C 4 1/ 8
D. 4 1/4
Answer:
C
Step-by-step explanation:
Multiply the 1.5 hours per pound by 2.75 pounds and we get 4.125 hours or 4 1/8
Answer:
C: 4 1/8
Step-by-step explanation:
i took the quiz
If
x = 3,
y = -5 and z-7, find
x +yz +xyz.
Answer:
143
Step-by-step explanation:
Since the values of x y and z are given
Substitute the value in the polynomial, so it'll become,
x+yz+xyz
= (3)+(-5)*(-7)+(3)*(-5)*(-7)
= 3+35+(3)*(-7)*(-5)
{Two negatives when multiplied becomes positive}
=3+35+3*35
= 3+35+105
=143
What’s the answer ??? Help
Answer:
It's B. (2x+5) (x+4)
Answer:
b
Step-by-step explanation:
2x²+13x+20
You can just try all the answers if you'd like and see which one equals 2x²+13x+20.
Using FOIL for all of them:
a. (2x-5)(x-4) = 2x²-8x-5x+20 = 2x²-13x+20
b. (2x+5)(x+4) = 2x²+8x+5x+20 = 2x²+13x+20
c. (2x+2)(x+10) = 2x²+20x+2x+20 = 2x²+22x+20
d. is obviously not correct since we already have an answer.
Our answer is b. (2x+5)(x+4)
A closed box has a square base with side length feet and height feet given that the volume of the box is 34 ft.³ express the surface area of the box in terms of length only
Answer:
[tex]\dfrac{2s^3+136}{s}[/tex]
Step-by-step explanation:
Let the side length of the square base =s feet
Let the height of the box = h
Given that the volume of the box = [tex]34$ ft^3[/tex]
Volume of the box =[tex]s^2h[/tex]
Then:
[tex]s^2h=34$ ft^3\\$Divide both sides by s^2\\h=\dfrac{34}{s^2}[/tex]
Surface Area of a Rectangular Prism =2(lb+bh+lh)
Since we have a square base, l=b=s feet
Therefore:
Surface Area of our closed box[tex]= 2(s^2+sh+sh)[/tex]
[tex]S$urface Area= 2s^2+4sh\\Recall: h=\dfrac{34}{s^2}\\$Surface Area= 2s^2+4s\left(\dfrac{34}{s^2}\right)\\=2s^2+\dfrac{136}{s}\\$Surface Area in terms of length only=\dfrac{2s^3+136}{s}[/tex]
√10·√8 is this equal to the √80?
Answer: yes
Step-by-step explanation:
They are both equal to 4/5
Answer each question and explain your reasoning.
How long is 75% of 60 minutes?
Answer:
45 minutes
Step-by-step explanation:
75% is the same as [tex]\frac{3}{4}[/tex]. This means that we can multiply 60 by [tex]\frac{3}{4}[/tex] to find 75% of 60.
[tex]60*\frac{3}{4} \\\\\frac{180}{4} \\\\\frac{90}{2}\\\\45[/tex]
Answer:
45 minutes
Step-by-step explanation:
Of means multiply
75% * 60
Change to a decimal
.75 * 60
45
45 minutes
the area that lies between Z= - 0.42 and Z= 0.42 is
Answer:
the answer is 0.84
Step-by-step explanation:
assume the two numbers are on a number line and take the absolute value of their difference
ANSWER THIS AND I WILL FRIEND YOU!!! What is x? 2x(3+4x) *2 -5
Answer:
Step-by-step explanation:
[tex]2*(3+4x) *2 -5\\6+8x*2-5\\16x =-6-5\\16x = -11\\x = 11/16[/tex]
How many cubes eith side lengths of 1/4 cm does it take to fill the prism? Please help
Step-by-step explanation:
In order to find Volume for a rectangle use the formula: L * W * H
2 1/4 * 3/4 * 1 1/4 = 2 7/64
A cube with the side lengths of 1/4: 1/4 * 1/4 * 1/4 = 1/64
Divide 1/64, by the prisms volume, 2 7/64 to get 135.
I'm not sure if this is right, but I hope that helps! :)
Find the sum of the first 44 terms of the following series, to the nearest integer. 10, 14,18,...
Answer:
4224
Step-by-step explanation:
Here, we want to calculate the sum of the first 44 digits
Term a which is first digit is 10
common difference which is difference of terms = 14-10 = 18-14 = 4
Now the nth term of an arithmetic sequence is
a + (n-1)d
44th term means n = 44
10 + (44-1)4
10 + 43(4)
10 + 172 = 182
To find the sum, we use the formula
Sn = n/2[a + L]
where a is the first term and L is the 44th term
Sn = 44/2 (10 + 182)
Sn = 22(192)
Sn = 4,224
The height, h in feet, a ball with reach when thrown in the ais is a function of time, t, in seconds,given by the equation h(t)=-16t2+35t+10. Find, to the nearest tenth, the maximum height, in feet, the ball will reach. The time when it reached its maximum height. How many seconds after the ball is thrown it will hit the ground?
Answer:
The maximum height the ball will reach is 29,141 feet.
The time when it reached its maximum height is 1.094 seconds.
2,443 seconds after throwing the ball, it will touch the ground.
Step-by-step explanation:
The function h (t) = - 16t² + 35t + 10 is a quadratic function of the form f (x) = ax² + bx + c, where a = -16, b = 35 and c = 10. To calculate the maximum height, you must then find the maximum of the function. In other words, Quadratic functions have a maximum (if a <0) or a minimum (if a> 0). This point is the vertex of the parabola.
The vertex coordinate on the x axis can be calculated by:
[tex]x=\frac{-b}{2*a}[/tex]
The value of the vertex on the y axis is obtained by substituting the value of "x vertex" in the function f (x), that is, by calculating f ([tex]\frac{-b}{2*a}[/tex]).
In this case, where h ([tex]\frac{-b}{2*a}[/tex]) is the maximum height:
[tex]t=\frac{-b}{2*a}=\frac{-35}{2*(-16)} =1.09375[/tex]≅ 1.094 seconds
So: h(1.094)= -16*1.094² + 35*1.094 + 10
h(1.094)=29.151
The maximum height the ball will reach is 29,141 feet.
The time when it reached its maximum height is 1.094 seconds.
To calculate the number of seconds after the ball is thrown it will hit the ground, you must calculate the roots of the quadratic function. For this you must apply:
[tex]x1,x2=\frac{-b+-\sqrt{b^{2}-4*a*c } }{2*a}[/tex]
where x1, x2 are the two roots of the function f(x)=a*x² +b*x + c
In this case:
[tex]t1,t2=\frac{-35+-\sqrt{35^{2}-4*(-16)*10 } }{2*(-16)}[/tex]
Solving, you get t1=-0.256 and t2=2.443
Since the time cannot be negative, 2,443 seconds after throwing the ball, it will touch the ground.
In a grade 11 class, 40% of the students are taking Geography, 30% are taking History and 10% are taking both. If 40 students are enrolled in the grade 11 class, how many students are taking neither Geography or History?
I put the wrong answer
Find the simplest pattern and fill in the missing number. 45, 30, 18, 9, ... 0
Answer:
3 the patten is the previous subtracted about decrease by 3
Step-by-step explanation: the pattern decrease the number subtracted by 3 so it starts with 15 and goes to 12 then to 9 so the last one would be six and 9 - 6 = 3
Scheels received a shipment of 400 water bottles. 30% were yellow.
How many yellow water bottles were in the shipment?
_________________________________
Solution,
30% of 400
= 30/100*400
=120
120 yellow water bottles were in the shipment.
Hope it helps
Good luck on your assignment
__________________________________
4x2 + 25y2
factor the following
Answer:
see explanation
Step-by-step explanation:
This polynomial is irreducible, that is cannot be factored.
4x² + 25y² ← is a prime polynomial
Answer:
1, the polynomial itself
Step-by-step explanation:
This is a prime polynomial since the terms have no common factor. The only factors it has are 1 and 4x2+25y2 (the number itself)
Find the surface area.
Please answer correctly !!!!!!! Will mark brainliest !!!!!!!!!!!!
Answer:
f⁻¹(-2)=3
f⁻¹(1)=0
Step-by-step explanation:
inverse function flips x any coordinate into y and x
