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Hatshy [7]
3 years ago
15

2. Find the theoretical probability of not rolling a 4.

Mathematics
1 answer:
mezya [45]3 years ago
8 0

Answer:If a die is rolled once, determine the probability of rolling a 4: Rolling a 4 is an event with 1 favorable outcome (a roll of 4) and the total number of possible outcomes is 6 (a roll of 1, 2, 3, 4, 5, or 6). Thus, the probability of rolling a 4 is 1/6.

If a die is rolled once, determine the probability of rolling at least a 4: Rolling at least 4 is an event with 3 favorable outcomes (a roll of 4, 5, or 6) and the total number of possible outcomes is again 6. Thus, the probability of rolling at least a 4 is 3/6 = 1/2

Step-by-step explanation:For example, when a die is rolled, the possible outcomes are 1, 2, 3, 4, 5, and 6. In mathematical language, an event is a set of outcomes, which describe what outcomes correspond to the "event" happening. For instance, "rolling an even number" is an event that corresponds to the set of outcomes {2, 4, 6}. The probability of an event, like rolling an even number, is the number of outcomes that constitute the event divided by the total number of possible outcomes. We call the outcomes in an event its "favorable outcomes".

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Consider the vectors a =3i +j −k, b =i +j +4k, c=i +3j +k, d =−i −3j +k, g =−3i −j +k. Which pairs (if any) of these vectors are
11111nata11111 [884]

Answer:

a and b are perpendicular to each other, as are b and d, b and g

Step-by-step explanation:

To check whether two vectors are perpendicular to each other, we need the angle between these vectors to be 90 degrees.

We can find the angle between to vectors a and b from the following relation:

The cosine of the angle \theta between two vectors is equal to the dot product of this vectors divided by the product of vector magnitude.

So

cos(\theta) = \frac{a.b}{|a||b|}

cos(90) = 0, so when the dot product between vectors a and b is 0, it means that these vectors are perpendicular to each other.

Now, for your exercise, let's compute the dot product between these vectors.

-----------

a.b = (3,1,-1).(1,1,4) = 3+1-4 = 0

So a and b are perpendicular to each other.

------------

a.c = (3,1,-1).(1,3,1) = 3+3-1 = 5

a and c are not perpendicular to each other.

--------------

a.d = (3,1,-1).(-1,-3,1) = -3-3-1 = -7

So not perpendicular

---------------

a.g = (3,1,-1).(-3,-1,1) = -9-1-1 = -11

Not

-----------------

b.c = (1,1,4).(1,3,1) = 1+3+4 = 8

Not

------------------

b.d = (1,1,4).(-1,-3,1) = -1 -3 +4 = 0

b.d = 0, so b and d are perpendicular to each other

--------------------

b.g = (1,1,4).(-3,-1,1) = -3-1+4 = 0

b.g = 0, perpendicular

---------------------

c.d = (1,3,1).(-1,-3,1) = -1-9+1 = -9

No

-----------------------

c.g = (1,3,1).(-3,-1,1) = -3-3+1 = -5

No

------------------------

d.g = (-1,-3,1).(-3,-1,1) = 3+3+1 = 7

No

7 0
3 years ago
Write the equation that represents the line shown.
Semmy [17]

Answer:

y =  - x + 2

Step-by-step explanation:

y = mx + b

y =  \frac{ - 2}{2} x + 2

y =  - x + 2

3 0
3 years ago
If f(x) = 3x^2 +1 and g(x) = 1-x, what is the value of (f-g)(2)
aleksley [76]

Answer:

14

Step-by-step explanation:

Let's find (f-g)(x)

3x^{2} + 1 - (1-x)\\3x^{2} + 1 -1 + x\\3x^{2} + x

Now let's plug in x=2, so to find (f-g)(2)

3(2)^{2} + 2\\12 + 2 = 14

8 0
3 years ago
17. ralph is 3 times as old as sarah. in 4 years ralph will only be twice as old as sara will be then. find ralph’s age now.
spin [16.1K]

Answer:

Sara is now 4, will be 8 in 4 years. Ralph is now 12, will be 16 in 4 years.

7 0
3 years ago
HELP ME ASAP PLEASEEEEEEE
Vlad [161]

Answer: a) about 450

Step-by-step explanation:

50 multiplied by 9 is 450 and its asking for an approximate so it would be anything near 450

3 0
3 years ago
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