Answer:
0, 1/18, and 1/36
Step-by-step explanation:
For i = 2, the probability it lands on 6 is 0, because you cannot sum to 2 with a 6. The same applies to i = 3 thru i = 6.
For the probability that at least one of a pair of fair dice lands on 6 for i = 7, there are only two possible ways, the first roll is a 6 and the second roll is a 7, and the first roll is a 1 and the second roll is a 6. The total amount of ways is 6 * 6 = 36, so the total probability is 1/18. This also applies to i = 8 thru i = 11.
For i = 12, there is only one way to get 12, the first dice lands on 6 and the second dice lands on 6. Assuming the dice are indistinguishable, the probability is 1/36.
The probability that at least one of a pair of fair dice lands on 6, given that the sum of the dice is i, where i ranges from 2 to 12, is 23/12.
We have,
The complementary probability of "at least one die lands on 6" is "neither of the dice lands on 6."
Therefore, you need to find the probability that neither of the dice lands on 6 for each possible sum i, and then subtract that probability from 1 to get the desired probability.
Let's go through the cases:
i = 2 (only possible sum with two dice):
In this case, both dice must show a 1.
The probability of this happening on a fair 6-sided die is
(1/6) * (1/6) = 1/36.
i = 3: The combinations are (1, 2) and (2, 1).
The probability of either happening is 2 * (1/6) * (1/6) = 1/18.
i = 4:
The combinations are (1, 3), (2, 2), and (3, 1).
The probability of any of these happening is 3 * (1/6) * (1/6) = 1/12.
i = 5:
The combinations are (1, 4), (2, 3), (3, 2), and (4, 1).
The probability of any of these happening is 4 * (1/6) * (1/6) = 1/9.
i = 6:
The combinations are (1, 5), (2, 4), (3, 3), (4, 2), and (5, 1).
The probability of any of these happening is 5 * (1/6) * (1/6) = 5/36.
i = 7:
The combinations are (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1).
The probability of any of these happening is 6 * (1/6) * (1/6) = 1/6.
i = 8:
The combinations are (2, 6), (3, 5), (4, 4), (5, 3), and (6, 2).
The probability of any of these happening is 5 * (1/6) * (1/6) = 5/36.
i = 9:
The combinations are (3, 6), (4, 5), and (5, 4).
The probability of any of these happening is 3 * (1/6) * (1/6) = 1/12.
i = 10:
The combinations are (4, 6) and (6, 4).
The probability of either happening is 2 * (1/6) * (1/6) = 1/18.
i = 11:
The combinations are (5, 6) and (6, 5).
The probability of either happening is 2 * (1/6) * (1/6) = 1/18.
i = 12:
The combination is (6, 6).
The probability of this happening is (1/6) * (1/6) = 1/36.
Now, sum up the probabilities for each case:
(1/36) + (1/18) + (1/12) + (1/9) + (5/36) + (1/6) + (5/36) + (1/12) + (1/18) + (1/18) + (1/36)
This simplifies to:
69/36 = 23/12
Thus,
The probability that at least one of a pair of fair dice lands on 6, given that the sum of the dice is i, where i ranges from 2 to 12, is 23/12.
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what is 15/2 into a mixed number
7 1/2.
2 goes into 15 7 times with one left over.
HELP ME PLEASE!!!!!!!!!!!!
Answer:
Your first equation y=1/2(1+0.3)^t is going to be growth
Your second equation y=0.3(0.95)^t is going to be decay
Your third equation y=((1+0.03)^1/2)^2t is going to be growth
your fourth equation y=200(0.73)^t is going to be decay
your last equation y=4(1/4)^t is going to be decay
Step-by-step explanation:
You can find this by graphing each of you equations on desmos
Answer:
Step-by-step explanation:
See attachment
During a job interview, you are asked to rate on a scale of 1 to 5 how happy you are. What type of test is the interviewer giving you
Answer:
Probably how much you want this job, if you say 0, than they are prob gonna assume you dont want to do this job, and you wont do your best. If you say 5, then you do want this job and your excited and youll give your all
Step-by-step explanation:
Questions regarding the level of excitement or happiness of one's self are called mental health or happiness test.
Happiness test are administered to evaluate personal feeling of excitement, hence, it cannot be taken on one's behalf as they are personified information. Happiness test are usually structured as "How happy are you". Hence, they are direct and usually measured using an Ordinal scale.Hence, the type of test on this context is Happiness test.
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Area of the figure 4cm 4cm 12cm and 8cm
8.
Write the equation of the parabola in vertex form.
A. y = –x^2 + 4
B. y = –x^2 + 3
C. y = –(x – 1)^2 + 3
D. y = –x^2 – 4
Answer:
A. y = –x^2 + 4
Step-by-step explanation:
Find the vertex form.
y = − ( x + 0 ) 2 + 4
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Down
Vertex:
( 0 , 4 )
Focus:
( 0 , 15 /4 )
Axis of Symmetry:
x = 0
Directrix:
y
=
17
4
x
y
−
2
0
−
1
3
0
4
1
3
2
0
Use properties to evaluate (-25) HIS O A. – 15 5 O B. 5 C. - OC. 15 O D. 1
Answer:
-15/4
Step-by-step explanation:
Answer: Its - 15/4 or 05/12 but the person above me is correct
Step-by-step explanation:
I don’t know how to do this…
Step-by-step explanation:
f^-1 means the inverse function that finds the x responsible for the creation of a given y (functional result) value.
y = 3x - 1
3x = y + 1
x = 1/3(y + 1)
and now we rename x to y and y to x, so that we get a normal function definition :
y = 1/3(x + 1) = (1/3)x + 1/3
now we create the first derivative d/dx of this function :
y' = 1/3
since both f(x) and f^‐1(x) are line functions with a constant slope, it is not surprising that the first derivative (the function of the slope of the base function) is a constant function.
so, for any value of x (incl. the requested x = 11) d/dx f^-1(x) = 1/3.
therefore also d/dx f^-1(11) = 1/3.
y = 2×sqrt(x)
sqrt(x) = y/2
x = y²/4
again we rename the variables, so that we get a normal function definition for the inverse function :
y = x²/4
the first derivative is :
y' = 2x/4 = x/2
so, d/dx f^-1(6) = 6/2 = 3
Use the inverse function theorem: if f(x) is continuously differentiable at x = a, and given f(a) = b, then f is invertible around x = a, and
[tex]\left(f^{-1}\right)'(b) = \dfrac1{f'(a)}[/tex]
Both the given functions f(x) meet the conditions above. Note that you don't need to actually compute the inverse function itself.
If f(x) = 3x - 1, then f(x) = 11 when
3x - 1 = 11 ⇒ 3x = 12 ⇒ x = 4
Now if f(4) = 11, it follows from the inverse function theorem that
[tex]\left(f^{-1}\right)'(11) = \dfrac1{f'(4)} = \boxed{\dfrac13}[/tex]
since f'(x) = 3.
If f(x) = 2√x, then f(x) = 6 when
2√x = 6 ⇒ √x = 3 ⇒ x = ±9
But note that f(x) is defined only for x ≥ 0, so we must take x = 9. Now if f(9) = 6, the inverse function theorem says
[tex]\left(f^{-1}\right)'(6) = \dfrac1{f'(9)} = \dfrac1{\frac1{\sqrt9}} = \boxed{3}[/tex]
since f'(x) = 1/√x.
mitchels room measures 10 inches by 6 inches on a scale drawing. what are the actual measermets of his room (in feet) of he uses a scale of 1 to 24?
width height
Answer:
20 ft by 12 ft
Step-by-step explanation:
(10 in x 24) / 12 ft = (240 in / 12 ft) = 20 ft
(6 in x 24) / 12 ft = (144 in / 12 ft) = 12 ft
A cylinder has a base radius of 10m and a height of 18m. What is its volume in cubic m, to the nearest tenths place?
Based on the question, the volume of the cylinder is approximately 56,520 cubic meters.
What is the cylinder volume?The formula for the volume of a cylinder is seen as:
V = πr²h
where
V = volume
r = radius of the base
h = height of the cylinder.
Then by Substituting the given values, we will have:
V = π(10m)²(18m)
= π(100m²)(18m)
= 18000π cubic meters
To be able to find the value to the nearest tenths place, we need to use π ≈ 3.14. hence:
V ≈ 18000 × 3.14
= 56520 cubic meters
Therefore, the volume of the cylinder is about 56,520 cubic meters to the nearest tenths place.
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What is the y-intercept of the graph of the equation 6x + 3y = 18?
HELPPPPPP plsssssssssss
Answer:
270°
Step-by-step explanation:
∠ PQR = 90° ( angle in a semicircle )
PRST is a cyclic quadrilateral
The opposite angles in a cyclic quadrilateral are supplementary, sum to 180°
Then
∠ PRS + ∠ PTS = 180°
∠ PQR + ∠ PRS + ∠ PTS = 90° + 180° = 270°
For a 100 ponits : 13+(-19)=
ANSWER:
Answer:
-6
Step-by-step explanation:
Two cubes are of sides 6 inches and 8 inches respectively. Find the ratio of (a) their sides, (b) their areas on one face, (c) their volumes.
Answer:
a. the ratio of the sides is 6: 8, or 3:4
b. the ratio of the surfaces is [tex]\frac{6\times 6}{8\times8}[/tex] or 9:16, the square of the ratio of the sides.
c. the ratio of the volumes is [tex]\frac{6\times6\times6}{8\times8\times8}[/tex] or 27:64, the cube of the ratio of the sides.
What is the total annual dividend received from owning 50 shares of stock A, if Company A issues a $0.10 quarterly dividend to its shareholders?
total annual dividend = [?]
Round to the nearest hundredth.
Answer:
20 dollars
Step-by-step explanation:
.10 x 4 (each quareter) = .40
.40 x 50 = 20.00
= $20.00
PLS SOLVE I WILL GIVE BRAINLIST
Answer:
first one, u can't ride a decimal of a ride
Step-by-step explanation:
y = 7.50 + 2.50x
║3x²+x+5║= 5x²- 3x+ 7
Is this what you needed ?
Find the equation of a line that passes through the point (3,-4) and has a gradient of
-1/2.
Leave your answer in the form
y=mx+c
10. What is the value of c?
Answer:
VALUE OF C = SUCK IT BRO
Step-by-step explanation:
can someone pls give me an example of an area of a trapezium
Answer:
I got this from one of my textbook for the previous years
Hope this helps:)
Would appreciate your help a lot!
Answer:
None of those answers are right. It should be
[tex] - \frac{23}{24} [/tex]
Step-by-step explanation:
You have to find common denominators first. Multiply -5/6 by 4/4 to get -20/24. Multiply 1/8 by 3/3 to get 3/24.
[tex] - \frac{20}{24} = z + \frac{3}{24} [/tex]
Subtract 3/24 from both sides since it is being added.
[tex] - \frac{20}{24} = z + \frac{3}{24} \\ - \frac{3}{24} \: \: \: \: \: \: \: \: \: \: - \frac{3}{24} [/tex]
Since there are two negatives on the left, add the fractions together and keep the negative sign.
[tex] - \frac{23}{24} = z[/tex]
You cannot reduce this fraction.
(334)÷(−212) dive it
What is the value of the expression x² + y² given x = 10 and y = 2?
A. 104
B. -98
C. 89
D. -89
Answer:
A. 104Step-by-step explanation:
Is the equation y + 1 = 5(x + 3) in point-slope form? Justify your answer.
Answer:
The given equation is in point-slope form. The slope is 5 and is seen on the right side before the parentheses. The point is (-3, -1).
Hope this helps! :)
Answer:
Yes
Step-by-step explanation:
The equation y + 1 = 5(x + 3) is in point slope form. Point slope form is y - y1 = m(x - x1). In the given equation the point would be (-3, -1) with a slope of 5.
4/5 x 2/35 I need help pls!
Answer: 8/175
Step-by-step explanation:
Answer: 8/175
Step-by-step explanation: to multiply fractions, multiply both numerators first then the denominators.
4x2=8
35x5=175
Evaluate. (4/5)^3this is a fraction, and an exponent, not 4 divided by 5, please get answer in quickly.
Answer:
[tex]\frac{64}{125}[/tex]
Step-by-step explanation:
[tex]\frac{4}{5} ^{3}[/tex]
To solve this you would cube the numerator and then the denominator:
4³ = 645³ = 125The answer is [tex]\frac{64}{125}[/tex]
Hope this helps!
Harvey is studying the polynomial f(x) = (4x – 3)(x – 3)(x2 +5) and determines that the polynomial has four real roots. Do you agree or disagree with Harvey’s statement? Explain your reasoning.
A.yes because there are 4 roots
B.yes because complex solutions do not matter
C.yes because when I solve he gets 4 x intercepts
D.no because there are two complex solutions
Yes because when I solve he gets 4 x-intercepts. The x-intercept is a point where the y value is zero.
The degree of a polynomial always determines the number of roots such polynomial function will have;
Given the polynomial function studied by Harvey as g(x) = (4x – 3)(x – 3)(x2 +5)
Taking the product of the leading variables
g(x) = (4x – 3)(x – 3)(x2 +5)
g(x) = 4x(x) (x^2)
g(x) = 4x^4
Since the degree of the polynomial is 4, hence the polynomial has four real roots.
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What is the Value of (-0.5) (-7.0)?
the answer is (-0.5) (-7.0)= 3.5
PLEASE ONLY ANSWER IF YOU KNOW THE CORRECT ANSWER!! I APPRECIATE IT THANK YOUUUU
Which relation is a function
Answer: The top right one
Step-by-step explanation: A function means that each input has exactly ONE output, so no x coordinate can have more than one y. The top right is the only one that fits that description. You can check to see if a point is exactly above a given point.
How to find area of a triangle.
Whoever helps me with this I'll give brainliest and extra points! :)
What are the options